Notes retrieval catalog

Markdown source

This catalog is a research retrieval aid for the maintained notes. Use STATE for the live queue and LLM.md for the established-result map at its stated date. The full notes retain proofs, assumptions, later corrections and reading levels; an index entry is a lead into that evidence.

Retrieval priorities follow the user’s independent analysis (2026-10-01): priority=3 (★★★) is the current spine or a map to consult immediately; priority=2 (★★) is a durable dependency or important obstruction; priority=1 (★) is specialist support; priority=0 (○) is normally omitted unless the query makes it relevant. flags=surprising records a non-obvious result in that analysis; flags=route-closure records a correction, closed route or superseded branch. These judgments concern retrieval, not mathematical quality or literature novelty. A closed route can retain a proved, reusable theorem.

Each entry separates role, status and value from priority. keys collect concrete search terms and result IDs. status classifies the current lesson as result, conditional, obstruction, open, historical or exploratory; proof_status=mixed means the note contains more than one proof level. Read its stated limits. used-calibration and infrastructure distinguish inputs and tools from new mechanisms. decisive-obstruction highlights a failure that changes the next calculation, including high-priority negative notes.

Before every research unit, follow the retrieval rule in AGENTS.md: search this catalog and the full corpus, then read relevant derivations and corrections. Search examples:

rg 'priority=3|decisive-obstruction' notes/index.md
rg -n -B1 -i 'moving saddle|coherence|action dilation' notes/index.md
rg -l -i 'mechanism|synonym|claim-id|counterexample' notes ideas references research claims papers docs --glob '*.md' --glob '*.bib' --glob '*.tex' --glob '*.txt'

Frequent gauge entry points are refinement composition, series/parallel halving, SU(2) midpoint, centre-sensitive cuts, mid-plane order t, and small-field control, followed by the 4D composition and parallel logarithm notes. The Newton spine runs through the fifth postulate, paper synthesis, unit and indeterminacy, indeterminacy routes, and recording closure.

Retrieve negative-route safeguards whenever their mechanism is proposed: local Agmon correction, blocking monotonicity, finite-certification correction, small-field threshold failure, ultraviolet Schur error, thermodynamic no-floor result, and failed confinement bridges.

Coverage verified 2026-10-01: 175 maintained notes, all read in full, including later corrections and appendices. The machine-readable catalog records titles, strongest current results, thematic areas, scope/status and typed relations. For current reading order use dependencies; for the long argument use the provisional book.

abelian-misses-the-box.md | priority=2 | flags=surprising | role=synthesis,result | status=result | proof_status=mixed | value=synthesis,surprising-result | keys=U(1);SU(3);strong coupling box;beta function;abelian photon;RG arrival | area=Yang–Mills/gauge Title: Why the abelian theory has no gap, in the language of the target box: its coupling does not run Summary: Both compact U(1) and SU(3) have volume-uniform strong-coupling Kogut–Susskind gaps; their weak-side flows distinguish them. Limit/reuse: Nonabelian arrival in the target box with generated interactions controlled remains conjectural; perturbative absence of abelian running does not itself prove every global phase claim. Use strong-coupling-target-box and the mass-gap position.
action-floor-yang-mills-gap.md | priority=2 | flags=surprising | role=result,synthesis | status=conditional | proof_status=mixed | value=surprising-result,synthesis | keys=G08;C133;transverse ellipse;matrix model valley;action unit;dimension four | area=Newton/action Title: An action floor on transverse phase-space area produces the Yang–Mills quantum-mechanical gap, and a gap forces an action unit Summary: A supplied transverse orbit-area floor confines the x²y² classical valley and reproduces the quantum-mechanical gap’s energy unit; a finite gap reconstructs an action unit in the mechanical model and dimensionful lower-dimensional cases. Limit/reuse: Semiclassical counting/levels are estimates; dimensional equivalence fails in 4D. Positivity of the floor is assumed; see low-dimensional-mass-gap.
action-scale-dilation.md | priority=2 | flags=none | role=obstruction,result | status=obstruction | proof_status=proved-unrefereed | value=known-boundary,decisive-obstruction | keys=A16;C056;C057;dilation closure;conformally symplectic;action infimum;preparation scaling | area=Newton/action Title: Dilation closure and the action-selection obstruction Summary: Space–time contraction q_a(t)=a q(t/a), V_a(Q)=V(Q/a) preserves mass, speed and energy while scaling orbit/Hamiltonian/covariance actions by a, giving zero infimum in contraction-closed classes. Limit/reuse: Couplings and force ceilings may break closure; fixed softened potentials still admit small actions. Read fixed-force-small-circles before treating broken similarity as sufficient.
action-scale-obstructions.md | priority=2 | flags=none | role=synthesis,obstruction | status=obstruction | proof_status=mixed | value=synthesis,known-boundary | keys=C002–C123;action observables;apparatus calibration;preparation precision;supplied scale;slow modes | area=Newton/action Title: Classical action scales: obstructions, conditional bounds and quantum premises Summary: Consolidates classical vanishing-action families, conditional excitation/composition bounds, finite-apparatus ambiguity/recovery, and the distinction between relaxation and physical Hamiltonian gaps. Limit/reuse: Premises remain model-specific; no universal selection theorem follows. Apparatus continuation is parked. Later necessity-unit-and-indeterminacy and refinement-results provide the current frame.
action-unit-dimensional-selection.md | priority=2 | flags=surprising | role=result,synthesis | status=result | proof_status=mixed | value=known-boundary,synthesis | keys=Q14;Buckingham theorem;fixed constants;action product;similarity;fine structure;k_e/c;C130 | area=Newton/action Title: A universal action floor needs a fixed action unit and no admitted similarity Summary: Dimensional homogeneity and universality require a finite positive floor to be a fixed-constant action product; admitted action-rescaling similarities force zero infimum. Classical k_e,c,G yield unique mass-independent unit k_e/c=αℏ. Limit/reuse: Unit existence does not select positivity or quantum normalization; singular Coulomb assumptions matter. Later necessity-unit-and-indeterminacy expands the unit/indeterminacy separation.
additive-noise-marks.md | priority=2 | flags=none | role=result | status=result | proof_status=proved-unrefereed | value=known-boundary | keys=body-independent noise;Weyl relation;Ozawa independent intervention;von Neumann mark;momentum transfer;Galileo recoil | area=Newton/action Title: Every mark with body-independent noise is a momentum-transfer mark Summary: Apparatus-only reading error and disturbances force a canonical error–impulse pair; position-undisturbed marks reduce to von Neumann momentum-transfer couplings, and the recoil bound extends to position-displacing marks. Limit/reuse: Strong Weyl commutation and unbounded continuous pointers are essential; general body-dependent noise requires record-costs-disturbance. Quantum action scale is supplied.
agmon-global-not-local.md | priority=2 | flags=route-closure | role=obstruction,result | status=obstruction | proof_status=proved-unrefereed | value=decisive-obstruction | keys=Agmon distance;global excess;local large field;extensive ground energy;gradient norm;Gibbs domination | area=Yang–Mills/gauge Title: The Agmon bound controls the global excess only: the local large-field estimate does not follow Summary: Explicit Kogut–Susskind Agmon constants yield extensive global magnetic-energy suppression, while a fixed local excess estimate degrades as inverse square-root volume. Limit/reuse: Corrects agmon-ground-state-suppression; total energy cannot supply the local RG estimate. The proposed pointwise Gibbs-comparison repair also fails by magnetic-energy-identities, Proposition 4.
agmon-ground-state-suppression.md | priority=1 | flags=route-closure | role=superseded,result | status=obstruction | proof_status=mixed | value=known-boundary | keys=Agmon identity;Kogut–Susskind ground state;weighted eigenfunction;global large deviation;local suppression correction | area=Yang–Mills/gauge Title: An Agmon bound for the Kogut–Susskind ground state: large fields are suppressed at rate \(1/g^2\) per plaquette Summary: Establishes the exact weighted ground-state Agmon identity and forbidden-region estimate on compact gauge configuration space. Limit/reuse: Its original n-plaquette/local-suppression interpretation is corrected by agmon-global-not-local; only global magnetic-energy excess control survives. Sections proposing local decimation control must be read through that correction.
ancient-cuts-provenance.md | priority=1 | flags=none | role=historical | status=historical | proof_status=reading | value=source-guardrail | keys=Aristotle 317a;Plutarch cone;Democritus;possible cuts;joint division;trajectory readjustment;I005 | area=historical/sources Title: Ancient cuts and modern readjustment: provenance Summary: Separates Aristotle’s individually possible versus simultaneous divisions from the project’s modern claim that re-solving a discretized trajectory can readjust vertices. Limit/reuse: Sampling, variational re-solving and exact marginal composition are distinct; no ancient path-integral or Newton-transmission claim is supported. cut-point-consistency treats fixed surrounding endpoints only.
arrow-not-sling.md | priority=0 | flags=none | role=historical,synthesis | status=historical | proof_status=reading | value=source-guardrail | keys=Zeno arrow;Plutarch 923C;sling moon;alātacakra;Vaiśeṣika;inertia;first second rung | area=historical/sources Title: Why the ancients argued about the arrow and not the sling Summary: Reads ancient arrow arguments as first-order motion questions, Newton’s sling as second-order deviation under inertia, and the firebrand circle as sampling/appearance. Limit/reuse: The corrected note explicitly retains Plutarch’s sling–moon witness; any claim that ancient philosophical sling arguments are absent is false. The force-rung analogy uses planck-gap-paper, not a historical transmission proof.
autonomous-finite-readout.md | priority=1 | flags=surprising | role=result,calibration | status=result | proof_status=proved-refereed | value=used-calibration,surprising-result | keys=R06;C068;C069;finite Hamiltonian apparatus;four momentum records;mechanical clock;delayed reconstruction | area=apparatus/reconstruction Title: A finite mechanical clock and four persistent readout records Summary: One finite mechanical clock and four probes reconstruct a known four-dimensional spring receiver at fixed latency with error/disturbance O(λ²), using preparation width b=λ³ and exact final momenta. Limit/reuse: Forces, masses, duration and clock energy stay bounded; preparation/record precision shrink. This is delayed reconstruction, not causal fresh measurements at each cut.
block-apparatus-composition.md | priority=1 | flags=none | role=result,calibration | status=result | proof_status=proved-refereed | value=used-calibration | keys=R15;C086;C087;independent block budgets;l^r;centre minimax;extensive composition;shared resource | area=apparatus/reconstruction Title: Independent apparatus blocks restore extensive composition Summary: Exact bounded-force centre risks add across independently budgeted record blocks; at r=3/2, k identical independent blocks give k times the saturated canonical risk product. Limit/reuse: A fixed global budget instead gives copy-count invariance. Regrouping preserves the original Cartesian constraints; replacing them with a global norm ball changes the apparatus class. Precision remains supplied.
blocking-criterion-monotone.md | priority=2 | flags=route-closure | role=obstruction | status=obstruction | proof_status=proved-unrefereed | value=decisive-obstruction | keys=Yarotsky polymer;block surface M²;block gap;Schur variation;projection blocking;effective coupling | area=Yang–Mills/gauge Title: The blocking criterion is monotonically worse in the block size: blocking gains nothing without a change of coupling Summary: Connected estimates are present in Yarotsky’s expansion, but the block-boundary norm/block-gap criterion worsens with block size: M² at strong coupling and M³ in the small-volume regime. Limit/reuse: Corrects blocking-step-obstruction; improvement requires RG coupling/effective-action change. The general monotonic statement explicitly assumes δ(g;M)≤M²δ(g;1); displayed asymptotic regimes supply its concrete examples.
blocking-step-obstruction.md | priority=0 | flags=route-closure | role=superseded,obstruction | status=obstruction | proof_status=mixed | value=known-boundary | keys=block Schur term;boundary energy;connected variation;generated couplings;RG step count;superseded induction | area=Yang–Mills/gauge Title: One blocking step: the obstruction is the variation, not the size, of the inter-block coupling Summary: Isolates scalar boundary-energy shifts from state-dependent Schur variation and counts tentative RG doublings to a strong-coupling threshold. Limit/reuse: Its proposed connected-estimate induction is superseded by blocking-criterion-monotone; the available connected estimate does not improve the criterion. One-loop doubling counts are orientation, conditional on controlled effective couplings, not continuum-gap bounds.
bound-orbit-action-observable.md | priority=1 | flags=none | role=result,calibration | status=result | proof_status=proved-refereed | value=used-calibration | keys=A15;C054;C055;uniform circular phase;orbital action;covariance determinant;rms emittance;transport response | area=Newton/action Title: Bound motion: transport variance and a canonical action estimator Summary: For a phase-uniform circular orbit, 2√det Cov(x,p_x)=RP equals normalized orbital action, while displacement-response coefficients vanish at short and long windows. Limit/reuse: Equality depends on preparation; point phase gives zero covariance despite nonzero orbit action. Invariance is affine symplectic in the selected plane; action-scale-dilation contracts between models.
bounded-acceleration-return.md | priority=1 | flags=none | role=result,calibration | status=result | proof_status=proved-unrefereed | value=used-calibration | keys=A07;C043;C044;bounded acceleration;velocity reversal;kinetic action;sharp 1/24;polygon mesh | area=Newton/action Title: A sharp mechanical cost for a finite-duration reversal Summary: A return with endpoint velocities ±u and acceleration ceiling a exists iff T≥2u/a and has unique minimum kinetic action mu³/(3a). Chord-action defect is bounded sharply by ma²T|π|²/24. Limit/reuse: Endpoint-conditioned cost and refinement excess differ; decreasing u closes the cost. External bounded control supplies the dynamics, not an autonomous conservative receiver.
bridge-crossover.md | priority=0 | flags=none | role=routing | status=result | proof_status=known | value=routing | keys=A09a;C037;C038;telegraph return;beta law;midpoint crossover;B17 | area=refinement/comparison Title: Midpoint crossover: consolidated manuscript Summary: Routes the former standalone midpoint-crossover derivation to maintained telegraph-return-bridge, sections 6–9, preserving C037–C038 and source links. Limit/reuse: This file contains no independent calculation; retrieve the consolidated manuscript for preparation, beta law, moments and mass/window constraints.
calibrated-canonical-ambiguity.md | priority=1 | flags=none | role=result,calibration | status=result | proof_status=proved-refereed | value=used-calibration | keys=R28;fixed q1;two energies;full final apparatus;implicit function;canonical fibre;x P risk | area=apparatus/reconstruction Title: Calibrated two-energy records still hide both canonical coordinates Summary: A fixed smooth pulse design admits an exact common-record receiver curve varying both x and P despite known nonzero first-probe displacement, receiver/apparatus energies and all ten final apparatus coordinates. Limit/reuse: Positive canonical risk is preparation/design-relative and uniform only over weak coupling in that fixed class; a curve does not establish projected area. Later calibration/recovery notes refine the boundary.
calibrated-displacement-ambiguity.md | priority=1 | flags=none | role=result,calibration | status=result | proof_status=proved-refereed | value=used-calibration | keys=R27;Borsuk–Ulam;S10;calibrated displacement;two initial energies;full-state ambiguity;inverse shear | area=apparatus/reconstruction Title: One calibrated displacement still leaves full receiver ambiguity Summary: A constrained eleven-coordinate preparation chart and Borsuk–Ulam yield distinct receiver states with identical ten-component final apparatus records and fixed energies/first displacement. Limit/reuse: The uniform full-receiver norm risk need not lie in x or P; it proves neither canonical action-product nor area floor. calibrated-canonical-ambiguity supplies a separate pulse-design construction for both canonical coordinates.
calibration-tolerance-recovery.md | priority=1 | flags=none | role=result,calibration | status=result | proof_status=proved-unrefereed | value=used-calibration | keys=R31;C119;calibration tolerance;inverse coupling;canonical minimax;common record ball;weak coupling saturation | area=apparatus/reconstruction Title: Calibration tolerance sets the recovery crossover Summary: On the fixed R30 apparatus box, receiver recovery error is O((record error+calibration error)/λ); exact final records give matching canonical-risk product order min{1,(ε/λ)²}. At sufficiently weak coupling one record hides the entire bounded receiver domain. Limit/reuse: Four calibration tolerances are supplied resources; exact calibration recovers the receiver by three-calibration-global-recovery.
causal-force-information.md | priority=2 | flags=none | role=result | status=result | proof_status=proved-refereed | value=used-calibration | keys=R07;C070;C071;delayed records;bounded-force lens;reachable region;canonical area;double integrator | area=Newton/action Title: New information behind a delayed record Summary: With exact past state but unknown future |f|≤F over delay ℓ, exact minimax errors are Fℓ²/(2m), Fℓ; the curved reachable lens has canonical area 2F²ℓ³/(3m). Limit/reuse: Delay/force resources set the scale; both vanish when refined. reachable-cut-composition composes the full phase-space region across cuts.
checkerboard-dynamics.md | priority=2 | flags=surprising | role=result,calibration | status=result | proof_status=proved-refereed | value=surprising-result,used-calibration | keys=A09b;C039;C040;checkerboard coin;Dirac strong limit;telegraph reversal;Born rule;observed corners | area=refinement/comparison Title: One action scale, two rules for composing paths Summary: An exactly unitary normalized checkerboard walk converges strongly on fixed L² wavepackets to Dirac evolution with supplied K; the corresponding real transition rule gives telegraph dynamics. Measuring direction every step yields a ballistic fixed-frequency limit. Limit/reuse: Complex amplitudes/Born probabilities are assumptions; action dimensionality alone selects neither composition rule nor positivity, and branch separation is not a field-theory vacuum gap.
classical-cut-state.md | priority=2 | flags=none | role=result | status=result | proof_status=proved-refereed | value=known-boundary | keys=R03;position-only cut;spring receiver;conditional kernel;momentum memory;independent reset;frozen limit;orbital preparation | area=refinement/comparison Title: What a classical cut must retain Summary: Fixed-energy spring position conditional kernels fail semigroup composition; independently refreshing hidden momentum at every cut freezes terminal position in L². Retaining canonical momentum restores exact composition on every partition. Limit/reuse: Observational cuts retain correlations; resets change the experiment. Orbit action E/ω remains preparation-selected, and three-body-cut-memory shows reduced tagged phase state can still need receiver memory.
classical-orientation-closure.md | priority=1 | flags=none | role=result,calibration | status=result | proof_status=proved-unrefereed | value=known-boundary,used-calibration | keys=Q01;C125;Bloch ball;hidden orientation;minimal composite;purification;Hardy subspace;operational closure | area=Newton/action Title: Finite operational closure does not select quantum composition Summary: Restricted affine measurements of classical random orientations yield ball states, capacity two, continuous reversible local motion and multiplicative composite dimensions/capacities. Minimal classical composites fail purification and Hardy’s subspace requirement. Limit/reuse: Measurement/operation restrictions are stipulated; no apparatus realization or action unit follows. reversible-interaction-premise tests the additional genuine-interaction premise.
classical-readout-refinement.md | priority=1 | flags=none | role=result,calibration | status=result | proof_status=proved-refereed | value=used-calibration | keys=R05;C066;C067;canonical shear probes;quiet preparation;cubic inverse sensitivity;mesh fourth power;growing apparatus mass | area=apparatus/reconstruction Title: Classical readout under cut refinement Summary: Two classical impulsive canonical probes per cut, prepared with phase widths O(mesh⁴), recover the hidden spring receiver uniformly with O(mesh) error and O(mesh³) accumulated disturbance. Limit/reuse: Probe count/mass grows, switching is external, final records are exact, and preparation precision improves. autonomous-finite-readout supplies the later finite-mass fixed-latency construction.
clock-position-local-recovery.md | priority=1 | flags=none | role=result,calibration | status=result | proof_status=proved-unrefereed | value=used-calibration | keys=R21;C098;C099;known clock position;energy transversality;local inverse;unknown clock speed;scaled records | area=apparatus/reconstruction Title: A known clock position permits stable local recovery Summary: Initial clock position, exact receiver energy and eight final pointer records recover receiver, probe positions and unknown clock momentum on one fixed transverse preparation patch, with record-error/coupling stability. Limit/reuse: Local-patch knowledge and known incoming probe momenta are premises; full-shell global recovery fails in global-clock-speed-ambiguity. The canonical risk product closes as record errors vanish.
closed-orbit-force-action.md | priority=2 | flags=none | role=result,calibration | status=result | proof_status=proved-unrefereed | value=used-calibration,known-boundary | keys=A18;C060;C061;Fenchel total curvature;speed floor;force ceiling;closed orbit;canonical action | area=Newton/action Title: Closed trajectories: action from total turning and persistent excitation Summary: Regular closed Newtonian trajectories with speed ≥v_* and force ≤F_max obey J≥m²v_³/F_max; relativistic momentum adds (1−v_²/c²)⁻¹. A smooth force-bounded central potential attains equality on a circle. Limit/reuse: Positivity is conditional on persistent excitation and a selected inertial frame; mechanical/canonical momentum identification needs care with vector potentials. Decreasing v_* closes the bound.
comparison-and-bridges.md | priority=1 | flags=none | role=synthesis | status=result | proof_status=mixed | value=synthesis,known-boundary | keys=Navier–Stokes;Yang–Mills;auxiliary clock;physical Hamiltonian;stochastic quantisation;scaling;gap limits;reconstruction | area=refinement/comparison Title: Navier–Stokes and Yang–Mills: comparison and bridges Summary: Derives fluid/gauge scaling and dissipation identities and distinguishes finite-box fluid decay, auxiliary Markov mixing and physical Hamiltonian spectral gaps. Lists invariant-law, continuum/volume, reconstruction and observable-completeness obligations for proposed bridges. Limit/reuse: Historical orientation, with lower-dimensional cited SPDE results and conditional transfers; three-continuum-limits and mass-gap-obligations-lattice carry the current programme.
composition-crossover-gap-checks.md | priority=0 | flags=none | role=calibration,infrastructure | status=result | proof_status=mixed | value=used-calibration,infrastructure | keys=P02;A08;A09;G01;product chain;telegraph midpoint;slow hidden mode;historical scripts | area=infrastructure Title: Composition, crossover and gap product: verified calculations for A08, A09 and G01 Summary: Early working calculations cover independent composition, telegraph bridge crossover, auxiliary spectral bounds and analytic continuation. Hidden slow modes preserve a velocity plateau while closing the full relaxation gap. Limit/reuse: Historical script/sampler evidence and uncompiled Lean are not active verification instructions. Retrieve maintained composition-universality, telegraph-return-bridge, checkerboard-dynamics and susceptibility-gap for durable statements.
composition-universality.md | priority=2 | flags=none | role=result | status=conditional | proof_status=conditional | value=known-boundary | keys=A08;C035;C036;mass composition;nonnegative additive function;Green–Kubo;reference reversal rate;preparation equivalence | area=Newton/action Title: A shared action coefficient from classical composition Summary: Nonnegative mass-only fluctuation coefficients preserved by independent centre-of-mass composition over every positive mass are constant K≥0. A supplied nonzero-speed finite-rate telegraph reference makes K positive within that preparation class. Limit/reuse: Whole-body versus independently composed preparation equivalence is essential; common reservoirs can violate it. Neither physical action selection nor universality across preparation classes follows.
cone-time-refinement.md | priority=1 | flags=none | role=synthesis,routing | status=result | proof_status=mixed | value=synthesis,known-boundary | keys=M05;Gaussian kernel;time convolution;cone sections;Rivero 1998;tangent groupoid;zero deterministic branch | area=refinement/comparison Title: From cone sections to time refinement Summary: Connects source-inspired spatial cutting to Gaussian time-kernel composition: convolution preserves any supplied variance coefficient κ/m, including the deterministic zero member. Limit/reuse: Positivity and oscillatory analytic continuation are separate physical premises. Historical source tasks and old next-step instructions are context; refinement-composition-and-limit develops the maintained insertion framework.
confinement-scale-bands.md | priority=2 | flags=none | role=synthesis,obstruction | status=obstruction | proof_status=mixed | value=synthesis,known-boundary | keys=Elitzur;Dobrushin block criterion;Wilson loop sub-block mixing;beta 5.7;glueball softening;physical crossover;bands A B C | area=Yang–Mills/gauge Title: The confinement scale in three bands, with published numbers, and the verification restated gauge-invariantly Summary: Gauge symmetry makes single-link block marginals Haar; useful finite-block certification must control gauge-invariant sub-block mixing. Published lattice scales orient the gap between rigorous strong coupling and physical crossover. Limit/reuse: Continuum-scaled glueball estimates near β≈5.7 need the explicit lattice-softening caveat; proposed small-box certification is superseded strategically by reasons-to-stop-as-research, which prioritizes weak-side RG.
conservative-harmonic-receiver.md | priority=1 | flags=none | role=synthesis,calibration | status=result | proof_status=mixed | value=used-calibration,synthesis | keys=C047–C049;harmonic receiver;low-frequency density;thermodynamic order of limits;hard speed ceiling;R03–R33;calibration recovery;correlated curvature | area=apparatus/reconstruction Title: A conservative receiver and the origin of a correlation scale Summary: Finite conservative spring receivers have zero long-window response; an increasing equal-mode-energy chain yields Θ√(m/k) only with size-first limits, and a common hard speed ceiling closes that plateau. Its 39 sections also consolidate cut memory and the full readout/calibration sequence. Limit/reuse: Specialized notes hold individual proofs; the final correlated-fibre curvature nonvanishing test remains open and parked.
correlated-calibration-response.md | priority=0 | flags=none | role=result,calibration | status=result | proof_status=mixed | value=used-calibration | keys=R33;C122;C123;correlated calibration line;hidden y;signed coupling symmetry;quadratic response;local fibre | area=apparatus/reconstruction Title: Correlated calibration errors suppress the canonical response Summary: A selected correlated calibration line suppresses canonical ranges on one common-record fibre. Signed-coupling symmetry cancels the proposed tangent coefficient exactly; moving-reference terminal quadratures give homogeneous quadratic response and a conditional curvature lower bound. Limit/reuse: This is local-fibre support, not global minimax recovery; both projected curvature coefficients remain unproved nonzero. action-scale-obstructions parks further apparatus continuation.
corpus-audit-2026-10-01.md | priority=2 | flags=route-closure | role=infrastructure,synthesis | status=result | proof_status=reading | value=infrastructure,source-guardrail | keys=Opus scores;interest and correctness;digest PDFs;factor 2 area form;q=4 tolerance column;uncorrected overclaims;closed-route drift;correction boxes | area=infrastructure Title: Corpus audit of 1 October 2026: two-axis scores for all 175 notes, the uncorrected errors they expose, and where the drift sits Summary: Claude Opus 5.5 scored every note from 1 to 10 for interest and for correctness under one rubric, and Claude Fable 5.1 reviewed the 26 selected digests against the notes. The Newton, refinement and gauge spine scores 8 or 9 for correctness; 24 notes keep uncorrected overclaims or inconsistent numbers, 20 of them closed mass-gap routes. Verified errors: planck-gap-derivation area forms off by a factor 2, strong-coupling-target-box q=4 column, small-field-step-decay abstract constants. Limit/reuse: Scores are a model reading with reasons on file, not refereeing; §3b items are the scorer’s reports, unverified; interest anchors measure what an outside expert would take, not novelty. The two digest PDFs and the score table are published on the director’s personal site, not here.
cut-measure-newton.md | priority=3 | flags=surprising | role=result | status=result | proof_status=proved-refereed | value=surprising-result | keys=Galileo cell action;Schauder hats;Cameron–Martin;arbitrary cuts;KL divergence;Zhuangzi rod;finite mark discernibility;Proposition 7 | area=Newton/action Title: Newton’s cell action as a measure on cuts Summary: Any cut spends 3s(1−s)K_τ in orthogonal hat energy; shares add and exhaust K_τ exactly when mesh vanishes. Gaussian bridge information and finite-grid optimal mark discernibility equal corresponding action/scale ratios. Limit/reuse: Proposition 7’s sharp value is a supremum, never attained by finite end marks. Cell floors and cut-share floors differ; noise/action scales remain supplied.
cut-paradox-two-faces.md | priority=1 | flags=none | role=result,synthesis | status=result | proof_status=proved-unrefereed | value=known-boundary | keys=I003;C032;scalar rigidity;ballistic support;Paley–Wiener;unitary translation;internal velocity;Compton branch points | area=refinement/comparison Title: The cut paradox in two signatures: sections of a solid and instants of a motion Summary: Ballistic-support scalar convolution probability semigroups are deterministic drifts; scalar translation-invariant strongly continuous unitary groups with compact light-cone kernels are translations times a phase. Limit/reuse: The unitary proposition is a working unrefereed derivation; nontrivial telegraph/Dirac dynamics retain internal state. Cone/arrow comparisons are modern heuristics, and the supplied crossover scale does not establish action positivity.
cut-point-consistency.md | priority=2 | flags=none | role=result | status=result | proof_status=proved-refereed | value=known-boundary | keys=A03;C027–C029;constant-force chord defect;arbitrary partitions;Gaussian restriction consistency;chi-square action;inserted node variance | area=refinement/comparison Title: A surviving action defect and consistency under inserting cuts Summary: Constant-force sampled-chord defects vanish as F²T|π|²/(24m); Gaussian bridge restriction consistency fixes any supplied κ, including zero. Fixed positive κ makes raw kinetic excess diverge while its per-node estimator converges. Limit/reuse: Changing κ with refinement changes preparations; a fresh inserted cut costs expected κ/2 only under the supplied Gaussian rule. Newton’s impulsive polygon is a different scheme.
dimension-ladder.md | priority=2 | flags=none | role=synthesis | status=result | proof_status=mixed | value=synthesis,open-mechanism | keys=0+0;1+n;thermodynamic action unit;wave equilibrium;dimensional transmutation;rotor;gravity least length;exponential ladder | area=refinement/comparison Title: The dimension ladder: from 0+0 to 1+3, and what the action constant does on each rung Summary: Organizes supplied action scales, rotor/string energies and generated YM scales by dimension, with explicit ℏ exponents and the 4D exponential. Proposes universal wave-field thermal consistency as an extension of Theorem U. Limit/reuse: That extension is conjectural; refinement error budgets alone establish no higher-dimensional construction. Paper-spine readings, gravity least-length route and renormalon comparisons require their stated premises.
discrete-substrate-actors.md | priority=0 | flags=none | role=historical,synthesis | status=historical | proof_status=reading | value=source-guardrail,routing | keys=’t Hooft automaton;Wolfram;finite information;Dedekind cut;Connes differential;equivalence classes;superdeterminism;groupoid zero fibre | area=historical/sources Title: From the continuum to discrete substrates: ’t Hooft and other turns Summary: Conversation provenance connects discrete/deterministic programmes to ancient cuts, information loss and the Newton refinement thesis; a later Gaussian groupoid test admits both zero and positive action branches. Limit/reuse: Most historical references/interpretations are explicitly from memory and unverified; three automaton DOIs are metadata-verified only. Information-loss equivalence classes lack a specified record-floor implication; no live queue change follows.
dobrushin-uniqueness-wilson.md | priority=2 | flags=none | role=result,obstruction | status=obstruction | proof_status=mixed | value=known-boundary,used-calibration | keys=Dobrushin;Wilson transfer gap;SU(3) g²444;single-link conditional;18 neighbours;Elitzur;sub-block mixing | area=Yang–Mills/gauge Title: Dobrushin’s uniqueness condition for the Wilson action: a two-line strong-coupling gap at \(g^2>444\), and the block criterion that is the finite verification Summary: The single-link coefficient α≤18(e^(4β_W)−1) gives a volume-uniform SU(3) Wilson transfer gap for g²>444 in physical units ℏc/a. Limit/reuse: Section 4’s single-link block criterion is explicitly corrected as vacuous in the interior by Elitzur; retrieve confinement-scale-bands for gauge-invariant sub-block mixing and reasons-to-stop-as-research for feasibility.
energy-constrained-apparatus-ambiguity.md | priority=1 | flags=none | role=result,calibration | status=result | proof_status=proved-unrefereed | value=used-calibration | keys=R26;C108;C109;backward terminal flow;receiver sign;two exact energies;ten final records;antipodal pair | area=apparatus/reconstruction Title: Exact apparatus energy leaves a receiver-sign ambiguity Summary: Terminal zero probe phase, backward Hamiltonian flow and an energy adjustment produce an exact receiver-sign pair with identical full final apparatus records and both initial energies fixed. Canonical risks stay positive as coupling decreases. Limit/reuse: Fixed preparation width and receiver excitation supply the scale; two points establish neither area nor exact minimax value. calibrated-displacement-ambiguity removes reliance on sign symmetry.
energy-depot-action-selection.md | priority=0 | flags=none | role=result,calibration | status=result | proof_status=proved-unrefereed | value=used-calibration,known-boundary | keys=Q03;energy depot;stimulated gain;finite fuel;pumped oscillator;Lyapunov attractor;power threshold;frequency dependence | area=Newton/action Title: Nonlinear feedback selects an action only while its energy source supplies power Summary: An explicit dissipative oscillator/depot model loses all action with finite fuel; replenishment above P_c gives attracting J_*=(P−P_c)/(2γω) for positive seeds. Limit/reuse: The power/frequency law supplies the scale, and exact rest persists. Equal power gives equal energy rather than universal action; the model is effective dissipative dynamics, not a closed Hamiltonian field construction.
final-clock-momentum-recovery.md | priority=0 | flags=none | role=result,calibration | status=result | proof_status=proved-unrefereed | value=used-calibration | keys=R23;C102;C103;final clock momentum;global inverse;unknown speed;bounded receiver domain;nine records | area=apparatus/reconstruction Title: Final clock momentum restores global receiver recovery Summary: Eight final pointer coordinates plus final clock momentum recover receiver, incoming probe positions and unknown clock speed globally on a fixed bounded domain at small positive coupling. Reaction is included; exact receiver energy is unnecessary. Limit/reuse: Initial clock position and incoming probe momenta remain supplied. Record precision controls the vanishing canonical risk product; full-clock-phase-recovery hides clock offset too.
finite-depth-spin-gap.md | priority=1 | flags=none | role=result,calibration | status=result | proof_status=known | value=used-calibration,known-boundary | keys=G05;cluster chain;controlled-Z;depth two;stabilizer;entangled ground state;uniform gap J;boundary degeneracy | area=refinement/comparison Title: Local entangling gates preserve an energy gap uniformly in chain length Summary: A depth-two controlled-Z circuit conjugates independent spins to a local interacting cluster Hamiltonian with unique entangled ground state and exact volume-uniform energy gap J. Removing endpoint terms yields four ground states, with gap J above the ground space. Limit/reuse: Quantum kinematics, energy normalization and time/action conversion are supplied; fixed-spacing volume uniformity establishes neither continuum construction nor generated gap.
finite-horizon-minimax.md | priority=2 | flags=none | role=result,calibration | status=result | proof_status=proved-unrefereed | value=used-calibration | keys=R13;C082;C083;bounded curvature;complete noisy history;three velocity regimes;transient aggregate loss;earliest saturation | area=Newton/action Title: Exact finite-horizon phase recovery Summary: Exact bounded-force position/momentum minimax risks have acceleration, two-arc and saturation regimes, with momentum saturation at T=4√(mε/F). Product fibres compose exactly; averaging records can lose both coordinates during mixed regimes. Limit/reuse: Known initial state, deterministic error band and complete-history access are premises; no speed ceiling or back-reaction is included. Refining ε closes the action-risk product.
finite-precision-cut.md | priority=1 | flags=none | role=result,calibration | status=result | proof_status=proved-refereed | value=used-calibration | keys=R09;C074;C075;clipped reachable lens;Minkowski area;position precision;residual delay;thin momentum fibre | area=refinement/comparison Title: Finite position precision and the reachable action area Summary: Derives exact terminal canonical area from a clipped bounded-force lens, with additive precision/delay and mixed extrusion terms; area vanishes uniformly when position error and residual delay vanish together. Limit/reuse: A central record can retain finite momentum width while area closes. Non-disturbing record access is supplied; two-position-recovery addresses recovery of both coordinates.
finiteness-half-flowed-susceptibility.md | priority=2 | flags=none | role=result | status=conditional | proof_status=conditional | value=known-boundary | keys=F1;Feynman–Bijl;flowed susceptibility;zero momentum;intensive bound;Hamiltonian equal-time flow;finite gap upper side;coupling cancellation | area=Yang–Mills/gauge Title: The finiteness half of the mass gap is the nonvanishing of one smeared susceptibility Summary: The zero-momentum Feynman–Bijl bound reduces finite excitation energy to one finite derivative expectation and positive flowed susceptibility, with volume cancellation. Limit/reuse: Continuum Hamiltonian equal-time flow limits and nontrivial susceptibility are hypotheses; Lüscher’s 4D Euclidean theorem does not discharge them. flowed-bound-free-field corrects the extra g² factor. This proves no lower gap bound.
fixed-coupling-calibration.md | priority=1 | flags=none | role=result,calibration | status=result | proof_status=proved-refereed | value=used-calibration | keys=R16;C088;C089;fixed nonzero coupling;exact nonlinear calibration;lower Lipschitz;preparation contraction;four persistent momenta | area=apparatus/reconstruction Title: Fixed coupling permits precise calibrated readout Summary: Exact nonlinear calibration of the finite four-record apparatus permits arbitrarily precise receiver reconstruction at one fixed nonzero coupling as preparation and final-record errors shrink. Accuracy times bounded disturbance also tends to zero. Limit/reuse: Dynamics/calibration knowledge, improved precision and fixed latency are resources; fixed coupling alone creates no floor. fixed-preparation-ambiguity holds incoming width positive instead.
fixed-force-small-circles.md | priority=2 | flags=none | role=result,obstruction | status=obstruction | proof_status=proved-unrefereed | value=known-boundary,decisive-obstruction | keys=A17;C058;C059;fixed smooth potential;bounded force;stable small circle;zero action infimum;excitation floor | area=Newton/action Title: Fixed force ceiling: small bound circles and an excitation floor Summary: One fixed smooth relativistic confining potential with globally bounded force supports radially stable circular orbits whose normalized angular actions behave as √(mK)R²→0. A supplied positive speed floor instead gives a conditional force-limited action bound. Limit/reuse: Binding, regularity and upper speed/force ceilings do not select positivity; closed-orbit-force-action extends the excitation-dependent bound beyond circles.
fixed-preparation-ambiguity.md | priority=1 | flags=none | role=result,calibration | status=result | proof_status=proved-refereed | value=used-calibration | keys=R17;C090;C091;fixed preparation box;exact four records;momentum compensator;receiver shell patch;canonical projected area | area=apparatus/reconstruction Title: Positive preparation width hides receiver states from exact records Summary: Unknown incoming probe momenta exactly compensate a two-dimensional receiver-shell patch at one common four-momentum record, giving positive position/momentum risk and projected canonical area bounds. Limit/reuse: Fixed-width Cartesian preparation support and four-record access supply the obstruction; this is reconstruction risk, not an accuracy–disturbance lower bound. Extra calibration/records change the compatible fibre.
flow-before-decimation.md | priority=2 | flags=route-closure | role=obstruction | status=obstruction | proof_status=proved-unrefereed | value=decisive-obstruction | keys=flow bijection;sup norm invariance;unitary spectrum;projection blocking;state-relative estimate;ground-state distribution;Agmon correction | area=Yang–Mills/gauge Title: Flowing before decimating leaves every norm-based criterion unchanged: what is needed is a statement about the state Summary: Flow conjugation preserves spectra and multiplication sup norms, so it leaves norm/gap blocking criteria unchanged. Useful smoothing requires measure/state-weighted or relative-form control. Limit/reuse: The addendum’s proposed local Agmon repair is superseded by agmon-global-not-local; magnetic-energy-identities also rejects the simple local Gibbs-comparison route. Keep the invariant-criterion theorem separate from those obsolete next steps.
flow-conjugation-truncation.md | priority=2 | flags=route-closure | role=obstruction,result | status=obstruction | proof_status=mixed | value=decisive-obstruction,known-boundary | keys=Wilson flow;unitary change of variables;pulled-back kinetic metric;free frequency cancellation;generated nonlocality;relative truncation | area=Yang–Mills/gauge Title: Conjugation by the flow preserves the spectrum, so the renormalization step is a truncation Summary: Finite-lattice flow is a diffeomorphism with unitary implementation; its exact Hamiltonian conjugation preserves the gap. Free magnetic damping cancels electric stiffening. Any locality-criterion gain needs a separate controlled truncation of generated terms. Limit/reuse: lattice-truncation-uniform corrects one-step pessimism; exact changes of variables themselves never establish new spectral separation.
flow-instability-large-field.md | priority=2 | flags=surprising,route-closure | role=obstruction,result | status=obstruction | proof_status=mixed | value=known-boundary | keys=Nielsen–Olesen;chromomagnetic saddle;curvature operator symmetric;Landau level;flow growth;large-field split;sharpness caveat | area=Yang–Mills/gauge Title: The flow Jacobian’s growth factor is sharp: it is the Nielsen–Olesen mode, so the large-field region cannot be flowed Summary: Symmetry of the curvature operator and the Nielsen–Olesen unstable chromomagnetic mode show that gradient descent can amplify perturbations near large-field saddles while lowering action. Limit/reuse: The note’s exact saturation claim needs care: its displayed Landau spectrum includes the positive covariant-Laplacian contribution, so it does not by itself establish growth equal to the curvature-only norm exponent. Lattice-step uniformity is separately corrected in lattice-truncation-uniform.
flow-jacobian-truncation-error.md | priority=1 | flags=route-closure | role=superseded,result | status=obstruction | proof_status=mixed | value=known-boundary | keys=linearized gauge flow;covariant heat kernel;Duhamel;Gaussian tail;curvature norm;continuum physical scale;lattice compactness | area=Yang–Mills/gauge Title: The truncation error of a flow step is Gaussian times \(e^{2t\|G\|_\infty}\), so the renormalization step is small exactly on small-field configurations Summary: Derives a covariant-flow Jacobian bound with Gaussian spatial decay multiplied by a curvature-growth factor, motivating small/large-field splitting and a range/flow-radius truncation budget. Limit/reuse: Its inference that one lattice step lacks uniform control is explicitly corrected by lattice-truncation-uniform. Kernel-tail estimates require further operator/relative-form justification; the linked instability note’s exact sharpness claim needs caution.
flowed-bound-free-field.md | priority=1 | flags=none | role=result,calibration | status=result | proof_status=exact | value=used-calibration,known-boundary | keys=free Maxwell;flowed magnetic energy;two-photon sum rule;g² cancellation;4.26;smearing radius;Feynman–Bijl upper bound | area=Yang–Mills/gauge Title: The flowed bound in free field theory: the coupling cancels, and the bound is informative only at the confinement scale Summary: Free flowed magnetic-energy susceptibility and derivative expectation give gap upper bound 8ℏc/(3√(πt)), independently matched by the two-photon spectral mean; g² cancels exactly. Limit/reuse: Corrects finiteness-half-flowed-susceptibility; the bound vanishes with increasing smearing in Maxwell theory. In interacting YM its coefficient becomes nonperturbative near confinement, and an upper bound cannot prove positivity.
four-dimensional-composition.md | priority=3 | flags=none | role=live,result | status=conditional | proof_status=mixed | value=open-mechanism,decisive-obstruction | keys=cell 4;Gaussian Schur composition;sharp flux covariance growth;background Hessian jets;generated cubic quartic vertices;common IR subtraction;equation 14;depth uniform matching | area=Yang–Mills/gauge Title: Four-dimensional composition: exact Gaussian blocking and one-loop matching Summary: Exact directional Gaussian composition preserves harmonic flux normalization but sharp blocked covariance grows with depth. Refereed determinant-jet estimates and conditional telescoping give universal average running; §7 supplies formal finite one-step vertices/matching constants. Limit/reuse: Depth-uniform continuum-subtracted generated contractions, infrared limits and interacting remainders remain open. §7’s review accepts formal structure while some Schur-test bounds are taken on trust.
four-dimensional-parallel-log.md | priority=3 | flags=none | role=live,result | status=conditional | proof_status=mixed | value=open-mechanism,known-boundary | keys=cell 4;three transverse planes;six anisotropic couplings;bridge Hessian;2b0;Ward identities;generated action;endpoint matching | area=Yang–Mills/gauge Title: Four-dimensional parallel insertions: one-loop shifts and the logarithm Summary: Computes formal one-step four-dimensional anisotropic shifts and conditionally recovers the universal inverse-coupling change −2b₀ log 2 from matched background determinants. Exact generated-action recursion retains every induced interaction. Limit/reuse: one-loop running requires matching hypotheses; sublinear endpoint corrections and controlled accumulated remainders suffice for its average. Uniform nonlinear iteration remains open in composition.
full-apparatus-preparation-ambiguity.md | priority=1 | flags=none | role=calibration,result | status=result | proof_status=proved-refereed | value=used-calibration | keys=R25;C106;C107;full apparatus preparation;ten final records;energy shell;exact compensation;minimax ellipse | area=apparatus/reconstruction Title: Full final apparatus records can hide the entire receiver energy shell Summary: Unknown incoming apparatus coordinates compensate receiver changes while preserving every final apparatus record; sufficiently weak positive coupling can hide the entire fixed-energy shell. Its projected ellipse gives exact coordinate minimax risks. Limit/reuse: the floor depends on preparation widths and receiver energy; supplying apparatus preparation restores recovery. Additional total-energy constraints are treated in energy-constrained ambiguity.
full-clock-phase-recovery.md | priority=0 | flags=none | role=calibration,result | status=result | proof_status=proved-unrefereed | value=used-calibration | keys=R24;C104;C105;ten apparatus records;clock phase;global inverse;known incoming momenta;weak coupling conditioning | area=apparatus/reconstruction Title: Complete final apparatus records replace the initial clock calibration Summary: Joint final pointer and clock phase-space data globally recover the receiver and unknown incoming positions/clock phase on a bounded domain, with reaction retained. At fixed nonzero coupling, record errors tending to zero remove reconstruction risk. Limit/reuse: incoming probe momenta remain supplied; unknown full apparatus preparation restores ambiguity in R25.
full-pointer-recovery.md | priority=0 | flags=none | role=calibration,result | status=result | proof_status=proved-unrefereed | value=used-calibration | keys=R19;C094;C095;eight pointer coordinates;clock calibration;global receiver recovery;free pointer shear;C1 perturbation | area=apparatus/reconstruction Title: Full pointer records recover receiver and unknown probe positions Summary: Eight final pointer coordinates globally recover a bounded receiver state and unknown probe positions at sufficiently small positive coupling, including clock reaction. Explicit inverse bounds make coordinate-risk product vanish with record precision. Limit/reuse: initial clock phase and probe momenta are supplied, and joint classical record access is assumed. Hidden clock removes that calibration premise.
galileo-two-path-interference.md | priority=2 | flags=surprising | role=result | status=result | proof_status=proved-refereed | value=surprising-result,known-boundary | keys=Galileo chord parabola;controlled unitary;F2 tau3 over 24m;Helstrom error;phase aliases;relative inverse-resolution averaging;noncommuting limits | area=Newton/action Title: Galileo’s comparison as two-path interference Summary: Endpoint-matched constant-force and impulsive propagators differ by the scalar phase Kτ/ε, yielding an exact independent-copy discrimination law. Refinement erases the signal; classical-first coherence oscillates, while relative-resolution averaging or calibrated attenuation gives specified noncommuting limits. Limit/reuse: coherent control, Born rule, supplied ε and resource budget are essential; this does not select positive action. See polygon phase.
gapped-set-critical-coupling.md | priority=2 | flags=surprising | role=synthesis | status=result | proof_status=mixed | value=synthesis,known-boundary | keys=T2 prime;gapped set;bulk transition;finite-lattice continuity;volume-uniform stability;closedness;scaling region;T3 | area=Yang–Mills/gauge Title: T2\('\) is the absence of a zero-temperature phase transition, and the missing input is closedness of the gapped set Summary: Separates finite-lattice continuity from infinite-volume gap closure and organizes possible obstructions using the gapped coupling set. Strong coupling supplies a nonempty region; global openness and closedness remain unproved. Limit/reuse: appended correction recognizes bulk transitions compatible with a continuum gap: only the weak-coupling trajectory and T3 are needed. Openings supersedes the all-coupling requirement.
gaussian-blocking-coupling.md | priority=3 | flags=none | role=result,live | status=result | proof_status=proved-refereed | value=infrastructure,known-boundary | keys=G1;Gaussian product blocking;alias sum;exact 2 forms;tree level coupling;plaquette centering;sharp flux surfaces;finite depth | area=Yang–Mills/gauge Title: Gaussian product blocking: the tree-level coupling never moves Summary: Exact Gaussian product blocking multiplies the small-momentum heat-time coefficient by 2^(4−D), preserving it in four dimensions at every finite depth. Centred nearest-plaquette input retains an O(K²) error. Limit/reuse: covariance must remain bounded near nonzero aliases; remainder constants need not be depth-uniform. Sharp-surface ultraviolet shape growth and interacting matching remain in composition.
global-clock-speed-ambiguity.md | priority=0 | flags=none | role=calibration,result | status=result | proof_status=proved-unrefereed | value=used-calibration | keys=R22;two clock speeds;equal-energy shell;eight pointer records;indefinite energy response;global branches;preparation width | area=apparatus/reconstruction Title: Distinct clock speeds give identical full pointer records on the shell Summary: An early-pulse apparatus admits two distinct clock speeds and equal-energy receiver states with identical full pointer records, persisting with positive-coupling reaction and separating both receiver coordinates. Limit/reuse: this is a design-existence, preparation-dependent coordinate-risk bound, not canonical area. It preserves local calibrated recovery; final clock momentum repairs the missing record.
ground-state-measure-transfer.md | priority=2 | flags=none | role=infrastructure | status=conditional | proof_status=mixed | value=infrastructure,known-boundary | keys=Kogut Susskind;anisotropic Wilson;Perron vector;Euclidean time-slice marginal;ground-state density;large-field action cost;probability transfer | area=Yang–Mills/gauge Title: The ground-state measure is the time-slice marginal of the Euclidean measure, and that imports the local large-field estimate Summary: Standard transfer-matrix spectral projection identifies the finite-lattice ground-state density with the infinite-time Euclidean slice marginal, transferring estimates actually proved for that marginal. It explains the scale-invariant four-dimensional large-field action cost. Limit/reuse: action cost alone supplies no normalized nonperturbative probability estimate or Hamiltonian operator inequality. The truncation-exponent competition is partly superseded by operator inequality.
halving-atlas.md | priority=3 | flags=none | role=live,synthesis | status=open | proof_status=mixed | value=synthesis,infrastructure | keys=dimension atlas;series parallel;arbitrary cuts;SU3 triality;Newton records;cell 4;weak recoupling;moving saddle | area=refinement/comparison Title: Atlas of halving: what one refinement step does, and what emerges, in each dimension Summary: Maintained map of directional and arbitrary-fraction refinement, grouped by dimension and gauge group, linking exact identities, formal running, corrections and open cells. Tracks gauge weak-strip activities, Newton recording and the positive completion/generated-shape tests in score-constrained ensembles. Limit/reuse: it adds no theorem; read linked derivations for hypotheses. Sharp Gaussian fixed-point assertions require the later composition correction.
hamiltonian-finite-closure.md | priority=1 | flags=none | role=obstruction,result | status=obstruction | proof_status=proved-unrefereed | value=decisive-obstruction | keys=C128;classical spins;J uz vz;finite observable closure;Vandermonde;all Borel preparations;nonlinear expectation update;operational descent | area=Newton/action Title: The spin interaction admits no exact finite observable repair Summary: The interacting two-spin flow generates arbitrarily many independent time-translated observables, excluding every finite bounded-observable repair containing the original effects. Nonlinear updates of finite expectations cannot evade the obstruction when all preparations are admitted. Limit/reuse: restricted preparations or effects change the premise; infinite observable dimension implies neither quantum structure nor a universal action. Extends moment descent.
hamiltonian-moment-descent.md | priority=1 | flags=none | role=result,obstruction | status=obstruction | proof_status=proved-refereed | value=known-boundary | keys=C127;classical orientations;Hamiltonian spin interaction;same first cross moments;product effect;quotient dynamics;missing quadratic moment;reversible closure | area=Newton/action Title: A reversible spin interaction separates identical operational states Summary: Two classical spin preparations share all retained first/cross moments and microscopic energy but evolve to different allowed product probabilities under H=J u_z v_z. Smooth microscopic reversibility therefore fails to descend to the operational quotient. Limit/reuse: supplied spin magnitudes fix action units; reconstruction needs a stable preparation/effect restriction or state enlargement. Finite closure excludes finite repairs for all preparations.
hidden-clock-ambiguity.md | priority=0 | flags=none | role=calibration,result | status=result | proof_status=proved-unrefereed | value=used-calibration | keys=R20;hidden clock phase;fixed energy receiver;eight pointer records;early pulse design;implicit function;coordinate risk product | area=apparatus/reconstruction Title: An unknown clock hides an exact fixed-energy receiver phase Summary: Unknown clock position/speed allows a smooth equal-record receiver family on an exact energy shell, with both canonical coordinates varying despite eight exact pointer records and known probe momenta. Limit/reuse: fixed pulse design and positive preparation widths give coordinate risks, not enclosed canonical area or a universal floor. Revealed clock information is progressively tested in local recovery.
holography-lowest-dimensions.md | priority=0 | flags=none | role=synthesis,historical | status=historical | proof_status=reading | value=synthesis | keys=Feynman Kac;Euclidean segment;thermofield double;JT gravity;Schwarzian;SYK;matrix ribbon graphs;infrared cap | area=refinement/comparison Title: Holography in the lowest dimensions: at \(d=0\) it is the wave-function identity, at \(d=1\) it is the Schwarzian Summary: Exploratory dictionary compares Euclidean ground-state marginals and segment factorization with low-dimensional holography, then distinguishes gapless Schwarzian/SYK scales from a confining infrared cap. Limit/reuse: references are metadata-level and holographic interpretations are orientation; large-N capped geometries prove no SU(3) theorem. The usable standard marginal identity is in measure transfer.
i003-double-limit-rigidity.md | priority=0 | flags=route-closure | role=superseded,synthesis | status=obstruction | proof_status=mixed | value=known-boundary | keys=I003;finite propagation;matrix semigroup classification;telegraph commutator;hidden slow modes;additive readout noise;double limit;probability conservation | area=Newton/action Title: I003: finite propagation, internal state and resolution Summary: Corrected exploratory draft retains exact two-state commutator scales and a specified additive-noise double-limit calculation, while withdrawing general zero-response and classification claims. Limit/reuse: the matrix finite-propagation classification is still conjectural; Markov conservation is an additional premise, and commutator norms can miss slow modes. Noise-selected limits do not force a physical floor. Two faces holds the scalar result.
indistinguishable-phase-bound.md | priority=2 | flags=none | role=result | status=result | proof_status=proved-refereed | value=infrastructure,known-boundary | keys=R11;C078;C079;bounded force;complete noisy history;blind delay;convex symmetric fibre;exact minimax risks | area=Newton/action Title: A sharp information bound from indistinguishable motions Summary: Convex symmetry and an explicit force-controlled pair give sharp coordinate minimax risks hidden by an entire bounded-noise position history, matching two-record recovery. At zero delay their product is 2√(mF) ε^(3/2). Limit/reuse: sufficient preparation time, deterministic error bands and known initial state are required; precision/delay refinement closes the bound. Short horizons are solved in finite-horizon minimax.
interacting-ising-gap.md | priority=1 | flags=none | role=result,calibration | status=result | proof_status=proved-refereed | value=used-calibration,known-boundary | keys=G03;C124;periodic Ising chain;heat bath;Hamming coupling;magnetization eigenmode;a one minus tanh 2b;per-site clock | area=refinement/comparison Title: A uniform relaxation gap with nearest-neighbour interactions Summary: A written coupling lower bound and magnetization eigenmode prove the known full relaxation gap a[1−tanh(2b)] for every periodic N≥3. Bounded coupling and a per-site clock floor give volume-uniformity. Limit/reuse: growing coupling or a fixed total clock closes it; this auxiliary stochastic rate selects neither a quantum Hamiltonian nor action normalization. See Hermitian transfer.
intermediate-region-finite-verification.md | priority=2 | flags=route-closure | role=superseded,synthesis | status=obstruction | proof_status=conditional | value=known-boundary,decisive-obstruction | keys=Dobrushin Shlosman;complete analyticity;finite block mixing;Wilson transfer matrix;interaction space;openness radius;RG finish line;screening | area=Newton/action Title: The intermediate region as a finite verification: complete analyticity, the transfer matrix, and the two numbers whose meeting closes the proof Summary: Conditional finite-block mixing certification would furnish a volume-uniform Wilson transfer gap and an open target for an RG trajectory in full interaction space. No certificate or reach estimate is supplied. Limit/reuse: all-coupling coverage and two scalar thresholds are unnecessary; oscillation bounds worsen with blocking. Physical-coupling certification is subsequently rejected as infeasible in reasons to stop.
ising-foundational-value.md | priority=0 | flags=none | role=synthesis,calibration | status=result | proof_status=known | value=used-calibration,synthesis | keys=Ising benchmark;relaxation gap;logarithmic mixing time;stochastic parent;physical clock;action conversion;publication premise | area=refinement/comparison Title: Foundational value of the established Ising gap Summary: Separates the known size-independent Ising relaxation gap, logarithmically growing global mixing time, and energy gap obtained by multiplying a stochastic parent by supplied action. Limit/reuse: equilibrium weights fix neither generator nor clock normalization; further spectra add no action-selection mechanism. Return only for a physical-generator comparison or distinctive conceptual claim. Uses interacting gap and Hermitian parent.
ising-hermitian-transfer.md | priority=1 | flags=none | role=result,calibration | status=result | proof_status=proved-refereed | value=used-calibration,infrastructure | keys=G04;C126;square-root Gibbs;detailed balance;three-site parent;frustration free;imaginary time;supplied K | area=refinement/comparison Title: The Ising gap gives a conditional local parent Hamiltonian Summary: The weighted-space unitary transform produces explicit positive three-site Ising terms, a unique square-root Gibbs ground state, and the exact inherited gap a[1−tanh(2b)]. Supplied action K converts this to energy. Limit/reuse: physical real-time dynamics, state interpretation, clock normalization and infinite-volume construction remain additional premises. Established stochastic-parent correspondence, with a derived local specialization; see foundational value.
jacobi-kernels-distinguishability.md | priority=0 | flags=none | role=routing | status=result | proof_status=mixed | value=routing | keys=action-gap-foundations;Jacobi Hessian;short-time kernel;Dirichlet variation;quantum first lobe;independent copies;relativistic speed margin | area=infrastructure Title: Variations, kernels and distinguishability Summary: Routes to the older technical manuscript’s action contractions, normalized Hessian bound, short-time kernel expansion and quantum two-arm discrimination threshold. Limit/reuse: the threshold assumes supplied phase/Born rules and independent-copy resources; increasing copies removes a fixed imperfect-confidence threshold. This note contains a location table rather than independent derivations. Later matched comparisons are in Galileo interference.
kogut-susskind-strong-coupling-explicit.md | priority=2 | flags=none | role=result,infrastructure | status=result | proof_status=proved-unrefereed | value=infrastructure | keys=T2;Kogut Susskind;continuous-time Duhamel;closed flux loops;Kotecky Preiss;general polymer tree;g2 388;hbar c over a | area=Yang–Mills/gauge Title: Continuous-time expansion for Kogut–Susskind: \(SU(3)\) gapped for \(g^2\ge388\), gap approaching \((8/3)g^2\,\hbar c/a\) Summary: A continuous-time electric-basis polymer expansion gives an explicit SU(3) volume-uniform KS lower gap (4/3)g² ℏc/a at g²≥388, retaining exact excited-link decay. The general connected-history tree count distinguishes this threshold from the adjacent-growth estimate g²≥79. Limit/reuse: this is a strong-coupling lattice finish line, not weak-side RG or continuum construction; compare Wilson expansion.
large-field-action-lower-bound.md | priority=2 | flags=none | role=result,infrastructure | status=result | proof_status=mixed | value=infrastructure,known-boundary | keys=flow monotonicity;flowed L2 block;eta2 over 4g2;four-dimensional action;scale invariant;constrained sharpness;normalized probability;large fields | area=Yang–Mills/gauge Title: The large-field action lower bound is immediate in the natural variable, and the constant field saturates it Summary: Flow monotonicity and positivity give the Euclidean action lower bound η²/(4g²) when the flowed block L² field exceeds η². The dimensional cancellation is independent of block scale. Limit/reuse: this is an action cost; claimed sharpness needs admissible boundary/flow control, and a normalized probability bound still needs partition-function estimates. See entropy model and operator obstruction.
large-field-entropy-count.md | priority=1 | flags=none | role=synthesis,infrastructure | status=exploratory | proof_status=formal | value=infrastructure,known-boundary | keys=Nielsen Olesen;Landau degeneracy;longitudinal disk;eta2 over 8pi2;action entropy ratio;constrained minimizer;large-field measure;bounded factor premise | area=Yang–Mills/gauge Title: The large-field region costs more action than it has unstable directions, by the factor \(2\pi^2/g^2\) Summary: Constant-background Landau counting estimates η²/(8π²) unstable modes per four-dimensional block, giving action-cost/count ratio 2π²/g². Limit/reuse: this is a model estimate, not a general entropy or convergent polymer theorem; bounded weight per mode and normalized measure control are additional premises. Compactness gives a constrained minimizer but does not itself supply a Gaussian expansion. The action bound is in lower bound.
large-field-operator-inequality.md | priority=2 | flags=route-closure | role=obstruction,result | status=obstruction | proof_status=mixed | value=decisive-obstruction | keys=rare negative well;IMS localization;local energy excess;surface vacuum cost;operator versus measure;positive perturbation;Euclidean polymers;truncation range | area=Yang–Mills/gauge Title: The large-field region in the Hamiltonian route needs an operator inequality, and the measure statement is weaker than that Summary: Exact min-max/trial-state inequalities distinguish harmless positive rare perturbations from negative wells that can reorganize low energy despite small measure. The attempted Hamiltonian large-field comparison loses cutoff-scale surface energy. Limit/reuse: rarity cannot replace the missing signed operator bound; Euclidean polymer estimates consume measure control directly. Growing truncation range removes the older fixed-range exponent competition in measure transfer.
lattice-gap-upper-bounds.md | priority=2 | flags=surprising | role=result,infrastructure | status=result | proof_status=mixed | value=surprising-result,known-boundary | keys=Feynman Bijl;double commutator;plaquette variance;U1 structure factor;linear electric field;semisimple Gauss law;Wilson dressing;flowed observable | area=Yang–Mills/gauge Title: Upper bounds on the lattice gap: the Feynman–Bijl inequality, the abelian structure factor and the non-abelian dressing obstruction Summary: Derives KS Feynman–Bijl upper bounds, fixes strong-coupling gap order, and exposes an abelian structure-factor gapless channel. For semisimple gauge groups, no nonzero c-number linear electric observable obeys Gauss law. Limit/reuse: the dressing discussion blocks this trial route, not all gapless states, and proves no lower bound. Ultraviolet plaquettes cannot control continuum finiteness; use flowed susceptibility.
lattice-truncation-uniform.md | priority=2 | flags=surprising | role=result,obstruction | status=obstruction | proof_status=proved-unrefereed | value=surprising-result,infrastructure | keys=lattice compactness;Wilson flow;coupling cancellation;dimensionless half time;Jacobian locality;exponential truncation tail;generated couplings;decimation | area=Yang–Mills/gauge Title: On the lattice one flow step has a uniformly bounded truncation error: the obstruction is decimation Summary: Compact lattice variables and coupling-independent Wilson flow bound one doubling’s Jacobian/locality constants, giving an exponentially small truncation tail with increasing lattice range. This corrects the claim that raw field supremum obstructs one lattice step. Limit/reuse: neither conjugation nor truncation removes variables; generated interactions and controlled decimation/iteration remain. Flow before decimation rejects improvement of the projection criterion by smoothing alone.
leibniz-continuity-records.md | priority=3 | flags=surprising | role=result,historical | status=conditional | proof_status=proved-refereed | value=surprising-result,source-guardrail | keys=Proposition L;Leibniz 1687;best verdict continuity;Gaussian mark floor;kappa zero;preparation ignorant;static shapes;Newton Rule III | area=Newton/action Title: Leibniz’s law of continuity, read on records, selects a positive action floor for motions Summary: In the non-adaptive Gaussian mark model with preparation-invariant tests, optimal force discrimination is continuous at zero force iff κ>0; finite schedules approach the spent-action supremum over κ. Historical passages support an explicitly modern record-level reading of continuity. Limit/reuse: each fixed protocol is continuous even at zero; static cases and unrestricted prepared apertures differ. The record-topology premise is additional physics, not Leibniz’s own theorem.
lieb-robinson-kogut-susskind.md | priority=2 | flags=none | role=result,infrastructure | status=result | proof_status=proved-unrefereed | value=infrastructure,known-boundary | keys=Kogut Susskind;unbounded electric term;single-link interaction picture;bounded plaquettes;volume-uniform locality;Nc over g2;gap stability;frustration free | area=Yang–Mills/gauge Title: A Lieb–Robinson bound for the Kogut–Susskind Hamiltonian, with velocity \(\propto Nc/g^2\) Summary: Treating commuting unbounded single-link electric terms exactly leaves bounded plaquette interactions with unchanged supports, permitting a volume-uniform Lieb–Robinson estimate with velocity proportional to Nc/g². Limit/reuse: the weak-coupling bound degrades and establishes no physical continuum light cone. Locality alone does not prove openness of the gapped set; the cited stability route still needs hypotheses absent from finite-coupling KS.
local-detector-coincidences.md | priority=0 | flags=none | role=result,calibration | status=result | proof_status=proved-unrefereed | value=known-boundary,used-calibration | keys=Q12;fixed passive splitter;monotone Bernoulli response;conditional independence;p12 ge p1 p2;full gate ensemble;shared readiness;dimensionless witness | area=Newton/action Title: Independent monotone receivers cannot suppress coincidences Summary: Independent monotone detectors fed fixed fractions of one scalar pulse energy obey p₁₂≥p₁p₂, with sharp efficiency/balance trade-offs. Saturation and dark counts preserve the premise package. Limit/reuse: fluctuating routing, anticorrelated readiness and outcome-selected gates explicitly evade it. This dimensionless exclusion witness selects no action unit; shared readiness CHSH tests the broader local model.
low-dimensional-mass-gap.md | priority=3 | flags=none | role=synthesis,result | status=result | proof_status=mixed | value=synthesis,infrastructure | keys=G07;supplied generated gap;homogeneous spectral dilation;xy valley;SU2 matrix model;transverse zero-point energy;two-dimensional flux;similarity anomaly | area=Yang–Mills/gauge Title: A gap is a scale the classical theory lacks: solved low-dimensional mass gaps and the positive-action question Summary: Dimensional and spectral scaling organize supplied versus generated gaps; written scalar/SU(2) matrix-model proofs explain transverse zero-point confinement and its ℏ^(4/3)g(2/3) scale. Includes finite-volume, two-dimensional flux and scale-anomaly examples. Limit/reuse: zero-mode gaps decay with box size; two-dimensional absence of local particles is dynamical, not absence of a mass unit. No result derives positive action structure from consistency alone.
magnetic-energy-identities.md | priority=2 | flags=none | role=result,obstruction | status=obstruction | proof_status=exact | value=infrastructure,known-boundary | keys=Wilson magnetic energy;Laplacian eigenfunction;gradient bound;ground-state sum rule;magnetic variance;Gibbs comparison;extensive Haar mean;local large field | area=Yang–Mills/gauge Title: Two exact identities for the magnetic energy, a ground-state sum rule, and why pointwise Gibbs domination fails as Agmon does Summary: Exact magnetic-energy Laplacian/gradient identities give a ground-state variance/kinetic sum rule. Exponential comparison functions reproduce the extensive threshold that prevents this argument from suppressing a local excess uniformly in volume. Limit/reuse: the failure concerns this eigenvalue-equation comparison, not a general impossibility of local estimates. Ground-state measure transfer imports Euclidean estimates once those estimates are proved.
mark-cost-and-statistical-floor.md | priority=3 | flags=none | role=result | status=result | proof_status=proved-unrefereed | value=infrastructure,known-boundary | keys=Theorems A B C;von Neumann mark;error recoil conjugacy;hbar over 2;Gaussian invariant test;Dirichlet energy;correlated squeezing;grid probe escape | area=Newton/action Title: The mark cost is exactly \(\hbar/2\), and the worst-case theorem survives as a statistical one Summary: Position-coupled quantum probes have exact error/recoil commutator and uncertainty cost ℏ/2. Independent Gaussian marks with preparation-invariant tests yield the sharp τΔE≥48z²κ bound; correlated probes lower its effective cost and can defeat it. Limit/reuse: arbitrary probes and prepared-body protocols escape the Gaussian floor. Recoil and disturbance provide the wider instrument statements; supplied ℏ remains a premise.
mass-gap-conditional-theorem.md | priority=3 | flags=none | role=synthesis | status=conditional | proof_status=conditional | value=synthesis,open-mechanism | keys=H1;H2;weak-side blocking;certified finite box;mixing neighbourhood;physical a star;minimum decay rate;continuum construction | area=Yang–Mills/gauge Title: The map as one conditional theorem: two hypotheses, both finite in kind, and an explicit lower bound \(m\ge\hbar c\,\gamma'/a_*\) Summary: Packages an RG fluctuation-decay hypothesis and robust finite-box mixing certificate into a proposed lattice decay/gap transfer, with physical lower scale ℏc min(γ,γ′)/a. Limit/reuse: both hypotheses remain unproved; continuum existence, nontriviality and observable/limit control are separate obligations despite the note’s endpoint rhetoric. Physical-coupling H2 certification is later rejected in reasons to stop; current progress follows the refinement spine.
mass-gap-obligations-lattice.md | priority=3 | flags=none | role=synthesis,result | status=open | proof_status=mixed | value=synthesis,infrastructure | keys=T1;T2;T2 prime;T3;T4;KS physical sector;volume then cutoff;asymptotic freedom;small-volume corner | area=Yang–Mills/gauge Title: The mass gap as a finite list of theorems: the Hamiltonian lattice route Summary: Canonical map distinguishes finite-lattice positivity, strong-coupling volume uniformity, weak-trajectory scaling, continuum axioms and the small-volume corner. T1 follows from compact resolvent and positivity improvement; δ(g) must scale with aΛ for a finite physical gap. Limit/reuse: ultraviolet stability is not a completed OS construction, and all-coupling T2′ is stronger than required. Openings supplies the scaling-region correction.
mass-gap-openings.md | priority=1 | flags=none | role=synthesis | status=exploratory | proof_status=mixed | value=synthesis,known-boundary | keys=scaling-region correction;Wilson bulk transition;negative adjoint action;Bakry Emery;centre stabilization;three dimensions;Simon valley;large N | area=Yang–Mills/gauge Title: Openings for the mass gap, and why it is not special to SU(3) Summary: Records four parked approaches—multiscale curvature, centre-stabilized compactification, three dimensions and spectral valley lifting—and clarifies group/action dependence of lattice bulk transitions. Continuum scaling needs positivity near g=0, not every bare coupling. Limit/reuse: curvature-threshold conversion is explicitly unchecked; deformed-theory continuity and SU(3) large-N transfer remain hypotheses. Its pause/next-task language is historical; use current STATE and atlas.
mass-gap-position.md | priority=3 | flags=none | role=synthesis,obstruction | status=open | proof_status=mixed | value=synthesis,decisive-obstruction | keys=mass-gap map;seven closed routes;operator norm;global Agmon;Gibbs comparison;Schur ultraviolet;H1 methods problem;H2 infeasibility | area=Yang–Mills/gauge Title: The mass gap: current position of this programme Summary: Earlier major synthesis collects finite-lattice/strong-coupling results, upper-bound tools, exact identities and seven failed approaches, with explicit weak/strong threshold asymmetry. Later sections reject correlation monotonicity and certified physical-coupling H2 as weak-side solutions. Limit/reuse: method closures have named scopes; claimed large-field measure closure exceeds action-cost/model-entropy ingredients. Follow reasons to stop and the current refinement construction.
mechanical-interference-action.md | priority=1 | flags=surprising | role=result,calibration | status=result | proof_status=proved-unrefereed | value=surprising-result,known-boundary | keys=Q08;classical string network;orthogonal junction;matched absorbers;finite pulse autocorrelation;attenuation;canonical action;divisible energy | area=Newton/action Title: Mechanical interference measures phase without fixing an action unit Summary: An explicit ideal string network produces mechanical work fringes whose normalized autocorrelation survives attenuation, while energy and canonical action shrink quadratically. The finite-pulse construction distinguishes canonical action from the traveling wave’s zero Lagrangian action. Limit/reuse: ideal junctions and sinks are supplied; deterministic work fractions are not exclusive click probabilities. Interference alone selects no action unit; threshold events tests detector additions.
millennium-problem-definitions.md | priority=2 | flags=none | role=infrastructure | status=historical | proof_status=reading | value=source-guardrail,infrastructure | keys=Clay definitions;Fefferman A B C D;forced breakdown;unforced existence;Jaffe Witten;nontrivial quantum theory;Wightman OS;finite positive mass gap | area=infrastructure Title: The two Millennium problems Summary: Source-backed digest states the Navier–Stokes alternatives and continuum infinite-volume Yang–Mills existence/gap target, including forcing distinctions, nontriviality, axiomatic strength and 0<m<∞. Limit/reuse: official originals govern details; confinement and isolated particles are additional questions. Its attributed 2026 announcement is recorded source context, not independent proof verification. Use this definition before interpreting lattice or auxiliary-clock gaps.
minimax-composition.md | priority=1 | flags=none | role=result | status=result | proof_status=proved-refereed | value=known-boundary,infrastructure | keys=R12;product central fibres;linear minimax radii;centre total momentum;aligned errors;extensive action product;aggregate record loss;variance mismatch | area=Newton/action Title: Worst-case information scales under mechanical composition Summary: Cartesian bounded-error experiments compose exact scalar minimax radii by sums of absolute weighted radii. Identical constituents make the canonical risk product extensive; discarding constituent records can strictly increase momentum risk. Limit/reuse: these are separate coordinate risks under product admissibility, not variance coefficients or simultaneous per-trajectory errors. A mass-independent positive product fails this law. Uses indistinguishable pair.
moment-hierarchy-upper-bounds.md | priority=2 | flags=route-closure | role=result,obstruction | status=obstruction | proof_status=mixed | value=decisive-obstruction,infrastructure | keys=spectral moments;log convexity;inverse moments;M0 over Mminus1;flowed correlator;positive spectral measure;gapless exponential tail;upper bound limitation | area=Yang–Mills/gauge Title: A monotone hierarchy of upper bounds from one flowed correlator, and why no bound of this kind can give \(m>0\) Summary: For a supplied positive spectral measure with finite nonzero moments, consecutive ratios upper-bound its spectral edge and improve toward negative indices. A gapless density suppressed faster than every power at zero has finite inverse moments, closing that positivity argument. Limit/reuse: correlator reconstruction, temporal-flow admissibility and infrared integrability need their own hypotheses; finite moment ratios prove no positive global gap. See finiteness.
necessity-unit-and-indeterminacy.md | priority=3 | flags=none | role=result,synthesis | status=result | proof_status=proved-refereed | value=synthesis,known-boundary | keys=Theorem U;Theorem I;radiation spectral integral;Kirchhoff Wien;prior density ceiling;two-pointer recoil monitor;instrument access;Rutherford correction | area=Newton/action Title: What a necessity argument for \(h>0\) must supply: a unit and an indeterminacy Summary: Radiation universality/scaling, finite positive integrated energy and low-frequency normalization define a positive enclosure-independent action unit. A specified classical two-pointer protocol defeats a prior-only density ceiling by sharpening the completed posterior. Limit/reuse: unit, posterior restriction and operational disturbance bound are distinct; the instrument-access premise is essential. Exact Rutherford scattering refutes the earlier universal Coulomb impulse floor. Continue in indeterminacy routes.
newton-NATP00385-audit.md | priority=1 | flags=none | role=historical,infrastructure | status=historical | proof_status=reading | value=source-guardrail | keys=H01;NATP00385;analysis discovery;synthesis demonstration;fluxions moments;first last ratios;diplomatic TEI;publication delay | area=historical/sources Title: Newton on discovery, demonstration and limiting ratios Summary: Passage-level Newton Project audit separates retrospective analytical discovery from synthetic Principia demonstration and documents generated quantities, limiting ratios and priority/publication revisions. Limit/reuse: the dossier supports no causal claim that shrinking-area doubts delayed publication. Draft layers, deletions and individual dating remain incompletely checked; selected diplomatic/TEI anchors carry the evidence. Book II methodological scholium and Book III Classical Scholia are distinct witnesses.
newton-indeterminacy-routes.md | priority=3 | flags=none | role=result,live | status=conditional | proof_status=conditional | value=open-mechanism,infrastructure | keys=Premise F;Theorem F;classical statistical angle;Hamiltonian translation speed;Gaussian symplectic covariance;h star 2 zeta;nonlinear generator escape;inflexion | area=Newton/action Title: Newton indeterminacy routes: the physical premise a record floor needs Summary: A conditional classical statistical-speed theorem reproduces the exact sagitta/impulse disturbance bound; Gaussian ensembles with affine generators satisfy its premise with h*=2ζ. Background and Newton inflexion candidates leave record closure and scale matching open. Limit/reuse: covariance alone fails for fine nonlinear generators, and indirect records can sharpen stationary priors. SED recording tests physical instruments and later nonlinear counterexamples.
newton-insertion-action.md | priority=3 | flags=none | role=result,synthesis | status=result | proof_status=mixed | value=infrastructure,synthesis | keys=N01;inertial falling parabola;3F over v;Galileo area;tau Delta E;matched endpoint chord;F minus F F reunion;controlled phase | area=Newton/action Title: Galileo’s falling parabola, Newton’s refinement and the Planck-scale question Summary: Establishes the geometric anchor (3F/v)A=τΔE and distinguishes it from matched-endpoint chord and force-centre sectors. Explicit F,−F,F return forces reunite both arms and give an exact scalar quantum phase for any body state. Limit/reuse: phase discrimination is supplied-ℏ/resource-dependent, and kinetic gain is not energy uncertainty. Independent positive-action necessity remains open; Galileo interference sharpens the controlled comparison.
newton-mark-floor.md | priority=2 | flags=none | role=synthesis,result | status=conditional | proof_status=conditional | value=known-boundary,source-guardrail | keys=N02;M1 M2 M3;Newton fits;Lambda p;two-mark floor;far-screen countermodel;worst-case widths;Gaussian replacement | area=Newton/action Title: The cost of a mark: a Newton-age floor for the Galileo comparison Summary: In an early worst-case mark model, added irrecoverable-recoil premise M3 yields a protocol-dependent Galileo action floor; determinate fits plus later screen records defeat it. Mathematical subdivision remains unrestricted. Limit/reuse: M3 is an added physical premise, not derived from Newton’s optics; finite support widths have no nonvacuous quantum instance. Statistical mark cost supplies the corrected ℏ/2 conjugacy and Gaussian bounds.
newton-record-parallel-move.md | priority=3 | flags=surprising | role=result,infrastructure | status=result | proof_status=exact | value=surprising-result,infrastructure | keys=Gaussian position instrument; forgotten record; Wigner momentum diffusion; inverse variance addition; continuous measurement; parallel insertion; supplied hbar | area=Newton/action Title: Newton’s record as a parallel move: what forgetting a record leaves Summary: Forgetting a Gaussian position record of width σ gives exactly momentum convolution with variance ℏ²/(4σ²); concurrent mark precisions add, and linear dynamics transports the resulting covariance. Limit/reuse: The continuous-measurement limit needs a summable noise budget; this standard channel supplies a Newton parallel-insertion analogy, not an independently selected positive ℏ.
ordered-beam-preparation.md | priority=0 | flags=none | role=routing,calibration | status=result | proof_status=proved-refereed | value=routing,used-calibration | keys=A13; C051; ordered collision beams; Palm residual; stationary preparation; zero long-window response | area=Newton/action Title: A13: ordered-beam preparation Summary: Routes to the reviewed collision manuscript: a stationary ordered two-stream preparation makes tagged motion periodic and kills its long-window response while preserving mass, speed, density and mean collision frequency. Limit/reuse: Joint position–velocity correlations change; this tests preparation dependence, not a general action-floor theorem.
passive-threshold-events.md | priority=0 | flags=none | role=result,calibration | status=result | proof_status=proved-unrefereed | value=known-boundary,used-calibration | keys=Q09; passive threshold; quartic barrier; no-click tradeoff; double clicks; preloaded detector; detector action scale | area=Newton/action Title: A passive threshold creates events, but its scale belongs to the receiver Summary: Independent equal-threshold detectors cannot maintain both exclusive clicks and unit efficiency over an open energy range; an explicit conservative quartic barrier realizes the crossing threshold. Limit/reuse: Near-saddle preparation makes additional signal energy arbitrarily small, and Δ/ω is detector-dependent. Conclusions concern the stated accumulator/impulse model; conservative crossing alone supplies no permanent latch.
physical-cut-speed.md | priority=2 | flags=none | role=result,calibration | status=result | proof_status=proved-refereed | value=used-calibration,known-boundary | keys=A05; C030; C031; C032; elastic return bridge; bounded speed; scalar convolution closure; velocity memory | area=refinement/comparison Title: A physical cut: elastic reversal, finite speed and memory Summary: Equal-mass elastic return bridges retain velocity memory and obey sharp bounded-speed midpoint variance bounds, while tracer action scales as mu²Δ/2 and vanishes under refinement. Scalar probability convolution semigroups with exact finite propagation reduce to deterministic drift. Limit/reuse: Prepared partner separation changes with the interval; internal-state models such as telegraph-return-bridge evade the scalar closure premise.
planck-gap-derivation.md | priority=1 | flags=route-closure | role=superseded,result | status=obstruction | proof_status=mixed | value=known-boundary,decisive-obstruction | keys=worst-case marks; feasibility box; Dirichlet certificate; bounded error-recoil product; constants 9 and 36; support width; Paley-Wiener correction | area=Newton/action Title: The Planck gap as a theorem: every marking protocol needs \(F^2\tau^3>9m\kappa\) Summary: Conditional classical bounded-error/bounded-recoil protocols require F²τ³>9mκ; a balanced two-mark construction succeeds above 36mκ. Limit/reuse: The quantum compact-support instantiation is vacuous and does not derive κ>0. Use planck-gap-probabilistic and record-costs-disturbance for valid resource-relative quantum statements; mark availability and incoming momentum assumptions remain explicit.
planck-gap-paper.md | priority=3 | flags=none | role=synthesis,result | status=conditional | proof_status=mixed | value=synthesis,infrastructure | keys=Newton Book I scholion; sagitta-impulse pairing; sharp Gaussian bound; arbitrary instruments; polygon phase; Opticks fits; ancient division; positive action unit | area=Newton/action Title: The cost of a mark: Newton’s vanishing sagitta and a floor of order \(\hbar\) Summary: Main synthesis combines sharp Gaussian recording bounds, general disturbance costs, state-independent polygon phases, and edition-labelled Newton/ancient division sources. Limit/reuse: Gaussian correlation restrictions, hybrid-state resource suprema and controlled-pass budgets matter; Newton’s fits give per-colour premises with a modern extension. Independent positivity/universality of the action unit remains open: consult necessity-unit-and-indeterminacy and the live SED notebook.
planck-gap-probabilistic.md | priority=3 | flags=surprising | role=result,obstruction | status=result | proof_status=proved-unrefereed | value=surprising-result,known-boundary | keys=arbitrary quantum instruments; adaptive protocol; Bures angle; hybrid marginal resources; aperture bound; squeezing aspect ratio; separated packets | area=Newton/action Title: The probabilistic Planck gap: \(F\tau(L+\tau P/2m)\ge\hbar\arcsin(1-2\epsilon)\), and why it is resource-relative Summary: Arbitrary adaptive quantum instruments obey JL+sP≥ℏ arcsin(1−2ε) when position/momentum resources are bounded on the required hybrid states. Separated packets permit arbitrarily small Galileo action with unbounded preparation aperture. Limit/reuse: Instrument universality is preparation-relative; an area bound LP alone fails without aspect-ratio control. Record-distance-path-length supplies the sharp geometric formulation.
polyakov-average-gap-bound.md | priority=2 | flags=none | role=result,infrastructure | status=result | proof_status=mixed | value=infrastructure,known-boundary | keys=spatial Polyakov loop; Feynman-Bijl; SU(N); Kogut-Susskind Hamiltonian; averaged loop variance; physical gap upper bound; self-averaging | area=Yang–Mills/gauge Title: The gap is bounded by the variance of the averaged spatial Polyakov loop, with the small-volume scaling built in Summary: The averaged fundamental spatial Polyakov loop gives Δphys≤ℏcg²N/[4L Var(averaged loop)] for the SU(N) Kogut–Susskind Hamiltonian. A positive volume-uniform physical gap therefore requires suitable loop self-averaging. Limit/reuse: This is an upper bound, never a positivity proof; proposed small-box scaling uses additional zero-mode estimates, and strong-coupling Haar variance yields a weak bound.
polygon-lift-phase.md | priority=3 | flags=surprising | role=result,infrastructure | status=result | proof_status=mixed | value=surprising-result,infrastructure | keys=Weyl central extension; inscribed polygon; insertion triangle; ordering holonomy; Dirichlet Green action; Gaussian distinguishability; Opticks refraction invariant | area=Newton/action Title: Newton’s inscribed polygon differs from the parabola by the phase of its segments Summary: Endpoint-matched polygon and forced motion differ by the exact scalar phase ΣKstep/ℏ; constant force gives F²Στj³/(24mℏ), with exact insertion and ordering identities. The same Dirichlet functional bounds Gaussian distinguishability by K/κ. Limit/reuse: Phase uses supplied Weyl relations; Gaussian sharpness requires one-sign force and uncorrelated marks. Newton fits interpretation needs a modern continuous-speed extension and remains per-colour.
position-preparation-ambiguity.md | priority=0 | flags=none | role=result,calibration | status=result | proof_status=proved-unrefereed | value=used-calibration,known-boundary | keys=R18; unknown probe positions; calibrated incoming momenta; clock reaction; narrow fixed pulses; equal-record shell fibre; lambda-squared response | area=apparatus/reconstruction Title: Unknown probe positions can hide the receiver after momentum calibration Summary: In a fixed admissible pulse design, unknown probe positions compensate a receiver-shell patch despite four initial and four final momenta being recorded; clock reaction supplies an invertible λ² response. Limit/reuse: The reconstruction lower-bound product scales as (λb)² and is preparation-relative, not universal or a risk-vanishing theorem. Full-pointer-recovery tests the richer-record endpoint.
principia-constant-force-action.md | priority=2 | flags=none | role=result,historical | status=result | proof_status=exact | value=infrastructure,source-guardrail | keys=Galileo parabola; inertial-line area; matched-endpoint chord; Lemmas X-XI; deterministic work; boost invariance; cubic action defect | area=Newton/action Title: Newton’s vanishing areas and the proposed action scale Summary: For constant force, the inertial–parabola area is vFτ³/(6m), and the endpoint-matched chord action defect is F²τ³/(24m)=τδE/12; polygon lens errors decay as N⁻². Limit/reuse: Deterministic work differs from quantum energy spread; the action defect survives boosts and endpoint gauge changes. Read English witnesses anchor the geometry; supplied phase resolution neither selects ℏ nor prohibits shrinking paths.
principia-fifth-postulate.md | priority=3 | flags=surprising | role=synthesis,result | status=conditional | proof_status=mixed | value=synthesis,known-boundary | keys=joint determinacy; velocitas ultima; affine symplectic covariance; Moyal uniqueness; Gaussian state restriction; Slepian concentration; zero branch | area=Newton/action Title: A fifth postulate for the Principia: joint determinacy of place and motion Summary: Under added affine-symplectic covariance, associative polynomial products reduce to the Moyal family; covariant noise-closed Gaussian state restrictions instead select a covariance threshold. Nonzero supplied constants give disturbance/concentration bounds. Limit/reuse: Both families retain the zero branch; interpreting Newton’s ultimate velocity as a record postulate is separate from the mathematical classification. Newton-indeterminacy-routes supplies the commutative alternative.
quantum-exclusion-premises.md | priority=1 | flags=none | role=historical,infrastructure | status=historical | proof_status=reading | value=source-guardrail,infrastructure | keys=Q01; Hardy continuity; CDP purification; finite simplex; operational closure; reversible transformations; action-time identification | area=historical/sources Title: Two ways to exclude a classical operational model Summary: Selected Hardy/CDP passages isolate continuous reversible pure-state connectivity and purification as distinct premises excluding standard finite classical simplexes/composites. Limit/reuse: These elementary exclusions neither reject every classical phase-space model nor supply a mechanical action scale; full reconstruction proofs were not read. Hamiltonian-finite-closure tests whether an interacting mechanical description can satisfy the required finite closure.
radiation-noise-action-selection.md | priority=2 | flags=route-closure | role=obstruction,result | status=obstruction | proof_status=conditional | value=decisive-obstruction,known-boundary | keys=Q02; cubic noise spectrum; dipole damping; oscillator stationary action; narrow resonance; free reservoir amplitude; ultraviolet cutoff; noncommuting limits | area=Newton/action Title: Radiation balance selects a spectral shape, but leaves its action amplitude free Summary: A finite-cutoff, externally Gaussian-driven harmonic probe has stationary action tending to supplied K in the stationary-first narrow-resonance limit, independently of charge/mass. Limit/reuse: K remains freely rescalable, including zero; removing the cutoff first causes ultraviolet energy divergence. This closes linear reservoir amplitude selection, not causal nonlinear field–particle models; SED-zeta-radiation-link keeps its physical assumptions explicit.
reachable-cut-composition.md | priority=2 | flags=none | role=result,infrastructure | status=result | proof_status=proved-refereed | value=infrastructure,known-boundary | keys=R08; C072; C073; bounded-force lens; sheared Minkowski sum; momentum fibre; conditional canonical area; exact cut observation | area=apparatus/reconstruction Title: Reachable information across a classical cut Summary: Bounded-force endpoint lenses compose exactly as K_T=S_bK_a+K_b when the joint phase state crosses a cut. Exact position observations leave a calculable momentum fibre and terminal area A(b)+(Fb²/m)D. Limit/reuse: Pointwise force admissibility and non-disturbing ideal observations are premises; refining the latest record collapses area without necessarily recovering momentum. Finite-precision-cut tests realistic record errors.
reasons-to-stop-as-research.md | priority=3 | flags=route-closure | role=obstruction,synthesis | status=obstruction | proof_status=mixed | value=decisive-obstruction,synthesis | keys=H1 weak-side RG; H2 mixing box; Griffiths monotonicity direction; truncated correlator; certified boundary supremum; physical Wilson coupling; small-field threshold | area=Yang–Mills/gauge Title: The two reasons to stop, as research problems: what a correlation inequality would buy, what a certified verification cannot, and where the research is Summary: Corrects the proposed correlation-inequality escape: even suitable monotonicity transfers control toward stronger coupling, and does not automatically control the truncated vacuum correlator. Known certification methods cannot supply the proposed physical-coupling H2 box. Limit/reuse: The target becomes weak-side RG control, with explicit small-field constants; small-field-step-decay-and-threshold later tests that constants programme.
receding-centre-area-audit.md | priority=1 | flags=none | role=result,obstruction | status=result | proof_status=proved-unrefereed | value=source-guardrail,known-boundary | keys=receding harmonic centre; divergent sector cancellation; matched endpoints; arc-chord lens; factor two; endpoint gauge invariance; threshold versus tiling | area=Newton/action Title: The surviving area is the matched-endpoint arc–chord defect Summary: An explicit receding-centre harmonic family retains the finite arc–chord lens Fvτ³/(12m), while arc–inertial-tangent sector differences cancel exactly before the limit. Limit/reuse: Subtract divergent references before limiting; comparison-path action has fixed normalization. A cell threshold does not imply exact action quantization without an additional tiling premise. Principia-constant-force-action supplies the maintained Galileo target.
reciprocal-coupling-normalization.md | priority=1 | flags=none | role=result,calibration | status=exploratory | proof_status=proved-unrefereed | value=used-calibration,known-boundary | keys=Q06; reciprocal spring; inertia ratios; cycle product consistency; diagonal kinetic energy; common action multiplier; small-amplitude escape | area=Newton/action Title: Reciprocal exchange fixes relative mechanical scales Summary: Directed acceleration responses admit a diagonal-inertia reciprocal-spring network exactly when cycle ratio products equal one; connected networks fix mass ratios up to one common positive multiplier. Limit/reuse: Overall action rescaling and small-amplitude orbits still reach arbitrarily small action. The conclusion concerns the chosen spring completion, not arbitrary mechanics; composition-universality separates relative universality from positivity.
record-costs-disturbance.md | priority=3 | flags=none | role=result,infrastructure | status=result | proof_status=proved-unrefereed | value=infrastructure,known-boundary | keys=Theorem U; arbitrary unitary instruments; body-dependent noise; hybrid states; sagitta-momentum pairing; impulse-position pairing; adaptive disturbance; Bures correction | area=Newton/action Title: The record costs disturbance: a floor for every instrument Summary: Arbitrary unitary marks deciding the force comparison for every pair of initial states satisfy (s/8)ΣsupΔD+(J/2)ΣsupΔX≥ℏ arcsin(1−2ε). Limit/reuse: Spreads are over conditional/interpolating hybrid states, not merely observed preparations; infinite spreads make the bound vacuous. Supplied canonical kinematics sets the exchange rate. Record-distance-path-length sharpens the original total-variation constant and combines accounting.
record-costs-recoil.md | priority=3 | flags=none | role=result,obstruction | status=result | proof_status=proved-unrefereed | value=infrastructure,known-boundary | keys=Theorem R; momentum-transfer marks; affine sagitta minimization; arbitrary probe states; grid counterexample; diverging recoil; Gaussian floor limitation | area=Newton/action Title: The record costs recoil: a floor for every probe state Summary: Momentum-transfer recording with arbitrary probe states obeys sΣΔ_j≥8ℏ arcsin(1−2ε); the stronger weighted form minimizes recoil against an affine displacement fit. Approximate grid probes defeat the Gaussian action bound at non-blind signals while recoil diverges. Limit/reuse: Adaptivity requires resource suprema; Gaussian three-mark comparison uses infinite endpoint recoil. Record-costs-disturbance extends beyond this coupling class.
record-distance-path-length.md | priority=3 | flags=none | role=result,infrastructure | status=result | proof_status=proved-unrefereed | value=infrastructure,known-boundary | keys=Theorem P; Bures angle; sharp single-shot constant; force waveform; Theorem K; split accounting; Dirichlet recoil length; attainment open | area=Newton/action Title: The record’s distance is a path length Summary: Bures-angle hybrid chains replace 1−2ε by arcsin(1−2ε) in aperture, recoil and disturbance bounds. A combined force split charges body aperture and mark disturbance; one-sign forces with von Neumann marks yield ∫|f|min(L,R)≥ℏ arcsin(1−2ε). Limit/reuse: Hybrid resource bounds and hypothesis preparation quantifiers matter; sharp single-shot constants do not prove protocol attainment or independently select ℏ.
refinement-composition-and-limit.md | priority=3 | flags=none | role=result,live | status=result | proof_status=mixed | value=infrastructure,open-mechanism | keys=local insertion; cubic correction; summable defects; arbitrary partitions; harmonic kick-order universality; exact retained weights; 2D heat-kernel convolution; physical spectral control | area=refinement/comparison Title: Inserting a point, subdividing a cell: how the limit is built Summary: Constructs constant-force composition and arbitrary-partition limits; later sections construct harmonic trajectories uniformly across start/end kick mixtures and identify their force law. Exact 2D gauge subdivision and a summable measure-consistency lemma frame higher-dimensional blocking. Limit/reuse: Classical normalization remains free; one-loop running and graph projective consistency supply neither OS construction nor physical gap. Live nonlinear recording and weak-strip control remain separate obligations.
refinement-results.md | priority=3 | flags=none | role=synthesis,infrastructure | status=result | proof_status=mixed | value=synthesis,infrastructure | keys=cut-measure theorem; Gaussian record supremum; verdict continuity; series-parallel halving; SU(2) covariant reference; third-order responses; large-field clusters; SU(N) one-loop transfer | area=refinement/comparison Title: What survives refinement: results on Newton’s vanishing sagitta and the halving of lattice gauge fields Summary: Theorem compendium links cut-action decomposition, Gaussian record optimality/continuity, exact gauge-halving factorization, compact bridge identities and barriered SU(2) small-field response/tail estimates. Limit/reuse: Source notes carry current proofs and corrections; finite-order derivative bounds and rare-cluster estimates are not polymer convergence. Newton continuity remains model-relative; SU(N) transfer stated here is one-loop, not a full nonlinear continuum theorem.
relativistic-kepler-threshold.md | priority=2 | flags=surprising | role=result,obstruction | status=result | proof_status=proved-refereed | value=surprising-result,known-boundary | keys=M07; singular relativistic Kepler; angular-action threshold; regular bound orbit; finite-time plunge; softened core; external potential | area=Newton/action Title: Relativistic Kepler: a singular-core angular-action threshold Summary: In an external relativistic −k/r potential, regular complete bound orbits require |L|>k/c; any fixed softened core −k/√(r²+a²) instead admits bound circles for every |L|>0. Limit/reuse: This continuous admissibility threshold depends on the singularity, coupling and domain; it is neither action quantization nor a universal floor. Rivero’s consistency test keeps the angular-state premise separate.
reversible-generator-constraints.md | priority=1 | flags=none | role=result,infrastructure | status=result | proof_status=proved-refereed | value=infrastructure,source-guardrail | keys=C129; Q01; B77; product-test positivity; two-sided reversibility; Bloch-ball tensor; seven-dimensional slice; necessary generator restriction | area=infrastructure Title: Product probabilities restrict reversible generators Summary: Product-test positivity under two-sided reversible evolution forces every local generator slice into a seven-dimensional space, hence X∈L⊗n. The expanded proof retains Taylor remainders and source conventions. Limit/reuse: This is a necessary ambient linear-space restriction, not a full admissible Lie algebra or reconstruction; later source steps and physical clock/action identification remain separate.
reversible-interaction-premise.md | priority=1 | flags=none | role=infrastructure,obstruction | status=conditional | proof_status=reading | value=source-guardrail,known-boundary | keys=Q01; C125; qubit local balls; separable composite; reversible operational descent; partial-transpose branch; identical-copy closure; action normalization | area=apparatus/reconstruction Title: Reversible interaction excludes the minimal orientation composite Summary: The cited reconstruction theorem excludes genuine connected reversible interactions that preserve C125’s minimal separable orientation composite; broader identical-copy closure selects quantum composition under additional premises. Limit/reuse: Mechanical interaction need not descend reversibly to retained moments. This source/hypothesis audit does not verify the full reconstruction proof or supply an action scale; generator constraints checks only its initial technical step.
rivero-1998-conjecture-central-forces.md | priority=3 | flags=surprising | role=result,obstruction | status=result | proof_status=proved-refereed | value=surprising-result,known-boundary | keys=1998 consistency conjecture; quartic stationary interference; arbitrary-partition product formula; Euclidean joint limits; scalar angular descent; Hooke-Kepler EBK; h-to-zero sequence | area=Newton/action Title: Rivero’s consistency conjecture: quartic paths and central-force angles Summary: Quartic real-time refinement exists for every supplied h>0; unrestricted multi-critical halving fails, while selected branches and the Euclidean zero-endpoint model have controlled limits. Scalar angular descent and both Hooke/Kepler EBK cycles still allow h→0. Limit/reuse: The failure concerns extending the original single-critical-point prescription; WKB/trivial-holonomy premises do not select a positive universal value. Rotation composition tests universality separately.
rotation-composition-universality.md | priority=3 | flags=none | role=result,infrastructure | status=result | proof_status=proved-refereed | value=infrastructure,known-boundary | keys=constituent action constants; derivation compatibility; mixed force derivative; additive mechanical angular momentum; faithful tensor algebra; connected interaction graph; common zero branch | area=Newton/action Title: One action constant from composition and spatial rotations Summary: In a shared canonical product, Newton derivation compatibility forces h_i=h_j whenever the mixed force derivative is nonzero. Faithful mechanical angular-momentum closure gives a separate conditional universality test. Limit/reuse: Rotation covariance alone permits unequal constants; closure identifies the measured mechanical sum with one rotation generator. Connected interactions propagate equality, but the common zero branch and absolute scale remain unselected.
schur-error-ultraviolet.md | priority=2 | flags=route-closure | role=obstruction,result | status=obstruction | proof_status=mixed | value=decisive-obstruction,known-boundary | keys=Feshbach Schur error; constant vacuum shift; energy derivative; Berry logarithm; cubic vacuum dressing; gNs small; fixed-cutoff proposal; ultraviolet uniformity | area=Yang–Mills/gauge Title: The Schur error of the small-volume reduction is an ultraviolet problem: a fixed-lattice theorem is available, the renormalized regime is not Summary: A proved refined transfer lemma removes scalar vacuum shifts but charges their energy derivative. Formal second-order bare-fibre estimates predict Berry logarithms and a cubic slope ∼g²(ΛL)², obstructing cutoff-uniform reduction. Limit/reuse: The proposed fixed-lattice gap theorem explicitly lacks its rigorous-constant proof here. Weak-coupling Feshbach reduction therefore still needs dressed-vacuum and uniform estimates, not merely subtraction of vacuum energy.
score-constrained-ensemble.md | priority=3 | flags=surprising,route-closure | role=result,obstruction | status=result | proof_status=mixed | value=surprising-result,open-mechanism | keys=classical sheet action; score constraint; Fisher Hamiltonian; population conjugate action; reservoir transport; inverse density; fourth order tangency; compact transfer shape; Gaussian width; evolving shape modes; positive nonlinear completion; Hermite Gaussian; forward time; quartic record tail; unread recoil energy; two-sheet realization; Nelson drifts; switching rates; sheet potential; mean power cancellation; nonexplosion; controller identification; pilot wave; many interacting worlds; two unread widths; variance witness; autonomous zero branch | area=Newton/action Title: Score-constrained ensembles and population transport Summary: Restricted classical sheet action gives the Fisher action and reservoir-aware population momentum; free sheets leave the constraint and fixed compact transfer shapes fail tangency. A width/phase mode has an exact positive non-Gaussian forward completion. Nonlinear copying generates a quartic exponential tail outside finite Hermite–Gaussian modes, with exact unread recoil energy. §§6–8: the two-sheet switching realization exists on every positive solution (rates from ρ_qq/ρ, force from the sheet potential, exact mean power cancellation) and for all forward time on the explicit orbit; rates or forces over an interval determine the field pair, so within this architecture the controller is the field and, after records, the record-dependent data of its family; branch controllers pass the two-unread-width test and the marginal-score replacement is refuted by a variance witness; closure under coordinate copies holds at every κ≥0 under a branch-dependent protocol. §§6–8 refereed by GPT-6.1 Sol (Codex) 2026-10-01: Props. 6, 8 accepted, 7, 9, 11, 12 refined, former Cor. 10 replaced, corrections applied. Limit/reuse: Field dynamics is supplied; the compact-shape obstruction needs zero-gradient preparations and fixed compact shapes. The completion is forward only and its linear tangent is Gaussian width/phase. The realization needs ρ>0 and is a stochastic pilot-wave representation (Nelson drifts, many-interacting-worlds as the finite closed form); composition closure selects no κ, so the apparatus-closure route to positivity is closed; impossibility of every other realization and literal full-history storage are not claimed. Terminal access, phase reunion, positivity, universality and calibration remain open.
sed-closure-under-recording.md | priority=3 | flags=none | role=live,result | status=result | proof_status=mixed | value=open-mechanism,decisive-obstruction | keys=complete physical memory; adaptive affine-body copies; limiting coordinate-record path; nonlinear curvature obstruction; unread-score excess; separated-packet coherence; positive-tail stability; additive bridge phase; inverse density; bridge resistance; fixed-density phase energy; unread current excess; common score sign; correlated momentum preparation; terminal conjugate escape; free fourth moment; Fisher ensemble; stationary switching; Zig-Zag; finite rescaled clock; preparation-dependent force; unread widths | area=Newton/action Title: Shared radiation and closure under recording Summary: A shared-sign positive classical preparation supplies nonlinear score correction under coordinate copies but fails full pointer access and Newtonian free transport. A stationary switching process repairs the Gaussian target with exact mean-energy balance and finite switch count; no continuous force on (q,p,sign) alone realizes all prepared means/widths (§§8.22–8.23). Limit/reuse: The repair prescribes actuators and selects neither a physical apparatus nor positive κ; terminal access and phase reunion remain open. Static bridge results are unrefereed; new constructions are written, internally checked. Universality and calibration remain separate.
sed-zeta-radiation-link.md | priority=2 | flags=none | role=synthesis,infrastructure | status=conditional | proof_status=conditional | value=known-boundary,synthesis | keys=Lorentz-invariant spectrum; free zero-point amplitude; resonant Gaussian area; off-resonant momentum divergence; cutoff breaks invariance; disputed SED Planck derivation; radiation-unit calibration | area=Newton/action Title: A Lorentz-invariant background and the state-route constant: a conditional link to the radiation unit Summary: Narrow-resonance Gaussian oscillator response links a supplied zero-point amplitude κ to covariance area ζ; conditional on the disputed SED Planck-spectrum derivation, 2ζ=[(π⁴/15)⅓/(2π)]h_rad. Limit/reuse: Lorentz invariance leaves κ free; full momentum variance diverges, and a fixed finite linewidth window captures only part of the resonance. Recording closure separately tests retained records rather than assuming equilibrium survives observation.
self-sufficiency-contrast.md | priority=3 | flags=surprising | role=result,live | status=result | proof_status=mixed | value=surprising-result,known-boundary | keys=self-sufficiency; Kepler collision time; collision set; Kato self-adjointness; global unitary dynamics; quartic contrast; branch rule; Ehrenfest exact; coherent state centroid; Hepp theorem; hypothesis L; smallest h; Dirac Coulomb threshold; Klein-Gordon threshold; gap in h; k over c unit | area=Newton/action Title: The self-sufficiency contrast: where Newton’s axioms leave motion undefined, the theory with \(h>0\) defines it Summary: Theorem 1 for Kepler’s force: (a) the classical flow is incomplete, with collision time t_c=(π/2)√(mr₀³/2k) for fall from rest and the invariant null collision set {L=0, inward or bound}, where the axioms give no continuation; (b) −h²Δ/2m−k/r is self-adjoint on H²(ℝ³) and generates a global unitary group for every state and every h>0 (Kato 1951, cited; hypothesis L²+L^∞ verified); (c) the quartic contrast between the fixed-h unitary limit and the classical-first construction needing a branch rule (1998-conjecture note); (d) the classical trajectory as derived centroid, exact Ehrenfest for quadratic forces (proved) and Hepp’s theorem for Kepler on a regularized potential with the Duhamel step under a stated localization hypothesis (L) (cited). Proposition 2: with finite c the self-sufficient theories have h ≥ k/(α_c c) (Dirac distinguished extension ν<1; Klein–Gordon s-wave ν≤1/2; cited), so the self-sufficient values of h form an interval with left endpoint h_min>0 and Newton at 0 outside: the gap, in two models under their selection premises. Thm 1 refereed ACCEPT (GPT-6.1 Sol via Codex, second pass); Prop. 2 assessed separately. Limit/reuse: (b), (d2) and Proposition 2 rest on cited theorems with hypotheses stated; (L) is unproved; the Klein–Gordon branch selection and the endpoints of (5) are additional premises; no value of h is fixed; nothing about long times or about the nonexistence of completions without h.
series-parallel-gauge-refinement.md | priority=3 | flags=surprising | role=result,live | status=result | proof_status=mixed | value=surprising-result,open-mechanism | keys=directional halving; heat-kernel series; mid-plane parallel integral; Brownian bridges; Hypothesis P; winding holonomy; U(1) vortices | area=Yang–Mills/gauge Title: Series and parallel: where the gauge insertion law stops closing Summary: Directional heat-kernel halving factors exactly into closing series convolutions and a coupled mid-plane theory; Gaussian defects and U(1) winding decompositions are explicit. Limit/reuse: Nonabelian normalized estimates and stability for generated actions remain conditional/open; fixed-torus holonomies require qualification. The full-plane calculation and small-field notebook continue the live gauge route.
shared-readiness-chsh.md | priority=1 | flags=none | role=result,calibration | status=result | proof_status=known | value=known-boundary,used-calibration | keys=Q13; CHSH; shared readiness; setting independence; conditional locality; heralding; action normalization | area=Newton/action Title: Independent settings test shared readiness, while leaving action units free Summary: Setting independence and conditional locality imply sharp CHSH ≤2 even with arbitrary shared readiness and setting-independent preselection; supplied singlet probabilities violate it. Limit/reuse: Setting-dependent censoring changes the tested ensemble. The witness is dimensionless and leaves every common action normalization admissible.
shared-record-budget.md | priority=1 | flags=none | role=result,calibration | status=result | proof_status=proved-refereed | value=used-calibration | keys=R14; C084; C085; shared record budget; minimax; ell-r norm; composition exponent | area=apparatus/reconstruction Title: A shared record budget changes the composition exponent Summary: Identical bounded-force bodies sharing an ℓr record-error budget have center-of-mass minimax radius εn^(-1/r) and saturated action-like product proportional to n^(1−3/(2r)). Limit/reuse: The anomalous exponent reflects apparatus-resource sharing; independent budgets in block composition restore the appropriate extensive composition.
shared-resource-events.md | priority=0 | flags=surprising | role=result,calibration | status=exploratory | proof_status=proved-unrefereed | value=used-calibration | keys=Q11; shared release; absorbing Markov receiver; fringe probabilities; inhibition delay; finite-window efficiency | area=apparatus/reconstruction Title: A shared release produces exclusive fringe-weighted events Summary: A classical single-permission Markov receiver with prescribed fringe-weighted hazards yields exclusive clicks and normalized fringe probabilities; spatial inhibition delay produces explicit double-click costs. Limit/reuse: Shared control, linear hazards and readiness are supplied architecture. At vanishing energy, finite-window detection probability vanishes; this supplies neither local independent detection nor a universal action floor.
single-calibration-fibres.md | priority=0 | flags=none | role=result,calibration | status=result | proof_status=proved-refereed | value=used-calibration | keys=R32; C121; B64; inverse response column; calibration fibre; Hermite interpolation; canonical diameter | area=apparatus/reconstruction Title: One uncertain calibration leaves an exact receiver curve Summary: One uncertain calibration leaves an exact equal-record receiver curve whose tangent is a column of the inverse response matrix; a fixed pulse design makes both canonical coordinate diameters positive. Limit/reuse: Projected curve area remains zero, arbitrary designs need nonzero cofactors, and ambiguity shrinks with calibration tolerance at fixed coupling. Uses tolerance recovery.
small-field-step-decay-and-threshold.md | priority=3 | flags=surprising,route-closure | role=obstruction,result | status=obstruction | proof_status=mixed | value=decisive-obstruction,known-boundary | keys=soft block constraint; Combes–Thomas; Kotecky–Preiss; nonlinear threshold; decay rate; weak coupling; methods deficit | area=Yang–Mills/gauge Title: One small-field blocking step, part 1b: the decay rate and the shape of the threshold, and why the weak side’s deficit is ten orders of magnitude Summary: Soft block constraints improve the explicit Gaussian decay rate, but plugging such rates into a heuristic nonlinear convergence estimate leaves an enormous weak-coupling deficit, even at idealized order-one decay. Limit/reuse: No nonlinear polymer expansion or rigorous impossibility theorem is proved; this diagnoses the limitation of the proposed constant-chasing method after the Gaussian step.
small-field-step-gaussian.md | priority=2 | flags=none | role=result,infrastructure | status=result | proof_status=mixed | value=infrastructure | keys=SU(3); four-dimensional block averaging; 32 components; tube Poincare; Gaussian covariance; 4/9; gauge intertwining | area=Yang–Mills/gauge Title: One small-field blocking step for \(SU(3)\), part 1: the Gaussian fluctuation integral with block averaging, with explicit constants Summary: Linearized four-dimensional SU(3) blocking has exact Gaussian covariance, gauge-compatible averaging and a tube Poincare lower bound 4/9, yielding fluctuation variance at most 9g²/4. Limit/reuse: This describes the Gaussian reference; nonlinear normalized estimates and iteration are separate. The decay/threshold continuation diagnoses why crude propagation constants do not close the weak side.
spin-action-patching.md | priority=2 | flags=surprising | role=result,calibration | status=exploratory | proof_status=known | value=known-boundary,used-calibration | keys=Q07; spin sphere; prequantization; chart transition; 2s/K; irrational spin ratios; common scaling | area=Newton/action Title: Global spin phases quantize a ratio, not an absolute action scale Summary: Patching exponentiated spin-sphere action phases requires 2s/K to be integral once phase unit K is supplied; classical sphere dynamics itself allows arbitrary symplectic area. Limit/reuse: Common rescaling of spin, Hamiltonian and K preserves motion and phases, while arbitrarily small trial-loop actions remain possible. Topology selects a ratio, not an absolute unit or dynamical action floor.
stabilized-topology-action-scale.md | priority=1 | flags=none | role=result,calibration | status=exploratory | proof_status=proved-unrefereed | value=used-calibration,known-boundary | keys=Q05; Skyrme; degree one; inverse stereographic trial; radius stabilization; b/c; common action scaling | area=Newton/action Title: Stabilizing a topological radius exposes an action coefficient Summary: A degree-one Skyrme trial family has competing aR and b/R energies, a preferred radius, and an action coefficient b/c; a separate topological energy lower bound holds. Limit/reuse: Common scaling of both coefficients preserves classical equations while scaling all actions, and vacuum excitations remain gapless. The calculation does not construct a full minimizer or prove dynamical well-posedness.
static-composition-classics.md | priority=0 | flags=none | role=historical,synthesis | status=historical | proof_status=reading | value=source-guardrail | keys=H10; Vasubandhu; six contacts; Ibn Sina; Liu Hui; Mohist shadow; parts and whole | area=historical/sources Title: Before the arrow: can the parts make a whole? Summary: Sources on atomic contacts, division and static assembly supply a historical counterpart to whether retained pieces determine a whole. Limit/reuse: Vasubandhu and Ibn Sina are differentiated from modern interface-state arguments; Chinese restorations and the Liu Hui witness need edition/facsimile qualification. Resemblance proves neither transmission, quantum structure nor an action unit; compare classical cut state.
stochastic-route-velocitas-ultima.md | priority=3 | flags=surprising | role=result,live | status=conditional | proof_status=proved-refereed | value=surprising-result,open-mechanism | keys=S1; S2; S3; Brownian free motion; universal mD; Cameron–Martin; ultimate velocity; zero branch | area=Newton/action Title: Brownian free motion: the velocitas ultima denied, one action constant, and the floor Summary: Continuous isotropic independent-increment free motion is Brownian; independent center-of-mass composition over all positive masses forces one nonnegative κ=mD. Additive force-independent position noise gives the sharp pinned Galileo discrimination floor. Limit/reuse: κ>0 remains assumed; Nelson dynamics needs additional state/phase laws. Uses cut measure within the fifth-postulate programme.
strong-coupling-target-box.md | priority=2 | flags=none | role=result,synthesis | status=conditional | proof_status=conditional | value=synthesis,infrastructure | keys=SU(3); target box; bounded local perturbations; electric deformation; locality q; exact low-energy reduction; physical gap | area=Yang–Mills/gauge Title: The target box: the strong-coupling gap survives local perturbations, so the renormalization group has an explicit finish line Summary: The continuous-time strong-coupling expansion admits explicit few-link perturbation tolerances and electric-energy deformation, giving a volume-uniform gap proportional to g²ℏc/a inside a target class. Limit/reuse: Tables separate adjacent-growth estimates from conservative general counts and retain the quoted expansion premises. Reaching the box by exact low-energy RG with controlled generated terms remains open; uses KS expansion.
strong-coupling-threshold-explicit.md | priority=2 | flags=surprising | role=obstruction,calibration | status=obstruction | proof_status=formal | value=known-boundary,used-calibration | keys=Yarotsky; time-discretized polymers; beta e^-465; g² 10^101; entropy; direct expansion; weak-side width | area=Yang–Mills/gauge Title: The strong-coupling threshold made explicit: Yarotsky’s proof gives \(g_0^2\sim10^{100}\), and only a direct expansion can give \(g_0^2\sim10^2\) Summary: Crude numerical extraction from Yarotsky’s proof yields an SU(3) sufficient threshold of order g²=10^101, exposing the cost of time-discretized polymer bounds. Limit/reuse: Expected direct-expansion thresholds 40–70 were estimates, not derived results; the later KS calculation supplies its actual threshold. The weak-side boundary still controls the crossover width.
strong-coupling-uniform-gap.md | priority=2 | flags=none | role=result,synthesis | status=result | proof_status=known | value=synthesis,known-boundary | keys=T2; Kogut–Susskind; Yarotsky; Peter–Weyl; volume-uniform gap; thermodynamic ground state; beta 54/g^4 | area=Yang–Mills/gauge Title: The strong-coupling gap of the Kogut–Susskind Hamiltonian is uniform in the volume Summary: A hypothesis check of Yarotsky’s theorem gives the KS Hamiltonian a unique ground state, thermodynamic limit and volume-uniform strong-coupling gap ≥γ(g²/2)C₂ℏc/a, including U(1). Limit/reuse: The threshold is existential here, with explicit improvements linked separately. This controls fixed-cutoff strong coupling, not the weak-bare-coupling continuum trajectory; see lattice obligations.
su2-midplane-order-t.md | priority=3 | flags=none | role=result,live | status=conditional | proof_status=formal | value=open-mechanism,infrastructure | keys=normalized mid-plane determinant; relative order t; cut positive transverse negative; SU(N) N/2; dimension six; winding obstruction; estimate (18) | area=Yang–Mills/gauge Title: SU(2) on the full mid-plane: the relative-order-t halving defect Summary: The formal full-plane one-loop defect has positive cut-coupling shifts, negative transverse shift, and remaining bulk smooth-field operators of dimension ≥6; refereed SU(N) scaling multiplies SU(2) coefficients by N/2. Limit/reuse: Flat-holonomy winding disproves literal fixed-torus flux-only control. Volume-uniform normalized interacting estimates and iteration remain open in the small-field continuation.
su2-midplane-small-field.md | priority=3 | flags=none | role=live,result | status=conditional | proof_status=mixed | value=open-mechanism,infrastructure | keys=normalized covariant comparison; retained barrier; weak recoupling strip; all-order bad-component tree (116); exact dressed activities (112); moving-mean quadratic source (177); nonlinear saddle; physical recoupling | area=Yang–Mills/gauge Title: The SU(2) mid-plane on its small-field set: bounds and the missing comparison Summary: Barriered covariant one-step bounds lead to all-order bad-component correlations and exact dressed hard-core activities in a weak auxiliary recoupling strip; a quadratic moving-mean test supplies the subtracted barrier source bound. Limit/reuse: Original flux-only Proposition 4 is rejected. Physical recoupling, nonlinear background transfer, other subtractions, late SU(3) estimates, full-integral comparison and iteration remain open; continues series/parallel.
su2-midpoint-exact.md | priority=3 | flags=surprising | role=result,infrastructure | status=result | proof_status=exact | value=surprising-result,infrastructure | keys=SU(2) bridge midpoint; all-spin character; spin-1 matrix; Gaussian tail; curvature softening; isolated cube; image bounds | area=Yang–Mills/gauge Title: The SU(2) bridge midpoint in closed form: the curvature term is exact Summary: Exact bridge character formulas cover every spin; spin-½ is scalar, while refereed spin-1 matrix entries retain axial anisotropy and explicit image bounds. Limit/reuse: Isolated-cube factorization uses independent bridges. Fixed-spin formulas do not control the full heat-kernel character sum or shared-edge mid-plane; image separation degenerates at the cut locus. Supplies curvature inputs to the full-plane calculation.
su3-constants.md | priority=2 | flags=none | role=infrastructure,synthesis | status=result | proof_status=known | value=infrastructure | keys=SU(3); Casimir 4/3; beta 54/g^4; Lieb–Robinson; Z3 flux sectors; one-loop doublings; magnetic identities | area=infrastructure Title: SU(3) in four dimensions: every constant of this programme, evaluated Summary: Evaluates group-dependent constants in the earlier SU(3) programme: Casimirs, strong-coupling normalization, locality velocity, magnetic identities, running coefficients and flux-sector counts. Limit/reuse: Lookup conventions remain useful; extrapolated doubling counts, small-volume interpretation and older route status are not new proofs. Retrieve maintained dependency notes for current thresholds and corrected physical/continuum scope.
sun-midpoint-centre.md | priority=3 | flags=surprising | role=result,live | status=result | proof_status=mixed | value=surprising-result,infrastructure | keys=compact group bridge; arbitrary cut; coroot images; coweight lattice; q-torsion centre; SU(3) triality thirds; signed amplitudes | area=Yang–Mills/gauge Title: The bridge midpoint on a compact group at any cut: windings and the centre Summary: Exact single/multiple-cut character moments classify central image phases by q-torsion; SU(3) trisections see triality while halvings reach only the identity centre element. Fundamental trisection shells are explicit. Limit/reuse: Signed polynomial amplitudes are not probabilities or homotopy sectors. Matrix orientations, normalized uniform image truncation and repeated RG stability remain open; uses SU(2) midpoint.
superdeterminism-floor.md | priority=1 | flags=surprising | role=result,calibration | status=conditional | proof_status=conditional | value=used-calibration,known-boundary | keys=Anosov setting device; Lipschitz preparation; measurement dependence; delta resolution; Ehrenfest logarithm; conditional setting laws | area=Newton/action Title: Superdeterminism lives below every resolution; a floor gives it a lifetime Summary: Exponential mixing of a connected Anosov setting device bounds hidden-variable/setting correlations for Lipschitz-resolved conditional preparations, with a logarithmic resolution-dependent onset. Limit/reuse: A supplied isotropic preparation floor turns this into an Ehrenfest-type lifetime; it neither derives that floor nor covers integrable devices, exact automaton labels or singular ensembles. Event bounds also require regular setting cells and suitable delays.
susceptibility-gap.md | priority=2 | flags=surprising | role=result,synthesis | status=result | proof_status=exact | value=surprising-result,known-boundary | keys=C041; C042; C045; susceptibility frame; hidden slow mode; relaxation gap; independent clocks; calibrated observability | area=refinement/comparison Title: When an action plateau controls a spectral gap Summary: Complete observable frames with bounded total susceptibility lower-bound a finite reversible chain’s relaxation gap; one positive velocity plateau only upper-bounds it. Explicit hidden/weakly observed slow modes preserve the plateau while closing the gap. Limit/reuse: Uniform calibrated coverage and physical clock normalization matter; interaction benchmarking uses Ising gap. This is not automatically a reconstructed quantum-field gap.
tangent-groupoid-trajectories.md | priority=3 | flags=surprising | role=synthesis,result | status=exploratory | proof_status=mixed | value=synthesis,infrastructure | keys=tangent groupoid; zoom action; principal symbol; time-graded groupoid; min-plus action; convolution; ballistic versus diffusive | area=refinement/comparison Title: The tangent groupoid, its zoom, and whole trajectories Summary: Relates tangent-groupoid zoom and principal symbols to single-step refinement, and time-graded composition to whole trajectories; constant-force action/kernel laws provide the explicit example. Limit/reuse: Geometric identifications are readings of established constructions. Diffusive quantum-path interpretation presupposes supplied positive ℏ and does not establish action necessity; uses refinement construction and fifth postulate.
telegraph-return-bridge.md | priority=2 | flags=none | role=result,calibration | status=result | proof_status=proved-refereed | value=used-calibration,infrastructure | keys=C033; C037; telegraph bridge; Bessel count; beta midpoint law; velocity memory; cubic crossover; small-mass nonuniformity | area=refinement/comparison Title: A finite-speed return bridge: cuts and midpoint crossover Summary: Exact count/simplex return paths give consistent velocity-resolved cuts, a midpoint atom plus beta-mixture law, controlled vanishing polygon-action error and an explicit long-window crossover to a supplied plateau. Limit/reuse: The right-continuous bridge differs from shrinking endpoint-window velocity conditioning; unscaled midpoint bias survives. Positive mass-universal plateaux need nonuniform small-mass windows, and the reversal rate still sets their value.
thermal-receiver-reliability.md | priority=1 | flags=none | role=calibration,result | status=conditional | proof_status=conditional | value=used-calibration,known-boundary | keys=Q10; Arrhenius receiver; dark retention; signal deadline; fixed attempt frequency; transduction; barrier reduction | area=apparatus/reconstruction Title: Thermal reliability selects a detector cost, not a universal action Summary: A capped activated-rate detector with fixed attempt frequency has exact feasibility and optimal signal barrier reduction kBT[log(cτ/(atg))]+. Limit/reuse: Incident-work bounds require a supplied transduction coefficient; variable prefactors evade barrier reduction. Temperature, deadlines and errors remain in the cost, which vanishes in admitted parameter limits and selects no universal action.
thermodynamic-records-no-floor.md | priority=2 | flags=route-closure | role=obstruction,result | status=obstruction | proof_status=conditional | value=decisive-obstruction,known-boundary | keys=Landauer; Sagawa–Ueda; posterior support area; mutual information; logarithmic work; no action floor; Bayesian records | area=Newton/action Title: Thermodynamics of records gives a trade-off and no floor Summary: For a uniform prior and bounded posterior support, the stipulated measurement-plus-erasure law gives W≥kBT log(A0/η); classical finite-precision protocols retain arbitrarily small positive η at finite increasing cost. Limit/reuse: This closes thermodynamic record pricing as a universal floor selector within the specified classical class, without proving sharp attainability of the work bound. Uses unit and indeterminacy.
three-body-cut-memory.md | priority=2 | flags=surprising | role=result,calibration | status=result | proof_status=proved-refereed | value=surprising-result,used-calibration | keys=R04; C064; C065; spring-chain memory; cosine kernel; tagged phase; two-time observability; preparation scaling | area=apparatus/reconstruction Title: Tagged momentum and the memory of a third body Summary: Eliminating the receiver of an equal-mass three-body spring chain yields an exact cosine memory kernel and inherited quadratures; tagged position/momentum alone fail to compose. Two nearby exact phase observations recover the missing state. Limit/reuse: Recovery is ill-conditioned as sampling shrinks, and all prepared modal actions contract while the memory law remains fixed; extends classical cut state.
three-calibration-global-recovery.md | priority=0 | flags=none | role=result,calibration | status=result | proof_status=proved-refereed | value=used-calibration | keys=R30; three calibrated positions; full ten-coordinate record; apparatus energy; global inverse; delta/lambda; fixed preparation box | area=apparatus/reconstruction Title: Three calibrated positions give uniform global receiver recovery Summary: Three exact initial probe-position calibrations, apparatus energy and full final apparatus data give uniform global receiver recovery on a bounded convex domain, for a fixed pulse design and suitably reduced fixed preparation box. Limit/reuse: Record-error amplification is O(1/λ); at fixed coupling its canonical product tends to zero. Calibration errors need the tolerance extension.
three-continuum-limits.md | priority=3 | flags=none | role=synthesis,live | status=conditional | proof_status=conditional | value=synthesis,infrastructure | keys=Newton necessity; pure SU(3); chiral pion; physical spectral measures; surviving weight; Ward identity; regulator limits; gap thesis; fringe visibility; Kepler swarm | area=refinement/comparison Title: What survives refinement: the pion, the Yang–Mills gap and Newton’s action Summary: Sets the joint-paper frame: Newton action necessity and pure SU(3) continuum gap are the two proof goals; massless/massive pion physics tests symmetry and surviving spectral weight. Two elementary spectral-measure limit criteria distinguish physical thresholds from disappearing eigenvalues. §4 now carries the gap thesis (2026-10-01): Newton’s surviving object is the fringe visibility of crossing streams in complete records of determinate swarms, with the record limit taken first; the Gaussian parabola is immune. Limit/reuse: Neither goal is proved; September 29 updates older H3-first routing to UV halving, and STATE controls today’s queue.
three-dimensional-gap-one-function.md | priority=2 | flags=surprising | role=synthesis,result | status=conditional | proof_status=conditional | value=synthesis,open-mechanism | keys=3D Yang–Mills; crossover f(x); g²hbar²c; small-volume x^-2/3; lattice gap ratio; stochastic auxiliary time; Karabali–Nair | area=Yang–Mills/gauge Title: In three dimensions the mass gap is the positivity of one function at infinity Summary: Conditional on physical construction, 3D Yang–Mills gaps have the one-variable form g²ℏ²c f(g²ℏL); a positive finite infinite-volume limit is the remaining spectral target. Constant modes identify the small-box scale. Limit/reuse: Strong lattice coupling and small-volume expansions are separate regimes; local stochastic dynamics supplies neither invariant measure nor OS theory. All-coupling positivity is sufficient, not necessary for the continuum target.
topological-sector-action-selection.md | priority=2 | flags=surprising | role=result,calibration | status=result | proof_status=known | value=known-boundary,used-calibration | keys=Q04; O(3) sigma model; degree one; 4pi rho; shrinking static soliton; crossing-time action; gapless vacuum | area=Newton/action Title: A topological energy floor survives shrinking while the action cost vanishes Summary: Smooth degree-one O(3) sigma-model static solutions of every radius saturate a fixed sector-energy floor, while their action magnitude over one radius-crossing time tends to zero. Vacuum waves remain arbitrarily soft. Limit/reuse: The specified energy-time action is not every action observable; topology fixes neither radius nor a unique gapped ground state. Stabilized topology tests added competing terms.
torus-valley-potential.md | priority=3 | flags=none | role=result,infrastructure | status=conditional | proof_status=formal | value=infrastructure,open-mechanism | keys=SU(2) torus; one-loop valley potential; Poisson summation; periodic centre minima; 2hbar c|a|; nonzero-mode correction; Feshbach H3 | area=Yang–Mills/gauge Title: The one-loop potential along the abelian valley of the torus is periodic, reproduces C133’s linear term at the origin, and saturates at order 1/L Summary: The regularized SU(2) one-loop torus valley potential is an explicit positive periodic Fourier series, with linear zero-mode term 2ℏc|a| and quadratic nonzero-mode correction; symmetry fixes that quadratic coefficient for general constant backgrounds. Limit/reuse: This is a one-loop effective potential, not an interacting excitation-gap proof or UV-uniform Schur estimate. Supports Feshbach H3; the cubic-lattice correction sign is borrowed.
two-calibration-branches.md | priority=0 | flags=none | role=result,calibration | status=result | proof_status=proved-refereed | value=used-calibration | keys=R29; two calibrated positions; energy shell; full apparatus record; local inverse; global two branches; canonical ambiguity | area=apparatus/reconstruction Title: Two calibrated probe positions give local recovery and two global branches Summary: Two calibrated probe positions and both exact energies remove local degeneracy in a fixed apparatus design but leave two globally distinct receiver preparations with identical complete records and positive canonical separation. Limit/reuse: The preparation-relative bound is neither positive area nor sharp global minimax risk. A third calibration gives uniform global recovery on its stated reduced domain.
two-position-recovery.md | priority=1 | flags=none | role=result,calibration | status=result | proof_status=proved-refereed | value=used-calibration,known-boundary | keys=R10;C076;C077;finite difference;bounded force;delay;epsilon over separation | area=apparatus/reconstruction Title: Two position records recover the phase state Summary: Two bounded-error position records give simultaneous sharp errors for the stated causal position/momentum estimator, and both errors vanish when precision improves faster than sample separation and delay vanishes. Limit/reuse: Known initial state, non-disturbing records and a force ceiling are inputs; this is not optimal minimax recovery. The equal-error optimum is δ*=2√(mε/F), with momentum error 2√(mFε).
two-regulator-audit.md | priority=2 | flags=surprising | role=result,routing | status=result | proof_status=proved-refereed | value=surprising-result,routing | keys=M05;C014;regulator limits;Gaussian bridge;dimension variance;uniform path;action defect | area=refinement/comparison Title: Two regulators: what survives when the paths shrink? Summary: Gaussian bridge polygons can converge uniformly to a classical path while retaining excess action ℓ/2 when dimension times the vanishing action coefficient tends to ℓ. Limit/reuse: The residual is regulator/preparation-selected, not a hard action-value floor; running bare mass to preserve a reference kernel is a different experiment. The full derivation is the regulator-limits manuscript.
typical-field-strength-window.md | priority=1 | flags=route-closure | role=superseded,calibration | status=obstruction | proof_status=mixed | value=decisive-obstruction,used-calibration | keys=flow time;typical magnetic variance;g over 4pi;supremum tail;compact lattice correction | area=Yang–Mills/gauge Title: On typical configurations the flow truncation is controlled at any coupling; the whole obstruction is the large-field tail Summary: Free flowed fields satisfy t√⟨|b_t|²⟩=g/(4π); the typical-field truncation estimate can be reduced by increasing range, while a volume supremum needs tail control. Limit/reuse: Interacting use is perturbative. Its lattice-step pessimism is corrected by compactness; this note does not prove an interacting normalized rarity bound.
uv-halving-ir-confinement.md | priority=3 | flags=none | role=synthesis | status=conditional | proof_status=mixed | value=synthesis,infrastructure | keys=UV IR;exponential ladder;dimensional transmutation;physical spectral weight;matching scale;C Lambda | area=Yang–Mills/gauge Title: Halving goes to the ultraviolet; confinement lives in the infrared Summary: Explains how one-loop exponential terms scale under halving and why fixed infrared observables require uniform ultraviolet transport, separating dimensional transmutation from a positive gap coefficient. Limit/reuse: The ladder is conditional on matching; coarse observations may miss fine spectral channels. Its finite-crossover-certification wording needs the later weak-side diagnosis, and some passages use g² for the classical coupling.
villain-monopole-refinement.md | priority=3 | flags=surprising | role=result,obstruction | status=result | proof_status=proved-refereed | value=surprising-result,decisive-obstruction | keys=Villain U1;Poisson monopole;flux sectors;TV;lambda3 a;D4 loop;Gross trajectory | area=Yang–Mills/gauge Title: Compact U(1) under refinement: an explicit total-variation bound in three dimensions, and why it fails in four Summary: Exact Villain monopole/flux decomposition gives a D=3 full-measure TV bound 2(L/a)³e^{(−π²/(6λ₃a))/(1−e}(−π²/(2λ₃a))) and removes compact defects at fixed coupling and volume. Limit/reuse: The same D=4 TV upper bound is useless at fixed coupling; an extensive lower bound proving TV separation is only expected. Blocked Gaussian fields still need smooth-observable comparison, not TV closure.
weak-coupling-feshbach-reduction.md | priority=3 | flags=none | role=live,conditional | status=conditional | proof_status=mixed | value=open-mechanism,infrastructure | keys=H1 H2 H3;Feshbach;relative Schur;fibered vacuum;small volume;zero mode;g two thirds | area=Yang–Mills/gauge Title: The weak-coupling gap in a small box reduces to three inequalities through the Schur complement Summary: A proved relative Schur-transfer lemma reduces the small-volume gap lower bound to nonzero-mode separation, a relative coupling error and an effective zero-mode gap. Limit/reuse: All three physical inequalities remain open; the bare sharp-cutoff vacuum fails UV control. The displayed cutoff calculation uses SU(2); transfer to SU(3) needs group-dependent estimates. A fibered projection and gauge-compatible cutoff identify the corrected estimates, not a completed fixed-lattice gap theorem.
what-would-unblock.md | priority=2 | flags=route-closure | role=superseded,synthesis | status=obstruction | proof_status=reading | value=decisive-obstruction,synthesis | keys=correlation inequality;Ginibre;centre flux;finite certificate;reflection positivity;weak side | area=Yang–Mills/gauge Title: What would unblock the confinement-scale region, and what was checked and fails Summary: Earlier confinement-route survey records where correlation cones, finite-size gap criteria and exact transformations fail to supply the weak-to-intermediate gauge bridge. Limit/reuse: Its claim of exactly two unblocking routes is corrected later: monotonicity would help only the strong side, and current physical-crossover certification is infeasible. Keep scoped ingredients, not the historical next-task queue.
wilson-strong-coupling-explicit.md | priority=3 | flags=none | role=result,calibration | status=result | proof_status=proved-unrefereed | value=infrastructure,used-calibration | keys=Wilson transfer;SU3;KP;rho;176 leading;1056 conservative;volume uniform;cyclic observables | area=Yang–Mills/gauge Title: An explicit strong-coupling gap for the Wilson transfer matrix: \(SU(3)\) is gapped for \(g^2\ge176\), with \(\Delta\ge(\hbar c/a)\,4\log(g^2/176)\) Summary: A closed-surface polymer criterion 20e²ρ≤0.84 yields volume-uniform local-observable decay and a Wilson-transfer gap lower bound in units ℏc/a. Limit/reuse: ρ=1/g² is a leading activity estimate; the conservative all-representation bound uses ρ=e^(6/g²)−1. Quoted 176/1056 thresholds use these different readings; positive gap needs a strict margin. Wilson and KS are distinct operators.
zero-branch-reachability.md | priority=3 | flags=surprising | role=result,live | status=result | proof_status=proved-refereed | value=surprising-result,known-boundary | keys=gap thesis; zero branch; theory space; complete records; smeared records; determinate preparation; fold time; caustic; stationary phase; almost periodic; Wigner transport; Gaussian marks; Egorov; Hepp; Wigner measures; singular limit; Ehrenfest time; all-time invariants; mean anomaly; lapping time; isochrony; Hooke; Kepler; Poisson summation; finite resolution; fringe visibility; gap invariant; contrast not scale; imprecision action; preparation thickness; coherence length; mutual coherence; coherence necessity; incoherent attachment; large-action regime; Kato self-adjointness | area=Newton/action Title: Which limits of Newton’s construction reach the zero branch Summary: States the gap thesis (Newton exists only with a positive scale; no zero branch continuously reachable) as a claim about limits and locates it. Thm 1: with Gaussian preparations, quadratic forces and minimal Gaussian marks the record family is the classical Gaussian process plus kicks of variance h²/(4σ²), continuous at zero: no gap on Galileo’s comparison. Thm 2: on any finite partition with several illuminated nondegenerate paths the complete record has an h→0 limit iff the signed cross amplitudes at each nonzero action difference cancel (almost periodicity), while smeared records converge to Newton’s branch-weighted density (final momenta distinct); a record of resolution δ reaches Newton if h/(δΔp)→0. Thm 3: exact for inertial motion with a graded velocity: fold interval, classical limit outside, three streams and no limit inside, affine profiles never fold, Airy h^{−1/3} at the fold. Thm 4: on the radial cycle Hooke’s anomaly record rotates rigidly for every h, while a monotone Kepler swarm loses the zero branch once its windings overlap, at the lapping time of order T²/ΔT when it spans more than half a turn. §§3b–3c: the invariant discontinuous at zero is the leading fringe visibility 2√(ρ₁ρ₂)/(ρ₁+ρ₂) of crossing streams, fixed by Newton’s branch densities, damped by |φ̂(δΔp/h)| at the record and |ŵ₀(ΔΔq₀/h)| at the preparation: a contrast, not a spectral gap. Thm 5 (exact for quadratic forces): the same swarm attached as an incoherent mixture of coherent states with widths vanishing with h has a complete record converging to Newton’s branch-weighted density at every fixed time, so the gap requires the coherence premise (Thm 5 refereed ACCEPT, GPT-6.1 Sol via Codex, third pass). Large-action proposition: scaling masses at fixed h, velocities, record resolution and velocity imprecision multiplies both imprecision actions by the scale, so Newton is recovered as the large-action regime of the h>0 theory, which is not its h→0 limit with exact data. Limit/reuse: holds in the complete-record topology for determinate preparations wherever streams cross; fails for smeared records, statistical preparations and refinement with records; no universal late-time persistence, no necessary resolution threshold, no positive Newtonian action scale; the second premise is an h-independent coherence length between the launch points of crossing streams (partial contrast e^{−Δq₀²/(8σ²)}, the same for every h>0), which remains a premise. Refereed by GPT-6.1 Sol (Codex) 2026-10-01 with corrections applied.
zero-spacing-any-action.md | priority=3 | flags=surprising | role=result,synthesis | status=result | proof_status=mixed | value=surprising-result,synthesis | keys=central Levy;Lindeberg;series convolution;parallel multiplication;D4 strict threshold;action universality | area=refinement/comparison Title: The zero-spacing limit for any plaquette action and any dimension Summary: Two-dimensional infinitesimal symmetric class-function refinement with finite representation exponents yields exactly central Lévy semigroups; a Lindeberg condition selects the Gaussian Yang–Mills member. Limit/reuse: Simple groups give a scalar diffusion constant; nonsimple groups need an invariant tensor. D≥3 error budgets and the strict 4D threshold 2b₀c>4 require normalized density, entropy, blocking stability and reconstruction; they do not prove universality.