Notes retrieval catalog

Markdown source

STATE holds the live question; this catalog locates the maintained proofs. Search the full corpus as directed by poormanrag, then read the argument and its hypotheses. Former filenames and completed task IDs are keys on canonical entries; the published pages redirect to those arguments. Short completed-work phrases in the JSON catalog replace historical handoffs and status/review records; git retains the original versions.

Question	Entry point
Does Newtonian completion require a positive physical action?	Newton construction, completion countermodels, quantum record bounds
What selects a classical action scale?	Units, symmetries and orbital thresholds
What do complete classical apparatus records determine?	Readout, calibration fibres, bounded-force records
Which estimates yield a physical continuum gauge gap?	Mass-gap position, halving atlas
What survives insertion and elimination?	Refinement, three limits
What do the historical sources say?	Planck manuscript, primary-source catalogue

Priority (0–3) concerns retrieval, not proof quality or novelty. Proof status, assumptions and route closures are separate. Model/coordinator reviews are internal checks, not independent peer review. The JSON catalog carries detailed limitations and typed dependencies; dependencies and obstructions provide compact routes.

Classical completion, action scales and records

action-unit-dimensional-selection.md | priority=2 | flags=surprising | role=result,obstruction | status=result | proof_status=written dimensional, dilation, orbit and countermodel proofs with exact hypotheses | value=known-boundary,decisive-obstruction | keys=Q14;Buckingham theorem;fixed constants;action product;similarity;fine structure;k_e/c;C130;action-scale-dilation;action scale dilation;A16;C056;C057;dilation closure;conformally symplectic;action infimum;preparation scaling;bound-orbit-action-observable;bound orbit action observable;A15;C054;C055;uniform circular phase;orbital action;covariance determinant;rms emittance;transport response;fixed-force-small-circles;fixed force small circles;A17;C058;C059;fixed smooth potential;bounded force;stable small circle;zero action infimum;excitation floor;closed-orbit-force-action;closed orbit force action;A18;C060;C061;Fenchel total curvature;speed floor;force ceiling;closed orbit;canonical action;relativistic-kepler-threshold;relativistic kepler threshold;M07;singular relativistic Kepler;angular-action threshold;regular bound orbit;finite-time plunge;softened core;action-scale-obstructions;action scale obstructions;C002–C123;action observables;apparatus calibration;preparation precision;supplied scale;slow modes;Jacobi;finite-copy distinguishability;first lobe;action-gap-foundations;jacobi-kernels-distinguishability;C131;generic observable dimension;Buckingham floor unit theorem;ACTION_FIELD_TARGET;P00;P03;P04;action-scale-consolidation-P04;dilation-B30;kepler-collapse-Q14;p04-routing-review;relativistic-kepler-B28;repository-review-2026-09-09;Sommerfeld radial action;Klein Gordon indicial threshold;Suslov 2401.07485;Bouaziz 1311.7405;scalar action continuity versus path topology;I004-bound-action-and-transport;I004;I004 bound action and transport | area=Newton/action Dimensional and similarity tests distinguish action units from floors. Sharp excitation and singular-Coulomb bounds retain their premises; the integrated C130 radial-action calculation gives the supplied-quantization Sommerfeld energy correspondence.
alpoge-balaban-newton-peek.md | priority=3 | flags=none | role=result,live | status=result | proof_status=proved-unrefereed | value=open-mechanism,infrastructure | keys=Alpoge Sussman source peek;pinned Yang-Mills LLM repository;connected fourth response;quartic cumulant identity;T to fifth cell scaling;scaled retained interaction;reflection positivity zero action;complete source-dependent density;Astra RPM1 attribution | area=Newton/action A pinned selected-source peek motivates an exact quartic connected-response test: m4-3m2^2=-(b/hbar)(m2 m6-m4^2)<0. The equal-cell cumulant is asymptotic to -3 lambda hbar^3 T^5/(256m4), while A_hbar fourth derivative divided by w tends to 6 lambda. A full Gaussian exponential-observable reflection test admits the zero-action member.
balaban-newton-time-blocking.md | priority=3 | flags=none | role=result,live | status=result | proof_status=proved-unrefereed | value=infrastructure,open-mechanism | keys=Balaban 0+1;Newton polygon;arbitrary intermediate times;Lipschitz;Dirichlet Green;action Hessian;Schur complement;hbar covariance;oscillator caustic;quartic continuation;Gaussian hat innovation;cut relative entropy | area=Newton/action For arbitrary unequal time grids, the exact Dirichlet Green row sum gives a contraction factor Lambda T squared over 8, polygon convergence and a uniform inverse-Hessian/source-response bound. Gaussian fluctuation widths retain an explicit hbar factor.
balaban-ode-lesson.md | priority=3 | flags=none | role=result,synthesis | status=result | proof_status=written proof; standard polygon methods and exact conservative examples; internal checks only | value=infrastructure,open-mechanism | keys=Balaban lesson;ODE existence;Newton polygon;causal initial value;Lipschitz stability;mixed kick orders;arbitrary partition;Gronwall residual;endpoint caustic;hbar weighting;newton-continuity-time-scales;newton continuity time scales;non-Lipschitz Newton force;conservative arrival criterion;logarithmic uniqueness threshold;beta equals two;annulus time sum;mixed polygon compactness;preparation instability;vanishing canonical action;explicit hbar WKB residual | area=Newton/action Arbitrary positive partitions and mixed kick/drift orders construct global-Lipschitz Newton motion with explicit mesh error. Conservative energy gives local continuation and magnetic global examples; exact logarithmic arrival criterion has threshold beta=2, vanishing annular action and local WKB residual. Unbounded slope is not a full-state merger; no action floor follows.
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 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.
causal-force-information.md | priority=2 | flags=none | role=result | status=result | proof_status=mixed | value=used-calibration | keys=R07;C070;C071;delayed records;bounded-force lens;reachable region;canonical area;double integrator;reachable-cut-composition;R08;C072;C073;sheared Minkowski sum;momentum fibre;conditional canonical area;finite-precision-cut;R09;C074;C075;clipped reachable lens;Minkowski area;position precision;residual delay;thin momentum fibre;two-position-recovery;R10;C076;C077;finite difference;bounded force;delay;epsilon over separation;indistinguishable-phase-bound;R11;C078;C079;complete noisy history;blind delay;convex symmetric fibre;exact minimax risks;finite-horizon-minimax;R13;C082;C083;bounded curvature;three velocity regimes;transient aggregate loss;earliest saturation;minimax-composition;R12;product central fibres;linear minimax radii;centre total momentum;aligned errors;extensive action product;aggregate record loss;variance mismatch;shared-record-budget;R14;C084;C085;shared record budget;ell-r norm;center of mass;minimax exponent;block-apparatus-composition;R15;C086;C087;independent block budgets;l^r;centre minimax;extensive composition;shared resource;C080;C081;block-apparatus-B46;causal-information-B38;cut-composition-B39;finite-horizon-B44;finite-precision-B40;indistinguishability-B42;minimax-composition-B43;shared-budget-B45;two-record-B41;I006-discovery-by-connecting-results;I006;I006 discovery by connecting results | area=Newton/action Exact force lenses and clipped-cut areas, a symmetric-fibre minimax theorem, all three finite-horizon phase-risk regimes, independent composition and shared/block budget laws are proved in one information model.
central-limit-canonical-gaussian-sector.md | priority=3 | flags=none | role=result,live | status=conditional | proof_status=proved-unrefereed | value=open-mechanism,infrastructure | keys=canonical mixing;independent copies;central limit;Gaussian covariance sector;cusp flow;entropy power;Wasserstein closure;density ceiling counterexample;selective records | area=Newton/action Copy-index symplectic mixers and weak or W2 closure admit a Gaussian with each admissible covariance; a positive infimum determines the entire Gaussian sector. The older density ceiling fails a two-copy mixer. A supplied entropy floor supports actual cusp transport and mixing with W2 closure but fails weak closure and, as a subsequent note proves, selective Gaussian-meter closure.
classical-orientation-closure.md | priority=1 | flags=none | role=result,obstruction | status=result | proof_status=mixed | value=known-boundary,decisive-obstruction | keys=Q01;C125;Bloch ball;hidden orientation;minimal composite;purification;Hardy subspace;operational closure;hamiltonian-moment-descent;hamiltonian moment descent;C127;classical orientations;Hamiltonian spin interaction;same first cross moments;product effect;quotient dynamics;missing quadratic moment;reversible closure;hamiltonian-finite-closure;hamiltonian finite closure;C128;classical spins;J uz vz;finite observable closure;Vandermonde;all Borel preparations;nonlinear expectation update;operational descent;reversible-interaction-premise;reversible interaction premise;separable composite;reversible operational descent;partial-transpose branch;identical-copy closure;action normalization;reversible-generator-constraints;reversible generator constraints;C129;B77;product-test positivity;two-sided reversibility;Bloch-ball tensor;seven-dimensional slice;quantum-exclusion-premises;quantum exclusion premises;Hardy continuity;CDP purification;finite simplex;mechanical action bridge;Q01-closure;Q01-descent;Q01-finite-closure;Q01-generator-audit;Q01-interaction;finite-closure-B74;orientation-closure-B69;quantum-premises-Q01;reversible-generator-B77;reversible-interaction-B70;spin-descent-B72 | area=Newton/action An affine-test orientation ball and its minimal composite have finite operational capacity, but a complete reversible spin interaction fails moment descent and admits no finite bounded-observable repair for all Borel preparations. Source reconstruction premises and the verified seven-dimensional generator restriction are integrated.
composition-universality.md | priority=3 | flags=none | role=result | status=conditional | proof_status=written classification, covariance and additivity proofs; borrowed probability inputs with stated reading levels; internal review only | value=known-boundary | keys=A08;C035;C036;mass composition;nonnegative additive function;Green–Kubo;reference reversal rate;preparation equivalence;C050;C051;ordered-beam-preparation;Palm residual;composition-crossover-gap-checks;mass-orthogonal coordinate;stochastic-route-velocitas-ultima;stochastic route velocitas ultima;S1;S2;S3;Brownian free motion;universal mD;Cameron–Martin;ultimate velocity;zero branch;A02-draft;A02;A13;P01-six-directions;composition-B16;ordered-preparation-B26;six-directions-2026-09-08 | area=Newton/action One nonnegative additive-function theorem controls mass-only independent fluctuation composition, including continuous Brownian free paths and Green-Kubo plateaus. A finite-rate reference supplies positivity; matched-scale ordered streams retain a zero plateau. Additive force-independent Brownian noise gives the sharp pinned-path record floor; symmetric Levy laws obey phi(m,k)=m Gamma(k/m).
cusp-quantum-preparation-selection.md | priority=3 | flags=none | role=result,live | status=result | proof_status=proved-unrefereed | value=open-mechanism,infrastructure | keys=bounded C1 cusp;same incoming trajectory;coherent Gaussian;vanishing momentum shift;branch selection;pure superposition;Wigner mixture;Athanassoulis Paul;Chabu | area=Newton/action Two Gaussian families have identical position densities and the same limiting incoming trajectory, yet converge to reflection or transmission through the C1 cusp; their superpositions yield any mixture of the two outgoing branches.
cut-measure-newton.md | priority=3 | flags=surprising | role=result | status=result | proof_status=written energy, Weyl and conditional Gaussian information proofs; historical interpretations explicitly qualified; internal reviews only | value=surprising-result | keys=Galileo cell action;Schauder hats;Cameron–Martin;arbitrary cuts;KL divergence;Zhuangzi rod;finite mark discernibility;Proposition 7;polygon-lift-phase;polygon lift phase;Weyl central extension;inscribed polygon;insertion triangle;ordering holonomy;Dirichlet Green action;Gaussian distinguishability;Opticks refraction invariant | area=Newton/action One canonical Dirichlet action treatment: orthogonal arbitrary-cut hat energies and mesh exhaustion; exact Gaussian bridge KL/testing and sharp finite-grid invariant mark information; Weyl polygon phase, positive ordering holonomy and partition identity. General force bound retains one-sign attainability. Historical Mohist/Archimedes sources and conditional Opticks fit-count proof distinguish source reading from quantum assumptions. No floor, Weyl law or universal physical hbar is derived from fits.
galilei-continuous-spin-classical.md | priority=1 | flags=surprising | role=result,synthesis | status=result | proof_status=mixed | value=surprising-result,known-boundary | keys=continuous spin;Bargmann group;zero central mass;transverse boost moment;mass dipole;signed masses;coadjoint orbit;fixed physical time;internal cylinder;Planck gap;mass gap;boost momentum uncertainty;hbar M | area=Newton/action The zero-mass continuous-spin label is a transverse boost moment, realized by a signed-mass dipole; elementary orbit curves have fixed physical time, and nonzero momentum precludes an energy lower bound. A supplied Poincaré energy gap gives a boost–momentum uncertainty floor proportional to ℏΔ/c², while a positive continuous-spin label still permits energy approaching zero.
galileo-two-path-interference.md | priority=2 | flags=surprising | role=result | status=result | proof_status=proved; repository-internal written review | 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 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.
gaussian-meter-entropy-floor.md | priority=3 | flags=surprising | role=result,live | status=result | proof_status=proved-unrefereed | value=decisive-obstruction,open-mechanism | keys=classical entropy floor;Gaussian meter;selective records;minimum action pointer;postselected covariance;non-Gaussian mixture;Wigner positivity;Gaussian mixture closure;nonlinear canonical shear;three point kernel;hbar explicit | area=Newton/action A single classical Gaussian meter with a supplied minimum-action pointer takes an entropy-floor input to arbitrarily small posterior action on a positive-probability coarse record. A Gaussian-mixture repair preserves the record and copy mixers but fails a nonlinear canonical shear.
leibniz-continuity-records.md | priority=3 | flags=surprising | role=result,historical | status=conditional | proof_status=proved; repository-internal written review | 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 In the non-adaptive Gaussian mark model with preparation-invariant tests, optimal force discrimination is continuous at zero force iff κ>0; finite schedules realize spent cut action/κ. Historical passages support an explicitly modern record-level reading of continuity.
lipschitz-certificate-quantum-lift.md | priority=3 | flags=none | role=result,live | status=result | proof_status=bounded theorem proved in writing with named analytic inputs; universal lifting remains conjectural | value=infrastructure,open-mechanism | keys=constructive lifting conjecture;classical polygon certificate;globally Lipschitz force;C1,1 potential;Nelson commutator;arbitrary partition;noncommutative Weyl observables;sqrt h sharpness;classical-quantum-existence-conjecture;classical quantum existence conjecture;constructive lifting;proof containment;classical refinement certificate;noncommutative target;Koopman representation;operator domains;oscillatory normalization;1998 consistency;positive action necessity | area=Newton/action Defines the universal constructive lifting conjecture with fixed certificate schema, noncommutative target, toolkit and joint observable limit; Koopman unitarity alone is insufficient. Proves the conservative global-Lipschitz C1,1 instance using graph estimates and Nelson: fixed-hbar product convergence and sharp mesh-uniform sqrt(hbar) classical recovery. Universal lifting, singular completion and positive-action necessity remain open.
local-detector-coincidences.md | priority=0 | flags=none | role=result,calibration | status=result | proof_status=written event, optimization and countermodel proofs under specified mechanical or stochastic receiver laws | 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;passive-threshold-events;passive threshold events;Q09;passive threshold;quartic barrier;no-click tradeoff;double clicks;preloaded detector;detector action scale;shared-resource-events;shared resource events;Q11;shared release;absorbing Markov receiver;linear hazards;fringe probabilities;inhibition delay;finite-window efficiency;thermal-receiver-reliability;thermal receiver reliability;Thermal reliability selects a detector cost, not a universal action;Q10;Arrhenius receiver;dark retention;signal deadline;fixed attempt frequency;transduction;barrier reduction;Q12-prior-state;local-detector-Q12;thermal-receiver-Q10 | area=Newton/action Fixed-split conditionally independent monotone receivers obey the sharp coincidence-product bound. Passive barriers, exact capped-Arrhenius retention/deadline optimization and shared-release countermodels retain their separate premises, energy accounting and causal timing. None selects a universal physical action.
mark-cost-and-statistical-floor.md | priority=3 | flags=none | role=result,obstruction | status=conditional | proof_status=mixed | value=known-boundary,decisive-obstruction | keys=Theorems A B C;von Neumann mark;error recoil conjugacy;hbar over 2;Gaussian invariant test;Dirichlet energy;correlated squeezing;grid probe escape;newton-mark-floor;newton mark floor;N02;M1 M2 M3;Newton fits;Lambda p;two-mark floor;far-screen countermodel;worst-case widths;Gaussian replacement;planck-gap-derivation;planck gap derivation;worst-case marks;feasibility box;Dirichlet certificate;bounded error-recoil product;constants 9 and 36;support width;Paley-Wiener correction;additive-noise-marks;additive noise marks;body-independent noise;Weyl relation;Ozawa independent intervention;momentum transfer;Galileo recoil;newton-record-parallel-move;newton record parallel move;Gaussian position instrument;forgotten record;Wigner momentum diffusion;inverse variance addition;continuous measurement;parallel insertion;supplied hbar | area=Newton/action Classical independent-box protocols obey the 9/36 conditional bounds, while Gaussian invariant tests have sharp constant 48. Supplied quantum probes give the standard-deviation cost hbar/2; correlations and non-Gaussian probes qualify it. Body-independent-noise classification and unread Gaussian channels are integrated.
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 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.
necessity-unit-and-indeterminacy.md | priority=3 | flags=none | role=result,obstruction | status=conditional | proof_status=written unit/record theorems and classical countermodels; response and calibration assumptions explicit | value=known-boundary,decisive-obstruction | keys=Theorem U;Theorem I;radiation spectral integral;Kirchhoff Wien;prior density ceiling;two-pointer recoil monitor;instrument access;Rutherford correction;radiation-noise-action-selection;radiation noise action selection;Q02;cubic noise spectrum;dipole damping;stationary oscillator action;narrow resonance;free reservoir amplitude;ultraviolet cutoff;sed-zeta-radiation-link;sed zeta radiation link;Lorentz-invariant spectrum;free zero-point amplitude;resonant Gaussian area;off-resonant momentum divergence;cutoff breaks invariance;disputed SED Planck derivation;radiation-unit calibration;energy-depot-action-selection;energy depot action selection;Q03;energy depot;stimulated gain;finite fuel;pumped oscillator;Lyapunov attractor;power threshold;frequency dependence;thermodynamic-records-no-floor;thermodynamic records no floor;Landauer;Sagawa–Ueda;posterior support area;mutual information;logarithmic work;no action floor;Bayesian records;radiation-noise-Q02 | area=Newton/action Normalized radiation spectrum defines an action unit under explicit scale and integrability assumptions, not universal quantum structure. Cross-field thermal extension remains conjectural. Reversible two-pointer records defeat a prior density cap; exact Rutherford, regulated radiation-response, pumped-depot and thermodynamic-work countertests retain their distinct hypotheses. Lorentz spectral form and any Planck calibration are conditional; work lower bounds are not attainable optima.
newton-branch-response-action.md | priority=3 | flags=none | role=result,live | status=conditional | proof_status=proved-unrefereed | value=open-mechanism,infrastructure | keys=double-well time cell;response ceiling;positive action bound;exact variance identity;tanh source layer;spinodal;classical branch memory;thermal countermodel;zero-action extension | area=Newton/action A double-well time-cell response ceiling gives a uniform positive lower bound on the supplied action multiplier using an exact variance identity. The small-action source transition has a tanh profile. A specified global-minimum zero extension is discontinuous, while classical branch memory and a thermal weight are explicit controls.
newton-cusp-preparation-floor.md | priority=3 | flags=none | role=result,live | status=conditional | proof_status=written conditional floor theorems, exact classical countermodels and Gaussian limit proofs; no physical selector or universal hbar identification | value=open-mechanism,infrastructure | keys=bounded cusp force;non-Lipschitz Newton ODE;full point-state merger;weak preparation closure;canonical covariance;positive covariance action;singular covariance;classical density ceiling;two-copy mixer counterexample;almost everywhere reversible flow;bounded-potential quantum completeness;cusp-history-records-continuity;cusp history records continuity;bounded cusp;reversible solution space;trajectory memory;complete records;classical conditional preparations;Gaussian branch selection;spontaneous stochasticity;weak discontinuity;W2 continuity selector;canonical mixing;uniform response modulus;zero action;Bell locality | area=Newton/action Bounded C1 cusp potential has full point-state mergers and global classical solutions. Conditional positive covariance floors follow either reversible instantaneous phase evolution plus canonical/weak closure, or actual Gaussian cusp transport plus W2 copying/continuity. Full-trajectory group is a distinct zero-floor classical completion; Gaussian branch limits have nonuniform zero-width continuity. Sharp density-cap witness 1/(4piM), entropy witness and fine joint-record contradiction delimit claims. Quantum dynamics at supplied hbar and quantum identification are separate.
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;I001-action-field;I001;I001 action field | area=Newton/action 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.
newton-insertion-action.md | priority=3 | flags=none | role=result,calibration | status=result | proof_status=mixed | value=known-boundary,used-calibration | keys=N01;inertial falling parabola;3F over v;Galileo area;tau Delta E;matched endpoint chord;F minus F F reunion;controlled phase;principia-constant-force-action;principia constant force action;Galileo parabola;inertial-line area;matched-endpoint chord;Lemmas X-XI;deterministic work;boost invariance;receding-centre-area-audit;receding centre area audit;receding harmonic centre;sector cancellation;matched endpoints;arc-chord lens;factor two;threshold versus tiling;B11;R01;newton-insertion-N01;ordinary point total derivative;velocity dependent endpoint counterexample;I002-newton-polygon-threshold;I002;I002 newton polygon threshold | area=Newton/action Canonical Galileo/Newton geometry, source paragraph map, matched-endpoint action and arbitrary-partition defect, receding-centre correction and exact controlled F,−F,F reunion. Conditional copy thresholds are kept separate from action quantization.
newton-nonlinear-time-cell.md | priority=3 | flags=none | role=result,live | status=result | proof_status=written conditional cell proofs and selected source passages; no selection of physical hbar | value=open-mechanism,infrastructure | keys=Balaban 0+1;nonlinear time cell;Gaussian integration;classical envelope;quartic flat centre;induced stiffness;conditional variance;normalized tails;one halving;inverse action estimate | area=Newton/action Convex Euclidean one-vertex integration has normalized tail, variance and curvature bounds; quartic integration generates positive stiffness at supplied hbar while minimization has zero central quadratic curvature. Retains finite constants, one-halving bad-event bound and precise Dimock/Balaban source evidence: noisy block average, generated terms, large fields and earned locality do not follow from a density-tower identity.
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;conditional Gaussian bound;arbitrary instruments;polygon phase;Opticks fits;ancient division;Kepler localization;selection-dependent endpoints;coherence premise;incoherent classical countercase;h versus hbar;closed Schur form;critical angular-channel counterexample;supplied positive action;universality and necessity open;arrow-not-sling;Plutarch 923C;firebrand circle;HANDOFF-2026-09-23 | area=Newton/action Integrated mathematical and historical manuscript: conditional Gaussian and quantum disturbance bounds, exact polygon phases and the source-based Newton comparison. Historical M3 is an interpretation; operator spreads, hard widths and posterior inference are distinguished.
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 covariance threshold;Slepian concentration;zero branch | area=Newton/action Added covariance classifies the Moyal algebraic route and a Gaussian state-restriction route, both retaining an unselected zero branch.
record-distance-path-length.md | priority=3 | flags=none | role=result,obstruction | status=conditional | proof_status=mixed | value=known-boundary,decisive-obstruction | keys=Theorem P;Bures angle;sharp single-shot constant;Theorem K;force split;Dirichlet recoil length;attainment open;planck-gap-probabilistic;planck gap probabilistic;arbitrary quantum instruments;adaptive protocol;hybrid marginal resources;aperture bound;squeezing aspect ratio;separated packets;record-costs-recoil;record costs recoil;Theorem R;momentum-transfer marks;affine sagitta minimization;arbitrary probe states;grid counterexample;diverging recoil;record-costs-disturbance;record costs disturbance;Theorem U;arbitrary unitary instruments;body-dependent noise;hybrid states;sagitta-momentum pairing;impulse-position pairing;adaptive disturbance | area=Newton/action One Bures-angle proof gives supplied-hbar aperture, general-disturbance and recoil-only bounds, with explicit hybrid-state envelopes and distinct preparation quantifiers. Separated packets and modular grid probes retain the resource counterexamples; force-split minimization needs envelopes uniform over splits.
rivero-1998-conjecture-central-forces.md | priority=3 | flags=surprising | role=result,obstruction | status=result | proof_status=proved; repository-internal written review | 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 Constructive quartic and angular-phase tests retain zero-action sequences despite valid refinement and cycle consistency.
rotation-composition-universality.md | priority=3 | flags=none | role=result,infrastructure | status=result | proof_status=written mechanical, canonical-algebra and spin-patch proofs with separate premise sets; standard source geometry | value=infrastructure,known-boundary | keys=constituent action constants;derivation compatibility;mixed force derivative;additive angular momentum;faithful tensor algebra;connected interaction graph;common zero branch;reciprocal-coupling-normalization;reciprocal coupling normalization;Reciprocal exchange fixes relative mechanical scales;Q06;reciprocal spring;inertia ratios;cycle product consistency;diagonal kinetic energy;common action multiplier;spin-action-patching;spin action patching;Global spin phases quantize a ratio, not an absolute action scale;Q07;spin sphere;prequantization;chart transition;2s/K;irrational spin ratios;common scaling | area=Newton/action Reciprocal spring responses fix compatible inertia ratios through a connected-graph cycle test. Newton derivation compatibility and mechanical rotation closure equate constituent algebra constants, admitting zero. A supplied spin phase imposes 2s/K integrality while common normalization and arbitrarily small local cap actions remain free.
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;shared score sign;terminal conjugate escape;Gaussian stationary switching;finite arctan clock;expected switch count;former SED 8.22;former SED 8.23;HANDOFF-2026-10-01-CLAUDE-NEWTON;PROMPT-CLAUDE-NEWTON-2026-10-01 | area=Newton/action Shared-score preparation and canonical copies lead to a restricted Fisher action, explicit positive forward orbit and switching representation. Terminal conjugate records and ordinary transport fail the restriction; branch controllers preserve unread energy while closure selects no kappa.
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;terminal Schur complement;complete physical memories;adaptive likelihood affinity;record norm;continuum controller recoil;former SED 8.1–8.21 | area=Newton/action Canonical classical recording treatment: regulated common-bath readout escape, terminal Gaussian closure, complete-record adaptive information, physical copy/refinement and continuum recoil, nonlinear-copy failures, and local phase/unread-energy tests.
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;Kato self-adjointness;Hepp theorem;hypothesis L proved;centered weighted Sobolev;Hardy singular multiplier;first moments;fixed delta fixed T;Dirac critical Schur domain;finite potential energy;Klein-Gordon charge space;critical no-log branch;selection-dependent h set;k over c unit;closed Schur form;critical angular-channel counterexample;2026-10-01-theorem1-self-sufficiency-contrast-referee | area=Newton/action Classical Kepler collision flow is incomplete while non-relativistic Coulomb dynamics is global for every h>0. The October 2 written derivation proves (L)=O(h^(3/2)) and position/momentum centroid errors O(sqrt(h)) on fixed collision-free intervals. Proposition 2 gives selection-dependent Dirac and Klein–Gordon h-sets, with explicit endpoint rules.
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 CHSH bounds arbitrary shared-readiness local models under setting independence but cannot select an action normalization.
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 Exponential mixing of a connected Anosov setting device bounds hidden-variable/setting correlations for Lipschitz-resolved conditional preparations, with a logarithmic resolution-dependent onset.
topological-sector-action-selection.md | priority=2 | flags=surprising | role=result,obstruction | status=result | proof_status=proved-unrefereed | value=known-boundary,decisive-obstruction | keys=Q04;O(3) sigma model;degree one;4pi rho;shrinking static soliton;crossing-time action;gapless vacuum;stabilized-topology-action-scale;stabilized topology action scale;Q05;Skyrme;inverse stereographic trial;radius stabilization;b/c;common action scaling;topological-sector-Q04 | area=Newton/action Actual two-dimensional degree-one sigma solutions keep energy 4πrho while their radius-crossing action vanishes. A three-dimensional quadratic/quartic trial family fixes radius but exposes the supplied action coefficient b/c and a free common stiffness normalization.
zero-branch-reachability.md | priority=3 | flags=surprising | role=result,live | status=result | proof_status=written stationary-phase and exact quadratic Gaussian-transport arguments; corrected branch/record scope; repository-internal review only | 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;equal-action cross cancellation;B_omega;two-branch fold counterexample;record family continuous not constant;support interval not global diffeomorphism;signed angular width;Kepler compression not prefold wrapping;half-turn criterion withdrawn;angle record versus radial measurement;2026-10-01-theorem5-coherence-necessity-referee | area=Newton/action Coherent finite-partition point records converge iff every nonzero action-frequency sum vanishes; equality to the classical value additionally requires cancellation of equal-action cross terms. Gaussian record laws vary continuously with the supplied action, and incoherent narrowing packets recover the classical swarm for quadratic forces. Includes local visibility, two-ended imprecision, free-fold and radial-angle constructions. The radial-angle model requires signed interval widths: positive Kepler action gradients compress before folding; T²/DeltaT is a dephasing scale, not an unconditional first wrapping time.

Complete apparatus state and recovery

autonomous-finite-readout.md | priority=1 | flags=surprising | role=result,calibration | status=result | proof_status=mixed | value=used-calibration,surprising-result | keys=R06;C068;C069;finite Hamiltonian apparatus;four momentum records;mechanical clock;delayed reconstruction;classical-readout-refinement;R05;C066;C067;canonical shear probes;quiet preparation;cubic inverse sensitivity;mesh fourth power;growing apparatus mass;fixed-coupling-calibration;R16;C088;C089;fixed nonzero coupling;exact nonlinear calibration;lower Lipschitz;preparation contraction;four persistent momenta;full-pointer-recovery;R19;C094;C095;eight pointer coordinates;clock calibration;global receiver recovery;free pointer shear;C1 perturbation;clock-position-local-recovery;R21;C098;C099;known clock position;energy transversality;local inverse;unknown clock speed;scaled records;final-clock-momentum-recovery;R23;C102;C103;final clock momentum;global inverse;unknown speed;bounded receiver domain;nine records;full-clock-phase-recovery;R24;C104;C105;ten apparatus records;clock phase;known incoming momenta;weak coupling conditioning;autonomous-readout-B37;classical-readout-B35;clock-position-B52;final-clock-B54;fixed-calibration-B47;full-clock-B55;full-pointer-B50 | area=apparatus/reconstruction One autonomous finite-mass Hamiltonian apparatus has vanishing-error/disturbance quiet-preparation limits; exact nonlinear calibration and complete pointer/clock records give bounded-domain recovery. Impulsive repeated-cut readout has separate growing-probe resources.
calibration-tolerance-recovery.md | priority=1 | flags=none | role=result,calibration | status=result | proof_status=mixed | value=used-calibration | keys=R31;C119;calibration tolerance;inverse coupling;canonical minimax;common record ball;weak coupling saturation;fixed-preparation-ambiguity;R17;C090;C091;fixed preparation box;exact four records;momentum compensator;receiver shell patch;canonical projected area;position-preparation-ambiguity;R18;unknown probe positions;calibrated incoming momenta;clock reaction;narrow fixed pulses;equal-record shell fibre;lambda-squared response;hidden-clock-ambiguity;R20;hidden clock phase;fixed energy receiver;eight pointer records;early pulse design;implicit function;coordinate risk product;global-clock-speed-ambiguity;R22;two clock speeds;equal-energy shell;indefinite energy response;global branches;preparation width;full-apparatus-preparation-ambiguity;R25;C106;C107;full apparatus preparation;ten final records;energy shell;exact compensation;minimax ellipse;energy-constrained-apparatus-ambiguity;R26;C108;C109;backward terminal flow;receiver sign;two exact energies;antipodal pair;calibrated-displacement-ambiguity;R27;Borsuk–Ulam;S10;calibrated displacement;two initial energies;full-state ambiguity;inverse shear;calibrated-canonical-ambiguity;R28;fixed q1;two energies;full final apparatus;canonical fibre;x P risk;two-calibration-branches;R29;two calibrated positions;full apparatus record;local inverse;global two branches;canonical ambiguity;three-calibration-global-recovery;R30;three calibrated positions;full ten-coordinate record;apparatus energy;global inverse;delta/lambda;single-calibration-fibres;R32;C121;B64;inverse response column;calibration fibre;Hermite interpolation;canonical diameter;zero projected area;correlated-calibration-response;R33;C122;C123;correlated calibration line;hidden y;signed coupling symmetry;quadratic response;local fibre;C092;C093;C096;C097;C100;C101;C110;C111;C112;C113;C114;C115;C116;C117;C118;C120;calibrated-canonical-B59;calibrated-displacement-B58;calibration-tolerance-B62;correlated-response-B65;correlated-variation-B66;energy-symmetry-B57;fixed-preparation-B48;full-apparatus-B56;global-clock-B53;hidden-clock-B51;position-preparation-B49;pulse-column-B64;single-calibration-B63;three-calibration-B61;two-calibration-B60 | area=apparatus/reconstruction A common inverse apparatus chart proves shell saturation, energy/calibration ambiguities, rank-controlled global recovery, matched tolerance/coupling crossover and directional calibration fibres. Signed-coupling symmetry cancels the proposed canonical tangent; finite-width quadratic quadratures retain a conditional curvature test.
conservative-harmonic-receiver.md | priority=2 | flags=surprising | role=synthesis,calibration | status=result | proof_status=mixed | value=used-calibration,synthesis,surprising-result | keys=C047–C049;harmonic receiver;low-frequency density;thermodynamic order of limits;hard speed ceiling;C062–C065;R03;R04;classical-cut-state;three-body-cut-memory;two-time memory;position-only cut;conditional kernel;momentum memory;independent reset;frozen limit;orbital preparation;spring-chain memory;cosine kernel;tagged phase;two-time observability;preparation scaling;A10;classical-cut-state-B33;harmonic-receiver-B23;three-body-memory-B34 | area=apparatus/reconstruction Finite conservative harmonic receivers have zero long-window response; the prepared increasing-chain plateau depends on limit order and closes under its hard speed-support condition. Exact two-body cut/reset and three-body elimination/observability proofs retain the missing classical memory.

Gauge construction and spectral estimates

blocking-criterion-monotone.md | priority=2 | flags=route-closure | role=obstruction | status=obstruction | proof_status=mixed | value=decisive-obstruction | keys=Yarotsky polymer;block surface M²;block gap;Schur variation;projection blocking;effective coupling;su3-constants;SU3 specialization;blocking-step-obstruction | area=Yang–Mills/gauge Surface-to-gap criteria scale unfavourably in specified regimes.
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 Derives the explicit one-link Wilson sufficient criterion g²>444 for SU3 and its transfer-gap rate. The proposed single-link block-marginal test is empty in the gauge interior; a joint invariant certificate and weak-trajectory control remain additional obligations.
finiteness-half-flowed-susceptibility.md | priority=2 | flags=none | role=result | status=conditional | proof_status=written variational and positive-measure proofs; free Gaussian calibration; continuum and spectral insertion hypotheses explicit | value=known-boundary | keys=F1;Feynman–Bijl;flowed susceptibility;zero momentum;intensive bound;Hamiltonian equal-time flow;finite gap upper side;coupling cancellation;free Maxwell;two photon sum rule;moment-hierarchy-upper-bounds;moment hierarchy upper bounds;A monotone hierarchy of upper bounds from one flowed correlator, and why no bound of this kind can give \(m>0\);spectral moments;log convexity;inverse moments;M0 over Mminus1;flowed correlator;positive spectral measure;gapless exponential tail;upper bound limitation;su3-constants;SU3 specialization;flowed-bound-free-field | area=Yang–Mills/gauge One variational and positive-spectral-measure treatment gives intensive susceptibility bounds, conditional moment ratios and exact spatially flowed Maxwell constants. Temporal-flow admissibility and infrared moments remain assumptions. All finite inverse moments can coexist with a zero edge; complete moment data may determine the observed channel, which need not be the global gap.
flow-conjugation-truncation.md | priority=2 | flags=route-closure | role=obstruction,result | status=obstruction | proof_status=written finite-lattice invariances, gauge variations, auxiliary kernel estimates and stationary-background calculation | value=decisive-obstruction,known-boundary | keys=Wilson flow;unitary change of variables;pulled-back kinetic metric;free frequency cancellation;generated nonlocality;relative truncation;lattice step coupling cancellation;local Jacobian;truncation correction;flow-jacobian-truncation-error;flow jacobian truncation error;Gauge flow: Jacobian domains, Gaussian locality and unstable backgrounds;linearized gauge flow;covariant heat kernel;Duhamel;Gaussian tail;curvature norm;continuum physical scale;lattice compactness;flow-instability-large-field;flow instability large field;Nielsen–Olesen;chromomagnetic saddle;curvature operator symmetric;Landau level;flow growth;large-field split;sharpness caveat;typical-field-strength-window;typical field strength window;flow time;typical magnetic variance;g over 4pi;supremum tail;compact lattice correction;three component radial tail;24 pi squared;trace variance;ground-state-measure-transfer free tail;flow-before-decimation;lattice-truncation-uniform | area=Yang–Mills/gauge Finite-lattice flow preserves spectra and multiplication norms and has a local first-derivative path bound. Exact continuum variation distinguishes the true Jacobian from an auxiliary Gaussian propagator with an absolute tail budget. Landau growth is gB-k_parallel^2; inverse metrics and relative Hamiltonian truncation remain open.
four-dimensional-composition.md | priority=3 | flags=none | role=live,result | status=conditional | proof_status=written exact Gaussian identities and regulated norm bounds; interacting one-loop matching formal or conditional as stated; internal checks only | 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 Exact directional Gaussian composition preserves harmonic flux normalization but sharp blocked covariance grows with depth. Internally checked determinant-jet estimates and conditional telescoping give universal average running; §7 supplies formal finite one-step vertices/matching constants.
four-dimensional-parallel-log.md | priority=3 | flags=none | role=live,result | status=conditional | proof_status=written formal one-loop identities and convergent coefficient integrals; conditional matching theorem with internal checks only | 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 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.
gaussian-blocking-coupling.md | priority=3 | flags=none | role=result,live | status=result | proof_status=proved; repository-internal written review | 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 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.
ground-state-measure-transfer.md | priority=2 | flags=none | role=infrastructure | status=conditional | proof_status=written identities and conditional tail/transfer theorems; local and continuum inputs open | value=infrastructure,known-boundary | keys=Kogut Susskind;anisotropic Wilson;Perron vector;Euclidean time-slice marginal;ground-state density;large-field action cost;probability transfer;agmon-ground-state-suppression;agmon ground state suppression;Agmon identity;Kogut–Susskind ground state;weighted eigenfunction;global large deviation;local suppression correction;magnetic-energy-identities;magnetic energy identities;Wilson magnetic energy;Laplacian eigenfunction;gradient bound;ground-state sum rule;magnetic variance;Gibbs comparison;extensive Haar mean;local large field;specific comparison not universal no-go;global sublevel threshold;agmon-global-not-local | area=Yang–Mills/gauge Exact magnetic Laplacian/gradient identities and variance sum rule feed finite-volume global Agmon tails with explicit all-path constants. Perron slab and anisotropic temporal limits conditionally identify ground-state slice probabilities; normalized local rarity and operator comparison remain separate.
large-field-action-lower-bound.md | priority=2 | flags=none | role=result,infrastructure | status=result | proof_status=written continuum inequality, equality conditions, constrained-minimum counterexample and specified spectral model; no uniform measure theorem | value=infrastructure,known-boundary | keys=flow monotonicity;flowed L2 block;eta2 over 4g2;four-dimensional action;scale invariant;constrained sharpness;normalized probability;large fields;large-field-entropy-count;large field entropy count;Nielsen Olesen;Landau degeneracy;longitudinal disk;eta2 over 8pi2;action entropy ratio;constrained minimizer;large-field measure;bounded factor premise | area=Yang–Mills/gauge Flowed-block continuum action floor eta_F^2/(4g2) has exact equality accounting and no proved positive-threshold saturation. Bianchi failure defeats the old localized-constant example. Finite-regulator minimum need not have nonnegative tangent-cone Hessian. Charged-background phase-space and exact box counts retain real/complex SU3 multiplicities and norm-dependent cost ratios. Normalized rarity, entropy and polymer convergence remain unproved.
large-field-operator-inequality.md | priority=2 | flags=route-closure | role=obstruction,result | status=obstruction | proof_status=exact perturbation and IMS identities; lattice localization coefficient conditional, local spectral comparison open | 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 Exact positive-perturbation min-max bound and negative-well ground-state trial identity distinguish measure from signed spectral control. IMS coefficient 32pi^2 c0^2/3 requires extra link-response, pointwise-field and locality assumptions. Local energy excess and vacuum surface subtraction are unproved targets for a specified construction; no exhaustion of Hamiltonian methods or automatic Euclidean closure.
lattice-gap-upper-bounds.md | priority=2 | flags=surprising | role=result,infrastructure | status=result | proof_status=written regulated variational, Gauss-law and Polyakov bounds; constant-mode substitution conditional | 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;polyakov-average-gap-bound;polyakov average gap bound;The gap is bounded by the variance of the averaged spatial Polyakov loop, with the small-volume scaling built in;spatial Polyakov loop;Feynman-Bijl;SU(N);Kogut-Susskind Hamiltonian;averaged loop variance;physical gap upper bound;self-averaging;su3-constants;SU3 specialization;centre neutral adjoint Polyakov trial;dual plane symmetry;fundamental loop mean zero;8 hbar c g squared over L variance | area=Yang–Mills/gauge The KS Feynman-Bijl identity gives plaquette strong-coupling order, an abelian structure-factor gaplessness test and an exact averaged-Polyakov susceptibility bound. Constant-colour electric trials vanish for semisimple gauge algebras; a universal string cost for all field-dependent dressed trials is unproved. An exact SU2 adjoint-loop bound targets the neutral centre sector; the one-patch fundamental variance is not a global vacuum variance.
lieb-robinson-kogut-susskind.md | priority=2 | flags=none | role=result,infrastructure | status=result | proof_status=written support-preserving reduction; locality/clustering theorems cited with metadata-level coverage; numerical prefactor not certified | 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;locality upper bound not propagation speed;microscopic range in clustering;uncertified prefactor 32e;su3-constants;SU3 specialization | area=Yang–Mills/gauge The support-preserving interaction picture reduces commuting unbounded single-link electric terms to bounded plaquette locality, with volume-uniform coefficient of order Nc/g². Numerical prefactors, clustering lengths, physical propagation and stability need their separate hypotheses.
low-dimensional-mass-gap.md | priority=3 | flags=none | role=synthesis,result | status=result | proof_status=written established matrix spectral proofs, explicit conditional classical bounds, labelled semiclassical estimates and corrected extension/domain statements; internal review only | 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;action-floor-yang-mills-gap;action floor yang mills gap;G08;C133;transverse ellipse;matrix model valley;action unit;dimension four;C131;C132;classical area floor not spectral gap;invariant sector gap;inverse-square two-sided tower;Friedrichs scale preserving;positive sublevel not positive energy floor;mass-gap-dictionary-G07 | area=Yang–Mills/gauge Scalar and SU(2) bosonic matrix oscillator bounds prove compact resolvent, a simple ground state and a supplied-hbar gap with exact hbar^(4/3)g(2/3) scaling. Classical area restrictions instead bound sublevels and their volume; the Weyl leading count and semiclassical channel levels remain distinct. Includes field-unit conversion, torus/invariant-sector limits, free/compact/2D flux and corrected singular-domain examples.
mass-gap-conditional-theorem.md | priority=3 | flags=none | role=result,synthesis | status=conditional | proof_status=proved conditional transfer; source applicability and physical hypotheses open | value=synthesis,open-mechanism | keys=H1;H2;weak-side blocking;certified finite box;mixing neighbourhood;physical a star;minimum decay rate;continuum construction;intermediate-region-finite-verification;intermediate region finite verification;Dobrushin Shlosman;complete analyticity;finite block mixing;Wilson transfer matrix;interaction space;openness radius;RG finish line;screening;confinement-scale-bands;confinement scale bands;Elitzur;Dobrushin block criterion;Wilson loop sub-block mixing;beta 5.7;glueball softening;physical crossover;bands A B C | area=Yang–Mills/gauge H1 multiscale fluctuation/quasi-local Gibbs control and H2 neighborhood mixing imply a volume-uniform Wilson-transfer gap, with continuum transfer conditional on existence and dense observables. Finite certificates, gauge marginal reduction, interaction robustness and numerical bands retain their distinct burdens.
mass-gap-obligations-lattice.md | priority=3 | flags=none | role=synthesis,result | status=open | proof_status=finite-lattice and conditional spectral proofs; linked strong-coupling theorems; weak trajectory, uniform estimates and continuum goal open | value=synthesis,infrastructure | keys=T1;T2;T2 prime;T3;T4;KS physical sector;volume then cutoff;asymptotic freedom;small-volume corner;gapped set;finite volume continuity;surviving spectral weight;lost spectral weight;mass-gap-position;mass gap position;mass-gap map;seven closed routes;operator norm;global Agmon;Gibbs comparison;Schur ultraviolet;H1 methods problem;H2 infeasibility;su3-constants;su3 constants;SU(3);Casimir 4/3;beta 54/g^4;Lieb–Robinson;Z3 flux sectors;one-loop doublings;magnetic identities;SU3 specialization;gapped-set-critical-coupling | area=Yang–Mills/gauge One canonical lattice-to-continuum spectral treatment contains T1 finite compact-resolvent positivity, strong-coupling and Wilson/KS distinctions, finite-volume analytic coupling dependence, conditional limiting spectral thresholds and lost-weight counterexample. Integrates former position map and exact Wilson sufficient constants. All-coupling positivity/phase equivalences, large-field rarity, relative flow truncation and exhaustive route closures remain unproved; continuum construction and physical spectral transfer stay separate.
mass-gap-openings.md | priority=1 | flags=none | role=synthesis | status=exploratory | proof_status=source-based scoped mechanisms and written comparison identities; proposed bridges conditional | value=synthesis,known-boundary | keys=scaling-region correction;Wilson bulk transition;negative adjoint action;Bakry Emery;centre stabilization;three dimensions;Simon valley;large N;reasons-to-stop-as-research;reasons to stop as research;Gauge crossover: comparison tools and their missing estimates;H1 weak-side RG;H2 mixing box;Griffiths monotonicity direction;truncated correlator;certified boundary supremum;physical Wilson coupling;what-would-unblock;what would unblock;correlation inequality;Ginibre;centre flux;finite certificate;reflection positivity;weak side | area=Yang–Mills/gauge One gauge-mechanism comparison keeps curvature, centre deformation, three-dimensional scaling and valley lifting beside correlation inequalities and finite certification. A weak scaling trajectory needs less than all-coupling positivity; temporal operators, rank and physical-hbar limits remain distinct.
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 convolution;mid-plane parallel theory;Brownian bridge;Hypothesis P;winding holonomy;U(1) vortex | area=Yang–Mills/gauge Directional heat-kernel halving closes in series but leaves an exactly defined coupled mid-plane parallel theory.
small-field-step-gaussian.md | priority=2 | flags=none | role=result,infrastructure | status=result | proof_status=written Gaussian, tube and soft-resolvent estimates; nonlinear expansion conditional | value=infrastructure | keys=SU(3);four-dimensional block averaging;32 components;tube Poincare;Gaussian covariance;4/9;gauge intertwining;small-field-step-decay-and-threshold;small field step decay and threshold;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;soft block constraint;Combes–Thomas;Kotecky–Preiss;nonlinear threshold;decay rate;weak coupling;heuristic polymer estimate | area=Yang–Mills/gauge Exact linearized four-dimensional tube blocking gives the 4/9 constrained gap and Gaussian covariance. A distinct soft constraint has gap 2/9 and a coefficient-specific decay criterion. Correct two-link normalization and infinity-norm shell sum replace the old threshold table; nonlinear KP control remains conditional.
strong-coupling-uniform-gap.md | priority=2 | flags=none | role=result,synthesis | status=result | proof_status=borrowed local stability theorem with written hypothesis checks; finite-volume and restricted-count proofs; general-history and RG transfer conditional | value=synthesis,known-boundary | keys=T2;Kogut–Susskind;Yarotsky;Peter–Weyl;volume-uniform gap;thermodynamic ground state;beta 54/g^4;abelian U(1);finite-volume min-max;SU(3) weak running;kogut-susskind-strong-coupling-explicit;kogut susskind strong coupling explicit;Continuous-time Kogut–Susskind expansion: corrected overlap bounds and an open explicit uniform threshold;Kogut Susskind;continuous-time Duhamel;closed flux loops;Kotecky Preiss;general polymer tree;withdrawn 388 threshold;hbar c over a;strong-coupling-target-box;strong coupling target box;The target box: the strong-coupling gap survives local perturbations with an existential tolerance; its explicit location is open;SU(3);target box;bounded local perturbations;electric deformation;locality q;exact low-energy reduction;physical gap;abelian-misses-the-box;strong-coupling-threshold-explicit | area=Yang–Mills/gauge Yarotsky stability gives an existential volume-uniform KS gap and a specified translation-invariant perturbed target region. Exact finite-volume electric-loop bounds, corrected all-root overlap obligations and restricted continuous-time counts share one proof structure; numerical uniform thresholds remain withdrawn.
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 Formal full-plane one-loop coupling shifts have explicit signs and SU(N) scaling, with a separate finite-torus winding obstruction.
su2-midplane-small-field.md | priority=3 | flags=none | role=live,result | status=conditional | proof_status=written estimates and conditional implications with incorporated counterexamples and repository-internal checks; no independent peer review | value=open-mechanism,infrastructure | keys=normalized covariant comparison;flat-holonomy obstruction;barrier covariance lower bound;inverse-curl pole;comb-tree strip Hessian;undifferentiated barrier;weak recoupling strip;all-order bad-component tree (116);exact dressed activities (112);moving-mean quadratic source (177);complex centered nonlinear factors;physical recoupling u=1;SU(3) transcription limits;generated-action iteration | area=Yang–Mills/gauge Covariant inverse decay, bridge tails and local convexity coexist with the flat-holonomy failure of the original normalized comparison. Exact barriered responses, large-field insertions and weak-recoupling dressed activities give (112)/(116); a centered quadratic moving-mean model gives (177), while nonlinear (113), physical recoupling and iteration stay open.
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 Exact bridge character formulas cover every spin; spin-½ is scalar, while internally checked spin-1 matrix entries retain axial anisotropy and explicit image bounds.
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 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.
three-dimensional-gap-one-function.md | priority=2 | flags=surprising | role=synthesis,result | status=conditional | proof_status=written dimensional and truncation identities; source-dependent strong-coupling theorem; continuum and small-volume transfer 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 Conditional physical 3D theory has gap E3 f(lambda3 L), with E3=hbar c lambda3 and lambda3=hbar g_cl². Exact SU2 constant-mode scaling and explicit nu=2 strong-coupling lattice constants control different regimes; nonzero-mode transport, construction and a positive finite spectral limit remain unproved.
torus-valley-potential.md | priority=3 | flags=none | role=result,obstruction | status=result | proof_status=written scalar benchmark theorem; specified one-loop calculation and conditional field transfer | value=infrastructure,open-mechanism | keys=SU(2) torus;one-loop valley potential;Poisson summation;periodic centre minima;2hbar c norm a;nonzero-mode correction;Feshbach H3;centre-odd variational bound;electric flux splitting;flat holonomy torus;cubic invariant charged sum;g8/3 exp minus c over g;Weisz Ziemann 1987 | area=Yang–Mills/gauge The one-loop SU2 valley has bounded periodic full potential and an unbounded nonperiodic subtracted correction. For the declared flat 4pi holonomy operator, centre-odd and cubic-invariant trials give an explicit g^(8/3) exp(-c/g) upper gap, so local g^(2/3) spacing is not its global gap.
villain-monopole-refinement.md | priority=3 | flags=surprising | role=result,obstruction | status=result | proof_status=proved; repository-internal written review | value=surprising-result,decisive-obstruction | keys=Villain U1;Poisson monopole;flux sectors;TV;lambda3 a;D4 loop;Gross trajectory | area=Yang–Mills/gauge 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.
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;Berry term;cubic vacuum shift slope;ultraviolet power counting;schur-error-ultraviolet | area=Yang–Mills/gauge Proves abstract Schur gap-transfer lemmas, including a constant-shift/relative-error version. Physical H1–H3, UV-uniform domains and bounds remain open, and H3 must identify the centre sector and observable algebra before a local matrix spacing can represent its compressed gap.
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 exact condition;rho exponential activity;1059 sufficient integer;1056 linearized;176 leading activity;volume uniform;strict positive rate;cyclic observables | area=Yang–Mills/gauge The all-representation activity rho=e^(6/g²)−1 yields a volume-uniform Wilson-transfer gap at the sufficient integer bound g²≥1059, with rate 4 log[1/(176 rho)] in units ℏc/a. Exact sufficient KP convergence uses rho≤21/(500e²); the unrounded rate is positive only at a strict margin.

checkerboard-dynamics.md | priority=2 | flags=surprising | role=result,calibration | status=result | proof_status=proved; repository-internal written review | value=surprising-result,used-calibration | keys=A09b;C039;C040;checkerboard coin;Dirac strong limit;telegraph reversal;Born rule;observed corners;checkerboard-B18 | area=refinement/comparison 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.
comparison-and-bridges.md | priority=1 | flags=none | role=synthesis | status=result | proof_status=source passage restatement; elementary identities proved under stated smoothness; bridges conditional | value=synthesis,known-boundary | keys=Navier–Stokes;Yang–Mills;auxiliary clock;physical Hamiltonian;stochastic quantisation;scaling;gap limits;reconstruction;first-milestone;millennium-problem-definitions;millennium problem definitions;Clay definitions;Fefferman A B C D;forced breakdown;unforced existence;Jaffe Witten;nontrivial quantum theory;Wightman OS;finite positive mass gap | area=refinement/comparison States the exact Clay data, forcing and quantifiers for fluid A–D and the axiomatic quantum Yang–Mills existence/finite-gap target. Derives scaling and dissipation identities, distinguishes physical from auxiliary clocks and states the obligations for each proposed bridge.
constructive-qft-one-time.md | priority=3 | flags=none | role=result,synthesis | status=result | proof_status=proved-unrefereed | value=infrastructure,synthesis | keys=P(phi)1;quartic oscillator;Feynman Kac;arbitrary time refinement;vacuum;reflection positivity;non-Gaussian;SU2 matrix;Gauss law;relativistic worldline | area=refinement/comparison Assembles the known quartic oscillator into a continuous full-time Euclidean process with a unique vacuum, positive gap, bounded-cylinder reflection positivity and a non-Gaussian one-time marginal; ground-state boundary-weighted lattice measures converge for arbitrary time partitions. The construction applies to the prior SU(2) matrix gap and its singlet sector.
cut-paradox-two-faces.md | priority=1 | flags=route-closure | role=result,synthesis,obstruction | status=result | proof_status=written scalar derivations and model identities; matrix conjecture open | value=known-boundary,decisive-obstruction | keys=I003;C032;scalar rigidity;ballistic support;Paley–Wiener;unitary translation;internal velocity;Compton branch points;matrix semigroup conjecture;telegraph commutator;hidden slow mode;independent additive readout noise;double limit;probability conservation;cone sections;Xylander 1570;Rivero 1998;time refinement;deterministic zero branch;i003-double-limit-rigidity;cone-time-refinement;I003-tests;I003-cut-paradox-arrow-obstruction;I003 cut paradox arrow obstruction | area=refinement/comparison Scalar ballistic-support probability convolution laws are deterministic drift, and scalar translation-invariant unitary groups with light-cone kernels are translations up to phase. Internal-state identities, the matrix conjecture, hidden slow mode and exact additive-readout double limit retain separate scope.
dirichlet-wall-impulse.md | priority=3 | flags=none | role=result,live | status=result | proof_status=written packet estimates and weak-measure limit for specified Dirichlet/Neumann states; Robin scattering comparison only | value=infrastructure,open-mechanism | keys=Dirichlet boundary force;impulse measure;elastic bounce;Neumann stress;Gaussian impact layer;error function;Robin reflection phase | area=refinement/comparison Imposed elastic bounce and quantum boundary choice are distinct. Explicit Dirichlet odd packet has uniform position recovery through impact, current recovery away, and positive boundary-force measure converging to 2|p0| delta. Full Neumann stress has same weak impulse; Robin phases and bound state retain boundary information absent from classical bounce. No self-adjoint half-line momentum is assumed.
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 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.
groupoid-quantum-newton-states.md | priority=3 | flags=none | role=result,synthesis | status=result | proof_status=written dilation, local heat-kernel and normalized-bridge proofs plus conditional state theorem; established analytic inputs; no universal positive-action selection | value=infrastructure,synthesis | keys=tangent groupoid;continuous field;coherent states;Weyl quantization;Egorov;joint mesh action limit;Euclidean scales;newton-dimock-balaban-guide;newton dimock balaban guide;October 27 28 synthesis;Newton quantum completion;conditional action floor;classical histories;Gaussian meter;record closure;Dimock Balaban;groupoid;renormalization;bare regulator;hard wall;quantum lift;refinement;ordering;two-regulator-audit;M05;C014;Gaussian bridge;dimension variance;uniform path;chi-square;residual action;action defect;tangent-groupoid-trajectories;tangent groupoid trajectories;zoom action;principal symbol;time-graded groupoid;min-plus action;convolution;ballistic versus diffusive;matched tangent scaling;interacting kernel dilation;normalized endpoint bridge;row normalization;Mehler kernel;strong versus norm limit;semiclassical heat symbol;Wigner Kirkwood;well-resolving scaling;harmonic versus quartic time scale;action mass normalization;inserted point;shifted kernel product;finite-scale base point;pair arrow factorization | area=refinement/comparison Exact interacting dilation commutes with kernel composition and normalized bridge marginalization. Matched hbar=epsilon S0 and time/distance epsilon give a local heat expansion with explicit second-order potential terms and a refinement-uniform Gaussian bridge limit. The shifted kernel product retains insertion centres lost at zero. Row-normalized harmonic transitions fail the semigroup law; well-resolving scaling differs. Retains the O(hbar+mesh) coherent-state field theorem, free zero-action control and bridge action defect.
halving-atlas.md | priority=3 | flags=none | role=live,synthesis | status=open | proof_status=maintained dependency synthesis; exact identities, formal scaling and open estimates distinguished | value=synthesis,infrastructure | keys=dimension atlas;series parallel;arbitrary cuts;SU3 triality;Newton records;cell 4;weak recoupling;moving saddle;uv-halving-ir-confinement;uv halving ir confinement;UV IR;exponential ladder;dimensional transmutation;physical spectral weight;matching scale;C Lambda;dimension-ladder;dimension ladder;0+0;1+n;thermodynamic action unit;wave equilibrium;rotor;gravity least length;refinement-results;refinement results;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 Exact series/parallel operations, arbitrary cuts and group image sectors organized by dimension and scientific dependency. Retains exact circle/rotor identity and one-loop scaling, separates depth/volume uniformities, fine-measure construction and spectral visibility. Corrects unsupported renormalon identification and stable-quartic non-Borel claim. No scale-to-gap or confinement implication is assumed.
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;thermofield double duration;entropy coefficient plus one;inverse temperature 2T over hbar | area=refinement/comparison 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.
interacting-ising-gap.md | priority=1 | flags=none | role=result,calibration | status=result | proof_status=mixed | value=known-boundary,used-calibration | keys=G03;C124;periodic Ising chain;heat bath;Hamming coupling;magnetization eigenmode;a one minus tanh 2b;per-site clock;ising-hermitian-transfer;ising hermitian transfer;G04;C126;square-root Gibbs;detailed balance;three-site parent;frustration free;imaginary time;supplied K;ising-foundational-value;ising foundational value;Ising benchmark;relaxation gap;logarithmic mixing time;stochastic parent;physical clock;action conversion;publication premise;ising-gap-B68;ising-hermitian-B71 | area=refinement/comparison The exact interacting heat-bath gap, its explicit positive three-site square-root Gibbs parent and logarithmic global mixing-time comparison are proved or source-matched together. Refresh-clock and supplied-action normalization remain independent of equilibrium weights.
lean-verification-quantum-newton.md | priority=3 | flags=none | role=synthesis,infrastructure | status=result | proof_status=mixed | value=synthesis,known-boundary | keys=Lean 4;newtonlean;constructive lifting;C1,1;Trotter;boundary impulse;cusp selection;relativistic;drift kick;ordering ambiguity;Gaussian overlap;literature priority | area=refinement/comparison Precise classical, operator, packet, sharpness, wall, cusp, relativistic and Euclidean Lean targets with close prior art and a finite rational drift-kick versus kick-drift comparison for newtonlean; exact constant-force overlap exposes joint-limit ray separation and a variable-mass example shows factor-ordering ambiguity.
quantum-blocks-construct-newton.md | priority=3 | flags=none | role=result,live | status=result | proof_status=mixed | value=open-mechanism,infrastructure | keys=Dimock Balaban;normalized density tower;Brownian bridge;quantum mechanics;coherent states;Newton ODE;joint time mesh and action limit;Cauchy Lipschitz;cut-point-consistency;cut point consistency;A03;C027–C029;constant-force chord defect;arbitrary partitions;Gaussian restriction consistency;chi-square action;inserted node variance;CUT_POINT_TARGET;cut-point-B12 | area=refinement/comparison Normalized supplied-hbar Euclidean blocks and coherent unitary products construct the unique smooth Newton initial-value trajectory with O(hbar+mesh) mean error and O(sqrt(hbar)) widths. Projective Gaussian preparation, raw kinetic divergence and its scale estimator are integrated.
refinement-composition-and-limit.md | priority=3 | flags=none | role=result,live | status=result | proof_status=written finite composition and harmonic estimates, supplied-action Gaussian and 2D law constructions; higher-dimensional transport conditional; internal review only | 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;M04 | area=refinement/comparison Exact constant-force elimination and supplied-action Gaussian composition accompany sharper harmonic insertion/mixed-kick bounds and an all-partition trajectory/force-law construction. Exact 2D gauge subdivision and a sufficient summable-defect law require different inputs from a classical initial-value theorem; higher-dimensional interactions and physical limits remain open.
relativistic-dispersion-blocks.md | priority=3 | flags=none | role=result,live | status=result | proof_status=proved-unrefereed | value=infrastructure,open-mechanism | keys=relativistic dispersion;positive energy;quantum time slices;joint h mesh c limit;strong resolvent;subordinate Brownian;spectral Dirichlet wall | area=refinement/comparison Bounded third derivatives give O(h+mesh+c^-2) mean and smooth Weyl convergence to Newton for the positive-energy relativistic particle; fixed h has strong-resolvent convergence, and a separate spectral Dirichlet wall has uniform position convergence through impact.
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;G01;G02;observable-access-B22;susceptibility-B20 | area=refinement/comparison 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.
telegraph-return-bridge.md | priority=2 | flags=none | role=result,calibration | status=result | proof_status=written exact path, support and moment derivations; classical models with explicit conditioning | value=used-calibration,infrastructure | keys=C033;C037;telegraph bridge;Bessel count;beta midpoint law;velocity memory;cubic crossover;small-mass nonuniformity;A09a;C038;B17;bridge-crossover;physical-cut-speed;physical cut speed;A05;C030;C031;C032;elastic return bridge;bounded speed;scalar convolution closure;A06;P02-six-direction-checks;bridge-crossover-B17;physical-cut-B13;telegraph-return-B14 | area=refinement/comparison Exact elastic equal-mass receiver and sharp kappa_mid<=mT(u-|v|)^2 support benchmark precede the velocity-resolved telegraph return bridge. Count/simplex law includes midpoint atom, Beta law, arbitrary-cut action error, exact Bessel crossover and small-mass/window nonuniformity. Scalar convolution rigidity is kept in cut-paradox-two-faces. Speeds, reversal rate, apparatus and limits are supplied.
three-continuum-limits.md | priority=3 | flags=none | role=synthesis,live | status=conditional | proof_status=source-based comparison, conditional chiral statements and written spectral-limit proofs; main goals open | 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;coherence premise;incoherent quadratic classical limit;Kepler localization and moments;selection-dependent endpoints;h versus hbar;Wilson explicit uniform bound;KS withdrawn numerical threshold;finite volume versus existential uniform | area=refinement/comparison Physical comparison retains a pure-SU3 gap, massless/massive two-flavour QCD pion channels and Newton record costs as different targets. Axial Ward/pole identity and two positive spectral-measure limit criteria include surviving weight and counterexample to eigenvalue-only convergence. Coherence, singular-domain selection and physical action necessity remain separate premises; chronological queue and repeated domain tables removed.
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 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.

Historical source questions

ancient-cuts-provenance.md | priority=1 | flags=none | role=historical | status=historical | proof_status=primary passage interpretation and scoped elementary modern comparisons; compatibility proposal unproved | value=source-guardrail | keys=Aristotle 317a;Plutarch cone;Democritus;possible cuts;joint division;trajectory readjustment;I005;discrete-substrate-actors;discrete substrate actors;’t Hooft automaton;Wolfram;finite information;Dedekind cut;Connes differential;equivalence classes;superdeterminism;groupoid zero fibre;Cvitanovic;Gisin;Del Santo;t Hooft automaton;Snyder;Yukawa;Adler trace dynamics;Nielsen random dynamics;Regge;Penrose spin networks;Finkelstein;Sorkin causal sets;Ambjorn Loll;Wheeler it from bit;von Weizsacker ur alternatives;classics-redirection-2026-09-09;static-composition-classics;static composition classics;H10;Vasubandhu;six contacts;Ibn Sina;Liu Hui;Mohist shadow;parts and whole;source restoration;I005-classical-cuts-and-relations;I005 classical cuts and relations;I007-static-compatibility;I007;I007 static compatibility;static compatibility;directional contact;Galileo cohesion;Nagarjuna traversal;Liu Hui dissection;Mohist apparatus | area=historical/sources Unifies Aristotle and Plutarch cut evidence with Indian contact, Avicennian, Chinese dissection/statics and cohesion witnesses, preserving editions and reading limits. Separates sampling, re-solving, marginalization and measurement, and retains fixed-time compatibility premises without an action-selection claim.
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 Passage-level Newton Project audit separates retrospective analytical discovery from synthetic Principia demonstration and documents generated quantities, limiting ratios and priority/publication revisions.

Notes retrieval catalog

Classical completion, action scales and records

Complete apparatus state and recovery

Gauge construction and spectral estimates

Composition, refinement and spectral comparisons

Historical source questions