What survives refinement?

Two proof goals guide this repository: derive a positive universal action scale from independently justified physical premises in Newton’s Galileo comparison, and construct pure SU(3) Yang–Mills in four dimensions with a positive finite physical mass gap.

Exact insertion laws, conditional record bounds and controlled lattice estimates are in hand. Both main goals remain open. The pion is a symmetry benchmark for the comparison.

Strong results to start with

Newton’s action decomposes under every cut

The cut measure gives exact additive refinement costs. Constant-force and harmonic curves can be constructed under the stated laws for arbitrary shrinking partitions: construction and limit. Consistency alone leaves zero action admissible.

A record costs disturbance

General quantum instruments obey a sagitta/impulse disturbance bound with supplied ℏ and explicit comparison-state resources. The sharp Gaussian floor has narrower mark and preparation-invariance hypotheses; prepared packets show why a universal cell-action floor needs more.

Kepler completion and a controlled classical limit

Coulomb quantum evolution exists at every positive phase constant. The October 2 written derivation controls the singular multiplier and both centroids on fixed collision-free intervals with a fixed smooth regularization. Relativistic action thresholds depend on the chosen point-source domain; full critical Klein–Gordon evolution remains open. These additions are unrefereed.

Series closes; parallel carries the generated action

Directional gauge halving factors exactly. SU(2) midpoint traces and general compact-group cuts are exact; interacting mid-plane comparison remains a separate estimate.

Connected bad sets and exact dressing in a weak strip

All-order marked estimates (116) and dressed activities (112) are proved in their retained-barrier weak-recoupling domain. Section 37 gives a quadratic moving-source test for part of (113). These results do not yet give the full nonlinear group integral or stable physical iteration.

Lattice gaps at strong coupling

The Wilson transfer bounds are explicit and volume-uniform. The KS numerical uniform threshold was withdrawn on October 2; its corrected explicit bound depends on volume. The Yarotsky application and perturbed target region retain existential uniform statements. Controlled arrival from the continuum scaling trajectory and continuum reconstruction remain open.

Current open fronts

Newton: independently justified physical premises for coherence through complete records, and for any singular-domain selection used to infer an action threshold. The incoherent-packet countercase reaches the classical branch for quadratic forces. The current packet/stability test uses supplied quantum free evolution as its reference.
Gauge local step: complex nonlinear centered bounds and decaying source dependence of the moving saddle, with the barrier retained. Current quadratic input.
Four dimensions and spectrum: depth-uniform generated-action matching, stable iteration, and the renormalized small-volume bridge. Continuum axioms, nontriviality, volume uniformity and physical spectral weight remain explicit.

Dependencies and exact next obligations · Live STATE. A gap at every bare lattice coupling (T2′) is an optional stronger statement; the continuum argument needs control along the appropriate weak-coupling scaling trajectory: correction.

Decisive corrections to retrieve

Local Agmon suppression: original route → global-only correction.
Finite crossover certification and monotonicity: earlier bridge → weak-side diagnosis.
Naive blocking, invertible flow and bare Feshbach UV control: scoped failures and surviving alternatives.
A prior covariance restriction is vulnerable to complete and nonlinear records: exact tests. Thermodynamic costs and phase consistency supply conditional trades or ratios, while positivity remains separate.

A short reading path

The illustrated argument, then the two goals and the spectral benchmark.
Exact insertion and what a limit requires.
Newton: record/disturbance synthesis → classical limits and coherence → Kepler completion and selection → physical premise and calibration.
Gauge: series/parallel split → order-t input → current normalized-control notebook.

For a specific calculation use the dependency paths and notation/scale map. The provisional book gives a longer reading architecture; the correspondence test states where the analogy is exact.

Complete archive and evidence

Every maintained note, with summary, status and retrieval priority · greppable catalog · syntheses, technical manuscripts and historical PDFs · primary sources and reading coverage · stable older claim IDs · dated established-result map.

The programme history, site audit and navigation test explain the reading architecture.

Retrieval priority measures usefulness to the current questions, not novelty or mathematical quality. Full notes govern their hypotheses and later corrections. Comments and corrections are welcome as repository issues.