Claim-status register
The register separates the origin of a statement from the recovery established here. A denotes a native admission result; B, a result conditional on the realized branch; C, a result of the supplied Yang–Mills construction; D, a recovery statement proved in this reconstruction; and E, an open selection question. A row can combine classes when a supplied construction also receives a new recovery proof. The hypotheses and exactness classes are part of the stated result.
Accessible table transcription
| Item | Class | Reconstruction status and recovery class |
|---|---|---|
| Admitted antecedent and lit- | A | Admission of the walking marked dependency; selects |
| eral preparation (Prop. 6.1) | no physics. | |
| Admitted fan supporting the | A | From the admission closure alone:no relation be- |
| family; its automorphisms and | tween leaves, no preferred labelling, finite statements | |
| fold map (Props. 8.1, 8.2) | over finite admitted supports. Selects no physics. | |
| Lift groupoid of a leaf; fibre | D | The realization is an equivalence of groupoids; lifts |
| law (Thm. 8.3, Cor. 8.4) | unique up to unique isomorphism; stabilizers pre- | |
| served. Checked on a finite model. | ||
| Interfaces and their discrepan- | B | Classification of the supplied construction’s interfaces |
| cies (Table 2) | by exactness class, each row proved where indicated. | |
| V | ||
| Frame realization, fibre, sec- | D | Exact: quotient equivalence Z/G≃U and normal- |
| tion, measure (Thms. 7.1, 7.2) | ized pushforward. |
Accessible table transcription
| Item | Class | Reconstruction status and recovery class |
|---|---|---|
| Reflectionpositivityand | C | Lifted with identical Gram matrices on the retained |
| rooted bounds | probe algebra. | |
| Activitydomains,budgets, | C, D | Definitionssupplied;frame-blindflags,ordered- |
| norm (AB1–AB12) | derivative recovery and isometry of the activity chart | |
| are new (Prop. 9.1, Thms. 9.2, 9.4). Exact embedding | ||
| with section. | ||
| Quadratic history contract | C | Five-row identities lifted through d1p (Prop. 11.1); |
| amendment recorded as a retained choice. | ||
| Primitiveintegrand(PRI1– | C | Regrouping is a bijection; marginal extension loses |
| PRI9) | only unread coordinates (Props. 13.3, 13.5). | |
| Stationary graph (AS, US) | C, D | Graph and response bounds supplied; recovery of the |
| vertical discrepancy from the residual with period-free | ||
| constants is new (Thm. 14.5). On-shell recovery with | ||
| explicit off-shell defect. | ||
| Exterior division, two-leg prim- | C | Division is a section of contraction; primitive not |
| itive (ED, TEL) | unique (Props. 14.8, Thm. 14.9). | |
| Loop moments (LM) | C | Quiet families are the zero fibre of an additive moment |
| readout (Prop. 14.10). | ||
| One-loopdriftands= | C | Coefficient derived inside the supplied construction |
| 2 | ||
| 11C/(24π) (DR, DP, MA) | from an exact pole integral (arithmetic recomputed | |
| A | ||
| here); actual couplings tied to the reference clock | ||
| by inequality (Thm. 14.12). Not a physical-coupling | ||
| identification. | ||
| Common calendar (CAL) | C | One common witness for all histories, cutoffs, periods, |
| observables (Thm. 14.16); non-unique, monotone un- | ||
| der admissible enlargement. | ||
| Startuprepresentative(SQ, | C | Exactdensityidentitywithnonzeroactivities |
| FST) | (Thm. 14.18); evaluation reader many-to-one. | |
| Forward recipe and shooting | C, B | Operation lift with zero defect (Thm. 14.20); cali- |
| (FCA, RSP, FCC, RET) | brated histories exist (Thm. 14.24); calibration is im- | |
| posed at the bottom and propagated. | ||
| Beacons, reference chart (RB, | C | Controlled approximation with stated rates;con- |
| PL, GL, RBG) | stants tied to fixed reference tori. | |
| Activitynorm,stepmaps | C | Descentofstepmapstothecommonchart |
| (LCN, ASP) | (Thm. 14.28). | |
| Stability and running (FCB, | C | BottomreaderinjectiveandLipschitz-invertible |
| RUN) | within the retained recipe (Thm. 14.29); slope clause | |
| of the public theorem recovered (RUN5). | ||
| Protected variables (PV) | C, D | Reading as a horizontal lift with equivariance under |
| the frame action is new. | ||
| Path books (SH) | C | Full-sequence limits for quadratic rows, subsequential |
| for nonlinear books (Prop. 15.3). | ||
| Radial jets (RJ) | C, D | Curl/radial reconstruction supplied; explicit gauge pa- |
| rameter and fibre description are new (Thm. 16.1). |
Accessible table transcription
| Item | Class | Reconstruction status and recovery class |
|---|---|---|
| Labels, calibration, free hierar- | C | Finite-order recovery of labels; invertible readout at |
| chy (PF, PC, FM, GP, FC, FS, | fixed level (Thm. 16.3); free sector is an imported | |
| HC) | comparison realization; faithful readout with bounded | |
| probes (Thm. 16.7). Numerical tables recomputed. | ||
| Physical quotient and deriva- | C, D | Supplied construction; its formulation as kernel of all |
| tives (CVP, CVR, QD) | spectator readers with operations descending is made | |
| explicit (Thm. 18.3). Quotient equivalence. | ||
| Slab insertions (BS) | C | Bounded on the reflection quotient (Prop. 19.1). |
| Euclideanrotations(RT, | C | Covariance of the readout derived, not a symmetry of |
| RSW, DB) | the lattice source (Thm. 19.3); elimination constant | |
| sharpened to 7K (Lemma 19.2). | ||
| Tracecandidate,Gaussian | C | Recovered with retained residuals; charges are rep- |
| comparison,scalingmaps, | resentable fields (Thm. 23.3);scaling comparison | |
| stress, charges (TF, IG, WS, | (Thm. 23.2). | |
| SR, SC, LCE, LR, TS) | ||
| Fullshort-distancelimit | C | Recovered for the selected phase (Thm. 24.1); value |
| 4 | ||
| (TLim) | 3 dimR g/πsupplied by the scalar Wick calculation | |
| of the sequential part. | ||
| Wightmanreconstruction, | C | Lifted through Thms. C.1, D.1 and Prop. E.1. |
| OPE,contactextensions, | ||
| mass-shell exclusion (sequen- | ||
| tial part) | ||
| Coverageandamendment | – | Every expanded-source heading unit and its depen- |
| record | dencies are mapped in both standalone papers. Four | |
| local recovery findings and two formula amendments | ||
| are resolved with their calculations in Section I.1. | ||
| Selection of the gauge group, | E | Not obtained and not claimed; inequivalent realiza- |
| dimension, action or coupling | tions over the same support exist (Section 8). | |
| history from source-side princi- | ||
| ples | ||
| Positive mass gap; identifica- | – | Not asserted by the source; not asserted here. |
| tion of the regulator coupling | ||
| with a physical coupling be- | ||
| yond the trace/Ward normal- | ||
| ization |
Source: Shadow Theory and the Wilson Yang–Mills Construction: A Source–Readout Reconstruction. Both papers belong to one Zenodo record. No external funding.