Remark: Revision log (audit 3)

Integration and proof audit following expert review; no new work package, no expansion; XVI-A–XVI-L, their artifacts and the GitHub repository are not modified.

1. Gate S-bv provenance. XVI-J already prints the formula (eq:W, eq:DF: $h_0=-W_0$, $d=W_0-i{E}_0^{\mathrm{A}}$, $S=-d$; eq:rational: $d=-\frac{1}{4{\pi }^2}(Q_{\mathrm{geom}}-i0{)}^{-1}$ on $z\ne 0$ including nonzero null points; prop:q uses it); XI-E, eq:h, only sets $h=-W$ and the jump. These are quoted in Section sec:wpA-identify, and Theorem thm:wpA-Sbv is reframed as a written check of XVI-J, eq:rational (corroboration, not a frozen XVI-L premise; the direct Fourier proof and Lemma lem:wpA-varreg stand independently). New Lemma lem:wpA-varreg proves the boundary value of the variable regulator $Q-2i\tau z^0-{\tau }^2$ near nonzero null points. The damping parameter is renamed $\epsilon \to \tau$ (and the Euclidean slice variable $\tau \to {\tau }_{\mathrm{E}}$) in the manuscript and the wpA fragment and script. The scope sentence on “extension across $z=0$” is replaced by: the predecessor $S$ is globally defined (XVI-J); what is not established here is its position-space identification at the origin.

2. Top versus full scale tensor. In the double plateau, the cutoff-independent $D=4$ component is variational and Lorentz covariant, but not linearized-gauge invariant. The full scale tensor has cutoff-dependent lower-degree components and need not be variational; its Lorentz covariance is not established (Theorem thm:wpB-dp). The relation to XVI-L, thm:L6 / rem:Lressretch, is recorded (Remark rem:wpB-topfull); $r=-i/(8{\pi }^2)$ discharges only the top contact.

3. Separating functional. Proposition prop:wpB-sep: $\ell =a+b-c+d+e$ annihilates $v_{R^2},v_{{\mathrm{Ric}}^2}$ and gives $\ell (v_{\mathrm{scale}})=-\frac{1}{16}$; basis order and signs verified against full_scale_collapse_certificates.json, COV4 and conventions.json; pure-gauge interpretation verified with sympy; the $f^{\prime \prime \prime \prime }$ coefficient $-\frac{1}{8}$ of $E^{00}[f{e}_{00}]$ is recomputed from the archived $C_{\mathrm{top}}$.

4. M-C split. Definition def:MCcurv: broad M-C is the matched-scale criterion (proved matching + explicit $\varpi$ and a functional representation of the entire collapsed scale variation); M-C${}_{\mathrm{data}}$ (matching + explicit prescription-dependent scaling formulas) is satisfied; M-C${}_{\mathrm{curv}}$ Proved obstructed (graph-specific); broad M-C not achieved (Unresolved) because XVI-L leaves $\varpi$ unspecified (thm:L6). The implication that ghosts/diagrams are the only enlargement is removed (Corollary cor:wpB-MC; release ladder; abstract).

5. Time-only. The step “By Lemma lem:to-indep this reduces to linear independence of the occurring switch jets” is removed; the sufficient condition is kept for the joint family $\{{{\sigma }_{\epsilon }}^{(k)}{\partial }^{\rho }{\chi }_{\mathrm{I}}\}$, with the counterexample Remark rem:to-joint. “Do not extend to any region where ${\sigma }_{\epsilon }$ varies” is replaced by “do not admit the stated universal time-only completion; the actual-ramp conclusion holds under Proposition prop:to-actual”. Corollary cor:wpB-timeonly was reviewed; its proof is complete relative to the reported computations and it is kept as a corollary.

6. Proof corrections. (a) Lemma lem:wpB-dw: the basis derivative is $\mu {\partial }_{\mu }{f}_{\gamma }=(E-|\gamma |)f_{\gamma }$, combined with $(|\gamma |-|\alpha |)$ from $M^{-1}$. (b) Lemma lem:bv(c): explicit $\widehat{uv}=\frac{1}{2\pi }\hat{u}\ast \hat{v}$ and Beta integral, with identification of the Hörmander product by the local Fourier formula; the “sequential continuity” shortcut is removed. (c) Proposition prop:M7-id(B${}^{\prime }$): weight-derivative terms arise in the Euler tensor and cancel in its divergence (cf.\ XII-C, eq:weighted-full-variation). (d) Shell annotations in the run listing and README are # comments. (e) regression_M.py labels current-status versus historical-record checks and has an audit-3 section.