Scale derivative versus dilation defect at every grade (work package B)

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wpB/higher_grade_scaling.py ($185$ checks; output higher_grade_scaling_out.txt), scale_derivative_coefficients.json, dilation_defect_coefficients.json, scale_defect_difference.json, full_scale_collapse_certificates.json, matched_scale_ledger.txt, _wpB_state.json, _wpB_sectionD.json. The script keeps $c^2$ symbolic; its status strings “CONDITIONAL on Input (S-bv)” predate Theorem thm:wpA-Sbv and are superseded by it.

.6 status.

• Dilation identity and $A_{\mu }=\mathcal{A}$ for $N=0$: Constructed (Proposition prop:M6-dil).

• $A_{\mu }={\mathcal{A}}_{\mu }$ ($B_{\mu }=0$) for all $N=0,\dots ,4$ and every admissible $\varpi$: Constructed (Theorem thm:wpB-B0).

• $S^2$ residue $r=-2i{\pi }^2{c}^2=-i/(8{\pi }^2)\ne 0$: Constructed (Theorem thm:M6-S2, with Theorem thm:wpA-Sbv).

• Top-order residues, all grades: Constructed, exact and $\varpi$-independent (units $i{\pi }^2{c}^2=i/(16{\pi }^2)$); lower-order values: Unresolved (depend on ${\nu }_k[\varpi ]$, $k=1,\dots ,4$; $\varpi$ not fixed by XVI-L; the radial comparison is a separately named specialization).

• $N=0$ anomaly component $C_{\mathrm{anom}}$ (higher-grade coordinates set to zero for this probe): Constructed (Definition def:M6-Canom).

• Collapse of the $N=0$ component: Constructed (Theorem thm:M6-collapse); it contributes no nonzero plateau matching (Corollary cor:M6-compat).

• Collapse of the full scale tensor: Constructed in all readings. In the double plateau, the cutoff-independent $D=4$ component is variational and Lorentz covariant, but not linearized-gauge invariant; it lies outside $\mathrm{span}(E_{R^2},E_{{\mathrm{Ric}}^2})$ (Theorem thm:wpB-dp, Proposition prop:wpB-sep). The full scale tensor has cutoff-dependent lower-degree components and need not be variational; its Lorentz covariance is not established. Time-only readings non-variational (Corollary cor:wpB-timeonly).

• Release: {M-C${}_{\mathrm{curv}}$ Proved obstructed} (graph-specific); broad M-C not achieved (Unresolved; $\varpi$ unspecified by XVI-L, thm:L6); {M-C${}_{\mathrm{data}}$ Satisfied} (Corollary cor:wpB-MC); not a claim about gravity generally.

Archives: scaling_anomaly.py, scaling_anomaly_out.txt, scaling_anomaly_cert.json, scaling_anomaly_cert.txt; wpB/.