Abstract

This note records the audit in results/tables/audit_manifest.json, source identifier 1eeba3536183. Fifteen unit tests passed. The runner label is singular_diagnostic; the admission field is not_claimed. A configuration labelled physical_identified is rejected by require_simulated.

For the cutoff in the package, $c_R=0.625$ and $c_{47}=0.15045103006514954$. The chart formula agrees to $1.96\times 10^{-13}$. At fixed $ϵ=0.1$, the $47$ mesh residual falls from $1.34\times 10^{-4}$ at $21$ nodes to $1.12\times 10^{-5}$ at $81$ nodes, which supports a grid-bias reading of the earlier stable residual. The amplitude probe has exact target $0.14179675523330723$, independent of $ϵ$.

The weighted atomic $5a$ integral at $\delta =0.35$ is $4.851387241020615$ by a Gauss cap rule and $4.845938176179326$ by a scrambled Sobol rule on $2^{12}$ nodes. The relative gap is $1.1\times 10^{-3}$. These quadratures do not share nodes. A scalar simulated ${\mathcal{P}}_{5a}$ integral on $\gamma \in [-1.2,-0.4]$ equals $-0.004633651977461527$. No inherited physical coefficient is claimed. The subsequent isolated-row run, source 05485aec7a9a, builds the specialized vertex and both adjoint constructions. They agree termwise to $2.8\times 10^{-14}$. The seven-dimensional seed integral changes sign from $-49.40$ to $21.20$ to $-8.25$ as the $U$-node count goes from 5 to 7, so no row value is released. The later overlap reduction separates that failure from the inner integral. At $s_{\ast }$ the factored inner value is $-2428.716$, and a 16-node overlap-box rule agrees to 0.28\%. The outer cone rules do not: Gauss gives $3.01,-0.15,-2.58$ and Sobol stays near $-4.3$. The row remains unreleased.