Macroscopic Core Rigidity and Endpoint-Amplified Non-Parseval Defects in Bandwidth-One Weil-Certificate Sources

Abstract

This paper studies the surviving common-depth branch of a bandwidth-one Weil-certificate source model after Stein normalization and weighted-exponential provenance have been imposed. The analysis develops a structural rigidity chain from deep-source order growth and fixed-scale fusion to a macroscopic irreducible core, quantitative difference-band coercivity, and an endpoint-amplified non-Parseval obstruction. In particular, every surviving deep common-depth corridor source must carry a fixed macroscopic amount of same-half Frobenius energy, $$\|Q_{\rm diag}\|_F^2\ge0.286153798088\ldots\,N-o(N),$$ and the exact half-interface geometry then forces superextensive endpoint-skew energy, $$\frac{\|V\|_F^2}{N}\to\infty.$$ Let $K$ denote the base Gram matrix and let $R,L$ be the two endpoint syntheses. Whitening the base frame gives an exact orthogonal-base spectral-pairing reference and yields the normalized amplified non-Parseval burden $$\|R(I-K^{-1})L^*\|_F^2\ge(0.030384878259\ldots-o(1))F_-(Q).$$ Writing $$B=RL^*,\qquadB_0=RK^{-1}L^*,$$ any surviving corridor source must satisfy $$\liminf\frac{\|B-B_0\|_F}{\|B\|_F}\ge0.328362234249\ldots,$$ while the full residual operator obeys $$\liminf\frac{\|Q-Q_0\|_F}{\|Q\|_F}\ge0.464374325046\ldots,$$ where $Q_0$ is the whitening-induced exact-pairing reference. An explicit two-center root-tuning construction shows that generic same-center provenance can produce a nonzero absolute amplified defect even when the base Gram approaches the identity. However, this deformation is perturbative relative to the actual directed endpoint transfer and therefore does not realize the corridor-grade burden. The remaining common-depth problem is consequently reduced to a genuinely collective, large-order, same-center realizability question. The paper is a structural rigidity result rather than a final zero-proportion theorem. Complete common-depth exclusion, heterogeneous-depth mixtures, and the global improvement beyond $$0.672500703679412\ldots$$ remain open. This work follows: Lee Byoungwoo, *Source Rigidity in Bandwidth-One Weil Certificates: Stein Normalization, Cubic Phase Skew, and a Two-Deck Pricing Barrier*, Version v1.0, Zenodo, DOI 10.5281/zenodo.21967182. The accompanying bundle contains the manuscript source, numerical and exact-rational verification scripts, a symbolic fusion-kernel audit, verifier outputs, and a SHA256 manifest.