Local H2/H2R Source Sufficiency, Blind Regge Transfer, and Conditional Curved-Regge Identity

Abstract

This article studies which finite local data suffice to determine selected mixed Regge responses when simplicial incidence changes. Here H2 denotes a germ-anchored local source descriptor and H2R its exact-normalization refinement. The analysis begins with a preserved negative result: a source-selected six-row transfer of a previously frozen interface operator failed by order-one margins on a response-sealed stellar refinement constructed and admitted without target responses. Here “blind” and “independent” denote this internal response separation, not external blinding, external replication, or a separate research group. An exact decomposition then separated target-edge normalization from local hinge-star content. H2 was discovered post exposure; on a response-unopened control it subsequently carried all 378 frozen response-vector predictions across 103 exact classes. H2R changes only two normalization tuples from binary floating serialization to exact rational serialization. In prospective changed-star tests, all 20 frozen two-parent predictions and all 94 frozen eight-parent predictions passed the componentwise $10^{-8}$ criterion; the latter covered 43 exact classes on 18 changed inherited stars. These are finite exact-class tests, not interpolation to unseen descriptors or arbitrary-composition theorems. A parameter-free local Regge mixed-Hessian functional then replaced registry lookup. On three authenticated fixtures, exact branch and nondegeneracy certificates establish equality with the direct Regge mixed derivative throughout a signed projective parameter strip $|\kappa|\le 1/256$. The generic result is separated into four claims: the elementary product-rule identity, descriptor-locality under exact isomorphism, finite admission of 1,818 historical occurrences under explicit hypotheses H1–H6, and the three-fixture parameter-domain certificate. The resulting theorem is descriptor-general and conditional; it does not establish automatic arbitrary-triangulation admissibility, arbitrary field-shape transfer, stronger curvature, refinement convergence, continuum general relativity, or external replication.

The failure is part of the result

The first broad transfer proposal failed, and that failure remains part of the evidence rather than being reclassified after later successes. Later local descriptions answer a narrower question; they do not retroactively repair the failed broad transfer.

Where it sits in the release

CUD-G1 takes its parent gravity architecture from TCG-F1. Its nonzero-response problem is deliberately distinct from the exact-zero mechanism of CUD-G2 — one branch asks what information is sufficient for a nonzero answer, the other what symmetry forces the answer to vanish.

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