[JoyboyBrian]

The actual encoded Gaussian coefficient producer needs a caller-bound enclosure audit before its scalar values can support matrix error claims. This package proves the frozen PR3851 Exponentials contract for every integer P,F>=1, rational 0<=f<=F, growth/decay sign and nonnegative binary normalization: the returned interval contains the exact coefficient, spans at most two target ulps, and its lower endpoint has error below 1.5 ulps. The proof also binds every Axis weight, kernel, wrapped cross-cell and normalized diagonal argument to that domain.

The independent-algorithm oracle uses positive arcsine and alternating decay, was frozen before source output capture, and requires containment of its entire finer interval. The unchanged encoded source runs with no_decode; the adapter only snapshots raw tapes and decodes after execution. The actual receipt covers 19 Axis + 10 isolated calls,523 Taylor steps, four domain rejections and growth/sign/normalization/endpoint controls. Ten additional source/oracle/receipt-corruption controls run in normal and optimized Python.

This resumes the unpublished result at b4596aa6 after the original quota-limited release. Both original commits are preserved by cherry-pick onto current canonical main 721c038; all 13 scientific input blobs are unchanged. Revision 8 freshness and scope review are the only new package changes. The original scientific base 32890bc and frozen oracle remain intact. Coordination: #3664 (comment).

Validation at final head 9fc80f1db55d4939c7b53c0799e6840cce35fbf8: metadata/pins, source history, committed bytes and owner-execute modes pass; the official export validates 24 files and 13 declared inputs. Serial normal and optimized actual-source commands passed in 151.1s and 152.9s, respectively, inside a read-only Git-free export with empty PATH (240s cap each). Both matched the entire frozen receipt, digest 7935bf9a08e3479b92a39cf91fb5ed71f73a8260bc4461848deb3b51594196ee; all 25 exported files including the export manifest remained unchanged. The ten package controls also passed. All 29 observed calls took early exit and had one-ulp width; the fixed cutoff and uniform two-ulp claim are established by the written proof, not these finite executions.

A separate read-only agent in the same AI-assisted team reviewed the universal inequalities, actual encoded source, Axis domains and cost paragraph at this exact head and reported no blocking correctness finding. That reviewer performed no heavy replay.

Scope: source-relative written proof and same-contributor independent-algorithm checks; no independent human/formal-kernel acceptance. Positive rounded-weight admission, full original-H perturbation and ideal rowgap remain separate. No LU/online-solve/Core/tensor/CRT admission, new kappa, selected-frontier change or bit-length-only tariff for huge normalization shifts is claimed.

Credit Jose Manuel/jmbarrancoml PR3851 and its retained physical-ring/Machin/Gaussian lineage, the distinct normalized scalar-backend audit, and source-specific notices. JoyboyBrian with substantial OpenAI Codex assistance; Apache-2.0.

[JoyboyBrian]

CI follow-up for 9fc80f1db55d4939c7b53c0799e6840cce35fbf8.

The plan failure reproduces on clean canonical main 721c03822c421b7f7fcbb2598993b947c4d88419: the two current-status navigation tests fail before this PR’s scientific replay. Existing PR #6050 (41ac3a47b91b4184e6c54af417bf576bfb429926) fixes both documentation mismatches; its exact two-file change passes all six tests locally, normally and with -O. Awaiting the shared upstream repair and a fresh CI run; this is not a successful scientific-replay claim.