[aliromman]

This source-bound application lowers the ordinary-decoder exclusion threshold for the actual 73-axis negative E endpoint from width 4198 to 296. For every width at least 296, every allowed ordinary endpoint has worst-case operator error at least 1541/1255956 in the fixed source chart. The complete kappa calculation is unchanged.

Proof and scope, exact checks, source pins, registered replay. Base: canonical main 32890bc5de034ab8fc93ac88ead7279a6a416d04, priority revision 7. Contribution head: b2ed5c35222665ceec0ab56c6937288f29635464.

The decoder observes the emitted negative bank and independent workspace. Ordinary address maps are columnwise monomial Cliffords; scalar mixing, instruction count and coefficients may depend on width. The source expansion has a unique nonmonomial Clifford path with fixed scalar coefficient 1541/418652. The pointwise Gram bound makes that coefficient impossible to cancel with the ordinary span. Correlated original-input histories, paid calls, cross-column operations and nonlinear rounding are outside this claim.

CPython 3.12.14 warning-strict registered normal and optimized checks pass. Three immutable source copies match their Git objects and SHA256 pins. Independent checks recompute the spectral/path coefficient, 147 sparse native columns, four Clifford generator identities, 36 finite rational Gram bounds and complete geometric tails; nine controls cover source changes, an unproved width, projective phases and scalar placement. Both modes print PASS_NEGATIVE_E_DECODER_GRAM_BOUND; the launcher prints PASS_REGISTERED_RESEARCH_PACKAGE.

python3.12 -B scripts/research_package.py --package research/negative-e-decoder-gram-bound

Python 3.12 and the standard library suffice. Committed-byte checks pass. The complete owner-path separation and general Clifford counting theorem are credited written premises, not newly audited theorems. Their full scientific suites, independent human/proof-kernel review, selected cold replay, physical emission, precision application and complete invoice were not run here. The norm floor is stated in the original endpoint chart and is not a paid-child lower bound. No smaller-width optimality or complete multiplication theorem is claimed. Hosted status is unconfirmed at publication.

Credit JoyboyBrian (@JoyboyBrian) for PR #5508, its pinned actual decoder/path proof and exact source result. Credit Ali Romman (@aliromman) for PR #5526 and its pinned pointwise Clifford Gram theorem. Both sources retain their native, fresh-stage, stabilizer and compiler lineage. The scoped claim reserves only this application.

Next: bind a changed paid decoder or correlated-history contract to its complete original-input identity and added-paid/lost-target ledger. Those interfaces may evade this obstruction, but all physical costs remain payable.

Prepared by Ali Romman with substantial OpenAI Codex assistance; Apache-2.0.