Research: sharp P104 dimension-98 prefix boundary

[AAAmirinu]

The P104 pooled-prefix minimum had an unresolved gap after cut 2717. This package proves dimension 99 through cut 2753 and 98 from cut 2754 through 2823, making 2754 the earliest prefix that can attain 98.

The new lower certificates force compressed determinants −2 and −1 for every rational residual in the source-bound operator space. A 46-contact witness attains the rank-98 upper bound at 2754. The existing 18-contact rank-99 witness is explicitly reused from PR #2345, commit 2a5fa34a967e7567abf01611f92a6ab69e8c901a. The proof and direct checks are self-contained; this branch starts from current main rather than stacking on that PR.

This is an algebraic pooled-information result. It does not construct a chronological correction, price a transport/hosting invoice, admit a supplier, or claim a new kappa. The reported later 97/96 prefix certificates are credited but not recertified here.

Validation:

• A fresh sparse exact replay checks all 4,059 cuts, 280 independent input columns, dirty restoration, frame/private-copy contracts, the original G/2 endpoint and unchanged local profile. It agrees with the earlier dense implementation on 110,814 target/snapshot pairs.
• Exact checks of the six/three annihilator constraints, every contact, the explicit rank-two residual, and direct 104-by-104 correction ranks pass. Optimized Windows CPython 3.12.11 primary replay: 12.0 seconds.
• All 13 controls are covered: 11 passed initially, then two test-fixture issues were corrected and both affected controls passed a targeted rerun. They cover coefficient/contact faults, endpoint restoration, equivalent representations and low-rank counterexamples when required lower-bound constraints are omitted. Metadata/source pins and patch checks pass. Full commands and limitations are in the package.

Reproduce:

python3.12 scripts/research_package.py --package research/p104-prefix-tail

Base: canonical main 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, priority revision 4. Only research/p104-prefix-tail/ is added. Canonical claim. TASK.json records checkpoint freshness and live overlap.

Credit Gonzalo Mier/#2173, Gareth Davidson/@bitplane/#2251, @josecarlosgonzalezroque-design's prefix handoff, the rank reduction/witness from #2345, and Rohan Arun/#1972, Chafik Boukhalfa/#1991, Adam Gall/#1940, Josie Elliston/#1071, Ali Romman/#1125 and their retained lineage. Frozen inputs and notices are unchanged.

Prepared for AAAmirinu with substantial OpenAI Codex assistance, including separate projection exploration, sparse replay implementation and mathematical review. No independent human review or formal proof-assistant claim. Native regeneration, chronological execution, global moment/owners, precision/all-size admission and selected cold replay are unrun; hosted CI is separate. Apache-2.0.