Research: exact 96-dimensional P104 shared correction space

[bitplane]

The fixed P104 snapshot model previously had a shared correction-space minimum between 96 and 97. This package attains 96, closing the explicit arbitrary-direction handoff in Gonzalo Mier’s PR #2173, pinned at d9b784ca86fba060f0264370536ccd322c89998a.

For each target, the existing source is the rational span of every other register snapshot ever available in the same binary frame subspace along the frozen channel. A 41-contact certificate constructs a 104×8 matrix A with RA=I, where R is the doubled root-coordinate matrix. Then K=(I−AR)(I−G/2) has rank 96, and each correction row differs from its row of K by an available pooled direction. The known lower bound 96 is independently re-certified by projecting all available snapshots into the eight-dimensional root code.

Scope: an exact algebraic minimum, not a chronological correction circuit, native transport saving, admitted supplier or new κ. Access at different cuts is pooled; constructing and hosting the shared directions remains unpriced. The known unfavorable 208-rank tail is not repriced as 96 ranks. Only research/p104-minimum-shared-space/ is added; selected and frozen predecessor files are unchanged.

Validation:

• Full registered CPython 3.12.3 replay passed: all 4,059 cuts, all 280 independent input columns, arbitrary dirty restoration, private lifetimes, inherited profile, all 104 full-space correction identities and exact rank 96.
• Separate implementations use sparse rational rows/reduced binary bases versus dense integer rows/explicit subspaces/dense rational elimination. Both produce receipt a8b78ea543762bb03984b2e228fc2652e9036153b7ad0ab51354cedff5766f1a.
• Seven control groups passed, including all 41 coefficient sign faults, unavailable/self contacts, removed dirty compensation/cleanup, wrong geometry/rank, schema/source/receipt corruption and basis-order invariance.
• Both isolated optimized CPython 3.14.4 replays passed from a read-only export without Git; all 14 export files stayed unchanged. Package metadata/source pins, clean patch application and whitespace checks passed.
• Native Clifford recompilation, new owner/hosting, global moment, precision/all-size admission and the selected cold replay were not run. Hosted CI is separate from these local results.

Reproduce: python3.12 scripts/research_package.py --package research/p104-minimum-shared-space. The README includes the complete proof, optional witness regeneration, source credits and the next chronological-realization handoff.

Base/current canonical main: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, priority revision 4. Exact contribution: 822bceef780d8da9605798f0836ae5320e8e291e. Original complex-mechanisms draw 04a0b5296b007400a2e6d4c67da47ad2 is preserved; revision 4’s central-handoff preference motivated this scoped override. The unimplemented gather claim #2032 is released. Canonical investigation: Discussion #2245. Final overlap completely paginated 480 open PRs and 956 Discussion records, with no warnings; the targeted search returned all 14 matches. Predecessor head and relevant upstream inputs were unchanged.

Credit Gonzalo Mier/#2173 for the pooled-span model, lower96/upper97 and handoff; Rohan Arun/#1972 for the channel, Chafik Boukhalfa/#1991 for native realization, Adam Gall/#1940 for the schedule, Josie Elliston/#1071 for the fixture, and their retained geometry/decoder lineage. Substantial OpenAI Codex assistance in mathematics, implementation, verification and writing; no subagents, independent human review or proof-assistant claim. Apache-2.0.