[mihir-s-05]

PR #4678 leaves the simultaneous-conjugacy state after Schur deletion open. This six-file package answers that handoff for the binary commuting projector pair with joint-sector dimensions (1,1,1,2). It finds seven ordered residual-pair orbits, retains their complete-header multiplicities, and counts the two remaining scalar guards. No new kappa.

The sample space is all 9,999,360 complete GL5(F2) headers for a fixed pair of rank-three projectors. Full guards require both requests' leading minors of orders 1, 2 and 3 to be nonzero.

• 93,564 headers pass every guard: exact fraction 2599/277760.
• The credited sharp one-block event has 60,480 headers. It reaches one orbit of 5,040 residual pairs with multiplicity 12 each; 3,240 headers continue through all guards, a conditional 3/56.
• Commutator rank loses continuation information: two rank-zero states have full-guard fractions 5/28 and 61/3360. Two other distinct states even share all displayed individual/product/sum/commutator ranks; their common-kernel dimensions distinguish them.

README.md proves the completion-fibre/orbit multiplicity reduction and guard equivalence. RESULT.json records all 172 admitted split pairs and their state assignments. The independently written standard-library checker imports no predecessor code. The contribution is the state distribution and continuation count; PR4678's one-block count is corroborated and credited.

Validation

python3.12 -B scripts/research_package.py --package research/schur-residual-orbits
python3.12 -B scripts/check_research_commit.py --package research/schur-residual-orbits --check-source-history

Normal and optimized registered replays pass. Coverage includes all 496 split pairs, full GL4 orbits, 141,120 literal complete-header checks using direct leading-minor determinants, an independent determinant census of 65,536 binary 4-by-4 matrices, and seven rejection controls. The direct header checks cover one full completion fibre per orbit; the written equivariance argument extends the counts to all split pairs. This is not a raw enumeration of all GL5 headers.

Committed bytes/source history, official export integrity, and a fresh Git-free optimized export replay are checked before publication. The export replay has an empty PATH, reads read-only files, and leaves every file hash unchanged. Detailed environment and overlap coverage are in TASK.json; hosted CI is reported separately after creation.

Scope and coordination

Started from canonical main b58ad9ef4d4e861b0eaa5dba41742bdc072dca51, priority revision 7. The scoped claim in Discussion #4653 takes PR4678's fresh handoff. formal-interface-lemma is explicitly changed to an algebraic side result. Final upstream/overlap freshness is recorded in TASK.json. The selected result remains 0.00302015.

This proves a finite classification with an exact counting reduction, not a general state recursion, physical supplier, human/proof-kernel acceptance or multiplication theorem. F2 is outside the retained odd-q normalizer executable domain. Production header covers, selection/emission, reads, restoration, stock, dispatch and complete consumer costs remain unknown. Lean, Docker and the selected scientific cold replay were not run. The open next question is an invariant-based transition law reproducing this table without enumerating GL4; no follow-up claim is held.

Credit ssafwann (#4678/#4671, OpenAI Codex assistance), Nick Petalas (#4597/#4278 and earlier header lineage), Ryanson Jonathan (binary sharpness and full-guard census, Claude Code assistance), lee-phys (binary dimension work), and Cinna Davis and the credited normalizer lineage. Exact citation/source pins are included. Prepared for Mihir Srivastava with substantial OpenAI Codex assistance, by one agent. Apache-2.0.
Publication head: 3a72fbad148294aa9ca7f900a48dbb10e64232be.

Hosted CI

Registered research packages run 39810654179 completed successfully at 3a72fbad148294aa9ca7f900a48dbb10e64232be. Onboarding/package selection, the registered package replay and unchanged-input checks passed. This hosted pass has the package's stated finite scope.