Research: verified T74 residue concentration (superseded by #2863)

[digitalis-p]

Superseded in reported κ before submission: pending #2863 at 34328b1d5e5bebac62d5cabec993dfbfd7b2123f reports 0.001720100805416885927944 − 10^-46 − 10^-70, above this T74 result. This PR preserves a simpler verified two-copy construction, separate chronological/moment checkers and bounded negative-search evidence. It makes no current-record or exclusive method-priority claim. PR2863’s full certificate was not reproduced in this run.

PR2857's T37 allocation leaves one rank-nine idle child. Interleaving two copies exposes a legal width-seven transfer that replaces two rank-nine children by ranks two and sixteen. Strict concavity lowers the complete recurrence moment.

This adds only research/shared-kernel-pair-concentration/: the deterministic generator, literal allocation, scoped proof, independent chronological and directed-integer moment checkers, source/dependency manifests, complete release evidence, bounded replay hook and research handoff.

The conditional multiplication exponent saving is exactly
κ = 0.001720097402339781716060 − 10^-46 − 10^-70.
The gain over PR2857 at 0b2e2537b368a0cade07ce3f71452ea018ebe394 is exactly
48353434319693/62500000000000000000000 = 7.73654949115088e-10.

Validation: PR2857's complete release reproduced with pinned dependencies; the derivative's complete frozen strict release passed. Actual inherited rejections: 119 admission, 12 bit, 25 controller, 8 owner, 6 geometry; 63 modern outer inequalities and 17 outer rejections. Independent checks cover all 271,728 roles and exact endpoint signs, with corruptions rejected. The registered Python 3.12 package check passes. Source-bound current native outputs are freshly generated by this session's baseline; older predecessors are explicitly reused, not claimed freshly cold-replayed.

On pinned unmodified main d311a18c6061af67d0aa35cbeced605b8b7472ed, repository-wide gates failed: make verify fails on singleton target unpacking in scripts/partial_swap/shared.py; make frontier1094-verify rejects a historical proof-supplement hash. Both failures are preserved. Canonical main was fetched again at 4cc9d09a124e06dd358fdc1c3d4b2af51dd44649; applicable guidance and the selected record were unchanged. Those broad suites were not rerun on that newer main. No check or historical expected result was weakened. No hosted CI, fresh Lean result or maintainer acceptance is claimed.

Scientific dependency: pending PR2857 and its full inherited lineage. The initial PR2853 improvement was superseded during the session; its useful negative/positive evidence is preserved. The research census identified PR2857 as baseline. The pre-submission refresh subsequently found the stronger pending PR2863; its body, pinned README, reviews and exact-head checks were inspected. Detailed coverage is bounded and disclosed, not a global priority guarantee.

Credit: Yiyang (@Lyy-iiis), Jeremy Kothe, Philippe Van Velzen, Marius-Paul Dumitrean (including related PR2856 vacancy concentration read before this construction), Dugongue, Tekalign and the retained outer/native contributors. Original licenses and notices are retained. Substantial OpenAI Codex assistance for research, implementation, separate checker implementations and packaging; no independent human review claimed.

All all-size/compiler, common-label/mutable-source, hosting, precision/tape, exact-recovery, analytic-transfer, corrected recurrence and bit H1–H5 obligations remain conditional. Finite certificates are not a formal complete multiplication theorem, and an exponent gain is not a measured speedup. No selected result or predecessor package changes.

Task and overlap: selected-packing, priority revision 5; scope changed to the strongest comparable pending construction identified by the donor-requested live run. The concrete bounded object is two interleaved T37 copies and one width-seven transfer. TASK.json, FRONTIER.json, and PUBLICATION-REFRESH.json preserve scope, exact sources and overlap.

Reproduce the bounded independent checks with:

python3.12 -B scripts/research_package.py --package research/shared-kernel-pair-concentration

The package README gives the pinned full native/admission/outer replay. The hosted tree was checked exactly against the local verified tree; the publication refresh changes documentation and its package manifest only.

Open next questions: independently reproduce #2863 and its claimed fixed-inventory packing optimum before further packing searches; alternatively, address one named all-size hosting/precision obligation in PROOF.md. No further large packing search is justified here.