[aliromman]

This adds a second rank-four P104 block and proves complete conditional κ = 0.00311325989, a gain of 0.00000012194 over PR #5756. The exact raw crossing is (0.00311325991155, 0.00311325991156).

Proof · Complete receipt · Exact plan · Source pins

This is a small, source-specific gain. Later PR #5786 claims the larger bound 0.00312265044. This PR does not supersede it. The new block is released for the separate composition investigation; composition needs a fresh whole-word replay.

The 102 scalar operations use roles 57,81,92,224,225,227,229,234,742 and move from chart 267 to span[11,21,38,448]. Helper 742 starts there and helper 225 ends there. Scalar order, coefficients, owned events and main endpoints stay fixed. The paid delta per local call is H1+H4-H5; the helper delta is -H1+H4+H5-H8. The full caller pays 66,870 calls for 13,390 productive fields, including every helper, native map, adapter, thin query, idle, COPY/CLEAR and route. Rank surplus remains 760. The raw ceiling is for this fixed full profile; less than 2.2e-11 headroom remains above the claim.

Python 3.12 and the standard library suffice:

python3.12 -B scripts/research_package.py --package research/p104-second-low-rank-block

Expected markers:

PASS_P104_SECOND_RANK4_BLOCK_KAPPA_00311325989
PASS_REGISTERED_RESEARCH_PACKAGE

Direct and registered normal/optimized replays pass: 602,176 scalar coefficients, separate dense transpose, 2,934 native maps with absolute phases, 208 main adapters, 1,118 helper normalizers, 7,488 physical contacts, 53,248 central-square columns, both rational engines, completion and all 54 strict/four functional compiler checks. The verifier rejects eight changed word/source/invoice controls and the native phase control. Metadata, committed bytes and official export pass. A separate read-only, Git-free -I -O -B replay with empty PATH passes in 128.974 seconds; every payload byte and mode stays fixed. Export SHA256: 53fb7049f089ffdba3af7afd32b155d943632d346774f25147fb8ad7671c0289.

The five inherited assumptions remain: native_all_columns, owned_erasure, compiler, precision_tape, analytic_recovery. The uniform word and rounded multiplier are not materialized. Full-history preflight and independent acceptance are not claimed. Hosted planning CI failed in the shared test_research_current_assignment.py suite, with eight failures and two errors. The package replay was skipped. That test, both picker scripts and the task catalogue are byte-identical to base main. No hosted scientific pass is claimed. The selected frontier is unchanged.

Base main: de5ec2e7a6074068452f45b1a191b5c72832df4a, priority 8. The exact PR #5756 source is frozen. The retained checker closure is PR #5751 at 8483f9a679d06c1e270141dbc686a7e76e7a7522; only declared pricing literals, labels and credit change. Joel Pulikkan (GamingPuzzled), with Claude Opus 5.5 assistance, supplied the R22 mechanism and the different source block. This PR claims the second block, not that mechanism. NOTICE retains flyingviper's distinct-boundary work and every P104/helper/native/controller/compiler/BIT predecessor.

New construction and package: Ali Romman with substantial OpenAI Codex assistance; no subagents. Apache-2.0. The complete public overlap refresh through 18:52 UTC covered 345 open PRs and 5,175 Discussion records. Unpublished work and sparse local notes remain coverage limits. Canonical scope.