[unpaidmoon]

Change and mathematical scope

Finite certificate. No new κ, and the selected frontier stays 605457647/200000000000.

For the full shared-arena CRT batch, replace one schoolbook product per tape action by the PR CrocSwap#4192 section-2 record comparisons. Charge each of the 4AJ key-field comparisons, and each of the V = N^2 - N - Nh/2 pairwise comparisons, at the same cap 8w^2. Keep the inherited tape, rotation and CRT charges. At both excluded corners the resulting batch is strictly below E = 2^{4 ell}(p+2)^{16}:

• (2,1,1): B = 822078336 < E = 68719476736
• (2,2,2): B = 12370604416 < E = 1099511627776

The inherited majorant stays above E there (75548846976 and 1241895956864). The new scalar term is strictly smaller than that majorant on the whole admissible domain, so the predecessor classification lifts the fit to every integer p >= 2 and 1 <= h <= ell <= p. One schoolbook cap per arena cell per charged access still fits the two corners. These are explicit majorant comparisons, not a machine lower bound, a supplier admission, or a multiplication theorem.

This branch is based on upstream CrocSwap main 32890bc5de034ab8fc93ac88ead7279a6a416d04. The reviewable change is only research/crt-p2-corner-record-inventory/.

Task and overlap

Task uniform-transfer-audit, priority revision 7, scope refined. Base commit 32890bc5de034ab8fc93ac88ead7279a6a416d04. Live inputs are research/crt-arena-root-axis/PROOF.md, research/crt-arena-batch-threshold/PROOF.md, and the vendored PR CrocSwap#4192 proof. The self-contained object is the two corners; the all-domain sentence cites the predecessor classification and does not re-prove it.

Nearest work: Nick Petalas's research/crt-arena-batch-threshold leaves this as open question 1. PR CrocSwap#4650 fits one axis and leaves the batch open. PR CrocSwap#4377 supplies the CRT and rotation tariffs. An overlap search on 2026-10-25T07:21Z covered 398 open pull requests, 4819 discussion records and 7404 local notes. No open pull request or discussion states this section-2 corner inventory. Closed pull-request bodies were searched only through local notes.

Validation

CPython 3.12, standard library, from the repository root:

python3 -I -W error -B research/crt-p2-corner-record-inventory/verify.py
python3 -I -O -W error -B research/crt-p2-corner-record-inventory/verify.py
python3 -B scripts/research_package.py --package research/crt-p2-corner-record-inventory
python3 -B scripts/check_research_commit.py --package research/crt-p2-corner-record-inventory --check-source-history

Observed on this commit: PASS_CRT_P2_CORNER_RECORD_INVENTORY, PASS_REGISTERED_RESEARCH_PACKAGE research/crt-p2-corner-record-inventory outcome=completed, and PASS_RESEARCH_COMMIT_BYTES at c1e15939664b47cfb92748ed2cbd34ca0817df8c.

The corner identities are exact arithmetic. The 45,759-triple box corroborates T_record < T_scalar; the written comparison has no p <= 64 cap. Not run: Lean, Docker, the Beneš simulator, and native replay.

Credit

Prepared by unpaidmoon with substantial Cursor Grok assistance.

Nick Petalas proved the inherited full-batch threshold and left these two corners open. The one-axis bill and its schoolbook cap are unpaidmoon's PR CrocSwap#4650. The CRT and rotation tariffs are unpaidmoon's PR CrocSwap#4377. ToikY's PR CrocSwap#4192 supplies the arena census, the four-field scan and the pairwise count. Cinna Davis supplies the shape of E in PR CrocSwap#4100. Predecessor files are unchanged. New work is Apache-2.0. Independent human and formal proof-kernel review are unclaimed.

Open next questions

1. Compose this allowance with reservoir placement and the paid repair-key service of PR Execute paid CRT key service at the actual repair port CrocSwap/integer-mult-bounds#4795. Begin with one complete entry, call and exit program, retaining every source-state query and restoration charge. The corner fit does not answer that composition.
2. Emit a literal scalar transition table for one four-field scan and price those steps at (2,2,2), keeping T_tape. The schoolbook-cap margin does not substitute for that table.

Workflow feedback (optional)

CrocSwap#1200

Fork main has diverged from upstream. Please review the package directory, or diff this head against 32890bc5de034ab8fc93ac88ead7279a6a416d04.