[commdata2338]

Change and mathematical scope

Adds research/crt-multitarget-row-audit/, an independent audit of the multi-target loop in PR #5496's current-row CRT join. PR #5496 connects current CRT offsets to a physical Beneš row query, but its completed joined fixtures have only one active target. This audit proves that its loop composes across several right targets: idle records are still consumed, successive active targets use their own offsets, padded coordinates are queried, one physical ROM bank is reused, and complete old tails and numerical outputs retire. No defect was found in this implication.

The result is conditional. The numerical Entry theorem (PR #5353's RowEntry over PR #5219/#5053) and the ROM producer theorem (PR #5092) are hypotheses of this audit, not re-proved here; the finite executions corroborate the implication and do not discharge those universal producer hypotheses.

The new exact storage lemma counts all 52 roles of the fixed-precision singleton-ROM bank. For nonempty active targets, guide width P and largest active width H,

B(P,H) = 5 P 2^H (H^2+3H+1) + 2^H(4H-1) + 48P + 2H + 104.

Each role's extent is nondecreasing in target width at fixed P, so the rolewise historical maximum is attained at H. The proof also counts the three disjoint coordinate/countdown/output backings. At P=11, the h=3→h=2 fixture retains 9,086 bank cells; billing only the last target would count 3,084 and omit 6,002. This is a rejecting control for an invalid shortcut, not a counterexample to #5496's conservative invoice. The inherited arena count and general historical-maximum principle are credited, not claimed as new.

Result kind: scoped conditional proof audit, exact footprint lemma, and finite independent corroboration. No implementation, recursive invoice, paid profile, selected result or κ changes. Retain the full numerical Entry/retirement, each complete ROM production, all-layer disposal and adapter work. Complete physical level/key composition and all-size transfer remain open.

Task and overlap

Task uniform-transfer-audit, priority revision 7, scope key ce7411fb7cf6f3460bfc; scope refined to pr5496-multi-target-current-row-bank-invariant. The chooser's adversarial-audit draw used seed 44f05f574fc586d49962b167a149c6d8, suggestion 2. TASK.json retains the full original card, selection, bounded method, stop rule, acceptance gate and remaining obligations. The card asks for one quantified CRT implication at its actual caller; #5496 supplies that concrete successor interface. The expansion decision is to stop after this audit.

Head 53a034436f17ef5b8fdf7a02f5066528cdfe5446 on base main 32890bc5de034ab8fc93ac88ead7279a6a416d04. Canonical main was checked again at 2026-10-25 05:50:02 UTC and 06:08:00 UTC and was unchanged, as was the #5496 head. certificates/selected-result.json on this base selects #5413 (κ = 0.003027288235, promoted 23 October); the priority page's 23 October note still names #4610. This audit neither replays nor changes either record.

Dependency	Exact binding
Audited pending #5496	a99afd7e0024af8367d5a2f6f4d2da57a1d13dd5, re-fetched unchanged; three byte-identical files and original credit retained in vendor/ and VENDORED.json
Main numerical/ROM inputs, including #5353/#5219/#5053/#5092	32890bc5de034ab8fc93ac88ead7279a6a416d04; twelve scientific files pinned individually by blob and SHA256 in SOURCES.json
#5353 retained predecessor	07a135eee3a8da9392c4a1e01d4b89db05b4ac03
Original #4100 construction	337d04939571a637aeab54a0f58f54fde811663a; context, not newly accepted

The claim is in Discussion #4709, comment 19173680, following #5496's record. Nearest overlap: #5496 constructs the join; this independently audits its multi-target boundary and exact storage. JoyboyBrian's #5505 treats changing-precision numerical-bank histories, while this treats the fixed-P ROM bank. JoyboyBrian's #5486 lowers a different fixed repair program to binary control. Earlier BIT/control/parking audits by this account are different objects.

Offline overlap queries covered the task, #5496/current-row-query, multi-axis/two-active-target work, ROM bank, producer footprint and 48P, together with main research/ledger inspection. The final snapshot covers 371 open PRs at 05:43:08.927390 UTC and 4,779 Discussion records at 05:44:30.637331 UTC, with complete pagination and all 7,404 local note records. Arbitrary remote code diffs and unpublished work remain outside that coverage; it is not a novelty guarantee.

Validation

Python 3.12.3, standard library only; serial execution. From the repository root:

python3 -B scripts/research_selected_baseline.py
python3 -B scripts/research_package.py --package research/crt-multitarget-row-audit --check-only
python3 -B scripts/research_package.py --package research/crt-multitarget-row-audit
python3 -B scripts/check_research_commit.py --package research/crt-multitarget-row-audit --check-source-history
python3 -B scripts/export_research_package.py export --package research/crt-multitarget-row-audit --ref HEAD --output crt-multitarget-row-audit.tar
python3 -B scripts/export_research_package.py check crt-multitarget-row-audit.tar

All passed. The registered replay executes normal and optimized Python serially, each with a 300-second limit. Each finishes:

PASS_CRT_MULTITARGET_ROW_AUDIT cases=9 producer_calls=13 controls=12 no_new_kappa=true

The nine cases execute 13 complete ROM calls at h≤3, covering distinct offsets, growing/shrinking banks, leading/trailing idle axes, padded current values, invalid left input, all-idle behavior and minimum-width nonroot entry. The independent oracle searches CRT congruences and exhausts network color constraints; it does not execute #5496's checker, the retained Caller oracle or the retained Beneš reference. Calibration covers 32 networks and all 236 addresses.

Twelve control groups cover seven execution faults, two algebraic discriminators, two storage omissions and JSON boolean/integer confusion. Every actual producer role extent, canonical table, bank identity, historical tail, borrowed input/head and all 63 numerical owned ports are checked. Adapter tape actions are measured separately against the inherited 4096F allowance; the complete instruction constant is not independently certified.

Committed bytes/source ancestry and the official 28-file export pass. An optimized direct replay from the extracted export without Git history passes and leaves all 29 extracted files (including the export receipt) unchanged. Separate corruption of a vendored source and a main scientific source is rejected before replay; both copies are restored. Registered normal+optimized replay took 125.77 seconds, peak 203,408 KiB; standalone optimized replay took 63.98 seconds, peak 22,544 KiB on the checking host.

Not run: h=4 joined pipeline, uninterrupted whole-level update, complete three-epoch key, binary numerical compiler, full E(p,ell), native/ordinary/outer or selected scientific replay, Lean. No independent human or formal-kernel acceptance is asserted.

Credit

Prepared for commdata2338 (@commdata2338), with substantial OpenAI Codex assistance.

JoyboyBrian supplies #5496's joined implementation, #5092's encoded ROM producer and #5053/#5219's numerical components. Ali Romman supplies #5353's RowEntry. Hiroki KUMAZAKI supplies the current-state CRT contract (#4716) and the #4169/#4174 repair and mixed-width reservoir audits; ToikY supplies the explicit-width mixed caller (#4195) and the Beneš arena refinement (#4192), including the inherited J count; Cinna Davis supplies #4100. (Several predecessor READMEs, including #5496's, credit Hiroki KUMAZAKI with the mixed-width caller; on main, research/crt-mixed-width-caller is PR #4195 by ToikY, which builds on #4169/#4174.) The general rolewise historical-maximum accounting is predecessor work, from Ross Richardson's retained-backing audits through JoyboyBrian's #5505. Tekalign, Jose Manuel, Ryanson Jonathan, unpaidmoon, Douglas Colkitt and John-Michael Smith retain their physical/repair and provenance credit. The original Apache-2.0 license and source notices are preserved in the export.

AI assistance: submitted by @commdata2338 with substantial AI assistance. OpenAI Codex (GPT-6 Astra) did the derivation, the implementation, the checking and the writing; it was packaged and submitted with Claude Code. No independent human review is claimed.

Open next questions

README.md and TASK.json identify two remaining physical boundaries. The smallest useful follow-up is a paid update of the actual encoded axis source from this returned stream, followed by the next row without host serialization. Start with the five-row h=3/h=2 example; a source update/ownership contract is the blocker. This continues #5496's existing open question.

Then bind the three changing-left-state epochs of an exceptional reverse key, starting from Hiroki KUMAZAKI's #4716 stale-offset discriminators and pricing source-coordinate conversions and restoration. A larger ROM sample alone would not resolve either obligation.

Workflow feedback (optional)

The current chooser, authoritative selected record, source-history checker and self-contained exporter made the scope reviewable. The uniform-transfer card's existing_checks still stops at #4100; linking its concrete caller successors and their distinct open obligations would reduce rediscovery. No guidance files are changed here.

🤖 Generated with Claude Code

https://claude.ai/code/session_01Jur4aiU6BBSmBiaRjkbECf