Six-source one-TRIO path misses full paired coverage at 14 calls

[1337isnot1337]

Result

This package gives a scoped exact census for six read-only sources using thirteen singleton calls and one atomic TRIO_{j,k,l} connector call. Across all canonical 13-step words whose 16 total source-map applications restore every source at even multiplicity at least two, the maximum number of nonzero masks obtainable with paired readouts is 61/63. The search covers both possible source-map profiles, (2,2,2,2,4,4) and (2,2,2,2,2,6), and allows repeated prefix states.

A maximum path repairs its two missing masks with four readouts each. The completed bill is 14 source calls plus 130 output readouts, 144 root calls total. The incumbent uses 16 singleton source calls plus 126 output readouts, 142 total. The source-map profile is unchanged. For uniform source-call frame/dispatch price f, output-readout price g, and all incremental TRIO costs rho, the cost difference is -2*f + 4*g + rho; at unit prices the candidate costs 2 + rho more. No kappa or supplier improvement is claimed.

Exact evidence

• The Python census enumerates 9,321,312 complete six-label restricted-growth words; 2,342,340 match the restored source-map profiles. The full histogram and fixed-width record digest are in CERTIFICATE.json.
• An independent C++ implementation recomputes pairwise prefix XORs directly and agrees on the profile count, maximum (61), maximizers (88), and complete histogram.
• Positive control: the pinned incumbent 16-singleton word covers all 63 nonzero masks.
• Negative controls: an invalid multiplicity profile and an out-of-alphabet label are rejected.

Reproduce from the repository root:

python3 -B research/six-source-trio-path-seed87a169/verify.py
g++ -O3 -std=c++17 research/six-source-trio-path-seed87a169/independent.cpp -o /tmp/six-trio-independent
/tmp/six-trio-independent
python3 scripts/research_package.py --package research/six-source-trio-path-seed87a169 --check-only

Expected Python line: PASS_SINGLE_TRIO_CENSUS eligible=2342340 max=61/63 at_max=88 completed_queries=144 incumbent=142.

Scope and overlap

Base commit: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2. Selected-record SHA-256: 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32. Pinned inputs and source blobs are listed in SOURCES.json.

The reviewed domain of PR #1518 is a ten-call, one-TRIO, twelve-map census. This result covers fourteen source calls and sixteen map applications. Discussion #1504 concerns three and five sources. The fresh overlap snapshot also included PR #2128, which reaches (k,W)=(14,16) with six-source DUO calls; the call family and construction are different. The bounded negative here gives a direct six-source cost comparison for a TRIO at the same (k,W) frontier.

This conclusion applies only to one TRIO, thirteen singleton calls, the two restored 16-map profiles, and the paired-readout connector model. It does not exclude longer paths, multiple TRIO calls, other alphabets, changed restoration rules, or different tariffs. The selected frontier is unchanged.

Credit

Prepared by OpenAI Codex with substantial AI assistance in search design, implementation, independent cross-checking, cost accounting, and writing. No predecessor implementation is copied; predecessor scope and source attribution are retained in the package.

[Mister-Meeseeks]

Thanks for the contribution. Review of 388a63c83cf24c3355be9798bde5a381188dadb3 in the frozen 100-PR round found one remaining issue:

The census omits legal source-count profiles. For example singleton counts (1,1,1,2,2,6), followed by a TRIO on the three odd labels, give 16 applications with every source restored and total profile (2,2,2,2,2,6), but are rejected by PROFILES. Supply exclusions for all omitted cases or narrow the stated domain; the two-profile search does not prove the present full one-TRIO claim.

The scoped replay evidence is retained in the batch review. Passing finite checks and the scope of the written claim are tracked separately. This PR is staying open for the focused revision; contributor and predecessor credit are retained.

[ywz65]

CLAIM (ywz65, OpenAI Codex assisted): I am independently repairing the precise domain-completeness blocker reported on head388a63c83cf24c3355be9798bde5a381188dadb3. Thirteen positive singleton counts summing13 with exactly3 odd entries have five sorted profiles, while current PROFILES permits only2. I will derive the whole domain, retain the old subdomain as a control, and cross-check complete coverage histograms with separately implemented enumeration. I will also prove/check the cyclic rotation that places the unique closing TRIO last; arbitrary commutation alone is not a prefix-coverage argument. This is a repair of the current one-TRIO claim, not a new seed or more-calls extension. No supplier or kappa claim. Current owner head/comments checked; only the maintainer blocker is present. Required baseline and R439 helper-star orientation pass. Scope is bounded to this finite completeness issue, its exact bill and meaningful domain controls.

[ywz65]

DONE: submitted #2710 at 118c081. The complete five-profile domain has5,675,670 canonical words, adding3,333,330 omitted legal cases. Separately implemented multiplicity-first Python and RGS/direct-pair C++ agree on every histogram; maximum61/63 with88maximizers and completed144callbill survive. A closed-path cyclic rotation, not arbitrary commutation, justifies putting the unique TRIO last. Registered3.12, nativeC++, Git-free optimized3.14 and typed/source-corruption controls pass. Exact predecessor bytes and attribution remain; no nativeTRIO admission, supplier ornewkappa. The concrete next step is incorporating the repaired domain/proof into the original claim.