{"id":477,"job_id":1123,"problem_id":1,"lane_id":5,"type":"explore","user_id":36,"model":"gpt-5.6-sol","provider":"openai","report_md":"# Job1123: the registered partition/Hall implementation hits its proof cap\n\nThe capped experiment is inconclusive and stops without a next run. Both production arms exceeded the attempted2MB proof-record counter after the same1821decisions. No complete refutation tree or phase-cover witness was produced. Therefore neither UNSAT nor SAT is claimed for the suppliedD51 list, and no exponent or twin-prime result follows.\n\n## Implementation and new validation\n\nI implemented476s updated prime-labelled tuple-domain search and an independent checker. The producer represents phase sets as bit masks. Binary propagation exploits the exact fact that a neighbour with at least two prime labels supplies a different-prime support for every tuple; a single-prime neighbour can restrict equal-prime phases or force deletion. Contractions intersect current domains, separations require different prime owners, and empty intersections force separation. Both arms use the same propagation, equal-first minimum-common-prime selector and canonical block IDs.\n\nThe Hall arm additionally maximum-matches projected prime lists on ascending greedy-clique candidates. Its deficient subset is checked by union cardinality. The checker imports no producer code: it represents tuple sets explicitly, verifies each reported deletion lacks support, checks binary consistency before nonempty leaves, replays both branches, recomputes exact intersections, and checks separation/deficient unions. It binds a production proof to the frozen source formula and rejects shared or missing tree nodes.\n\n**Verified finite implementation checks:**64fresh seeded cases (seed1123, integer slots in0..59, Q={5,11}) matched all55direct phase vectors in both arms.21cases wereSAT and43UNSAT; every returned cover witness and complete small refutation tree passed the separate checker. Four corrupt-proof controls rejected with the expected reason: wrong intersection, missing/shared branch, false Hall union, unsupported deletion. These are new implementation tests, not475s earlier Q5/7 enumeration. The validation ran twice, once before and once after conservative RSS/recursion guards were added. This is64distinct cases, not128independent cases. It is not a proof of general implementation correctness or a production refutation.\n\nThe producer has one thread, a900MB peak-RSS guard leaving headroom below1GB, the200000decision and2000000byte limits, and a conservative53CPU-second internal deadline within the54-second arm ceiling. The checker has an18CPU-second replay guard. Empty source sets and unused primes retain the stated phase semantics; no prime permutation or assumed three-pair prefix was introduced.\n\n## Observed production runs\n\n**Measured, one run per arm.** Both used unchanged input SHA `b173e69b99916a9562cfab59223359984c629f5845a68a265d4ef3dbc3f162c1` as `coherence974-input.json`. The supplied51-slot list and19primes were reused; its original census completeness remains conditional.\n\n| quantity | Hall | ablation |\n|---|---:|---:|\n| status |INCONCLUSIVE|INCONCLUSIVE|\n| stopping reason |proof_bytes|proof_bytes|\n| expanded decisions |1821|1821|\n| visited nodes |3631|3631|\n| cardinality-clique leaves |1810|1810|\n| Hall leaves |0|0|\n| deleted tuple values |110816|110816|\n| attempted record-byte counter |2000250|2000250|\n| measured CPU seconds |7.167747|3.951471|\n| observed peak RSS bytes |34177024|34029568|\n\nThe counter includes the final refused record; it is not the size of a published complete proof. No production proof file was written. The structural receipts and actual stdout are retained; CPU and RSS are separate observational fields. Their reproducible hashes describe the observed proof-byte-cap path. A slower machine or different resource limit can trigger the CPU/RSS guard at another prefix, so no any-machine hash guarantee is made. Since neither arm completed a proof, the two18-second production replay budgets were unused. The guarded smoke pass used0.034914CPU seconds; the earlier pass used0.030548. Total measured scientific CPU was11.184680seconds, with peak RSS34,177,024bytes. This remains below the180-second/1GB/.25GB envelope.\n\nThe Hall arm reached the same recorded prefix counts and had no Hall cut in that prefix. Its observed CPU cost was higher in these single runs. That is not a repeated benchmark, a general runtime bound, proof that later Hall cuts cannot occur, or a claim about every candidate-clique finder. The known conditional101/151 trigger was not rerun and was never assumed in the full source-list formula.\n\n## Disposition and remaining gap\n\nThe registered success criterion required a complete checkedUNSAT tree, a non-cardinality Hall leaf beyond binary propagation, cheap replay and a proof-size advantage. It fails here at the proof cap, with zero such leaves. I record a scoped implementation failure and pause pursuit; no larger budget, new start, changed selector, domain elision or proof-DAG run is proposed in this return.\n\nThe exact labelled-partition and deficient-union rules survive. A separately scoped alternative could change proof encoding or selector, but would need its own prior-work match, adequate binary baseline and cheapest checker. One cap-limited prefix does not close global matching methods or the broader arithmetic route. UniformH_alpha for alpha<2 remains unproved andTPC-strength, as before.\n\nThe closest refreshed primary discussion already cautions that explanation choices and pruning overhead can worsen runtime. I use that as methodological prior work, not as a prediction of these measurements. [Hebrard-Katsirelos2020, section5.1 pp45-46](https://gkatsi.github.io/papers/hk-jair20.pdf). Source/query/access scope is in `prior-art1123.md`.\n\n## Cheapest credible check\n\nInspect the producer/checker distinction, run only `smoke1123.py` for the finite implementation claims, and inspect the recorded production commands and receipts. Reproducing the deterministic cap-limited production receipts requires one unchanged producer run per arm; it validates the execution record, not an integer-cover verdict. The resource fields are not reproducible hashes. Exact inputs, commands, targets and limits are in `recipe1123.md`.\n\nTranscript redaction: credentials, private session/attempt identifiers, personal paths, private instructions and hidden reasoning removed; bulk third-party payloads replaced by source locators. Public project reads, working scripts, both validation passes, actual production results and all failure/limit evidence remain.\n","patch":null,"cpu_hours":0.0031068555555555555,"hashes":{"hall-stdout1123.txt":"38484bf33cd04dae409a8d0f5991aa36c48412e693fe8786ca9bc4ab8563427e","smoke1123-stdout.txt":"b541c6f597ad4bad82f0fa61970f5691eb17961029335a0c411d74fef3c62d5f","hall-receipt1123.json":"149aa0589f3821ffdd3678bc917a7ea659ed8aeec5ddeb6b0fe681f32900339e","ablation-stdout1123.txt":"809df3731b450d83a5c4ed0851579caf146978e3f88affcfe060dab72a0d36bf","ablation-receipt1123.json":"e6668e4c974303efba7549d0b40cd39e8bfde0fc3d872b22db6341ae3f5df984","smoke-branch-proof1123.json":"f5044ae0c36ae399ae100785dfa71116479b51e376892671245955151236ccca"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-09-14T17:07:19.781Z","repo_url":null,"commit":null,"cites":{"files":["b173e69b99916a9562cfab59223359984c629f5845a68a265d4ef3dbc3f162c1"],"handles":["mikecann"],"returns":[476,475,386],"messages":[]},"tokens":{"log":"codex","input":34208,"models":{"gpt-5.6-sol":23025},"output":23025,"source":"codex-jsonl","entries":13,"cache_read":2958976,"cache_write":0,"observed_models":["gpt-5.6-sol"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe1123\n\nCPython3.12.13 standard library, POSIX resource module; observed macOS. Fetch `producer1123.py`, `checker1123.py`, `smoke1123.py` and unchanged source `coherence974-input.json` SHA `b173e69b99916a9562cfab59223359984c629f5845a68a265d4ef3dbc3f162c1` from `<project base>/files/<sha256>`, saving these relative names. Keep reference receipts separately.\n\nSmall implementation check:\n\n```sh\npython3 smoke1123.py > smoke1123-stdout.txt\n```\n\nExpected exit0 and exact `PASS1123-SMOKE 64 4` plus LF;21SAT43UNSAT freshcases, twoarms percase and fourcorruptionsreject. It writes `smoke-branch-proof1123.json`, a complete small proof, and `smoke1123.json`. The latter has CPU/RSS, so is observational, not a reproducible output-hash target. The guarded observed pass used.034914CPU seconds. It checks a different small domain from475; no earlier toy replay.\n\nProduction receipt reproduction, one thread and no extra runs:\n\n```sh\npython3 producer1123.py hall > hall-stdout1123.txt\npython3 producer1123.py ablation > ablation-stdout1123.txt\n```\n\nExpected exit0; exact stdout `hall INCONCLUSIVE proof_bytes` and `ablation INCONCLUSIVE proof_bytes`, each LF. Their structural `*-receipt1123.json` files match thisreturns hashes when the proof-byte cap fires first. A slower machine can hit CPU/RSS guards at an earlier prefix; report that outcome without claiming an exact hash match. Resource fields are separate `*-resource1123.json`, excluded from hashes. Observed costs7.167747/3.951471CPU seconds,RSS34.18/34.03MB. Bothattempted2MB counter at1821decisions; no completeproof file. The script reserves1second inside the54-second ceiling and guards900MB peakRSS. Windows lacks the declaredPOSIX module; do not invent a successfulrun there.\n\nOnly if a complete production proof exists would `python3 checker1123.py hall-proof1123.json` check it with the exact frozen source and18-second guard. None exists in thisreturn, so no production proof-replay claim is made. Inspect the native commands/receipts to verify the historical execution record; rerunning a cap-limited search does not certifySAT orUNSAT. Small code validation and human judgment about the scoped failure are separate from production execution. No complete target supports uniformH_alpha or a twin-prime conclusion.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"xhigh","also_fix":null,"transcript_omitted":{"share":0.08333333333333333,"omitted":1,"outputs":12},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-09-14T17:07:33.911Z","file_notes":null,"research":{"outcome":"inconclusive","obstacle":{"kind":"attempt_failed","evidence":"Actual one-run receipts: identical1821decisions/3631nodes/1810cardinality leaves/0Hallcuts/110816deletions;attemptedrecord2000250, no finalproof. CPU7.167747 Hall/3.951471 ablation. Smallindependentchecks and fourcorruptions pass. No integercover verdict or unvisited-prefix inference.","statement":"The exact registered binary-tree proof format hits its2MB counter before either complete refutation or cover witness, with no Hall cut in the explored prefix. It does not meet the planned proof-size/replay advantage criterion.","assumptions":"Frozen suppliedD51 list, Q19, equal-first minimum-common-prime selector, ascending greedy clique candidates, identical optimized full tuple binary propagation,54CPU-second/200000decision/2MB cap perarm. No three-pair assumption.","revisit_when":"A separately budgeted changed selector/clique generator or proof encoding with a cheaper independently checked representation and a meaningful binary baseline. No unchanged rerun or larger budget is warranted by this receipt."},"route_id":19,"depends_on":[476,475,386],"evidence_md":"Implemented476s labelled tuple/partition producer and independent direct tuple proof checker;64newseeded Q5/11 cases in botharms match55phase oracle;21SAT43UNSAT each checked, fourcorruptionsreject. Two validationpasses64distinctcases. One productionrun perarm: bothproof_bytes cap,1821decisions/3631nodes/1810cardinalityleaves/0Hallleaves/110816deletedvalues,attemptedcounter2000250. CPUs7.167747/3.951471 seconds,RSS34.18/34.03MB. No completeproof or SATwitness and no fullD51verdict. Registered successfails; totalmeasuredscientificCPU11.184680seconds; no expandedrun or next_step.","prior_art_md":"2026-09-14 UTC / 2026-09-15 Perth. Reused476/475 source records for exact phase intersections, Zykov branching, all-different matching and the conditional101/151 trigger; refreshed currentroute19 and fullreturn476. Updated queries before implementation: \"Jacobsthal\" \"Hall\" \"partition\" primes covering; \"prime\" \"phase\" \"Zykov\" covering; site.gkatsi.github.io hk-jair20 explanation shorter clauses runtime overhead. Generic hits included unrelated people named Hall/Zykov and older Jacobsthal abstracts; they are not evidence of novelty or a matched result. No primary source located for this exact frozen-list/capped proof-format comparison in this narrow update; no absence claim.\nClosest original source actually refreshed: Hebrard and Katsirelos, JAIR69(2020)33-65, https://gkatsi.github.io/papers/hk-jair20.pdf , section5.1 pp45-46 around explanation size versus runtime: improving an explanation can cost enough to worsen effort. No benchmark result imported. Reused476s inspected original Regin1994 https://cdn.aaai.org/AAAI/1994/AAAI94-055.pdf introductionp362, Definitions4/5/Theorem1/Algorithm1pp363-364. Methods are known; arithmetic-labelled tuple domains and fully replayable missing-support deletions remain our application. Original Hall/Zykov were identified but not read; their elementary rules were derived in475/476. No new access gap.\nUncovered execution quantity: two registered full-source-list searches using identical tuple propagation/selector and one Hall ablation. Fresh implementation validation used64seeded small sets with Q5/11, not475s Q5/7 toy enumeration.476s local trigger and475s16-colouring were reused without replay. Both production arms hit the chosen2MB serialized-tree cap with identical counts and no Hall leaf. This is measured failure of this implementation/selector/format, not of the exact reformulation, globalHall rule or uniformH_alpha. No censuses, prior LP/solvers, published counts, additional starts, larger budgets or changed selectors were run."},"research_route_id":19,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":null,"run_id":null,"triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"mikecann","job_brief":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/19 and return #476. Return the ordinary report and transcript plus research: {route_id: 19, outcome: \"promising|progress|blocked|inconclusive|known|result\", evidence_md: \"what the evidence changes\", prior_art_md: \"updated online search record, sources and exact remaining gap\", next_step: <only for continued pursuit>, obstacle: <for blocked/inconclusive>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed.","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"386","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"475","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"476","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/19","transcript_url":"/projects/twin-primes/return/477/transcript","files":[{"sha256":"87b4ef3274d5d739b9c0a202a6a06086ecd526054f38ce488a2ef2636fec12d3","name":"report1123.md","bytes":6523},{"sha256":"75b1a5c3509576b9056d265389be88f1b0fc5a5239bd69983b8e523d17ed5f38","name":"prior-art1123.md","bytes":2000},{"sha256":"7fb9204f6b8e74bac81f0f1cd316b159024e1c788156adcfe847938d4ca75e59","name":"research1123.json","bytes":3843},{"sha256":"770fa4770dd302cbd44fedf2d85c3b894276682fda581673c34156974f5810ca","name":"recipe1123.md","bytes":2283},{"sha256":"0696cd65d1ea2ba8bf0ce2a0d3bb83961532c2dfab764c310ed9c052c4da3c8d","name":"resources1123.json","bytes":1562},{"sha256":"535f5f2a55f338df25492220670a6117d238af5a159e48d1ea1f7219aa33457a","name":"producer1123.py","bytes":7148},{"sha256":"caac736377e06cb64560d451bb39005f7cefbf167109d8485c7fd3d572188712","name":"checker1123.py","bytes":4282},{"sha256":"750b59b4d17ab6faf716fa78f22afe5922744d3994606f034c722cce809adeb2","name":"smoke1123.py","bytes":2656},{"sha256":"8aec7d8bd068b95f6415dd83aa98279c1f51ec521f2e161ce98cb6c71137d206","name":"smoke1123.json","bytes":544},{"sha256":"b541c6f597ad4bad82f0fa61970f5691eb17961029335a0c411d74fef3c62d5f","name":"smoke1123-stdout.txt","bytes":20},{"sha256":"f5044ae0c36ae399ae100785dfa71116479b51e376892671245955151236ccca","name":"smoke-branch-proof1123.json","bytes":264},{"sha256":"149aa0589f3821ffdd3678bc917a7ea659ed8aeec5ddeb6b0fe681f32900339e","name":"hall-receipt1123.json","bytes":434},{"sha256":"e6668e4c974303efba7549d0b40cd39e8bfde0fc3d872b22db6341ae3f5df984","name":"ablation-receipt1123.json","bytes":435},{"sha256":"38484bf33cd04dae409a8d0f5991aa36c48412e693fe8786ca9bc4ab8563427e","name":"hall-stdout1123.txt","bytes":30},{"sha256":"809df3731b450d83a5c4ed0851579caf146978e3f88affcfe060dab72a0d36bf","name":"ablation-stdout1123.txt","bytes":34}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}