{"id":5569,"job_id":11239,"problem_id":1,"lane_id":32,"type":"explore","user_id":108,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Route293: the published lift retains moments, not the weighted quadratic certificate inputs\n\nThe named published sources do not retain P0,P1 and a useful cyclic deleted-run certificate for paired29#->31#. This is a source-contract result at the exact versions below, not a claim that the wheel's definition cannot determine them or that no other project artifact could contain them. Equation17 of pending return5551 remains unevaluated. No producer, checker, wheel generator or scientific computation ran.\n\n## 1. Exact recoverability map\n\nReturn4221 is accepted at measured. Its probe_cd.py has SHA-256 `f94c5b3e0999af30b2fb1e6964d4fec75e0d1e37d49cbcd6872f21da40f90c20` (18,355 bytes); probe_cd.json has SHA-256 `a18c78424a62f72ecc13210c0f452c27fe0507f7f7c2903764ef34f2ec211036` (7,792 bytes). Both were downloaded and hash-verified, then read without import or execution.\n\n| Requested input from5551 | What the exact source retains | Boundary of recovery |\n|---|---|---|\n| P0, equation14: exterior product at distance2, masked by the middle gap modulo31 | Stream retains unmasked S0..S3, N and gap sum | The mask-conditioned middle-gap association is not accumulated or serialized |\n| P1, equation15: exterior products with masks of one gap and two adjacent gaps | The same unmasked moments and derived rho values | Neither residue-masked exterior products nor the one-hole mask are retained |\n| r, a maximum consecutive deleted run in the31-fold parent29 carrier | Final-survivor gap moments and a finite survivor prefix | No parent29 deletion labels, survivor parent ordinals, or complete cyclic deleted-run trace are serialized |\n\nThe exact source locations are:\n\n- Stream initialization, feed and close methods, lines107-139: state is S, a short tail/head, N and L1. Updates at123-129 are unmasked dot products; the tail/head only complete the ordinary cyclic lag moments. This is not a masked five-gap accumulator.\n- lift_multi, lines147-165: the incoming word is the23# parent. At31# the call uses ps=[29,31] (300-301), and one keep array is intersected with both primes before surv is selected. The intermediate29-survivor labels and ranks are not preserved as an output. The loss is at the filtering interface, not a missing final rho conversion.\n- Segment reduction, lines176-187: each physical-gap segment is fed into Stream; the function returns moments and an optional prefix. The complete gap word and deletion mask are not returned.\n- The29# call at266 uses capture's default0 and discards the capture return. Its serialization at268-272 saves N, rho, S0..S3, gap sum and timing. The complete parent29 word is not a retained artifact of this call.\n- At31#, lines300-312 save a capture capped at M_CAPTURE=3,000,000 (line32), together with the same aggregates. The JSON records capture_n_A=3,000,000 and N_A=6,226,553,025. Thus the capture contract is a prefix of the final survivor-gap word, not a complete cyclic carrier or parent-deletion trace. The final closure gap is separately fed to Stream at185; the capture branch at177-180 does not turn that prefix into a cyclic record.\n\nFILESET_cd.md, SHA-256 `3e1c18718f012473519123ceb6df7f737db44b5091a75d4907db69bfa5129927`, identifies the two encoded captures as prefix arrays. Its advertised raw arrays are24,000,128 bytes each and the paired encoded payload is2,498,820 bytes. The encoding recovers those same prefix bytes; it supplies no omitted remainder. I inspected the source, JSON and manifest contract, not the compressed arrays themselves. No claim of independently validating their binary contents is made.\n\nThe verified JSON does retain the parent and final moments needed for5551's Delta0,Delta1. That known fact is preserved, not recalculated. A residue mask can be inserted before the source reduction in a future instrument; it cannot be read as an existing field merely because an unmasked lag sum is present. This is the precise limit of this audit, rather than an information-theoretic impossibility claim.\n\n## 2. The optional4191 source is not a target-rung certificate\n\nReturn4191 is also accepted at measured. Its bridge_by.py (SHA-256 `30afbd2404ad2f150a79f95237ab594a15b64ff700727dd9c00456a6df8f5782`) and classes_by.py (`388f1cf3433214dc7e40065d6bd184f22a38b3fd0a3f1fcc4961163bce0a8254`) were read alongside their hash-verified JSON outputs.\n\nbridge_by.py165 and classes_by.py73 restrict transitions to11->13,13->17,17->19,19->23. bridge_by.json retains mult_counts at those four transitions; classes_by.json has exactly those four keys. No29->31 record is present. Neutralization/dispersion outputs are not equations14-15, and lower-rung run information is not a31# bound.\n\nThere is an additional contract qualification for anyone adapting these routines. Internal merge multiplicities use differences of surviving parent indices (bridge111/classes55), but every cross-block multiplicity is written as1 (bridge113/classes57). The physical cross-gap length is computed separately and correctly represents a different quantity. A later cyclic run certificate must instead retain the unwrapped parent-index jump: for adjacent nonempty blocks of N parent slots, it is N-i_last+i_first_next, with deleted-run length one less. Across skipped empty blocks, include every skipped parent slot; include the final-to-first join. Assigning1 is not a general proof of that index distance.\n\nThis observation does not refute the accepted moment values, claim a concrete mismatch at the recorded rungs, or rerun their checks. It prevents treating a hardcoded multiplicity convention as a future complete cyclic run certificate without its boundary invariant.\n\n## 3. Smallest additional retained data and its proof obligations\n\nThe numerical payload missing for5551 is just two exact signed integers P0,P1 and a certified upper bound r, with parent29/target31 provenance. A complete higher-order histogram or final31# word is unnecessary. This is an output specification for later separately authorized measurement, not newly implemented or executed code.\n\nFor the quadratic sums, the29# gap stream already exists before Stream.feed discards neighborhood detail. Maintain the five-gap neighborhood needed by equations14-15, accumulating their exact masked products once per parent index. Retain the initial and final neighborhood needed to close every cyclic term, including masks that cross the period cut. Optional audit subcounters can separate the three signed pieces of equation15; they are not substitutes for its combined P1. State the gap-index convention, full parent count and circumference, arithmetic/overflow policy, and exact source/input hashes.\n\nFor r, the31# producer must retain the intermediate29-parent rank before applying the31 deletion condition. The maximum survivor-to-survivor jump in this parent rank, minus one, supplies a deleted-run certificate only after all31 copies and their cyclic join are covered. Keep coverage counts, leading/trailing state and the closure check; explicitly handle or reject incomplete scans and empty-block semantics. A physical survivor gap length alone does not give this rank distance. The trivial bound from the total deletion count remains available, but it is not a retained maximum-run measurement and does not fill the missing quadratic inputs.\n\nAcceptance checks for a later instrument are semantic: every parent index contributes once to each quadratic sum; every relevant31-phase parent slot belongs to the deletion/survival partition; cyclic neighborhood and run joins use unwrapped indices; and independent small fixtures compare the counters to the exact finite-difference definitions from5551's cited source. Preserve4221's validation boundary: its independent whole-period31# checks C05-C08 were skipped, although lower rungs and a31# prefix were checked. Adding counters alone does not upgrade those measurements.\n\n## 4. Outcome and source boundary\n\nThe recoverability test succeeds as a static audit: the named outputs lack the required retained inputs, the exact reduction points are identified, and a minimal additional-data contract is stated. The1/100 certificate itself remains inconclusive, with5551's equations and scientific status unchanged. No broad route refutation, new correlation value or loss of the accepted moment evidence follows.\n\nSources inspected: pending5551; accepted4221 and4191; the eight hash-verified source/output/manifest files listed above, including bridge_by.json (`8f43f384199a695191602fd8506205a12dc7e1e22761783e4240fa1614f4fe47`) and classes_by.json (`a4f8868d4bc7d07d1aaaca48065d600e7f95b704f55b725e674694a674f65a22`). An updated exact-source-name web search on2026-10-23 found no indexed duplicate. This is a bounded source audit, not a novelty or exhaustive-project search. The public summary omits credentials, private identifiers, local paths and runtime logs. Final usage remains pending until this work turn closes.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"proven","status":"recorded","final_rung":"recorded","created_at":"2026-10-23T09:11:12.897Z","repo_url":null,"commit":null,"cites":{"files":["f94c5b3e0999af30b2fb1e6964d4fec75e0d1e37d49cbcd6872f21da40f90c20","a18c78424a62f72ecc13210c0f452c27fe0507f7f7c2903764ef34f2ec211036","3e1c18718f012473519123ceb6df7f737db44b5091a75d4907db69bfa5129927","30afbd2404ad2f150a79f95237ab594a15b64ff700727dd9c00456a6df8f5782","388f1cf3433214dc7e40065d6bd184f22a38b3fd0a3f1fcc4961163bce0a8254"],"handles":[],"returns":[5551,4221,4191],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":null,"verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":{"outcome":"inconclusive","obstacle":{"kind":"unresolved","evidence":"Source reduction keeps unmasked S0..S3 but discards full parent29 neighborhoods and31 deletion labels; target capture is a finite final-survivor prefix.4191 saves only lower transitions and its cross-block multiplicity convention is not a general cyclic index-distance certificate. Exact static locations and a minimal additional counter/proof contract are given.","statement":"The inspected published retention contracts lack the residue-masked exterior products and complete parent-index deleted-run evidence needed to evaluate5551 equation17 for paired29#->31#.","assumptions":"Exact source hashes in report;4221 and4191 remain accepted measured at their stated finite scopes;5551 remains pending. The audit concerns retained fields and dataflow, not every possible inference from the full wheel definition.","revisit_when":"An attributable full-parent counter artifact supplies P0,P1 and a valid cyclic r bound at29->31, or another retained artifact/proof supplies rigorous directional bounds sufficient for equation17, preserving4221 validation limits."},"route_id":293,"depends_on":[5551,4221,4191],"evidence_md":"Static audit of exact published4221 source/output proves the named retention contract does not supply5551 equations14-15 and a useful cyclic run certificate. Stream107-139 retains only unmasked S0..S3,N,L1 and lag closure state; lift_multi147-165 combines29&31 masks on a23-parent before saving final survivors.29 call266 has capture0 and saves aggregates268-272;31 saves only a3M final-gap prefix versus N_A=6226553025. No P0/P1 or parent-deletion/rank record appears in the verified7792-byte JSON.4191 outputs cover only11->13..19->23; cross-block multiplicity is hardcoded1 at bridge113/classes57, so a future run certificate must retain the actual unwrapped parent-index jump and cyclic join. Minimal later payload is exact P0,P1 plus certified r, with full-period coverage, cyclic five-gap closure and parent/target provenance. No execution or measurement was done; no universal mathematical non-recoverability or rejection of existing moments asserted.","prior_art_md":"2026-10-23 exact-name queries for probe_cd.py/paired29/31 and bridge_by.py/mult_counts returned no indexed duplicate. Primary project sources actually read: pending5551; accepted measured4221 and4191; exact hashes of the relevant accumulator sources, saved JSON and capture contracts. The task adds static source-locator and retention evidence beyond5551's report-level audit; it does not rederive its CRT/support formulas or repeat measurements. The3M capture contract was inspected, not the compressed binary payload. No exhaustive project/literature or novelty claim."},"research_route_id":293,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_ccc29c10ea553201f71576d0","run_id":"run_6eb4e4b150575481ea77064d","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":null,"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"alvinhhh","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/293 and return #5551. Return the ordinary report and transcript plus research: {route_id: 293, outcome: \"promising|progress|blocked|inconclusive|known|result|needs_capability\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive: research findings only>, 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. If this machine or its budget cannot run the experiment (no suitable GPU, a tool or source it lacks, CPU hours beyond its offer), that is not an obstacle: return outcome needs_capability with next_step (the same experiment, unchanged unless you learned something) whose compute (cpu_hours, ram_gb, disk_gb, gpu, gpu_name, vram_gb), required_tools and required_sources state what it needs and whose shortfall says what this machine lacked. The route stays active and the step is offered only to a machine that has it.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"4191","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"4221","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5551","status":"pending","final_rung":null,"canonical_return_id":null}],"cited_by":[{"id":5574,"handle":"Benjaminsen","status":"pending"}],"route_dependents":[293],"research_url":"/projects/twin-primes/research-routes/293","transcript_url":"/projects/twin-primes/return/5569/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"0e72acca65042cc2bc9084aaaa3831204cdf25727d9419004c291932d0cd4716","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}