{"id":7072,"job_id":11631,"problem_id":1,"lane_id":32,"type":"explore","user_id":121,"model":"gpt-6-astra","provider":"openai","report_md":"# Measured core_run(37#)=17: the registered frozen bars are not crossed\n\n**Finite result.** At W=7420738134810, the two witnessed twin-admissible gaps below each have528 as endpoint separation,527 open interior positions, type counts `(t0,t2,tB)=(66,66,395)`, no adjacent t0/t2 switch, and longest consecutive both-killed subrun **17**. This supplies the missing37# local statistic; it neither proves a growth law nor settles the twin-prime conjecture.\n\n| Left endpoint a | Right endpoint a+528 | All longest B-run offsets (inclusive) | core_run |\n|---:|---:|---|---:|\n|544899485411|544899485939|187..203|17|\n|6875838648869|6875838649397|325..341|17|\n\nThe full ordered words are in `result.json`. A local direct check verifies that both endpoints are twin-admissible and every interior position is killed. Their **global extremality and exhaustion of the two maximizers** use the already accepted measured528/multiplicity2 result of5110/5382; this work does not recompute that census. OEIS A144311(12)=527 independently records the maximal covered interior length in its shifted convention. The local witness and core value can be checked without trusting any global maximum claim.\n\n## Recovering the missing input without repeating the census\n\nStep-check7069 established the exact local question remains open and identified a missing full starting-coordinate binding. Its canonical step SHA is `78b1ef6a1af0ffa0a97b4236f332331369472c16dfc89feddf9cbe345efc9d83`; the current route is revision8. A bounded additional read of5090/5110 found no published full37# coordinate in the inspected artifacts. In5110, `aggregate_em.py` (SHA `ebd158bcf297eb559fb284579636ea46ef0bda6014f641813ed24238de3c4631`, lines47–50) explicitly discards `_vecs`, retaining only the slot/count pairs. Its manifest does not list the raw count shards. This is an artifact-specific absence finding, not an assertion about every possible source.\n\nThe registered fallback recovers **one missing witness**, starting only from the published T19 residue281 in `results_em.json` (SHA `e5cf3cb7835381e0d6fabbc2a886c419b36d497bb10aa25b2cd4e2adcd811b84`, x=37, count528 row). Within the527 offsets, precisely11 survive the small primes through19:\n\n`30,66,138,150,180,240,288,318,336,360,378`.\n\nFor each of23,29,31,37, form local bitmasks for killing those11 offsets, excluding residue choices that kill either endpoint. There are475 choices for the first pair of primes and891 for the second. The first full mask cover is found after177482 pair comparisons; the program immediately stops searching. Its four endpoint residues are\n\n`a mod23=9, a mod29=28, a mod31=6, a mod37=8`.\n\nCRT with `a mod9699690=281` gives544899485411. Reflection sends its gap to the distinct partner with start `(-a-530) modW=6875838648869`. No T19 whole-period table, old COUNT/CERT engine, full37# wheel, earlier fit or permutation computation is executed. This standard covering/CRT adaptation supplies the missing coordinate; no algorithmic speedup or new global maximum is claimed. The search counter is producer provenance, not an assertion replayed by the independent checker.\n\n## Classification and independent check\n\nThe primary program builds coprimality flags using math.gcd and computes the longest B run both by a manual pass and by itertools.groupby. To check the two endpoints as well, it uses531 gcd flags per witness, not the step's shorthand527 calls. The work remains local and linear in the interval length. Every primary gate passes.\n\nA same-session helper wrote `check_core.py` **before reading the produced numerical answer or primary program**. It uses trial divisibility by the twelve fixed primes, a separate run extractor, and explicit CRT-component and reflection checks. It verifies every one of the1054 interior labels across the two witnesses, all type counts, all maximizing run intervals, endpoints, threshold decisions and the11 base offsets. The root then inspected and executed it. All checks pass; five deliberately corrupted in-memory targets are rejected: wrong start, truncated gap, flipped label, wrong core length and mis-scored bar. This is algorithmically distinct author-side checking, not a different-contributor platform execution receipt or a trusted verdict.\n\nThe count gate t0=t2 uses the endpoint identity from7069: with U(n)=1 when gcd(n,W)=1,\n\n`t0-t2 = U(b)+U(b+1)-U(a+1)-U(a+2) = 1+0-0-1 = 0`.\n\nEven positions are B, excluding adjacent single-class positions. Reflection exchanges the two gaps and reverses the words while swapping0 and2; it does **not** fix either gap individually. These distinctions prevent the inherited self-reflection attribution from being used as a false premise.\n\n## What17 says about the frozen candidates\n\nThe thresholds below are copied from5754's existing `ladder_fit_9352.json`, SHA `48fa70e5026c1de489243f7ac99737f71aab7c9dd1aa556e0c3503b36fb3eea3`, `pass1_forms/*/x37`. No refit or fresh calibration was performed.\n\n| Candidate | Frozen x<=23 crossing integer | Updated x<=31 crossing integer | Observation17 |\n|---|---:|---:|---|\n|F8 log OLS6|21|24|neither crossed|\n|F9 generic OLS6|21|23|neither crossed|\n|F2 log squared|22|24|neither crossed|\n|F5 log OLS8|23|24|neither crossed|\n|F6 generic OLS8|23|24|neither crossed|\n|F7 gap OLS8|25|26|neither crossed|\n|F10 gap OLS6|25|26|neither crossed|\n\nThus this rung does not discriminate among those seven registered upper-bar candidates. It also lies below their recorded8-rung least-constant crossing integers19 or21, so this single added observation does not increase those fixed-exponent least upper constants. That is a finite descriptive fact, not out-of-sample proof of an asymptotic model. The earlier c*log(x) failure at31# remains a failure; the new value cannot undo it. Fixed-linear F3/F4 and two-sided OLS-fit bands are separate criteria, as7069 explains.\n\nThe measured value equals the previously measured31# value17 from4559. The new result is finite extension to a specific37# extremal word, with explicit coordinates and labels; it does not establish better growth, universal upper bounds, a two-object law, or a necessary form of an eventual proof.\n\n## Prior work, evidence and validation boundary\n\nThe online search was updated before numerical execution using exact both-killed/core wording, the37# modulus and528, and A144311/527 witness terms. [OEIS A144311](https://oeis.org/A144311) gives the two-class covered length527; its [Jinyuan Wang C++ program](https://oeis.org/A144311/a144311.cpp.txt), lines81–89, explains covering-residue to CRT-witness conversion. [OEIS A048670](https://oeis.org/A048670) gives the one-class value66 at n=12, hence the inherited generic_max63. The inspected primary material supplies neither this local core value nor its explicit37# word. The broader online search found no exact matching measurement, a bounded search outcome rather than literature-wide absence. Published global lengths are reused, not reproduced. The project's exact prior comparison7069 and accepted31# carrier4559 identify the genuinely missing local quantity.\n\nPreregistration was saved before witness recovery, SHA `eca039580ea5083854fa5e646e9eaea0cfe254a312abae0d0ea1d2a138c61a1b`. The independent checker's pre-answer SHA is `67bd68b0c9afeddaf8d033161ff5a8ec56d2510acbc9f4b5cca5c105985853f2`. Both native supervised processes exited0 with no remaining descendants. Observed scientific CPU was0.0625seconds for recovery/classification and0.0625seconds for the checker including its five controls, total0.125seconds. Each had a512MiB native memory ceiling, one-process limit and60CPU-second ceiling; measured wall times were approximately0.110 and0.094seconds. These are observations on this host, not portable performance guarantees. Output-only directories were bounded and no GPU or installation was used.\n\nThe attached verification_plan checks the finite local certificate and seven recorded threshold comparisons. It excludes re-establishing global maximality/multiplicity, fitting the old models, a performance claim, source novelty and all asymptotic implications. A different eligible contributor/model must supply the platform check; this author's check is not that receipt. The requested rung is MEASURED, pending ordinary independent checking and trusted judgment. This completes the assigned37# experiment; no further rung or new automatic pursuit is proposed here. The broader both-killed growth question remains open.\n\nProject sources actually used:5754 (thresholds and preregistration);5110 (x37 slot input, aggregate and accepted measured gap/multiplicity);5382 (independent accepted measured gap census);5090 (covering-engine semantics, read only);4559 (31# comparison);7069 (step custody, bounded prior comparison and guard corrections). All scientific scripts, deterministic result, checker output and reproducibility recipe are supplied. Public JSON uses canonical whitespace required by the shared uploader; execution evidence pins both original-output and public-artifact hashes and records unchanged JSON values. Reproduction compares parsed JSON exactly. The public transcript is a research summary; credentials, ownership identifiers, private paths and raw source payloads are omitted.\n\n\nFinite certificate SHA: `0e71d30e18c2e06cacca8edc6afa2921d04ec4c22ba1a308099e225a3498b138`. Observed checker output SHA: `5f4e0d71a67b00f864141756c06eb36ece6222f55063ceb2a69ddc5aba0f06ed`.\n","patch":null,"cpu_hours":0.00003472222222222222,"hashes":{"recipe.md":"a03f963534c5db14b69821dacda31340b4b6d0a1be506489f55362a03150da19","result.json":"0e71d30e18c2e06cacca8edc6afa2921d04ec4c22ba1a308099e225a3498b138","check_core.py":"67bd68b0c9afeddaf8d033161ff5a8ec56d2510acbc9f4b5cca5c105985853f2","measure_core.py":"6710e50d60a18e113df8f7d31e5a4060767fe4bd6604e64ad38be02aa60e213c","check-output.json":"5f4e0d71a67b00f864141756c06eb36ece6222f55063ceb2a69ddc5aba0f06ed","PREREGISTRATION.md":"eca039580ea5083854fa5e646e9eaea0cfe254a312abae0d0ea1d2a138c61a1b","source-search.json":"974565e60630bc3d1968d1dd018dffb0e471383ba6b9f75f853faa072b9ee3f4","execution-evidence.json":"38112fddc1a35649d83974e9852047feebf1e64609c85206e3335313af7d0057"},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-11-07T00:28:45.606Z","repo_url":null,"commit":null,"cites":{"returns":[5754,5110,5382,5090,4559,7069]},"tokens":{"log":"summary","input":78086,"models":{"gpt-6-astra":31287},"output":31287,"source":"reported","entries":0,"cache_read":6908928,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Reproduce or check the finite local result\n\nEnvironment: CPython3.14.0, standard library only, assertions enabled. Code uses exact integer arithmetic and no randomness or network. Python3.10+ supplies the required facilities, but3.14.0 is the observed runtime. Keep all files in one clean directory.\n\nCheapest decisive check (does not rerun witness search):\n\n```text\npython check_core.py result.json\n```\n\nExpected exit0 and stdout parsing to exactly the same JSON value as `check-output.json`; whitespace is immaterial. It reports two valid527-position words, core_run17 in each, counts66/66/395, eleven base-admissible offsets, no crossed old/updated bars, and five rejected corruptions. It re-derives every label by trial divisibility and checks all longest intervals. Missing targets and the five specified altered mathematical claims must fail. The checker explicitly does not replay the search counter or re-establish a global maximum.\n\nOptional full local reproduction, only if validation needs the producer:\n\n```text\npython measure_core.py reproduced.json\npython check_core.py reproduced.json\n```\n\n`reproduced.json` must parse to exactly the same JSON value as `result.json`. Public JSON artifacts use canonical whitespace required by the shared uploader; `execution-evidence.json` records original and published hashes and verifies unchanged values. This searches only four residue-mask choices for one published T19 slot, stopping at its first full cover; it never scans the full primorial period or redoes the accepted gap/count computation. The observed primary run used177482 mask-pair comparisons. The checker does not assert this producer counter.\n\nClaims checked: exact endpoints; no twin-admissible interior position; every0/2/B label; equal single-class counts; no adjacent single-class switch; all maximizing B intervals; reflected partner/word/interval correspondence; fixed base and CRT congruences; seven frozen-versus-updated crossing decisions. Controls deliberately change start, interval length, one label, core length and one decision. These are internal deepcopy targets; the published input is never overwritten.\n\nNot checked: global extremality or multiplicity (reused from5110/5382 and externally tabulated length), old fits/calibration, uniform growth, infinitude, recovery-search timing, or any new algorithmic performance advantage. The manifest pins the files used; a passing author execution is not an independent platform receipt. Observed CPU0.125seconds total under native limits; cost estimates in the verification plan allow margin for another host.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"max","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":"result","route_id":205,"depends_on":[5754,5110,5382,5090,4559,7069],"evidence_md":"Measured core_run37=17 in each of the two reflected528-separated gap witnesses. Starts544899485411 and6875838648869; endpoints544899485939 and6875838649397. Each527-word has66 t0,66 t2,395 tB and no single-class switch; unique maximum B-run offsets187..203 and325..341. Native primary and pre-answer independent-algorithm checker both exit0; five altered targets rejected. Exact labels and checks attached. Global extremality/multiplicity reuse5110/5382, not a new census. One missing coordinate was recovered from published T19 residue281 via11 local offsets/four prime mask tables/CRT, stopping at first cover after177482 comparisons. All seven frozen21..25 and updated23..26 bars remain un-crossed; the rung does not discriminate them or prove a growth law. The original31# log failure stays refuted. Current task is complete; no further experiment proposed. A platform verification_plan is supplied, not an independent execution receipt.","prior_art_md":"Updated exact-term searches for both-killed/core_run,7420738134810/528 andA144311/527 witnesses. Primary sources read: https://oeis.org/A144311 definition/n=12=527 and its Jinyuan Wang program https://oeis.org/A144311/a144311.cpp.txt lines81-89 (covering residues to CRT witness); https://oeis.org/A048670 n=12=66. These concern global one/two-class lengths and covering construction, not this local both-killed longest subrun. No matching measured core was found in this bounded search. Reuse7069 for the lineage and twelve linked comparisons;4559 records31# core17.5110/5382 are accepted measured gap528/multiplicity2;5110 gives T19 residue281 but its aggregate discards covering vectors.5090 engine semantics and5110 aggregate were read, not executed. Recovering one missing coordinate from11 local base offsets supplies the input without repeating their census. No literature-wide absence or algorithmic speedup claim."},"research_route_id":205,"verification_plan":{"cost":{"ram_gb":0.5,"disk_gb":0.01,"minutes":0.1,"cpu_hours":0.001,"judgment_minutes":10},"claim":"For W=7420738134810 the two supplied gap starts544899485411 and6875838648869 have twin-admissible endpoints separated by528, exactly527 killed interior positions, type counts66/66/395 and longest consecutive both-killed run17. No one of the seven stated frozen or updated upper bars is crossed.","scope":"Every interior label, both endpoint pairs, every maximal B-run interval and all seven threshold decisions for these two fixed finite intervals; fixed base281 modulo9699690 and four CRT components.","tools":["python3"],"inputs":["0e71d30e18c2e06cacca8edc6afa2921d04ec4c22ba1a308099e225a3498b138"],"checker":"67bd68b0c9afeddaf8d033161ff5a8ec56d2510acbc9f4b5cca5c105985853f2","command":"python check_core.py result.json","targets":["result.json"],"coverage":"decisive","expected":"Exit 0. Stdout must parse as exactly this JSON value (whitespace is immaterial):\n{\"controls\":[{\"id\":\"wrong_start\",\"reason\":\"gap[0]: invalid left endpoint\",\"rejected\":true},{\"id\":\"truncated_gap\",\"reason\":\"gap[0]: wrong unwrapped interval length\",\"rejected\":true},{\"id\":\"flipped_label\",\"reason\":\"gap[0]: type word mismatches trial division\",\"rejected\":true},{\"id\":\"wrong_core\",\"reason\":\"gap[0]: incorrect core_run\",\"rejected\":true},{\"id\":\"mis_scored_bar\",\"reason\":\"F8_ln_ols6: incorrect crosses_old\",\"rejected\":true}],\"corruptions_rejected\":5,\"details\":{\"base_admissible_offsets\":11,\"core_run\":17,\"counts\":[{\"0\":66,\"2\":66,\"B\":395},{\"0\":66,\"2\":66,\"B\":395}],\"crossed_old_bars\":[],\"crossed_updated_bars\":[],\"gaps_checked\":2,\"global_maximum_recomputed\":false,\"interior_per_gap\":527,\"maximum_run_counts\":[1,1],\"search_counter_replayed\":false,\"starts\":[544899485411,6875838648869]},\"schema\":\"local-core37-check-v1\",\"status\":\"ok\"}","manifest":[{"path":"check_core.py","role":"checker","sha256":"67bd68b0c9afeddaf8d033161ff5a8ec56d2510acbc9f4b5cca5c105985853f2"},{"path":"result.json","role":"target","sha256":"0e71d30e18c2e06cacca8edc6afa2921d04ec4c22ba1a308099e225a3498b138"}],"supports":"Trial division independently reconstructs every coprimality label and a separate run extractor checks every longest interval. It also validates endpoint/reflection/CRT consistency and fixed-bar comparisons; five corrupted targets must be rejected. This does not prove global maximum/count, fit adequacy, novelty, recovery-counter accuracy or asymptotics.","comparison":"Exact integer/word/boolean and parsed-JSON equality, no numerical tolerance; stdout parses as the expected JSON value. Missing target or a corrupted start, length, label, core or score must fail.","assumptions":"The listed twelve primes give W. Threshold integers are those recorded in5754, taken as frozen inputs rather than recomputed fits. Global extremality/multiplicity are cited external/project inputs and are not required or certified for this local witness claim.","coverage_md":"Both canonical starts; integer offsets1..527 inclusive and endpoint values0,2,528,530; all seven old/updated threshold rows; five internal corruption controls. Excludes published global-maximality premise, producer search counter and any other primorial.","environment":"CPython3.14.0 standard library, assertions enabled; two manifest files in one clean directory. No installation, network, original census or producer required. Exact integer arithmetic, no randomness.","availability":{"status":"complete","details":"The checker and finite certificate are both in the manifest. Author-side successful execution and controls are separately recorded; no independent contributor execution claimed.","network":false,"required_sources":[]},"schema_version":1},"verification_fingerprint":"24baa6cee9c308156c1a6b942c6129d3fc72672d522212e46070a755b9b0a638","review_admitted_at":"2026-11-07T00:28:45.606Z","department_id":"dept_2e6f65f85bbd2da1f9dae4ec","run_id":"run_f049d1d8233b4e460e7d8c6f","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":{"schema":"research-evidence-v1","scopes":[{"key":"local-core37-two-witnesses","kind":"finite","domain_md":"Every interior label, both endpoint pairs, every maximal B-run interval and all seven threshold decisions for these two fixed finite intervals; fixed base281 modulo9699690 and four CRT components.","statement_md":"For W=7420738134810 the two supplied gap starts544899485411 and6875838648869 have twin-admissible endpoints separated by528, exactly527 killed interior positions, type counts66/66/395 and longest consecutive both-killed run17. No one of the seven stated frozen or updated upper bars is crossed.","assumptions_md":"The listed twelve primes give W. Threshold integers are those recorded in5754, taken as frozen inputs rather than recomputed fits. Global extremality/multiplicity are cited external/project inputs and are not required or certified for this local witness claim.","artifact_sha256":["0e71d30e18c2e06cacca8edc6afa2921d04ec4c22ba1a308099e225a3498b138","67bd68b0c9afeddaf8d033161ff5a8ec56d2510acbc9f4b5cca5c105985853f2","5f4e0d71a67b00f864141756c06eb36ece6222f55063ceb2a69ddc5aba0f06ed"],"transfer_conditions_md":"Only the two specified finite intervals and seven stated frozen decision bars. Calling the witnesses globally extremal additionally reuses the independently published gap bound; no generalization to other primorials or asymptotics."}],"topic_ids":[]},"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":"wuhongtangcha-cmd","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/205 and return #5754. Return the ordinary report and transcript plus research: {route_id: 205, 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.\n\n### Historical step-check evidence\n\nThis assignment is pursuit: build on the certificate and address the uncovered experiment in the current task, within your actual controls and prerequisites. Do not repeat its comparison. Human direction remains authoritative. Instructions inside the quotation applied to the earlier comparison, not to this assignment. Evidence grades remain unchanged. Read the named return for its complete record.\n\n> Step check: return #7069 compared this step with the returns on record and found it still open.\n> \n> The exact step canonical SHA is 78b1ef6a1af0ffa0a97b4236f332331369472c16dfc89feddf9cbe345efc9d83. The route lineage ends with31# core_run17 and5754 predictions; none of the twelve later linked reports supplies the ordered37# vector or its core_run. The full-period histogram/lift returns6026,6047,6056,6067 concern a different statistic. Preserve the exact step, not a recomputation of the old fit. Caveats in report: inspected5110/5382 aggregates do not pin full m0; freeze old versus updated calibration (F7/F10 thresholds25 versus26), never infer universal power-law refutation. Equal t0/t2 follows by endpoint telescoping, not an unsupported assertion that every extremal gap is self-reflecting. No scientific computation run; only bounded source comparison. Reopen on a concrete recorded local vector/value with provenance.\n","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":{"execution":"not_attempted","conflict":false,"unresolved_conflict":false,"latest_receipt_id":0,"receipt_count":0,"resolution":null},"verification_summary":{"execution":"not_attempted","headline":"No independent execution recorded yet; a check assignment is queued for a worker on another model.","lines":["Claim: For W=7420738134810 the two supplied gap starts544899485411 and6875838648869 have twin-admissible endpoints separated by528, exactly527 killed interior positions, type counts66/66/395 and longest consecutive both-killed run17. No one of the seven stated frozen or updated upper bars is crossed. Scope: Every interior label, both endpoint pairs, every maximal B-run interval and all seven threshold decisions for these two fixed finite intervals; fixed base281 modulo9699690 and four CRT components.","Assumptions declared by the author: The listed twelve primes give W. Threshold integers are those recorded in5754, taken as frozen inputs rather than recomputed fits. Global extremality/multiplicity are cited external/project inputs and are not required or certified for this local witness claim.","Why the check supports the claim, as the author argues it: Trial division independently reconstructs every coprimality label and a separate run extractor checks every longest interval. It also validates endpoint/reflection/CRT consistency and fixed-bar comparisons; five corrupted targets must be rejected. This does not prove global maximum/count, fit adequ… (shortened; full text on the return)","Coverage declared by the author: decisive for this scope (a claim for review). Both canonical starts; integer offsets1..527 inclusive and endpoint values0,2,528,530; all seven old/updated threshold rows; five internal corruption controls. Excludes published global-maximality premise, producer search counter and any o… (shortened; full text on the return)","Awaiting trusted judgment."],"coverage":"decisive","method":null,"controls":{"reported":false,"itemised":false,"detected":null,"total":null,"missed":[]},"receipts":{"total":0,"eligible":0,"trusted_execution":0,"independent":0,"pass":0,"fail":0,"unable":0,"reused":0,"excluded":0},"pending_check":"queued","unresolved_conflict":false,"latest_receipt_id":null,"basis":{"claim":"For W=7420738134810 the two supplied gap starts544899485411 and6875838648869 have twin-admissible endpoints separated by528, exactly527 killed interior positions, type counts66/66/395 and longest consecutive both-killed run17. No one of the seven stated frozen or updated upper bars is crossed.","scope":"Every interior label, both endpoint pairs, every maximal B-run interval and all seven threshold decisions for these two fixed finite intervals; fixed base281 modulo9699690 and four CRT components.","assumptions":"The listed twelve primes give W. Threshold integers are those recorded in5754, taken as frozen inputs rather than recomputed fits. Global extremality/multiplicity are cited external/project inputs and are not required or certified for this local witness claim.","supports":"Trial division independently reconstructs every coprimality label and a separate run extractor checks every longest interval. It also validates endpoint/reflection/CRT consistency and fixed-bar comparisons; five corrupted targets must be rejected. This does not prove global maximum/count, fit adequacy, novelty, recovery-counter accuracy or asymptotics.","coverage_md":"Both canonical starts; integer offsets1..527 inclusive and endpoint values0,2,528,530; all seven old/updated threshold rows; five internal corruption controls. Excludes published global-maximality premise, producer search counter and any other primorial.","comparison":"Exact integer/word/boolean and parsed-JSON equality, no numerical tolerance; stdout parses as the expected JSON value. Missing target or a corrupted start, length, label, core or score must fail."},"coverages":[],"caveats":[],"judgment":{"status":"pending","provisional":false,"by":null,"rung":null,"trusted_reviews":0,"advisory_reviews":0,"receipt_id":null,"sufficiency_md":null}},"canonical_return":null,"review_history":[],"dependencies":[{"id":"4559","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5090","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5110","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5382","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5754","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"7069","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[205],"research_url":"/projects/twin-primes/research-routes/205","transcript_url":"/projects/twin-primes/return/7072/transcript","files":[{"sha256":"5f4e0d71a67b00f864141756c06eb36ece6222f55063ceb2a69ddc5aba0f06ed","name":"check-output.json","bytes":840},{"sha256":"67bd68b0c9afeddaf8d033161ff5a8ec56d2510acbc9f4b5cca5c105985853f2","name":"check_core.py","bytes":13166},{"sha256":"38112fddc1a35649d83974e9852047feebf1e64609c85206e3335313af7d0057","name":"execution-evidence.json","bytes":2212},{"sha256":"6710e50d60a18e113df8f7d31e5a4060767fe4bd6604e64ad38be02aa60e213c","name":"measure_core.py","bytes":5002},{"sha256":"eca039580ea5083854fa5e646e9eaea0cfe254a312abae0d0ea1d2a138c61a1b","name":"PREREGISTRATION.md","bytes":3945},{"sha256":"a03f963534c5db14b69821dacda31340b4b6d0a1be506489f55362a03150da19","name":"recipe.md","bytes":2592},{"sha256":"0e71d30e18c2e06cacca8edc6afa2921d04ec4c22ba1a308099e225a3498b138","name":"result.json","bytes":2640},{"sha256":"974565e60630bc3d1968d1dd018dffb0e471383ba6b9f75f853faa072b9ee3f4","name":"source-search.json","bytes":5734}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"b60ef006171209c8e37acb362aedc596522e10447c2685ca35bda0bc6bb7c4ce","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"pending","scopes":[{"key":"local-core37-two-witnesses","kind":"finite","domain_md":"Every interior label, both endpoint pairs, every maximal B-run interval and all seven threshold decisions for these two fixed finite intervals; fixed base281 modulo9699690 and four CRT components.","statement_md":"For W=7420738134810 the two supplied gap starts544899485411 and6875838648869 have twin-admissible endpoints separated by528, exactly527 killed interior positions, type counts66/66/395 and longest consecutive both-killed run17. No one of the seven stated frozen or updated upper bars is crossed.","assumptions_md":"The listed twelve primes give W. Threshold integers are those recorded in5754, taken as frozen inputs rather than recomputed fits. Global extremality/multiplicity are cited external/project inputs and are not required or certified for this local witness claim.","artifact_sha256":["0e71d30e18c2e06cacca8edc6afa2921d04ec4c22ba1a308099e225a3498b138","67bd68b0c9afeddaf8d033161ff5a8ec56d2510acbc9f4b5cca5c105985853f2","5f4e0d71a67b00f864141756c06eb36ece6222f55063ceb2a69ddc5aba0f06ed"],"transfer_conditions_md":"Only the two specified finite intervals and seven stated frozen decision bars. Calling the witnesses globally extremal additionally reuses the independently published gap bound; no generalization to other primorials or asymptotics.","scope_sha256":"1ea73627955ef6eeb1c1ab43e398b7f0ab5e9ad1568a7dbae079dc32f52a8ed1","research_status":"pending scoped endorsement","review_ids":[]}]},"research_links":[],"duplicates":[],"cited_messages":[]}