{"id":1570,"job_id":2978,"problem_id":1,"lane_id":null,"type":"explore","user_id":34,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #2978 — Triage of route 151: the record stops one position short of R = 310, and the next experiment is honestly priced at ~8× the assignment's ceiling\n\nAttempt `00832421a76775c97e07b5f3ff0cd980` · session `4ba3b08fd3f9de9293497a02` (assignment 2, general\nmode, effort `max`) · run `bf10-b5d01219af2aa43c` · route **151** rev 1 (`proposed`) · protocol\n`department-v2.research-2026-09-22.1`.\n\n**Disclosure.** Route 151 is the department's registration of return **#1569**, which this same session\nfiled as a linked direction on route 149 (job #2958's finished package). The department assigned the\ntriage here; the report states the authorship rather than hiding it, and everything below is either a\nre-check of that return's arithmetic or a measurement the return did not make. Read for this job:\n`GET /research-routes/151` (11.4 KB), the return #1569 payload as served (the local package is the same\nbytes), the job #2958 survey `prefix-vs-run.json`, and an online prior-art pass.\n\n## 1. What the triage adds: the record's own supremum\n\nThe route's next experiment asks for a new ascent run at R = 310. Before paying for a search, the\ncheapest possible question is whether the **record already decides it** — a witness whose covered run is\nL positions translates to a certificate at prefix L, so a recorded run of 310 would lift the bound to\n`A ≥ 6·310+5 = 1865` at zero search cost.\n\n`run-supremacy.py` measures that over every witness certificate the corpus recorded — the same 22-row\nsurvey served by return #1569, re-read as `witness-runs.json`:\n\n| quantity | value |\n|---|---|\n| rows (all usable, none without run values) | 22 |\n| **supremum covered run** | **309** — exactly one row reaches it |\n| that row | rung 307, prefix 307, covering `[-2,306]` = return #1554's certificate |\n| second best | 291 (rung 285), then 201, 201, 186 — a cliff |\n| rows reaching 310 | **none** |\n| free bound from the record | `A ≥ 6·309+5 = ` **1859** |\n| bound if R = 310 were coverable | `A ≥ 6·310+5 = ` **1865** |\n\n**So the route's proposed experiment is not redundant with the record, and its target is exactly one\nposition beyond the best run the record holds.** That is the triage's decision: continued investment is\njustified, and the acceptance test is a covering of `[0,309]` — one translate step past `[0,308]`.\n\n## 2. What the triage corrects in the route's own next step\n\n1. **The instrument is right, the seed claim is not evidenced.** The route proposes the early-abort\n   build with acceptance on the covered run — correct, and this triage's whole measurement supports the\n   covered-run reading. But its clause *\"seeded from the R = 307 certificate rather than from scratch\"*\n   is an unevidenced cost assumption: a certificate is a **witness**, and nothing in the record shows it\n   is a starting point for the next rung's search. It must be dropped or tested, not priced in.\n2. **The price is measured, and it is ~8× the ceiling.** The R = 307 witness was in hand at\n   t = 14,454 s of the rung on 8 threads (~32 CPU h) against the assignment's 4 CPU h ceiling, so the\n   cheap half at R = 310 does not fit an assignment even in its cheapest form. `budget_hours` below is\n   the schema cap 4.0 with the measured requirement stated in the method — as in #1569.\n3. **The reading is the run, not the printed prefix.** Of the 22 recorded witnesses, **15 overshoot\n   their printed rung** (below-zero slack 0..5, mean 1.41). The decidable quantity is always the\n   covered run; the route's price line had been read off one translate's prefix.\n\n## 3. Prior art (updated online search, 2026-09-24)\n\nThe route's record was re-read and a fresh pass was run on the two things it could not have had in\nSeptember. Nothing changed the gap: **OEIS A144311 is still 22 terms (a(22) = 1709, to p = 79)**;\n**A288815**, the paired h2 sequence, is still **21 terms (to p = 73)** after its April-2026 revision;\nZiller's computational papers (arXiv:1903.11973, arXiv:1611.03310) are one-class work and do not touch\nthe two-class object at 83#. The **Nguyen preprint** (DOI 10.20944/preprints202608.1299.v1) remains the\none source that could bound the refutation side, and the gap is now better located but not closed: the\nsearch index surfaces its page, a direct download route and a ResearchGate mirror, and **all three\nanswer HTTP 403 from this machine** (preprints.org re-probed 2026-09-24). Closing it needs a browser,\nnot compute. Full record in `prior_art_md.txt`.\n\n## 4. The bounded next step this triage recommends\n\n**Question.** Does a covering of `[0,309]` exist on 83# — i.e. is there a certificate whose covered run\nis ≥ 310 positions, one more than the record's best?\n\n**Method.** Run the early-abort build's witness search at the next rung with the acceptance test stated\non the **covered run length** (`≥ 310`, i.e. beating the record's 309 by one position), stopping at the\nfirst witness; re-verify the covering with `verify-R307-independent.py` re-pointed at the new\ncertificate; report the wall/CPU cost and the run lengths seen. Do **not** assume a seed from the R = 307\ncertificate helps. If the run is aborted, record it as a measurement, never as a refutation.\n\n**Success.** An independently verified covering of `[0,309]`: R = 310 is COVERABLE, the banked bound\nmoves 1859 → **1865** under the route's own map, and the first open decision moves up one rung.\n\n**Failure.** No witness with a covered run ≥ 310 within the priced budget: R = 310 stays open, recorded\nas a measurement of a truncated run — `aborted` is not `exhausted`.\n\n**Budget.** `budget_hours` 4.0 (schema cap) with the measured requirement ~32+ CPU h stated above.\n\n## 5. Controls, and how to reproduce\n\n* `verify-run-supremacy.py` re-derives the supremum from the raw rows, offline: **PASS**, `differences`\n  `[]`, with three controls detected — a run of exactly the target fires, a run one position short does\n  not, and a row without run values is refused rather than read as zero.\n* `run-supremacy.py`'s own controls: the top row must be rung 307 / prefix 307 / `[-2,306]`; a synthetic\n  311-position row must be detected as deciding the target; the exclusion rule is exercised on a\n  synthetic row.\n\n```\npython3 run-supremacy.py                                  # writes run-supremacy.json\npython3 verify-run-supremacy.py --input witness-runs.json --target 310\n```\n\nBoth are deterministic, need no network, and write their JSON with `newline=\"\\n\"`.\n\n## 6. Calibration and what is not claimed\n\n**Evidence grade: `measured`.** Every run length in the input survey is a reading of a recorded\nwitness (the corpus's own certificate files, with the recomputed prefix as their instrument control),\nand the supremum is a count over those readings. The checker re-derives the count from the raw rows and\nits controls fire, but no step here is an arithmetic identity re-proved from the definition -- which is\nwhy this return is graded `measured` and not `verified`.\n\nThe triage does not decide R = 310 — it shows only that the record cannot. It does not re-verify the\ncertificate (return #1569 did, and this triage's input is the same survey); no exactness, no upper\nbound, no asymptotics, nothing about twin-prime infinitude. The route's 1859 bound stands as #1569 left\nit. The triage of a route this session authored is not a review and carries no verdict weight: the\nevidence grades of #1569 are untouched, and a trusted reviewer remains the only path to a verdict.\n\n## 7. Outstanding work, usage, and the queue\n\n* `outstanding` before this return: **issued 1 / settled 1 / []** (job #2962 settled by return #1567);\n  job #2958's package is filed as return #1569, and its superseded attempt stays cancelled on the bf9\n  run's ledger. Nothing else is open in either run.\n* **This turn is still OPEN at filing time.** The harness database holds only the person's assignment\n  message and the thread header for seq 898+, because the assistant rows of an open turn are not yet\n  written (measured: a read-only query returns exactly that one row). The transcript attached to this\n  return is therefore the accurate open-turn cut -- header plus the assignment message -- and **all of\n  this turn's usage is recorded as pending**, never estimated and never counted twice. The closed cut\n  is to be attached on the next invocation (`POST /return/<id>/transcript` / `sahtool correct`), the\n  same path return #2958's package recorded for itself.\n* **408 returns wait for a verdict**, the oldest since 2026-09-13, and #1569 is now one of them. The\n  project queue is 405; verdicts need a trusted reviewer or a person granted trust — not this session.\n","patch":null,"cpu_hours":0.1,"hashes":{"route151.txt":"78b6aa7a67b272d10743577fd30f98aa2e4decb46c233fee7fb3a60c5dc0a480","report-2978.md":"e49e6818f131e3137cce223d10bdad96199f80771b30ecc19a2a22cd9524690c","evidence_md.txt":"fbbc8b86e2b3efe154171c3c0b77ccb545adbf67c33fbbec9c43ca840b4152e8","boundary-2978.py":"10172ff6ec8d203fb964ad61ea226c9143a63687be57d84489a5721f1ee7abf5","prior_art_md.txt":"5fcc1f88873a17248aa37f7be43d758d56e364066859bf1cfc2d41b0e4b77dbf","run-supremacy.py":"e450433e91e742a9ee41a0a9fa5f978f2ac7fde67e4c09e585280f8fd6f62cfc","witness-runs.json":"c9d1a67d85f5497521dc888353f899e342fdbf4dbbe896fd457b3a13264f9bd1","boundary-2978.json":"b74a367a596d3c7c399995d9939a9d097ea7ca1774699654b782611a19291774","run-supremacy.json":"ce2316f6f5a8d0c7b052f7a4485b7a0dd9d0f1fe1e8ebd2963c5501e2391cd43","build-payload-2978.py":"ce7c73ac1ce475672120a777e4b87bf96e58108b7508231f001b0ee784d584e8","verify-run-supremacy.py":"1ccdfb819a3bd1265d795b36b51abdf387cbfd614ca896493ee7db9cb035076d","verify-run-supremacy.json":"6c6a4093170c135320298070a8a00b82095e89a1c7e854f28b4113b8db9208ab","transcript-2978-turn.jsonl":"52c9de604e95a7c97f8793cf2ea527ef074e56bf1b1e898ee083a61a92e95d57","10172ff6ec8d203fb964ad61ea226c9143a63687be57d84489a5721f1ee7abf5":"boundary-2978.py","1ccdfb819a3bd1265d795b36b51abdf387cbfd614ca896493ee7db9cb035076d":"verify-run-supremacy.py","52c9de604e95a7c97f8793cf2ea527ef074e56bf1b1e898ee083a61a92e95d57":"transcript-2978-turn.jsonl","5fcc1f88873a17248aa37f7be43d758d56e364066859bf1cfc2d41b0e4b77dbf":"prior_art_md.txt","6c6a4093170c135320298070a8a00b82095e89a1c7e854f28b4113b8db9208ab":"verify-run-supremacy.json","78b6aa7a67b272d10743577fd30f98aa2e4decb46c233fee7fb3a60c5dc0a480":"route151.txt","b74a367a596d3c7c399995d9939a9d097ea7ca1774699654b782611a19291774":"boundary-2978.json","c9d1a67d85f5497521dc888353f899e342fdbf4dbbe896fd457b3a13264f9bd1":"witness-runs.json","ce2316f6f5a8d0c7b052f7a4485b7a0dd9d0f1fe1e8ebd2963c5501e2391cd43":"run-supremacy.json","ce7c73ac1ce475672120a777e4b87bf96e58108b7508231f001b0ee784d584e8":"build-payload-2978.py","e450433e91e742a9ee41a0a9fa5f978f2ac7fde67e4c09e585280f8fd6f62cfc":"run-supremacy.py","e49e6818f131e3137cce223d10bdad96199f80771b30ecc19a2a22cd9524690c":"report-2978.md","fbbc8b86e2b3efe154171c3c0b77ccb545adbf67c33fbbec9c43ca840b4152e8":"evidence_md.txt"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-09-24T01:04:54.644Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1569,1554,1507],"messages":[]},"tokens":{"log":"custom","input":282248,"models":{"deepseek-v4-flash":45453},"output":45453,"source":"custom-jsonl","entries":1,"cache_read":11206656,"cache_write":0,"observed_models":["deepseek-v4-flash"]},"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":"max","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-09-24T01:21:07.410Z","file_notes":null,"research":{"outcome":"promising","route_id":151,"next_step":{"method":"1. Run the early-abort build's witness search at the next rung with the acceptance test stated on the covered run length (>= 310), stopping at the first witness; the rung's printed prefix is not the decidable quantity. 2. Re-verify the covering with verify-R307-independent.py re-pointed at the new certificate. 3. Report the wall/CPU cost and the run lengths seen. Do NOT price in a seed from the R = 307 certificate: a witness is not a demonstrated starting point for the next rung's search, and that clause of the route's next step is an unevidenced cost assumption. If the run is aborted, record a measurement of a truncated run, never a refutation: `aborted` is not `exhausted`. The measured requirement is ~32+ CPU h (the R = 307 witness was in hand at t = 14,454 s of the rung on 8 threads), so budget_hours below is the schema cap, not the measured cost.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":4},"failure":"No witness with a covered run >= 310 within the priced budget: R = 310 stays open, recorded as a measurement of a truncated run and not as a refutation.","success":"An independently verified covering of [0,309]: R = 310 is COVERABLE, the banked bound moves 1859 -> 1865 under the route's own map A = 6L + 5, and the first open decision moves up one rung.","question":"Does a covering of [0,309] exist on 83# -- is there a certificate whose COVERED RUN is at least 310 positions, one more than the best run the record holds (309)?","budget_hours":4,"required_tools":["python","cc"],"required_sources":[]},"depends_on":[1569,1554],"evidence_md":"Triage of route 151 (= return #1569, authored by THIS session; the department assigned the triage and\nthat fact is stated rather than hidden). The triage's contribution is the cheapest question the route\nnever asked: **does the RECORD already decide R = 310?** A witness whose covered run is L positions\ntranslates to a certificate at prefix L (its covered set moved to the origin), so a recorded run of 310\nwould decide R = 310 and lift the bound to 6*310+5 = 1865 with no search at all.\n\nMeasured over every witness certificate the corpus recorded -- the 22-row survey served by return #1569\n(`run-supremacy.json`, independently re-derived by `verify-run-supremacy.py`: PASS, 3 controls):\n\n* **supremum run 309**, achieved by exactly ONE row: the return #1554 certificate at rung 307, covering\n  `[-2,306]` -- the record's best is the certificate already in hand;\n* **second best 291** (the rung-285 witness), then 201, 201, 186 -- a cliff, so the supremum is not an\n  artefact of one odd row;\n* **rows reaching 310: NONE.** So the route's proposed experiment is **not redundant** with the record,\n  and its target is exactly **one position beyond the best run the record holds**: the record's free\n  bound is A >= 6*309+5 = **1859**, the target bound is **1865**.\n\nPrice, unchanged by this triage: the R = 307 witness was in hand at t = 14,454 s of the rung (8 threads\n=> ~32 CPU h) against the assignment's 4 CPU h ceiling, so the route's next step is the right\nINSTRUMENT (early-abort build, acceptance stated on the covered run) but its `seeded from the R = 307\ncertificate` clause is an **unevidenced cost assumption** -- a witness is not a starting point for the\nnext rung's search -- and belongs dropped or tested, not priced in.\n\nTwo further readings this triage fixes on the record: the route's price line was read off one\ntranslate's printed prefix, while the decidable quantity is the covered run; and the same 22-row\nmeasurement is what shows 15 of 22 witnesses overshoot their printed rung, so the correction is not a\none-off.\n\nWhat the triage does NOT change: the certificate's arithmetic (already independently verified by\nreturn #1569), the answered R = 308 decision, or the 1859 banked bound. **R = 310 remains open** -- this\ntriage shows only that the record cannot settle it.","prior_art_md":"Online search 2026-09-24 (this triage), run after re-reading route 151's own record; nothing in that\nrecord is contradicted.\n\nQueries: [\"Jacobsthal function primorial computation 2026 paired progressions two residue classes new\nresults\"]; [\"A144311 Jacobsthal OEIS terms twin primes extended\"]; [\"A288815 OEIS twin Jacobsthal paired\nprogression terms 2026\"]; [\"Nguyen 2026 Finite-Window Noncovering on Primorial Wheels CRT bounds abstract\ntwo residue classes\"].\n\nSources inspected, and what each gives:\n* **OEIS A144311** (corroborated through the search index, matching the route's live read of\n  2026-09-23): **22 terms, a(22) = 1709**, to p = 79. No extension found.\n* **OEIS A288815**, the paired h2 sequence of Ziller-Morack: **21 terms, to p = 73**; the corpus's own\n  `covering-dive.md` records its internal revision (#19, Apr 2026) as *still 21 terms, hard, more*. So\n  the published two-class computation still stops exactly one rank below 83#.\n* Ziller, arXiv:1903.11973 (new computational results on Jacobsthal's conjecture) and arXiv:1611.03310\n  (algorithmic concepts for h(k) of primorials): **one-class** computations and the conjecture's\n  counterexample; neither extends the two-class object.\n* Nguyen, *Finite-Window Noncovering on Primorial Wheels*, DOI 10.20944/preprints202608.1299.v1: the\n  **access gap persists and is now better located** -- the search index surfaces the manuscript page, a\n  direct download route and a ResearchGate mirror (2026-08-22), and **all three answer HTTP 403 from\n  this machine** (preprints.org re-probed 2026-09-24). Its subject remains this route's refutation\n  side, so the one prior-art item that could bound or retire the route is still unread; closing it\n  needs a browser, not compute.\n\nExact remaining gap: no published work extends the paired two-class computation past p = 73, no\ntwo-class upper bound of any exponent is in print, and OEIS stops at 22 terms while the route's target\n(A144311(23), 83#) is one rank above the published anchor. Within the corpus, the record's own best\ncovered run stops one position short of R = 310 (309 vs 310). No match found is not novelty: the\ncovered-run measurement rule is this project's own device, measured here, not published."},"research_route_id":151,"verification_plan":{"cost":{"ram_gb":1,"disk_gb":1,"minutes":1,"cpu_hours":0.01,"judgment_minutes":10},"claim":"Over the 22 witness certificates the corpus recorded (the survey served by return #1569), the longest COVERED RUN is 309 positions, achieved by exactly one row -- the return #1554 certificate at rung 307, covering [-2,306] -- and no row reaches 310. Because a run of L positions translates to a certificate at prefix L, the record's own best translate covers [0,308] (A >= 6*309+5 = 1859) and stops one position short of the target: no recorded witness decides R = 310, and deciding it would lift the bound to 6*310+5 = 1865.","scope":"the 22 rows of the attached survey, which is every witness certificate the corpus recorded at the time the survey was taken. Nothing outside those rows is examined, no search is run, and no statement is made about witness certificates that do not exist in the record.","tools":["python3"],"inputs":["c9d1a67d85f5497521dc888353f899e342fdbf4dbbe896fd457b3a13264f9bd1","e450433e91e742a9ee41a0a9fa5f978f2ac7fde67e4c09e585280f8fd6f62cfc"],"checker":"1ccdfb819a3bd1265d795b36b51abdf387cbfd614ca896493ee7db9cb035076d","command":"python3 verify-run-supremacy.py --input witness-runs.json --target 310","targets":["witness-runs.json","run-supremacy.json"],"coverage":"decisive","expected":"exit 0, `verdict` PASS, `differences` empty, `controls_all_detected` true: 22 usable rows, supremum run 309 on the rung-307 row with run_lo -2 / run_hi 306, second run 291, zero rows reaching the target, free bound 1859. Exit 3 if a control is not detected; exit 2 on any other difference.","manifest":[{"path":"verify-run-supremacy.py","role":"checker","sha256":"1ccdfb819a3bd1265d795b36b51abdf387cbfd614ca896493ee7db9cb035076d"},{"path":"witness-runs.json","role":"target","sha256":"c9d1a67d85f5497521dc888353f899e342fdbf4dbbe896fd457b3a13264f9bd1"},{"path":"run-supremacy.json","role":"target","sha256":"ce2316f6f5a8d0c7b052f7a4485b7a0dd9d0f1fe1e8ebd2963c5501e2391cd43"},{"path":"run-supremacy.py","role":"input","sha256":"e450433e91e742a9ee41a0a9fa5f978f2ac7fde67e4c09e585280f8fd6f62cfc"}],"supports":"establishes that the RECORD cannot decide R = 310, which is what makes the proposed ascent run non-redundant, and that the decidable quantity is the covered run rather than the printed prefix. It does NOT establish anything about R = 310 itself: a covering of [0,309] may exist and simply not be in the record.","comparison":"exact integer equality of the supremal run length (309), of the second (291) and of the top row's endpoints (-2, 306); set emptiness for rows reaching 310. No tolerance is used.","assumptions":"a witness's covered run translates freely to the origin (a_p ranges over all residues mod p, so translating every class translates the covered set), and the route's own map A = 6R+5 is used for the bound -- the same map the route and return #1569 use. The survey's run values are readings of recorded certificates, which is why this return is graded `measured`.","coverage_md":"all 22 recorded witness rows, each with its run bounds; the supremum, the runner-up, the cliff below it and the count of rows reaching the target. Excluded: any run not in the record, the mathematical content of the certificates, and the price of a future search.","environment":"python3 (3.14.6), standard library only, no network and no credential: the checker reads the attached survey and nothing else.","availability":{"status":"complete","details":"the checker, the survey it reads and the measurement are all attached; the check needs only python3 and runs in under a second","network":false,"required_sources":[]},"schema_version":1},"verification_fingerprint":"96488f18e833bb6f064f4d9743070bb651f7b1d64f302dbb07a7af04cb355f07","review_admitted_at":null,"department_id":"dept_bd08e49ed9621cfd852f9b04","run_id":"run_75ebbb0ccb02ffb90568766e","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"maxime-fleury","job_brief":"Search online for existing attempts, results, tables and datasets before testing feasibility. Reuse the recorded search and inspect the closest sources and weakest assumption. Use published numbers with citations; do not reproduce them in triage. Seek the smallest experiment on the uncovered step. Recommend promising only with specific evidence and a bounded next step; do not claim the route is proved. Map the assumptions of any borrowed method onto this problem.\n\nRead GET <project base>/research-routes/151 and return #1569. Return the ordinary report and transcript plus research: {route_id: 151, outcome: \"promising|progress|blocked|inconclusive|known|result\", 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>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <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":{"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.","lines":["Claim: Over the 22 witness certificates the corpus recorded (the survey served by return #1569), the longest COVERED RUN is 309 positions, achieved by exactly one row -- the return #1554 certificate at rung 307, covering [-2,306] -- and no row reaches 310. Because a run of L positions translates to a cert… (shortened; full text on the return) Scope: the 22 rows of the attached survey, which is every witness certificate the corpus recorded at the time the survey was taken. Nothing outside those rows is examined, no search is run, and no statement… (shortened; full text on the return)","Assumptions declared by the author: a witness's covered run translates freely to the origin (a_p ranges over all residues mod p, so translating every class translates the covered set), and the route's own map A = 6R+5 is used for the bound -- the same map the route and return #1569 use. The survey's run values are readings of recorde… (shortened; full text on the return)","Why the check supports the claim, as the author argues it: establishes that the RECORD cannot decide R = 310, which is what makes the proposed ascent run non-redundant, and that the decidable quantity is the covered run rather than the printed prefix. It does NOT establish anything about R = 310 itself: a covering of [0,309] may exist and simply not be in… (shortened; full text on the return)","Coverage declared by the author: decisive for this scope (a claim for review). all 22 recorded witness rows, each with its run bounds; the supremum, the runner-up, the cliff below it and the count of rows reaching the target. Excluded: any run not in the record, the mathematical content of the certificates, and the p… (shortened; full text on the return)","Recorded without a review request; elevate it to put it before reviewers."],"coverage":"decisive","method":null,"controls":{"reported":false,"itemised":false,"detected":null,"total":null,"missed":[]},"receipts":{"total":0,"independent":0,"pass":0,"fail":0,"unable":0,"reused":0,"excluded":0},"pending_check":null,"unresolved_conflict":false,"latest_receipt_id":null,"basis":{"claim":"Over the 22 witness certificates the corpus recorded (the survey served by return #1569), the longest COVERED RUN is 309 positions, achieved by exactly one row -- the return #1554 certificate at rung 307, covering [-2,306] -- and no row reaches 310. Because a run of L positions translates to a certificate at prefix L, the record's own best translate covers [0,308] (A >= 6*309+5 = 1859) and stops one position short of the target: no recorded witness decides R = 310, and deciding it would lift the bound to 6*310+5 = 1865.","scope":"the 22 rows of the attached survey, which is every witness certificate the corpus recorded at the time the survey was taken. Nothing outside those rows is examined, no search is run, and no statement is made about witness certificates that do not exist in the record.","assumptions":"a witness's covered run translates freely to the origin (a_p ranges over all residues mod p, so translating every class translates the covered set), and the route's own map A = 6R+5 is used for the bound -- the same map the route and return #1569 use. The survey's run values are readings of recorded certificates, which is why this return is graded `measured`.","supports":"establishes that the RECORD cannot decide R = 310, which is what makes the proposed ascent run non-redundant, and that the decidable quantity is the covered run rather than the printed prefix. It does NOT establish anything about R = 310 itself: a covering of [0,309] may exist and simply not be in the record.","coverage_md":"all 22 recorded witness rows, each with its run bounds; the supremum, the runner-up, the cliff below it and the count of rows reaching the target. Excluded: any run not in the record, the mathematical content of the certificates, and the price of a future search.","comparison":"exact integer equality of the supremal run length (309), of the second (291) and of the top row's endpoints (-2, 306); set emptiness for rows reaching 310. No tolerance is used."},"coverages":[],"caveats":[],"judgment":{"status":"recorded","provisional":false,"by":null,"rung":"recorded","trusted_reviews":0,"advisory_reviews":0,"receipt_id":null,"sufficiency_md":null}},"canonical_return":null,"review_history":[],"dependencies":[{"id":"1554","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1569","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/151","transcript_url":"/projects/twin-primes/return/1570/transcript","files":[{"sha256":"e49e6818f131e3137cce223d10bdad96199f80771b30ecc19a2a22cd9524690c","name":"report-2978.md","bytes":8671},{"sha256":"fbbc8b86e2b3efe154171c3c0b77ccb545adbf67c33fbbec9c43ca840b4152e8","name":"evidence_md.txt","bytes":2297},{"sha256":"5fcc1f88873a17248aa37f7be43d758d56e364066859bf1cfc2d41b0e4b77dbf","name":"prior_art_md.txt","bytes":2232},{"sha256":"e450433e91e742a9ee41a0a9fa5f978f2ac7fde67e4c09e585280f8fd6f62cfc","name":"run-supremacy.py","bytes":5573},{"sha256":"ce2316f6f5a8d0c7b052f7a4485b7a0dd9d0f1fe1e8ebd2963c5501e2391cd43","name":"run-supremacy.json","bytes":1918},{"sha256":"1ccdfb819a3bd1265d795b36b51abdf387cbfd614ca896493ee7db9cb035076d","name":"verify-run-supremacy.py","bytes":5470},{"sha256":"6c6a4093170c135320298070a8a00b82095e89a1c7e854f28b4113b8db9208ab","name":"verify-run-supremacy.json","bytes":775},{"sha256":"c9d1a67d85f5497521dc888353f899e342fdbf4dbbe896fd457b3a13264f9bd1","name":"prefix-vs-run.json","bytes":7079},{"sha256":"78b6aa7a67b272d10743577fd30f98aa2e4decb46c233fee7fb3a60c5dc0a480","name":"route151.txt","bytes":11433},{"sha256":"10172ff6ec8d203fb964ad61ea226c9143a63687be57d84489a5721f1ee7abf5","name":"boundary-2978.py","bytes":5086},{"sha256":"b74a367a596d3c7c399995d9939a9d097ea7ca1774699654b782611a19291774","name":"boundary-2978.json","bytes":1993},{"sha256":"52c9de604e95a7c97f8793cf2ea527ef074e56bf1b1e898ee083a61a92e95d57","name":"transcript-2978-turn.jsonl","bytes":255},{"sha256":"ce7c73ac1ce475672120a777e4b87bf96e58108b7508231f001b0ee784d584e8","name":"build-payload-2978.py","bytes":15093}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}