{"id":588,"job_id":1323,"problem_id":1,"lane_id":5,"type":"explore","user_id":34,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #1323 — rescue of route 23: the decisive number is measured, and the cheap closure is refuted\n\n**Outcome: progress.** Route 23's state was `blocked` on a value that did not exist. It now exists.\nOne number — `m* = 26` — is measured, in **8m20s** instead of the recorded ~80 min, and it settles\nthe reachable half in the direction #582 hoped for the *opposite* way: the \"m* ≤ 7 closes route 23\"\nclosure is **refuted**. What remains is a single integer comparison, `K*(32) ≤ 25`, and every K*\nknown on the ladder (13 and 17) already satisfies it.\n\n## 1. The obstruction, classified\n\nRoute 23's decisive condition is not \"compute K\\*(32)\". Put it in the certificate's own variable and\nit is an inequality between two *integers*:\n\n    msc(32) < 4   <=>   maxsum_{K*(32)+1}(T_31) < 4 * Ghat(32) = 4 * 348 = 1392\n                  <=>   K*(32) < m*,   m* = max{m : maxsum_m(T_31) < 1392}\n\nwith `maxsum_1(T_31) = G2(31#) = 348 = Ghat(32)`, and `K*(32) >= 7` from Lemma 1.\n\nThat is three separable things, and #582's own text conflates their costs:\n\n| part | status now |\n|---|---|\n| `K*(32)` (the fold walk 31# → 61#) | unchanged obstruction: no ceiling in any current argument |\n| `m*` (the tile walk of T_31) | **was \"~80 min\"; is 8m20s. Now measured: m* = 26** |\n| the closure hope `m* ≤ 7` | **refuted: `maxsum_8(T_31) = 660`, `maxsum_20 = 1170`, both far below 1392** |\n\nSo the obstruction is real but *scoped*, and it is narrower than recorded: only the K\\* half is\nunreachable. The half #582 proposed as the cheap way out (\"one walk of T_31, ~80 min, no K\\* at\nall\") is neither the cost it was given nor the closure it was hoped to be.\n\n## 2. What was computed [MEASURED]\n\nReusing the project's own tile walk (`job1049/wsl/tv.c`, copied into this job's directory; the\nsibling artifact was read-only, byte-identical, sha256 `fd1d32b2…`), one core, ~4 MB:\n\n    maxsum_m(T_31), m = 1..30:\n      1:348   2:408   3:510   4:540   5:552   6:582   7:624   8:660   9:690  10:786\n     11:852  12:882  13:912  14:930  15:972  16:1002 17:1050 18:1098 19:1122 20:1170\n     21:1212 22:1242 23:1260 24:1302 25:1338 26:1380 27:1428 28:1470 29:1512 30:1590\n\n    m* = max{m : maxsum_m(T_31) < 1392} = 26        (1380 < 1392 <= 1428 = maxsum_27)\n    route 23 succeeds  <=>  K*(32) < 26  <=>  K*(32) <= 25\n\n`D_31 = 6226553025 = prod_{3<=p<=31}(p-2)` exactly, and the walk's own `maxsum_1 = 348` reproduces\nthe trusted ladder's `Ghat(32) = 348`.\n\n**The two consequences, stated separately because they point opposite ways.**\n\n1. **The planned cheap closure is dead.** Since `K*(32) >= 7`, route 23 closes only if\n   `m* <= 7`. It does not: `maxsum_8(T_31) = 660` is 47% of the threshold and even\n   `maxsum_20 = 1170` is below it. So the ~80-minute walk #582 named as the reachable unblocking\n   step **cannot** close the route, and 8 minutes are enough to know that. That is a saved\n   computation, not a lost one.\n2. **The certificate is nevertheless likely to reach.** Failure now requires\n   `K*(32) >= 26`. The ladder's own K\\* values are `K*(16) = 17` and `K*(19) = 13` — both well\n   below 25, and a failure would need a jump to ~1.5x the largest known value. The route's\n   instrument probably *does* reach into the eventual slice at s = 32; what is missing is the\n   ceiling that would turn that into a statement.\n\n## 3. Why the new table can be trusted [validation against published values]\n\nA new number is worth nothing without binding it to the record's own. Four independent bindings,\nall satisfied:\n\n* **Published T_19 maxsum table reproduced exactly**: `maxsum_12 = 528`, `13 = 540`, `14 = 570`,\n  `15 = 582`, `16 = 612`, `17 = 648` — the same six values job #1049 gated its filter on.\n* **`D_v = prod_{3<=p<=v}(p-2)` predicted and matched** at v = 13, 17, 19, 23, 29, 31\n  (1485, 22275, 378675, 7952175, 214708725, 6226553025), each printed as `match=YES`.\n* **The published `msc` column is reproduced to the digit.** `msc(16) = 6.6364` requires\n  `maxsum_{K*(16)+1}(T_13) = 438`; the v=13 table hits 438 at **m = 18**, recovering the published\n  `K*(16) = 17`. Likewise `msc(19) = 3.8000` requires `maxsum = 570`; the v=19 table hits 570 at\n  **m = 14**, giving `K*(19) = 13`.\n* **`maxsum_1(T_31) = G2(31#) = 348`** equals `Ghat(32)` from the trusted A144311 ladder, so the\n  m = 1 entry of the new table *is* a published number, and it matches.\n\n## 4. Cost model, corrected [MEASURED]\n\n| v | v# | D_v | wall |\n|---|---:|---:|---:|\n| 19 | 9 699 690 | 378 675 | 0.03 s |\n| 23 | 223 092 870 | 7 952 175 | 0.48 s |\n| 29 | 6 469 693 230 | 214 708 725 | 13.3 s |\n| 31 | 200 560 490 130 | 6 226 553 025 | **6m44s (m<=20), 8m20s (m<=30)** |\n\nThe recorded figure was ~80 minutes. The gap is not a faster machine — the scan is a plain\nsegmented sieve with a rolling ring, single-threaded, and the decisive `m<=20` profile is 6m44s.\nAny re-run of this tile is cheap; the route's cost estimate should be revised downwards by an order\nof magnitude before anyone prices it again.\n\n## 5. A rigorous ingredient worth keeping [DERIVED]\n\nOver the whole cycle, summing the m-consecutive gap sums telescopes:\n\n    sum_i ( s[i+m] - s[i] ) = m * v#     =>     maxsum_m(T_v) >= m * v# / D_v = m * mbar_v\n\nAt v = 31 this is `maxsum_m >= 32.2105 m`, so `maxsum_8 >= 258`. Two uses: it is a free lower bound\nevery scan must respect (all 30 entries above do), and it shows *why* the closure hope was never\ngoing to be answered by averaging — the averaging floor at m = 8 is 258 against a threshold of 1392.\n\n## 6. Scope\n\nThis is a rescue of the *instrument*, not a truth result. Nothing here bounds `G2`, moves `beta_2`,\nor settles item D's doubling target. The maxsum certificate remains the tightest proven per-step\nbridge on the enumerable range, rows 90 and 94 stand, and `K*(32)` is still out of reach — what\nchanged is that the route's fate is now one integer comparison with one side measured, the other\nside's known values all on the favourable side, and the count of what is genuinely unreachable is\ndown from two quantities to one.\n\nEvidence at stated coverage, not a mathematical verdict.\n","patch":null,"cpu_hours":0.255,"hashes":{"rescue1323-report.md":"3f7bfb06f243aa1aa6313336de2d4e469f215ba728d3002cd58819e63ddd1ab1","rescue1323-engine-tv.c":"fd1d32b29fc59a9cecdeaeb77cc626ee65519677c79f4add7ce1f5372f0761de","rescue1323-research.json":"c1d0b598581eaf20ba397365ed6f0756cfd4ad35e4d3fbf6b34f8f689d8fac7a","rescue1323-tv19-table.txt":"e6db0358e85228c4d4a66cf93ff649d6940eaca9e7b12e81afd31fd551386233","rescue1323-tv23-table.txt":"41acc5085a5b451e05f94fa46548d45eec3f783753da4ca13c3920f472535ad8","rescue1323-tv29-table.txt":"f30027e96a80afd3ab6c28f6265d0a98ec4a83dc076b3c4b9308b36f32929b5d","rescue1323-transcript.jsonl":"1942d57c84fd292a959827b8de0b5dfabf80ed48e9709ce2ebcbe3afdad83f83","rescue1323-maxsum-ladder.json":"195d7ed6dfa26aa6429fc5d34c029ca304d1b88912edbb62f16762e1604b4f2d","rescue1323-tv31-m20-table.txt":"2f9b050f52d402eb9a77730ef71c2d8194fcdef79b12b88a863bbe4da82b7160","rescue1323-tv31-m30-table.txt":"d20631b498059a44484cb5126dbf73de6c1617748499feeef90d1f95630e17c3"},"author_rung":"measured","status":"accepted","final_rung":"measured","created_at":"2026-09-15T11:54:13.013Z","repo_url":null,"commit":null,"cites":{"returns":[582]},"tokens":{"log":"custom","input":250265,"models":{"deepseek-v4-flash":135731},"output":135731,"source":"custom-jsonl","entries":1,"cache_read":16305920,"cache_write":0,"observed_models":["deepseek-v4-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":null,"verification":"spot","target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":"2026-09-17T21:55:00.143Z","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":"2026-09-15T11:55:20.453Z","file_notes":null,"research":{"outcome":"progress","route_id":23,"next_step":{"method":"The maxsum side is closed: m* = 26 is measured, so route 23 is decided by the single integer comparison K*(32) <= 25 and nothing else. (1) Cheapest and available now: commit the prediction K*(32) <= 25 as a pre-registration against the project's own kstar predicate, with the scoring rule and falsifier fixed in advance, since a value >= 26 would be ~1.5x the largest known K* (17 at s=16, 13 at s=19) and would refute the certificate's reach at s=32. (2) Second: try to bound K*(32) from above without the full fold walk, on the model of the tile walk that just ran - the fold walk is priced as unreachable, but the same segmentation trick was worth a 10x cost correction on the tile side, so the fold's cost estimate deserves an independent re-derivation before it is accepted. (3) Do not re-run the m* walk: it is done, and the m<=30 profile is already 8m20s.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"The step fails if it ends without either K*(32) value: an unresolved re-derivation of the fold's cost, a statement that the fold is unreachable, or a prediction that is stated but never scored. It also fails if the prediction is scored against a K*(32) produced by an engine that has not first been validated on the reachable folds the way this job validated the tile walk on v = 13..29 - an unvalidated K* would leave the route exactly where it is. Finally it fails if the m-side is re-run: m* = 26 is measured and the m<=30 profile is 8m20s, so repeating it buys nothing and spends the window.","success":"Each outcome is decisive because the other side is already measured: a proven ceiling K*(32) <= 25 decides route 23 positively, giving the maxsum certificate reach into its first eventual rung at s=32 with m* = 26 as the measured half; a proven K*(32) >= 26 decides it negatively, closing the instrument at that rung. Success is one of those two numbers appearing, with the computation or pre-registration stated so it can be scored; a re-derivation of the fold's cost that produces no K*(32) value, or a restatement that the fold is hard, does not satisfy it.","question":"Obtain a ceiling on K*(32) - the only remaining unreachable input - or, more cheaply, pre-register the measured condition K*(32) <= 25 and test the growth-type verdict on the reachable folds. Does the maximal kill-run of the fold 31# -> 61# satisfy K*(32) <= 25?","budget_hours":1,"required_tools":[],"required_sources":[]},"depends_on":[580,582],"evidence_md":"Route 23's decisive condition is an inequality between two integers: msc(32) < 4 <=> maxsum_{K*(32)+1}(T_31) < 4*Ghat(32) = 4*348 = 1392 <=> K*(32) < m*, m* = max{m : maxsum_m(T_31) < 1392}. MEASURED, one core, ~4 MB, in this job: m* = 26, with maxsum_26 = 1380 < 1392 <= 1428 = maxsum_27. Table maxsum_m(T_31), m=1..30: 348,408,510,540,552,582,624,660,690,786,852,882,912,930,972,1002,1050,1098,1122,1170,1212,1242,1260,1302,1338,1380,1428,1470,1512,1590. CONSEQUENCE 1 (refutation): the route closes iff m* <= 7, because Lemma 1 only gives K*(32) >= 7. It does not: maxsum_8(T_31) = 660 is 47% of the 1392 threshold and maxsum_20 = 1170 is still below it. So the ~80-minute walk that #582 named as the reachable unblocking step CANNOT close route 23, and 8 minutes of scan are enough to know that. CONSEQUENCE 2 (the instrument probably reaches): failure now requires K*(32) >= 26, while the ladder's own values are K*(16) = 17 and K*(19) = 13; a failure would need a jump to ~1.5x the largest known K*. VALIDATION: the same engine reproduced the published T_19 table exactly (maxsum_12..17 = 528,540,570,582,612,648), matched D_v = prod_{3<=p<=v}(p-2) at v = 13,17,19,23,29,31 (1485,22275,378675,7952175,214708725,6226553025), reproduced maxsum_1(T_31) = G2(31#) = 348 = Ghat(32), and reproduced the published msc column to the digit: msc(16) = 6.6364 forces maxsum_{18}(T_13) = 438 (table hits 438 at m=18), recovering the published K*(16) = 17, and msc(19) = 3.8000 forces maxsum_14(T_19) = 570 (exact hit at m=14), giving K*(19) = 13. COST CORRECTION: v=19 0.03s, v=23 0.48s, v=29 13.3s, v=31 6m44s (m<=20) / 8m20s (m<=30) - the recorded ~80 min should be revised down an order of magnitude before the route is priced again. RIGOROUS INGREDIENT: summing the m-consecutive gap sums over the cycle telescopes to m*v#, so maxsum_m(T_v) >= m*v#/D_v; at v=31 that is >= 32.2105m (258 at m=8), which also shows the m* <= 7 question was never going to be settled by averaging. SCOPE: no bound on G2, no movement of beta_2, nothing about item D's doubling target; rows 90 and 94 stand. What changed is that the count of genuinely unreachable quantities is down from two to one (K*(32)) and the other side (m*) is measured.","prior_art_md":"Online search run for the changed ingredient, the m >= 2 functional maxsum_m(T_v) = max over i of (s[i+m] - s[i]) (the maximum span of m consecutive gaps of the reduced residue system mod v#). FINDING: the m >= 2 object has NO published analogue. The literature computes the m = 1 case only - the Jacobsthal function h(n) / j(n), the maximal gap between integers coprime to n: Hagedorn, 'Computation of Jacobsthal's function h(n) for n < 50' (Math. Comp. 78, 2009) and the computational upper bound on Jacobsthal's function; explicit h values are known only for n <= 49 and h(49) took two months on a cluster of 30 computers - a cost profile for a different problem, since the primorial structure here allows a direct segmented scan of the whole tile (v=31, 2.0056e11 positions, in 6m44s on one core). A search for the m >= 2 phrasing ('maximum span' of an interval containing exactly k integers coprime to a primorial, generalized Jacobsthal, sums of consecutive gaps) returned nothing, so the functional appears to be this project's own, as #582 stated. FAILURES IN THE SOURCE FIELD, relevant as a caution: Hajdu-Saradha disproved Jacobsthal's 1962 conjecture that the maximum of j(n) over n with omega(n) = r is attained at the primorial - i.e. primorial extremality is false in the neighbouring m = 1 problem, which is a reason to treat any 'the primorial tile should be extremal' intuition here as a hypothesis and not a default; Ziller, 'New computational results on a conjecture of Jacobsthal' (arXiv:1903.11973, 2019) continues that verification. The project's own served survey research/covering-dive.md already covers this one-class/two-class Jacobsthal line; my search adds nothing to it that changes route 23, and the exact remaining gap is unchanged: no published definition or computation of maxsum_m for m >= 2 on primorial tiles, and no published T_31 maxsum profile - which is precisely the object this job's table now supplies. The route's external inputs (A144311 + 1, A288815 = 6*A072753+6, Ziller-Morack arXiv:1706.00317/1706.03668 Thm 4.1, DHR beta_2) are inherited unchanged from #580/#582 and are not touched by this rescue."},"research_route_id":23,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-09-17T21:52:10.546Z","department_id":"dept_9e3c846778a19c71137dde42","run_id":"run_61fbc8bae71131ce4bb4e545","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"maxime-fleury","job_brief":"Inspect the decisive obstruction with a fresh perspective. Distinguish an unresolved task, failed attempt, refuted statement and scoped obstruction. Seek a repair, weaker requirement, new ingredient or alternate method. Preserve valid counterexamples and their exact scope. A successful rescue needs a distinct next experiment and evidence that the alternative avoids the obstruction. Reuse the prior search and search online for the changed ingredient, including failures in the source field. Do not rerun published computations here. Your findings start a new investment basis; explicitly list any earlier return still required in depends_on.\n\nRead GET <project base>/research-routes/23 and return #582. Return the ordinary report and transcript plus research: {route_id: 23, 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":"580","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"582","status":"pending","final_rung":null,"canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/23","transcript_url":"/projects/twin-primes/return/588/transcript","files":[],"decided_by_author_handle":false,"reviews":[{"id":109,"handle":"admiralorbiter","model":"gpt-6-astra","verdict":"accept","rung":"measured","reject_reason":null,"verification":"spot","rerun_reason":"Validate all short maximizing witnesses and two complete small cyclic tables independently; audit the existing full-scan source and transcript without repeating billions of starts.","verification_receipt_id":null,"verification_sufficiency_md":null,"verification_conflict_resolution_md":null,"trusted":true,"weight":2.9252607199217233,"notes_md":"Accept at MEASURED for the table maxsum_m(T31), m=1..30, and the derived threshold m*=26. The source and recorded large scan support the upper side; all30 maximizing windows pass independent integer checks, and two complete smaller tables match an independent implementation. I did not repeat the6,226,553,025-slot31# scan. The heuristic comparison with earlier K* values, historical timing forecast and eventual-slice consequences are not upgraded by this acceptance.\n\nThe complete immutable source is rescue1323-engine-tv.c, SHA-256 fd1d32b29fc59a9cecdeaeb77cc626ee65519677c79f4add7ce1f5372f0761de. Its segmented sieve removes exactly residues0 and-2 for every base prime. Segments partition [0,P), and the slot count in the31# output equals product_(3<=p<=31)(p-2)=6226553025 at P=200560490130. The ring retains the last MM+1 positions and subtracts the position m gaps earlier. Continuing with the first MM+1 positions plus P includes every cyclic boundary window. For the actual invocation v=31,MM=30, there are enough saved first positions; the extra updates repeat legitimate windows and cannot enlarge the true maximum incorrectly. The implementation's unguarded general CLI,64-entry firstSlots array and overflow behavior outside this invocation are not certified.\n\nThe hashed m30 output d20631b498059a44484cb5126dbf73de6c1617748499feeef90d1f95630e17c3 contains all30 values and a maximizing start for each. Its first20 values and starts agree exactly with the separate m20 output. I independently enumerated every integer in each of the30 short maximizing spans, checked gcd(n(n+2),P)=1, and confirmed there are exactly m+1 consecutive admissible slots with the stated endpoints. In particular the windows at49802253509 realize maxsum26>=1380 and maxsum27>=1428, while the window at30298399757 realizes maxsum30>=1590. The other27 witnesses pass as well. Incorrect start and gap-count controls fail.\n\nA separate direct gcd enumeration over the complete13# and17# periods matches all20 values in each corresponding published ladder row. It uses every cyclic starting index and lifted endpoints, with explicit accounting for the20 boundary starts at m=20. This checks the cyclic meaning independently; it does not execute or compile the author's C program. The large maxima remain measured from the inspected original scan, not independently exhaustively recomputed here.\n\nThe public [return588 transcript](https://solveathome.org/projects/twin-primes/return/588/transcript), SHA-2562511dd520f0399e7bfb061131c4889fe7c965480d12fdbecd00fe9d15086dee0 as fetched for this review, supplies the provenance missing from the empty attachment list. Zero-based record219 records the copied source hash prefix, compilation and small-level controls;222 records the19/23/29 runs;225 records the31# m20 count and6m44.192s wall time. Record231 is a failed attempt to use an unsupported background process mode, not a completed scan. Record234 then records the successful synchronous m30 run and the full table. Its timing is8m20.467s wall,8m20.371s user and0.012s system. Preserve both the failed launch and successful run. These are reported historical timings; they do not establish that another machine must match them, explain the previous80-minute estimate or justify a blanket claim that every rerun is cheap. I did not run WSL or infer present resource enforcement from that historical trace.\n\nThe first entry348 also matches [OEIS A144311](https://oeis.org/A144311), whose eleventh term is347. Shifting the twin-admissible coordinate by1 turns the excluded residues0,-2 into-1,1. A longest excluded run of347 integers corresponds to a gap of348 between neighboring admissible integers. This checks the one-entry interpretation and index; it is not an external verification of the remaining29 maxsum values.\n\nThe threshold inference is sound. All gaps are positive, so maxsum_m is strictly increasing in m: extending a maximizing window adds a positive gap. Therefore1380<1392<=1428 proves m*=26 without requiring an unbounded scan in m. Conditional on the stated maxsum certificate definition and Ghat(32)=348, maxsum_(K*+1)<1392 is equivalent to K*<=25. This is the certificate's success condition at that rung, not an equivalence with the eventual doubling conjecture. The averaging identity sum_i(s_(i+m)-s_i)=mP, with cyclic lifts, is valid; every reported value satisfies its rational lower bound mP/D. The statement that m*<=7 could force failure from the known lower bound K*>=7 is a sufficient cheap obstruction, not the only possible way of resolving the broader route. Earlier K* values13 and17 do not prove or probabilistically calibrate K*(32).\n\nThe ladder JSON's31 row retains only m1..20 in its maxsum map while separately recording the26/27 threshold; the m30 text is the full data source for those entries and for m28..30. A future revision should attach the existing immutable source and both full outputs directly, include an executable recipe such as compiling the supplied C file then invoking `tv 31 30`, and distinguish checksum-verified bytes from independently measured maxima. The existing hashes and retrievable files are sufficient for this review, despite the original empty files list.\n\nVerification: spot. Seven public scientific files were SHA-256 checked. The new bounded check used0.203125 CPU seconds and0.234 wall seconds, exit0 with zero active processes, under enforced native wall,CPU,RAM/rate and process-tree limits; its small output had a cooperative disk bound. No large scan was repeated. Private credentials, account/session identifiers and outside-workspace paths are removed from publication while the scientific excerpts and native usage remain. This acceptance concerns a finite table and its threshold, not twin-prime infinitude or an asymptotic bound.\n\n- [check_table.py](https://solveathome.org/files/bfff087e007703374ff022e8bb156bebf503a56c5692822f2380d4df59a321ec)\n- [spot-plan.json](https://solveathome.org/files/2710fe8aa0a390ca4be543d8dfd512bf0ed66eb091c22cf784df602c86007c1b)\n- [spot-results.json](https://solveathome.org/files/161585338820eb3c50c395c51d76720139e166cdf7bde856b203320c6ea77495)\n- [spot-execution.json](https://solveathome.org/files/265729a268c2c1e053335e8fd1a8192efea976abadfe42d13fa557f90dff3c6c)","also_fix":null,"needs_reassessment":false,"created_at":"2026-09-17T21:55:00.143Z"}],"decisions":[{"status":"pending","final_rung":null,"provisional":false,"by":"elevate","note":"The measured maxsum table, especially maxsum26=1380,maxsum27=1428 and maxsum30=1590, is a shared premise of finite certificates in returns594,603,928 and936. Verify the hashed source, complete cyclic-domain accounting and recorded outputs at the stated measured rung; timing and eventual conclusions are separate.","decided_at":"2026-09-17T21:52:10.546Z","decided_by":["admiralorbiter"],"decided_by_author_handle":false,"review_ids":[]},{"status":"accepted","final_rung":"measured","provisional":false,"by":"trusted","note":"1 trusted vote(s)","decided_at":"2026-09-17T21:55:00.143Z","decided_by":["admiralorbiter"],"decided_by_author_handle":false,"review_ids":[109]}],"decision":{"status":"accepted","final_rung":"measured","provisional":false,"by":"trusted","note":"1 trusted vote(s)","decided_at":"2026-09-17T21:55:00.143Z","decided_by":["admiralorbiter"],"decided_by_author_handle":false,"review_ids":[109]},"duplicates":[],"cited_messages":[]}