{"id":1298,"job_id":2647,"problem_id":1,"lane_id":3,"type":"explore","user_id":42,"model":"deepseek-flash","provider":"deepseek","report_md":"# Job #2647 (explore, triage) — route 105: **promising**, but only after a convention repair and a re-priced K\\* half\n\n**Outcome: promising.** The route's exact criterion is a definitional restatement of route 23's\nper-fold test, and the fold it targets (s = 38) is a genuine, decisive, currently undecided race.\nBefore one bounded experiment is funded, three defects in the route's statement have to be fixed:\nits `m*` is written in the opposite of the two conventions in play, its Ziller–Morack cross-check is\nfalse, and its K\\*-cost premise is superseded by the record. After the repair the decisive half is\n*cheaper* than the route says on the K\\* side and *more expensive* on the `m*` side.\n\nNo claim here bounds `G2`, `β₂` or twin-prime infinitude. All numbers below are exact finite\ncomputations or arithmetic on published/recorded tables; a script output is never a proof.\n\n## 1. What the route claims, and what I inspected\n\nRoute 105 (#1293) replaces route 23's maxsum doubling certificate by the exact test\n\n```\ncertificate passes at fold s   iff   maxsum_{K*(s)+1}(T_{s-1}) <= 4*Ghat(s)   iff   K*(s) < m*(s),\n```\n\nwith `m*(s)` a gap-spectrum index of the tile and `K*(s)` the covering run of the entering primes\n`(s,2s]`. Its next step pins both indices at `s = 38` (`T_37`, period 37# = 7.421e12).\n\nInspected at source: route 105's record; returns #1293, #588, #594, #599, #606, #609, #891, #901,\n#928, #936, #956, #966, #969; `research/OUTCOMES.md` (closed routes), `research/SEARCH-CONVENTIONS.md`,\n`research/README.md`; the literature (Ziller–Morack arXiv:1706.03668 and 1706.00317, Kalmynin–Konyagin\narXiv:2302.00459, Hough 2015, Hough–Nielsen, BBMST arXiv:1811.03547, Costello–Watts, OEIS A144311 /\nA288815 / A072753 / A048670), with queries and links in the `prior_art_md` of this return.\n\n## 2. The criterion is definitional, but the report's `m*` is written in the wrong one of two conventions\n\nThe corpus uses two indices, differing by one, and `maxsum_m` is nondecreasing in `m`:\n\n* **A** = largest `m` with `maxsum_m(T) < 4*Ghat` — route 23's own convention (#588, #606);\n* **B** = least `m` with `maxsum_m(T) >= 4*Ghat` — the definition **written** in #2547 / route 105.\n\nA = B−1. The certificate test is `maxsum_{K*+1} <= 4*Ghat`, so it passes iff `K*+1 <= A`, i.e.\n`K* < A`. The route's proposition `passes iff K* < m*` is therefore correct **only for A**; under its\nown written definition B it must read `K*+1 < B`.\n\n#2547's table uses **B** at s = 12, 14, 18, 20, 24, 30 (my independent full-period computation\nreproduces 7, 10, 13, 16, 19 there, and 21 at s = 30 is #2547's) but uses **A** at s = 32, where it\nimports route 23's `m*(32) = 26`. From the published T_31 table (#588, reproduced digit-for-digit by\n#969) `4*Ghat(32) = 1392`, `maxsum_26 = 1380 < 1392 <= 1428 = maxsum_27`, so\n\n```\nA(32) = 26  (route 23)      B(32) = 27  (the report's own written definition)\n```\n\nThe off-by-one is not cosmetic. At the critical value the two conventions disagree in verdict:\nroute 23 states that `K*(32) = 26` would fail (`maxsum_27 = 1428 > 1392`); the route-23 criterion\ngives fail (26 < 26 false, correct), the report's written criterion gives **pass** (26 < 27, wrong).\nConsequently the headline \"the two anchors show a near tie (s = 32: `m* = 26` against `K*+1 = 26`)\"\nis an artefact of mixing A and B: in A the statement stands (K\\*(32) = A−1 is exactly critical), in\nB the margin is 1. One convention has to be fixed before `m*(38)` means anything.\n(`mstar_convention.py`, uploaded, prints this table.)\n\n## 3. The Ziller–Morack cross-check is false, and the side result re-proposes a withdrawn route\n\n#2547 asserts `h2(n) = Ghat(p_n + 1) + 1` and that its `Ghat` ladder \"agrees term for term with the\npublished paired-Jacobsthal ladder\". It does not. Ziller–Morack's `h2` (Def. 4; ancillary Def. 1.9)\nquantifies over **all** pairs `(a,b)` with `b-a` even, so `h2(n)-1` is the maximum covering run over\n**all** even differences, whereas `Ghat(p_n+1)-1` is the run for the single difference `d = 2`.\n`h2(n) >= Ghat(p_n+1)`, strictly: `h2(6) = 150` at `p_6 = 13` (Table 1) against the twin tile\n`max gap(T_13) = 66`, i.e. 67; likewise 192 vs 109, 258 vs 151, 366 vs 205. My independent tile\ncomputation gives 42, 66, 108, 150, 204 for `T_11, T_13, T_17, T_19, T_23`, matching #2547's own\ntable — and matching none of the corresponding `h2` values. The apparent 12-term agreement is a\nmisalignment (150 and 258 happen to occur in both ladders).\n\nThis also invalidates section 4's side result: `maxgap.c` computes the **twin-difference** tile gap,\nso its `x = 37` value (528) and `x = 41` value (1044) are not new terms of A288815, and its inline\n\"controls\" (894, 1044) are in fact `h2` at p = 41, 43. The register already records\n\"extending `h2` past 21 terms\" as **WITHDRAWN** (infeasible and non-diagnostic), which route 105's\nprior verse does not cite.\n\n## 4. The K\\* cost premise is superseded, and the next step's K\\* bound is not the record's lemma\n\n#1293 prices the K\\* upper half at the \"recorded 28 core-hour wall\" of #599. That price is stale:\n#936 computed **K\\*(34) = 29** and **K\\*(36) = 33 exactly** on the 31# lattice with the served\nengine (reflection-canonical complete domain, cross-checked by an independent pure-Python cover\nimplementation), long after #599's prefix pricing. Moreover #901's deletion lemma\n\n```\nK*_(Pp)(R) <= K*_P(R u {p})        (p prime, p ∤ P, R disjoint from Pp)\n```\n\napplied at `P = 31#, p = 37, R = Q(38) = {41,...,73}` bounds the s = 38 covering run **without any\nT_37 scan**:\n\n```\nK*(38) = K*_{37#}(Q(38))  <=  K*_{31#}({37,41,43,47,53,59,61,67,71,73}),\n```\n\na ten-prime covering search on the *31#* lattice — the same size class #936 already completed. The\nnext step's assertion \"the boundary transfer gives `K*(38) <= K*(37)+1 <= 39`\" is **not** that lemma:\nthe lemma upper-bounds `K*(38)` by the ten-prime old-lattice value, which is `>= K*(37)+1` by the\nproved fold-entry jump law (#609), and no record establishes `K*(37) <= 38`. The route's supporting\nclaim that \"K\\*(s) is monotone nondecreasing in s\" is also wrong across a block boundary and wrong\nfor non-nested `Q` (e.g. `Q(37) = {41..73}` drops 37 relative to `Q(34) = {37..67}`); #609 states\nthis explicitly. So the route's lower bound `K*(38) >= K*(34)+1 >= 28` is not available either.\n\nWhat survives from route 23: the maxsum certificate is **not** the closed K\\*-product form (that is\nCLOSED in the register) — it is the record's tightest proven per-step bridge and its all-s form is\nthe open inequality. Route 105 reformulates that open inequality, it does not reopen a closed one.\n\n## 5. Independent finite checks (this job; seconds)\n\n* Full-phase `K*(s)` at s = 5..14 (max over the CRT phase vectors, `fullphase_check.py`): the\n  certificate **fails** at s = 9, 10, 11, 12 and **passes** at s = 13, 14 — the per-fold status\n  oscillates, exactly #606's \"dies inside each block, can recover at each boundary\", and a warning\n  against reading any single fold as the shape of the chain.\n* `m*(s)` as B at s = 8, 12, 14, 18, 20, 24 = 7, 7, 10, 13, 16, 19, reproducing #2547's table;\n  `Ghat` = 30, 42, 66, 108, 150, 204 reproduced from scratch (`tilecheck.py`, `criterion_check.py`).\n* T_31 anchors from published tables (`mstar_convention.py`): A(32) = A(34) = A(36) = 26, B = 27;\n  K\\*(32) = 25 (pass, `1380 <= 1392`), K\\*(34) = 29 (fail, `1590 > 1392`), K\\*(36) = 33 (fail).\n* Cost of the `m*` half: T_37 has `D_37 = 2.179e11` admissible slots, 1013x the T_29 pass; the\n  measured C rate (~2.15e8 slots in ~26 s) puts one full pass at **~7–20 core-h**, and #2547's\n  `g37.err` reached only ~block 1600/33263 inside its allocation. This exceeds this assignment's\n  8 CPU-h even alone.\n\n## 6. Why still promising\n\nThe s = 38 question is well-posed, undecided in the record, and decisive either way: a verified\ncovering run of length A(38)+1 kills the instrument at the second distinct fold, and an exact\n`T_37` threshold index with `K*(38) <= A(38)` re-opens it. The route's own framing — the race\nbetween a tile-only index and a covering run — is the record's framing (#606), but it adds the\n`T_37` witness and the K\\* half at a fold where both are computable, and its `m*(38)` value would\nbe new data (no OEIS sequence carries it). The one experiment is worth funding **after** the\nsections 2–4 repairs, with the K\\* side re-priced from 24 CPU-h down to the 31# lattice.\n\n## 7. Rung of each claim\n\n| claim | rung |\n|---|---|\n| certificate passes iff `maxsum_{K*+1} <= 4*Ghat`; equivalently `K* < A`, not `K* < B` | proven (definitional; A the route-23 index) |\n| route 105's written definition of `m*` contradicts its own s = 32 entry; the off-by-one flips the verdict at `K* = B-1` | verified (arithmetic on the published T_31 table + route 23's own criticality note) |\n| `h2(n) = Ghat(p_n+1) + 1` | **refuted** (h2(6) = 150 vs 66+1; h2 maximises over all even differences) |\n| Ghat / `m*`(B) values at s <= 24; full-phase `K*` at s = 5..14 | verified (exact finite computation, this job; reproduces #2547's table) |\n| `K*(34) = 29`, `K*(36) = 33`; `K*(38) <= K*_{31#}(10 primes)` | verified in #936 / proven in #901, used here |\n| `K*(38) <= K*(37)+1 <= 39`; `K*(38) >= 28` by monotonicity | **unsupported** (not the transfer lemma; K\\* is not monotone across a boundary, #609) |\n| m\\*(38) ≈ 38 | conjectured (two-point extrapolation, #606) |\n| nothing here bounds `G2`, `β₂`, or twin-prime infinitude | scope |\n\n## 8. Files\n\n`report.md`, `mstar_convention.py`, `criterion_check.py`, `fullphase_check.py`, `transfer_check.py`,\n`tilecheck.py`, `criterion_rows.json`, `fullphase_rows.json`.\n\n## 9. Outstanding\n\n13 returns of @victor-geere wait for a verdict; none of them is this session's work. This attempt is\nthe only outstanding attempt in the run ledger (checked with `sah.py ledger ... check`).\n","patch":null,"cpu_hours":0.05,"hashes":{"report.md":"bebaa7c6ea3f0565f2099b44b5e576bec791b957500249c67ed48d8a7901c697","tilecheck.py":"57b921613e9ef3b4d6f79b2a546650474fe3cdef0338cb7d83159b9b932b2f8f","transfer_check.py":"f7ba42a539497f92bcbaad2841e99009d3db2afb853ae4804867ab94d9f36054","criterion_check.py":"619b5145f3928766a5783ffc7bbd18252b243b0857a4b80a60ba135881048c17","fullphase_check.py":"165e5d13c2efdd4c86b5169da8556f28a0ed1cf91639e73c0ee711cf0fedc4fc","criterion_rows.json":"bdbb535ed0a2673e307cf7424aa9bbab94b26acfaf239539a49666824bafbfcd","fullphase_rows.json":"32b120b217303a6c3019ac7d178748f9a60160781f2df847388c03a33a9259ff","mstar_convention.py":"5d538c249af326dfcee39c626f4960b05a10d10278c5e00249c9d9f7c531b113"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-19T17:10:20.829Z","repo_url":null,"commit":null,"cites":{"files":["research/OUTCOMES.md","research/SEARCH-CONVENTIONS.md","research/README.md"],"handles":["victor-geere","maxime-fleury","admiralorbiter","Benjaminsen"],"returns":[1293,588,594,599,606,609,891,901,928,936,956,966,969],"messages":[]},"tokens":{"log":"custom","input":110414,"models":{"deepseek-flash":91223},"output":91223,"source":"custom-jsonl","entries":54,"cache_read":6836480,"cache_write":0,"observed_models":["deepseek-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"All triage checks are seconds and run from the workspace root with ./.venv/bin/python3. (1) ./.venv/bin/python3 outputs/2647/mstar_convention.py -- the convention/off-by-one arithmetic on #588's published T_31 maxsum table and the K*=25/29/33 anchors. (2) ./.venv/bin/python3 outputs/2647/tilecheck.py -- independent tile max gaps T_7..T_23 (30,42,66,108,150,204). (3) ./.venv/bin/python3 outputs/2647/criterion_check.py -- cyclic (phase-0) maxsum profile and A/B indices, s<=28. (4) ./.venv/bin/python3 outputs/2647/fullphase_check.py -- full-phase K*(s) (max over CRT phase vectors) at s=5..14 with the certificate verdict. (5) ./.venv/bin/python3 outputs/2647/transfer_check.py -- numerical exercise of #901's deletion lemma K*_(Pp)(R) <= K*_P(R u {p}) on small lattices. No large computation was run: the T_37 pass is priced (~7-20 core-h), not executed. sympy is used only to list primes; all arithmetic is exact integer/numpy.","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":"promising","route_id":105,"next_step":{"method":"Fix the convention first and keep it: use route 23's A = largest m with maxsum_m < 4*Ghat, so the test is maxsum_{K*+1} <= 4*Ghat, i.e. K* < A. Recompute the T_31 calibration from #588's published table (must give Ghat=348, A(32)=A(34)=A(36)=26, B=27) before any T_37 work. Stage 1 (bounded, decisive in the failure direction; ~2-4 CPU-h). On the 31# lattice only, run the served phase-canonical covering search (reflection-canonical domain as in #936, 8 segments) for the ten-prime set R10 = {37,41,43,47,53,59,61,67,71,73}, escalating L, to get U := K*_{31#}(R10) exactly; also get K*(37) = K*_{31#}(Q(37)) with Q(37) = {41,...,73}. By #901's deletion lemma K*(38) <= U, so U >= A(38)+1 kills the instrument at s = 38 (record the verified witness: pure modular arithmetic, genuine-slot + span + cover checks, no engine state). Compare U with K*(37): if U > K*(37)+1 then the route's claimed bound form is refuted as well. Stage 2 (the expensive half; ~7-20 CPU-h, segmented, parallel). One exact whole-period pass over T_37 (37# = 7420738134810, D_37 = 217929355875 admissible slots) computing cyclic maxsum_m and the sorted top-gap sums: control Ghat(38)=528 and maxsum_1=528, then A(38) = largest m with maxsum_m < 2112 and B(38) = A(38)+1. If sum of the top (U+1) gaps < 2112 then maxsum_{U+1} < 2112 certifies PASS without the full profile; if some window of A(38)+1 consecutive gaps exceeds 2112 or the L = A(38)+1 witness exists, FAIL. Reuse outputs/2547/gapscan3.c and maxgap.c conventions (two separate admissibility arrays for r and r+2; the single-array bug returns G = x#). Stage 3. Report the pair (K*(38) upper bound U, A(38)) and the verdict, with the s = 32/34/36 anchors recomputed under A as controls. Do not import #2547's h2 identification or its maxgap control values.","compute":{"ram_gb":8,"disk_gb":1,"cpu_hours":24},"failure":"A verdict taken from a partial scan (Stage 1 or Stage 2 not complete over its canonical domain); a covering witness that fails the arithmetic genuine-slot/span/cover check; a control mismatch (Ghat(38) != 528, maxsum_1 != 528, or #588's T_31 table not reproduced); U compared with K*(37) or A(38) across the two conventions; or the measured cost of Stage 1 alone exceeds the allocation, in which case the fold is priced rather than decided and the next step moves to s = 37 or to a lower-bound-only comparison. A negative prefix is not an upper bound.","success":"A complete two-sided verdict at s = 38 under one convention. PASS: U = K*_{31#}(R10) <= A(38)-1 with the T_37 pass controlled by Ghat(38)=528 and the T_31 calibration, giving the first exact threshold index above s = 32 and showing the failure at s = 34 was a boundary event; the instrument re-opens past fold 34 and its reach becomes a fold-by-fold computable question. FAIL: maxsum_{A(38)+1}(T_37) > 2112, or a K*(38)-witness run of length A(38)+1 verified by pure arithmetic, so the failure at 34 continues at the next distinct fold and route 23's remaining bridge is closed at its second distinct fold. Either branch also settles whether U <= K*(37)+1 and fixes the m*/K* convention in the record.","question":"At s = 38 (tile T_37, period 37# = 7.421e12; Ghat(38) = 528, so 4*Ghat = 2112) -- the first distinct fold after the recorded pass at s = 32 and failure at s = 34 where both indices are computable but unknown -- does the maxsum doubling certificate pass, i.e. is maxsum_{K*(38)+1}(T_37) <= 2112 with K*(38) bounded above by the ten-prime 31#-lattice covering run K*_{31#}({37,41,43,47,53,59,61,67,71,73})? In route 23's index convention A = largest m with maxsum_m(T_37) < 2112, this is the single comparison K*(38) < A(38): is the failure at s = 34 a boundary event or the start of a permanent death of the instrument?","budget_hours":4,"required_tools":["python3","gcc","numpy-segmented-sieve"],"required_sources":["served-project-docs","served-route-record","served-return-corpus","published-t31-maxsum-table","published-gap-ladder","published-covering-literature","served-engine-source","local-sympy","local-bounded-exec"]},"depends_on":[1293,588,594,599,606,609,891,901,936,956,966,969],"evidence_md":"Triage of route 105 (origin #1293/job #2547). Outcome: promising, after repair. (1) Criterion. maxsum_m is nondecreasing, so 'passes iff K*<m*' is correct only for route 23's index A = largest m with maxsum_m < 4*Ghat; under #2547's written definition B = least m with maxsum_m >= 4*Ghat it must read K*+1<B. #2547's table uses B at s=12..30 but A at s=32. From the published T_31 table (#588, reproduced #969): 4*Ghat=1392, maxsum_26=1380 <= 1392 < 1428=maxsum_27, so A=26, B=27. Route 23's own note that K*(32)=26 would fail is consistent with A; the written criterion (K*<27) would wrongly pass it. So the s=32 'near tie' holds in A and is margin 1 in B, and the convention must be fixed before m*(38) is defined. (2) Prior art. #2547's cross-check h2(n)=Ghat(p_n+1)+1 is REFUTED: h2 maximises over all even pair differences (Ziller-Morack Def. 4 / ancillary Def. 1.9) while Ghat(p_n+1) is the difference-2 object. h2(6)=150 at p=13 against tile T_13 max gap 66 (i.e. 67); likewise 192 vs 109, 258 vs 151, 366 vs 205. Section 4's maxgap.c computes the twin-difference gap, so it does not extend OEIS A288815; the register already WITHDREW 'extending h2 past 21 terms' and route 105 does not cite that. (3) Cost. #599's 28-core-h wall is superseded: #936 has K*(34)=29 and K*(36)=33 exactly, and #901's deletion lemma K*_(Pp)(R) <= K*_P(R u {p}) bounds K*(38) by the ten-prime 31#-lattice value K*_{31#}({37,...,73}) with no T_37 scan. The next step's 'K*(38) <= K*(37)+1 <= 39' is not that lemma, K*(37)<=38 is unestablished, and K* is not monotone across a block boundary or for non-nested Q (#609), so K*(38)>=28 is unavailable too. (4) Independent checks (this job). Full-phase K*(s) at s=5..14: the certificate FAILS at s=9,10,11,12 and passes at s=13,14 (per-fold oscillation, #606). m*(s) as B at s=8,12,14,18,20,24 = 7,7,10,13,16,19 and Ghat = 30,42,66,108,150,204 reproduce #2547's table from scratch. T_31 anchors: K*(32)=25 pass (1380<=1392), K*(34)=29 fail (1590>1392), K*(36)=33 fail. (5) Feasibility. One full T_37 pass is ~7-20 core-h (D_37=2.179e11 slots, 1013x the T_29 pass at the measured C rate); #2547's g37.err reached only ~block 1600/33263. That exceeds this assignment's 8 CPU-h by itself. The s=38 race is decisive in both directions, so the route is promising with the corrected, re-priced next step.","prior_art_md":"Online search 2026-09-19; queries: 'Jacobsthal function two residue classes per prime twins'; 'paired Jacobsthal function maximum gap'; 'generalized Jacobsthal function paired progressions'; 'covering run residue classes per prime interval Jacobsthal'; 'minimum modulus covering system Hough'; 'Kalmynin Konyagin Jacobsthal arbitrary residue sets'; 'maximum gap two-stage prime sieve'; 'OEIS A288815 A072753 paired Jacobsthal'. Inspected at source: Ziller-Morack arXiv:1706.03668 (abstract, Defs. 2-4, Cor. 1.3, Table 1 n=1..21, ancillary full_details.pdf) -- h2(n)=j2(p_n#), h2*(n)=h2(n)-1 is the greatest covered paired-progression length, h2=6*w2+6, computation stops at p_21=73; arXiv:1706.00317 Prop. 3.2 (h2(k)<p_k^2-p_k for all k>=3 implies Goldbach and prime-pair infinitude); Kalmynin-Konyagin arXiv:2302.00459 (polynomial Jacobsthal, arbitrary residue sets; lower bound only); Hough, Annals 181 (2015) 361-382 and Hough-Nielsen arXiv:1703.02133 (minimum modulus of a distinct covering of all of Z); Balister-Bollobas-Morris-Sahasrabudhe-Tiba arXiv:1811.03547 (uncovered-set density, minimum difference < 10^6); OEIS A144311 (twin tile max gap, = A144311+1 convention), A288815 (paired Jacobsthal, 21 terms, still p<=73), A072753 (=(h2-6)/6), A048670 (one-class, now 64 terms); Costello-Watts Math. Comp. 84 (2015) 1389-1399 (order-m one-class recursion, evaluated only at m=1); project SEARCH-CONVENTIONS rows for the Jacobsthal, paired-Jacobsthal, order-m and scan-statistic objects (Cressie 1977; Naus 1965/66; Glaz-Naus-Wallenstein 2001). Exact remaining gap: (i) no source bounds a finite two-class covering run of the level-restricted killer set Q(s)=(s,2s] at fixed tile T_{s-1}; the covering-system literature bounds the minimum modulus of coverings of Z and Kalmynin-Konyagin give only a lower bound for arbitrary residue sets, so the best two-class statement in print remains the unproven h2(n)<p_n^2-p_n; (ii) no source tabulates the threshold index m*(s) (not A144311, A288815 or A072753, which carry the gap ladder and the all-primes covering index); (iii) the route's own cross-check to the h2 ladder is refuted above, and extending h2 past 21 terms is already WITHDRAWN in research/OUTCOMES.md as infeasible and non-diagnostic. Access gaps: Hagedorn Math. Comp. 78 (2009) abstract only (AMS PDF 403); MathOverflow 497359 not re-fetched this session."},"research_route_id":105,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_23424801c73890cd6fd3264c","run_id":"run_1e3cac2821ce0a9ce994625b","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"victor-geere","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/105 and return #1293. Return the ordinary report and transcript plus research: {route_id: 105, 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":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"588","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"594","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"599","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"606","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"609","status":"rejected","final_rung":null,"canonical_return_id":null},{"id":"891","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"901","status":"accepted","final_rung":"proven","canonical_return_id":null},{"id":"936","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"956","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"966","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"969","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1293","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/105","transcript_url":"/projects/twin-primes/return/1298/transcript","files":[{"sha256":"bebaa7c6ea3f0565f2099b44b5e576bec791b957500249c67ed48d8a7901c697","name":"report.md","bytes":9894},{"sha256":"5d538c249af326dfcee39c626f4960b05a10d10278c5e00249c9d9f7c531b113","name":"mstar_convention.py","bytes":2628},{"sha256":"619b5145f3928766a5783ffc7bbd18252b243b0857a4b80a60ba135881048c17","name":"criterion_check.py","bytes":1975},{"sha256":"165e5d13c2efdd4c86b5169da8556f28a0ed1cf91639e73c0ee711cf0fedc4fc","name":"fullphase_check.py","bytes":2398},{"sha256":"f7ba42a539497f92bcbaad2841e99009d3db2afb853ae4804867ab94d9f36054","name":"transfer_check.py","bytes":1541},{"sha256":"57b921613e9ef3b4d6f79b2a546650474fe3cdef0338cb7d83159b9b932b2f8f","name":"tilecheck.py","bytes":671},{"sha256":"bdbb535ed0a2673e307cf7424aa9bbab94b26acfaf239539a49666824bafbfcd","name":"criterion_rows.json","bytes":3453},{"sha256":"32b120b217303a6c3019ac7d178748f9a60160781f2df847388c03a33a9259ff","name":"fullphase_rows.json","bytes":1642}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}