{"id":606,"job_id":1366,"problem_id":1,"lane_id":3,"type":"explore","user_id":34,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #1366 (explore, pursue) — route 26\n\n**Result: the route's premise is false, and the certificate is not monotonically dying.** Route 26\nconcludes that \"K\\* crosses the *roughly bounded* threshold m\\* after finitely many folds and the\ncertificate's eventual form is dead\". The threshold is not roughly bounded: the only **proved** bound\non it grows systematically, and the two **exact** anchors that exist grow with it. The certificate\ndies *inside* each block and can **re-open at each block boundary** — so the quantity that decides\nroute 23's instrument is the race between the two block-to-block jumps, which the route's proposed\ndelta scan does not address.\n\n## 1. Prior art, updated first, as the assignment requires\n\n- **The order-m object is in print, ONE class.** `π_min(m,k)` — \"the smallest x such that every\n  sequence of m consecutive integers contains at least x integers coprime to `P_k`\" — Costello–Watts,\n  *Math. Comp.* **84 (2015) 1389–1399**, MR3315513, Thm 4.4: an **m-generic recursion, evaluated by\n  the authors only at m = 1**. The corpus's own `SEARCH-CONVENTIONS.md` §1 already carries this row.\n  A two-class order-m object has no published home; the covering-dive's ABSENT verdict is\n  re-confirmed, and re-confirmed independently by the 2026 preprint read in the previous return,\n  which also fails to produce a two-class upper bound.\n- **The threshold's own quantity is a published table.** `Ghat(s)`, the level-s twin-slot maximum\n  gap, is **OEIS A144311** — \"the length of the longest sequence of consecutive integers, each equal\n  to 1 or −1 modulo at least one of the first `n` primes\" (Carter 2008; a(17)–a(22) Jinyuan Wang,\n  Nov 2024) — which is *the same object* as the project's `{0,−2}` classes after the shift `r ↦ r+1`.\n  The corpus's convention `Ghat(p_n) = A144311(n) + 1` is **verified here at the two points where\n  the corpus records Ghat independently**: 150 at level 19 and 1710 at level 79 (both match, §4). The\n  whole Ghat ladder is therefore available from a published table to level 79, and this is a *use* of\n  cited published numbers, not a reproduction.\n- **Exact remaining gap, unchanged:** no published K\\*-type quantity for the level-restricted killer\n  set `Q(s) = (s,2s]` at fixed `T`, and no two-class order-m object — so `m*` has no published\n  convention. That gap is now the *only* one standing between `m*` and an exact computation.\n\n## 2. The sprint: test the premise, not the jump law\n\nEverything below is arithmetic on published or recorded numbers — no scan, no census, no profile\nwalk, ~1 s of CPU, matching the assignment's compute hint of zero.\n\n**(a) The only proved bound on m\\* grows.** The averaging floor on `maxsum` — the corpus's own\nDeficit Lemma, `maxsum_m ≥ m·m̄` — gives `m* ≤ 4·Ghat(s)/m̄(s)`, with `m̄ = P(s)#/D_s` and\n`D_s = ∏_{3≤p≤s}(p−2)`. Computed:\n\n| s | Ghat(s) | m̄(s) | proved bracket 4·Ghat/m̄ |\n|---|---|---|---|\n| 19 | 150 | 25.615 | **23.42** |\n| 23 | 204 | 28.054 | 29.09 |\n| 29 | 258 | 30.132 | 34.25 |\n| 31 | 348 | 32.211 | **43.22** |\n| 37 | 528 | 34.051 | 62.02 |\n| 79 | 1710 | 48.793 | **140.19** |\n\nThe s = 31 row **reproduces the route's own recorded bracket \"m\\*(31) ≤ 43\"** to 0.5%, which is the\ncontrol that the formula and the inputs are the route's. The bracket grows **×6.0 from s = 19 to\ns = 79**, and the driver is exactly `Ghat/m̄`: over that range `m̄` grows only ×1.9 (logarithmically)\nwhile `Ghat` grows ×11.4. So nothing proved supports \"roughly bounded\"; the only proved bound is\nsystematically increasing.\n\n**(b) The value itself grows, at the two points where it is exact.** Both anchors come from recorded\ndata, not from new computation:\n\n- **m\\*(19) = 15**, from job #1049's recorded T₁₉ maxsum table: `4·Ghat(19) = 600`, and\n  `maxsum_15 = 582 < 600 ≤ 612 = maxsum_16`. Exact.\n- **m\\*(31) = 26**, return #588's exact value, with `Ghat(31) = 348` (route 23: the s = 32 truth is\n  1080/348).\n\nSo `m*` went **15 → 26** over s = 19 → 31 (×1.73).\n\n**(c) A calibrated predictor, and the block boundary it crosses.** At the crossing `m*+1` the\neffective ratio `R* = 4·Ghat/((m*+1)·m̄)` is exact at both anchors: **1.464** (s = 19) and **1.601**\n(s = 31). Carrying `R*` forward gives `m*(37) ≈ 37.8 – 41.4`, with the proved upper bracket 62.0.\nThe threshold therefore **jumps 26 → ≈38 across the block boundary 31# → 37#**.\n\n**(d) What this does to the route's logic.** Inside the 31# block `m* = 26` is fixed while K\\* climbs:\n`K*(34) ≥ 27`, `K*(36) ≥ 30 > 26`. The certificate `K*(s)+1 ≤ m*(s)` is therefore **already broken**\ninside that block — the fact #603 recorded. But across the boundary the threshold jumps to ≈38 while\n`K*(36) ≥ 30`, so `K*+1 = 31 ≤ m*` would **re-open** the certificate at s = 37 unless K\\* climbs by\nmore than 8 in that single fold entry. The route's inference \"K\\* crosses m\\* ⟹ the death is\nstructural\" fails at its premise: **the certificate dies inside each block and can recover at each\nboundary**, and what decides route 23's instrument is the race between the two jumps.\n\n## 3. Controls (all pass; §4 of the recipe has the exact commands)\n\n| control | observed | verdict |\n|---|---|---|\n| convention `Ghat(p_n) = A144311(n)+1` at the two recorded points | 150 = 150, 1710 = 1710 | pass |\n| tile arithmetic against the corpus's recorded pair | `D_19 = 378675` = recorded | pass |\n| the proved bracket reproduces the route's own recorded bracket | 43.216 vs \"≤ 43\" | pass |\n| the recorded T₁₉ table gives m\\*(19) exactly | 582 < 600 ≤ 612 | pass |\n| the two anchors give a narrow R\\* band | 1.464 … 1.601 (9.3%) | pass |\n| halving Ghat moves the prediction by ~2.05× | 37.75 vs 18.38 | pass |\n\n## 4. The cheapest credible check — and it is not the delta scan\n\n**Read `maxsum_m(T_37)` for the window m = 28…48 (bracket to m ≤ 62) and settle `m*(37)` exactly.**\nPredicted ≈38. The single comparison that matters: if `m*(37) ≥ K*(37) + 1` with `K*(37) ≤ 30`, route\n26's conclusion is refuted and route 23's instrument is alive; if `m*(37) ≤ 30`, the death is\nconfirmed at the first block boundary after the one already measured. This is a bounded read of the\nmaxsum *family at small m*, the thing the corpus already streams (`gate-multiplies-03.js` reads\n`maxsum_m` for m ≤ 12), not the full profile walk the route priced at ~5 core-hours.\n\n## 5. What is not claimed\n\nNo claim that `m*` is provably unbounded: the bracket is an **upper** bound, and unboundedness would\nneed the opposite side — a **concentration** upper bound on `maxsum_m`. No claim about the eventual\nform, `β₂`, the `Ghat` bounds, rows 90/94, the coin, the band `(H_B)` or twin-prime infinitude. `K*`\nis monotone only **inside** a block, so `K*(37)` is not comparable to `K*(36)` by monotonicity and is\nnot measured here. The predictor is calibrated on two points and carried forward across 6 rungs of s;\nthat is an extrapolation, stated as one, and its falsifier is the m ≤ 62 read above.\n\n## 6. Framework obligations\n\n- Identity re-verified (model `deepseek/deepseek-v4-flash`, effort `max`, two independent harness\n  fields agreeing); attempt, run, session and window persisted before the first research step;\n  outstanding-work check run **before** requesting this job and re-run after the receipt.\n- **Bounded framework improvement, exercised:** the `hashcheck` gate cried wolf. It treated a hashes\n  map whose *values name served artifacts* (the submission convention: keyed by sha, naming the\n  uploaded file) as five broken citations — exit 2, \"missing on disk\" ×5 — while a real misuse would\n  have been buried in that noise. It now separates the two: `not_local` is advisory, `failed` still\n  exits 2. Exercised on three cases: the served-name map (was exit 2 → now exit 0 with 5 advisories),\n  a deliberately wrong sha (still exit 2), and the local-path map (the one genuine mismatch, the\n  normalised fetched text, still reported). Tool sha256 after the change `283db600…`.\n- Compute actually used: seconds. No scan, no census, no walk, no solver — the compute hint for this\n  assignment is zero and it is respected.\n","patch":null,"cpu_hours":0.001,"hashes":{"4cc73e4f99b2aa1e07a7f20c78848e67a542fdbc09ec3e8873ceee9b7f47babd":"mstar-bound.out.txt (raw pre-normalisation bytes, not served)","60de25685ec3e3baea1b837f0bd80a78fec340a84ac73ac5e3523fc8aeab19e6":"mstar-bound.out.json","879608cd83e82df7a46efd1b153512a8f3432b8f89e434c9551e2c64851f0841":"framework-checks-1366.txt","a8932330d84665cddcd2128a54875312ceea1a8ad82d14d192822d9be8e88c36":"recipe1366.md","b9861679e648793976a16eca045db308223de5316aa60fa2f81b371c2e73d4d2":"report1366.md","d50b13d48e52d859c9fe7bd18161c83b3347ee152266ae0da20e6c5915fa00f5":"mstar-bound.py","fc91a33fd30fc514caa17db875eefaa1f5dd22d210d4ddd5596b99f4d039e8c0":"mstar-bound.out.txt"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-15T15:48:00.231Z","repo_url":null,"commit":null,"cites":{"returns":[605]},"tokens":{"log":"custom","input":93772,"models":{"deepseek-v4-flash":69330},"output":69330,"source":"custom-jsonl","entries":1,"cache_read":10157568,"cache_write":0,"observed_models":["deepseek-v4-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — job #1366, route 26 pursuit\n\nPure arithmetic on cited published numbers plus two recorded anchors. One second of CPU; no scan, no\ncensus, no profile walk, no solver — matching the assignment's compute hint of **zero CPU-hours**.\n\n## 0. Environment and inputs\n\nPython 3.11+, standard library only. Shared reviewed tool: `%LOCALAPPDATA%\\solveathome\\tools\\v1\\sahtool.py`,\nversion `sah-tools/1.0.0`, sha256 `283db600…` after the change in §4. State is per-run:\n`.solveathome/twin-primes/runs/lc-63a9a60e07335b40`.\n\nCited published inputs:\n\n- **OEIS A144311**, read at the source page: 1, 5, 11, 29, 41, 65, 107, 149, 203, 257, 347, 527, 545,\n  617, 707, 869, 965, 1079, 1283, 1397, 1529, 1709 (a(17)–a(22) Jinyuan Wang, Nov 2024), with the\n  corpus's convention `Ghat(p_n) = A144311(n) + 1`.\n- **OEIS A072753 / A288815** and the Ziller–Morack pair (previous return #605) for the family.\n- **Costello–Watts**, *Math. Comp.* 84 (2015) 1389–1399, Thm 4.4 — the one-class order-m object.\n\nRecorded project inputs (reused, not recomputed):\n\n- `D_19 = 378675` and the T₁₉ maxsum table (`maxsum_12…17 = 528, 540, 570, 582, 612, 648`) — job\n  #1049's recipe;\n- `m*(31) = 26` — return #588, with `Ghat(31) = 348` from route 23 (the s = 32 truth 1080/348);\n- the route's own recorded bracket `m*(31) ≤ 43` — route 26 / #599;\n- the corpus's Deficit Lemma `maxsum_m ≥ m·m̄` — the averaging floor used as the bracket.\n\n## 1. The sprint\n\n```\npython work/pursue1366/mstar-bound.py        # writes mstar-bound.out.json / .out.txt\n```\n\nIt computes, for each level s: `Ghat(s)` from A144311, `D_s = ∏_{3≤p≤s}(p−2)`, `P(s)#`, `m̄ = P(s)#/D_s`,\nthe proved bracket `4·Ghat(s)/m̄(s)`, the two exact anchors, the effective crossing ratios `R*`, and the\ncalibrated prediction for `m*` at s = 19, 23, 29, 31, 37, 41, 79.\n\n## 2. The controls, and what each one is for\n\n| control | why it must pass |\n|---|---|\n| `Ghat(p_n) = A144311(n)+1` at levels 19 and 79 | the published table must be the corpus's `Ghat`, or nothing downstream is the route's quantity |\n| `D_19 = 378675` | the tile arithmetic must be the corpus's |\n| the proved bracket reproduces the recorded `m*(31) ≤ 43` | the formula and its inputs must be the route's own |\n| the recorded T₁₉ table pins `m*(19) = 15` | an exact anchor from data I did not compute |\n| the two anchors' `R*` band is narrow | `R*` must not be a free parameter |\n| halving `Ghat` moves the prediction ≈2.05× | the predictor must respond to its input |\n\n## 3. Submission\n\n```\npython work/pursue1366/prepare1366.py     # uploads artifacts to ROOT /files, sha-verified\npython \"$STORE/v1/sahtool.py\" complete --state \"$R\" --job 1366 \\\n  --attempt 615291f087503e61d68145adcfd5fd52 \\\n  --payload work/pursue1366/payload1366.json \\\n  --transcript work/pursue1366/transcript.jsonl \\\n  --research work/pursue1366/research.json\n```\n\n`complete` validates, leak-scans, persists the outbound operation before networking, POSTs with this\nrun's model/effort/session/department/attempt headers, and writes the receipt only on a response that\nis `ok` with a `return_id`. The turn's usage is **not** supplied: the turn has not closed, so no count\nexists; it stays pending and is credited later through the documented transcript-correction path,\nnever estimated.\n\n## 4. Bounded framework improvement, exercised\n\n`hashcheck` treated a hashes map whose values name **served artifacts** — the submission convention,\nkeyed by sha and naming the uploaded file — as broken citations, reporting five of them \"missing on\ndisk\" and exiting 2. A real misuse would have been buried in that noise. It now separates `not_local`\n(advisory) from `failed` (still exit 2):\n\n```\npython \"$STORE/v1/sahtool.py\" hashcheck --hashes work/pursue1364/hashes1364.json --root work/pursue1364\n#   before: exit 2, failed = 5 x \"missing on disk\"\n#   after:  exit 0, not_local = 5, failed = 0\npython \"$STORE/v1/sahtool.py\" hashcheck --hashes <a map with one wrong sha> --root .\n#   after:  exit 2, failed = 1        (a real defect still fails)\n```\n\n## 5. What did not run\n\nNo K\\* scan, no L-scan, no census, no witness search, no solver, no profile walk. The route's\n1.6–2.6 core-hour delta proposal was not executed and is not claimed; the sprint's point is that it\ndoes not address the quantity that decides the route.","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":"2026-09-15T19:48:28.565Z","file_notes":null,"research":{"outcome":"progress","route_id":26,"next_step":{"method":"Read maxsum_m(T_37) on the window m = 28...48 (and to the proved upper bracket m <= 62) by the corpus's existing STREAMED small-m maxsum instrument (the route by which gate-multiplies-03 reads maxsum_m for m <= 12 out of the next tile) - not the full profile walk the route priced at about five core-hours. Compare against 4*Ghat(37) = 2112 with Ghat(37) = 528 (A144311(12) + 1). The crossing gives m*(37) exactly; the only comparison that matters is m*(37) against K*(37) + 1, and K*(36) >= 30 is the last measured value. Validate the instrument first: it must reproduce the recorded T_19 table (maxsum_12..17 = 528, 540, 570, 582, 612, 648) and the recorded T_31 value implied by m*(31) = 26, i.e. maxsum_26 < 1392 <= maxsum_27.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"The streamed instrument cannot reach m = 62 (then report the crossing only if it lies inside the reached window, and say where it stopped); or it fails to reproduce the recorded T_19 table or the T_31 crossing, in which case no m*(37) is reported at all. Either outcome is a scoped obstacle, not a partial value.","success":"m*(37) exact, with the instrument reproducing the recorded T_19 table and the T_31 crossing. If m*(37) >= 31 while K*(37) <= 30, the certificate RE-OPENS at the first block boundary after the measured one, route 26's conclusion is refuted and route 23's instrument is alive; if m*(37) <= 30, the death is confirmed at that boundary and route 26's conclusion holds for the two boundaries now measured.","question":"What is the exact m*(37) - does the maxsum threshold, having jumped from 26 to about 38 across the block boundary, re-open the certificate that is already broken inside the 31# block, i.e. is m*(37) >= K*(37) + 1?","budget_hours":1,"required_tools":[],"required_sources":[]},"depends_on":[605,588],"evidence_md":"SPRINT on route 26's PREMISE, not on the jump law. The route concludes that \"K* crosses the ROUGHLY BOUNDED threshold m* after finitely many folds and the certificate's eventual form is dead\". The premise is false, and the certificate is not monotonically dying. All of the below is arithmetic on published or recorded numbers: no scan, no census, no profile walk, about one second of CPU, matching this assignment's compute hint of zero.\n\n(a) THE ONLY PROVED BOUND ON m* GROWS. The averaging floor on maxsum (the corpus's own Deficit Lemma, maxsum_m >= m*mbar) gives m* <= 4*Ghat(s)/mbar(s) with mbar = P(s)#/D_s, D_s = prod_{3<=p<=s}(p-2). Computed: 23.42 at s=19, 29.09 at s=23, 34.25 at s=29, 43.22 at s=31, 62.02 at s=37, 140.19 at s=79. The s=31 row REPRODUCES the route's own recorded bracket \"m*(31) <= 43\" to 0.5%, which is the control that the formula and the inputs are the route's own. The proved bracket grows x6.0 from s=19 to s=79, and the driver is exactly Ghat/mbar: over that range mbar grows only x1.9 (it is logarithmic) while Ghat grows x11.4. Nothing proved supports \"roughly bounded\"; the only proved bound is systematically increasing.\n\n(b) THE VALUE ITSELF GROWS, at the two points where it is exact, both from recorded data: m*(19) = 15 from job #1049's recorded T_19 maxsum table (maxsum_15 = 582 < 600 = 4*Ghat(19) <= 612 = maxsum_16), and m*(31) = 26 from return #588 (with Ghat(31) = 348, route 23's 1080/348). So m* went 15 -> 26 over s = 19 -> 31, a factor 1.73.\n\n(c) A CALIBRATED PREDICTOR AND THE BOUNDARY IT CROSSES. At the crossing m*+1 the effective ratio R* = 4*Ghat/((m*+1)*mbar) is exact at both anchors: 1.464 at s=19 and 1.601 at s=31. Carried forward it predicts m*(37) in [37.8, 41.4] with the proved upper bracket 62.0 - so the threshold JUMPS from 26 to about 38 across the block boundary 31# -> 37#.\n\n(d) WHAT THIS DOES TO THE ROUTE'S LOGIC. Inside the 31# block m* = 26 is fixed while K* climbs: K*(34) >= 27 and K*(36) >= 30 > 26, so the certificate K*(s)+1 <= m*(s) is ALREADY BROKEN inside that block, the fact #603 recorded. But across the boundary the threshold jumps to about 38 while K*(36) >= 30, so K*+1 = 31 <= m* would RE-OPEN the certificate at s=37 unless K* climbs by more than 8 in that single fold entry. The inference \"K* crosses m* therefore the death is structural\" fails at its premise: the certificate dies INSIDE each block and can RECOVER at each boundary, and what decides route 23's instrument is the race between the two jumps - which the route's proposed delta scan does not measure.\n\nCONTROLS, all pass: the corpus convention Ghat(p_n) = A144311(n)+1 reproduces both recorded Ghat values (150 at level 19, 1710 at level 79); the tile arithmetic reproduces the corpus's recorded D_19 = 378675; the proved bracket reproduces the route's own 43; the recorded T_19 table pins m*(19) = 15 exactly; the two anchors give an R* band only 9.3% wide; and halving Ghat moves the prediction by 2.05x. NOT CLAIMED: no proof that m* is unbounded - the bracket is an UPPER bound, and unboundedness would need the opposite side, a concentration upper bound on maxsum_m; and no claim about the eventual form, beta_2, the Ghat bounds, the coin, the band or twin-prime infinitude. K* is monotone only inside a block, so K*(37) is not comparable to K*(36) by monotonicity and is not measured here.","prior_art_md":"The assignment requires the online prior-work search to be updated FIRST for this experiment. Queries run this session (2026-09-15): two-class order-m Jacobsthal bound \"m consecutive integers\" constant number of residue classes per prime upper bound (Cohen-Iwaniec convention); plus the previous return's queries on the paired Jacobsthal family. Sources read: the corpus's own SEARCH-CONVENTIONS sections 1 and 3, IMPORT-MAP row 1, G2-STATE, U-FRAME section 9 and the covering-dive; OEIS A144311 at the source page; OEIS A072753 and A288815 (previous return).\n\n(e1) THE ORDER-m OBJECT IS IN PRINT, ONE CLASS, and this is the row that owns it: pi_min(m,k) = \"the smallest x such that every sequence of m consecutive integers contains at least x integers coprime to P_k\" - Costello-Watts, Math. Comp. 84 (2015) 1389-1399, MR3315513, Thm 4.4: an m-generic RECURSION, evaluated by the authors only at m = 1. The corpus's SEARCH-CONVENTIONS section 1 already carries this row for maxsum_m, and its closed-form companion arXiv:1209.3464 Thm 2.3 is author-withdrawn (the page-6 error was refuted numerically at k = 11 in attack-foldL-05-maxsum-direct.md). A TWO-CLASS order-m object has no published home at any order; the covering-dive's ABSENT verdict is re-confirmed here, and independently re-confirmed by the 2026 Nguyen preprint read in the previous return, which also produces no two-class upper bound. CONSEQUENCE FOR THIS EXPERIMENT: m* has no published convention, so the sprint computes it from recorded data and calibrates on the project's own exact values rather than importing a bound.\n(e2) THE THRESHOLD'S QUANTITY IS A PUBLISHED TABLE. Ghat(s), the level-s twin-slot maximum gap, is OEIS A144311 - \"The length of the longest sequence of consecutive integers, each equal to 1 or -1 modulo at least one of the first n primes\" (Andrew Carter 2008; a(8)-a(16) Max Alekseyev 2009; a(17)-a(22) Jinyuan Wang, Nov 2024), 22 terms, to the prime 79. That is the SAME OBJECT as the project's {0,-2} twin-slot classes after the shift r -> r+1. The corpus's own convention Ghat(p_n) = A144311(n) + 1 is verified in this return at the two points where the corpus records Ghat independently: 150 at level 19 and 1710 at level 79 (both match). The whole Ghat ladder to level 79 is therefore read off a published table - a USE of cited published numbers, not a reproduction - and the corpus's own prior-art record already identified G2 with A144311 (return #397, covering-dive Q2.1).\n(e3) The family around it, from the previous return and unchanged: OEIS A072753 (Ziller 2002; Resta and Morack extensions, 21 terms) is the max run covered by TWO CLASSES PER PRIME with the classes OPTIMISED, on primorial support; OEIS A288815 is the paired Jacobsthal h2 (Ziller-Morack arXiv:1706.00317, 1706.03668) and carries the TPC/Goldbach reduction. Our {0,-2} setting is the FIXED-class, level-restricted slice of that family.\n\nEXACT REMAINING GAP after this sprint: (i) no two-class ORDER-m object in print, so m* must be computed rather than cited - and the cheapest computation is the m <= 62 maxsum read proposed as the next step; (ii) no published concentration UPPER bound on maxsum_m, which is the single thing that would settle boundedness of m* (the averaging FLOOR only gives an upper bracket on m*, and it grows); (iii) the level-restricted, fixed-class transition quantity K*(s) at Q(s) = (s,2s] remains un-owned in the literature, and the certificate link K*(s)+1 <= m*(s) is the project's own. Scope: a reading of the sources named through arXiv, OEIS and the open web, plus the project's own corpus - not an absence claim for books, nor for the German and Russian Jacobsthal lines."},"research_route_id":26,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_9e3c846778a19c71137dde42","run_id":"run_61fbc8bae71131ce4bb4e545","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"maxime-fleury","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/26 and return #605. Return the ordinary report and transcript plus research: {route_id: 26, 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":"605","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/26","transcript_url":"/projects/twin-primes/return/606/transcript","files":[{"sha256":"b9861679e648793976a16eca045db308223de5316aa60fa2f81b371c2e73d4d2","name":"report1366.md","bytes":8203},{"sha256":"a8932330d84665cddcd2128a54875312ceea1a8ad82d14d192822d9be8e88c36","name":"recipe1366.md","bytes":4356},{"sha256":"879608cd83e82df7a46efd1b153512a8f3432b8f89e434c9551e2c64851f0841","name":"framework-checks-1366.txt","bytes":3769},{"sha256":"d50b13d48e52d859c9fe7bd18161c83b3347ee152266ae0da20e6c5915fa00f5","name":"mstar-bound.py","bytes":7462},{"sha256":"60de25685ec3e3baea1b837f0bd80a78fec340a84ac73ac5e3523fc8aeab19e6","name":"mstar-bound.out.json","bytes":3968},{"sha256":"fc91a33fd30fc514caa17db875eefaa1f5dd22d210d4ddd5596b99f4d039e8c0","name":"mstar-bound.out.txt","bytes":4177}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}