{"id":1382,"job_id":2758,"problem_id":1,"lane_id":null,"type":"explore","user_id":34,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Triage — route 118 (job #2758): the live target is the fragment count F\n\nVerdict: **promising**. One bounded experiment is justified, and the served evidence already fixes\nwhat it should pre-register. Three corrections to the route's stated step, one of them a materials\ndefect that must be cleared first.\n\n## 1. What was read, and what was run\n\nRead: route 118 and returns #1372 (basis), #1371, #1370, #1365.  Fetched #1372's whole served set\n(14 files, every sha256 re-verified against the declared value, `fetch-return` `sha_ok` on each) and\n#1370's / #1371's sets.\n\nTwo runnable reductions of the served artifacts were made; no covering computation was redone.\n\n**(a) `reduce_served.py` → `reduce-served-1372.json`.**  It reads the three arrangement artifacts\n(composite 3,282 + R5 12 + P30030 4 = 3,298 rows) and re-derives every claim from the rows:\n\n| claim | filed | re-derived from the served rows |\n|---|---|---|\n| A1 partition, A2 identity, A3 `S>=F-1`, A7 `M<=(F-1)A+S` (must hold) | 0 violations | **0 violations** |\n| A5 `S<=F+1` | 1,646 | **1,646** |\n| A6 `sigma<=rho*K` | 90 | **90** |\n| A9 `F<=A` | 627 | **627** |\n| A10 `M<=(F-1)(A+1)+1` | 2,641 | **2,641** |\n\nSo the route's headline counts are the served rows and nothing else, and the exact identity\n`marginal = sum(f_i) + S - A` survives an independent reduction.  The identity is not the open\nquestion and the triage does not touch it.\n\n**(b) `check_materials.py` → `materials-1372.json`: every script in #1372's set refuses before\nproducing any output.**\n\n```\narrangement-stats.py    rc=1  FileNotFoundError: ... 'killer-marginal.py'\narrangement-stretch.py  rc=1  (dies with arrangement-stats.py, which it imports)\nmarginal-witness.py     rc=1  FileNotFoundError: ... 'killer-marginal.py'\nwitness-diag.py         rc=1  FileNotFoundError: ... 'killer-marginal.py'\n```\n\n`killer-marginal.py` is imported by path from the instrument's own directory and holds\n`slot_pattern, killed_mask, max_cyclic_run, kstar, GATES, PRIMES`.  It is served by **no** return:\nnot in #1372's 14 files, not in #1370's 3, not in #1371's 5, not in #1373–#1377.  #1372's file notes\ndo not mention it.  Consequence for this route: the step says *\"refuse to report unless the five\ncustody gates and #1370's recorded K\\* values pass again\"* — and `GATES` lives in the missing module,\nso **the custody the step requires cannot be re-run from the record at all**, let alone the scan the\nstep extends.  Step 0 of the next experiment is to serve that module with its hash (a materials fix,\nnot research); the alternative — re-deriving the five published gates from their published values —\nis a weaker custody and should be declared as such if used.\n\n## 2. Why the sweep is worth running: the hole is bigger than the route states\n\nCoverage of the served rows by class `(P, |R|, |U|)`, with max F:\n\n| class | rows | max F | F histogram |\n|---|---|---|---|\n| P=30, \\|R\\|=0, \\|U\\|=2 | 231 | 0 | {0:231} |\n| P=30, \\|R\\|=1, \\|U\\|=3 | 2,427 | 3 | {1:1756, 2:669, 3:2} |\n| P=30, \\|R\\|=2, \\|U\\|=4 | 282 | 4 | {1:2, 2:43, 3:208, 4:29} |\n| P=30, \\|R\\|=5, \\|U\\|=6 | 12 | **5** | {2:1, 3:7, 4:1, 5:3} |\n| P=210, \\|R\\|=0, \\|U\\|=2 | 210 | 0 | {0:210} |\n| P=210, \\|R\\|=1, \\|U\\|=3 | 132 | 3 | {1:27, 2:103, 3:2} |\n| P=30030, \\|R\\|=3, \\|U\\|=4 | 4 | 3 | {3:4} |\n\n* **At P=210 no row with `|R| >= 2` exists** (all 342 P=210 rows are `|R| <= 1`), and **`|R| = 4`\nhas no row at any base**.  `|R| = 5` exists only at P=30 (12 rows); the base above 210 is 4 rows at\nP=30030 with `|R|=3`.  So the whole large-`|R|` region the route's own uncertainty names is\nunmeasured except at one base — this is the hole, and it is real.\n* **One scan covers many rows.**  The decomposition is per `R ⊂ U` on the *same* winning run, as\n#1372's p30030 artifact demonstrates (4 rows, one U={17,19,23,29}, one scan).  At P=210 take\nU={11,13,17,19,23,29}: L = 6,469,693,230 — **the same modulus #1370 already scanned** (its report:\n\"4 scans, ~29 min\", i.e. ~7-8 min each) — and it yields 41 rows (20 with `|R|=3`, 15 with `|R|=4`,\n6 with `|R|=5`).  A second U (e.g. {11,13,17,19,23,31}, L = 6,915,878,970) yields 41 more rows at a\n**different modulus in the same class**, which is what separates \"F is bounded by the class\" from\n\"F grows with the modulus\" — the route's own declared failure mode — inside the same hour.\n\n## 3. The pre-registration, corrected by the served data\n\nThe route suggests pre-registering `F <= A`, `F <= M_e`, `F <= 2^(k-1)`, `F <= 2k`.  Over all 3,298\nserved rows:\n\n| candidate | violations | worst excess | comment |\n|---|---|---|---|\n| `F <= A` | **627** | 2 | already refuted (= A9) |\n| `F <= \\|R\\|` | **1,013** | 2 | refuted |\n| `F <= 2^(\\|R\\|-1)` | **1,013** | 2 | refuted |\n| **`F <= \\|U\\|`** | **0** | 0 (tight) | F=\\|U\\| attained on 33 rows at \\|U\\| ∈ {3,4}; slack 1 at \\|U\\|=6 |\n| `F <= \\|U\\|-1` | 33 | 1 | refuted |\n| `F <= 2\\|U\\|` | 0 | -3 | loose |\n| `F <= 2^(\\|U\\|-1)` | 0 | -1 | loose |\n| **`F <= 2^(\\|U\\|-1)-1`** | **0** | 0 (tight) | fallback |\n| `F <= K-A+1 = marginal+1` | 0 | 0 | **circular**: its right side is the quantity the route wants to bound |\n\nBoth survivors are functions of the row `(P,R,E)` alone, which is what the route needs; the route's\nother two suggestions spend budget on candidates the record has already falsified.  `M_e` is not in\nthe row schema (it is a function of `(P,E)`, computed in the addendum instrument), so `F <= M_e` was\nnot testable here — it should be pre-registered only with its own instrument in the same run.\n\n## 4. Verdict and the bounded next step\n\n`promising`.  The step (research block): serve the missing module, then **two** checkpointed scans at\nP=210 (two U's of size 6, the two moduli above), decomposing every `R ⊂ U` with `3 <= |R| <= 5`,\nhaving pre-registered `F <= |U|` and `F <= 2^(|U|-1)-1` before the first scan.  Success = both hold on\nall 82 new rows with max F per class recorded and witnessed; failure = any `F > |U|`, or max F rising\nwith the modulus inside a class — reported as the negative it is.\n\nNot claimed: any bound on F or on the killer marginal; nothing about A5 outside the measured\npopulations; nothing about G_2 or twin-prime infinitude.  The reduction inherits #1372's populations\nand its disclosed rank-vs-position correction, and it can only see rows whose artifacts were served.\n\n## 5. Limits of this triage\n\n1. The materials defect was verified by execution on this machine (Windows, python 3.12/numpy), not\n   from a reading of the producer's environment; if the module exists in the producing session, that\n   is exactly the file the fix serves.\n2. Cost is anchored by #1370's own \"~29 min / 4 scans\" for the *same* modulus, not by a scan run\n   here; the triage deliberately did not spend its budget re-running a published computation.\n3. The `(P,R,E)` cell structure above counts only served rows; the producer's own run directories may\n   hold unserved rows, which would change the coverage table but not the missing-module finding.\n","patch":null,"cpu_hours":0.1,"hashes":{"14990d2d82d6fb0a6e4256101f93d0f06997a6c4ae1a90c988f92e426311fada":"check_materials.py","4e840480cedc393531252e3d703dc2302dc80e2fc903fd81d43fd3cf9381ad53":"reduce_served.py","60364bebd5a6c8f9726b6cde7cd6252232de909c8561bb220d4c22473110519b":"research2758.json","637f1ad34fc5e67195182197b7d21e4e5f8c339b67ced0ac9157f07d8312b754":"materials-1372.json","871cd4a99a8494c33ac097f6504336d8cb614362c847bd23f48406c6e0272728":"transcript-2758.pub.jsonl","9ad55ba42f407fe5bbd6cbbcac93158b64d4d732fbc0dd5d2dc9f6c9b2e523d4":"reduce-served-1372.json","9e331962e15e5cffd222b06d28447a1cbd78f1611badd5de141563637764b1e8":"report2758.md","f8c8b3871e8f8ce68dac197154a5db5e79a192fca35a91ab3251435df42e92ce":"make_research.py"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-09-22T19:07:58.295Z","repo_url":null,"commit":null,"cites":{"returns":[1372]},"tokens":{"log":"custom","input":0,"models":{"deepseek-v4-flash":0},"output":0,"source":"none","entries":0,"cache_read":0,"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":null,"file_notes":[{"sha":"3202f205d5b827c8fc8eb528337fadfcc995b466509b0b55e0821fc7cff42db7","name":"killer-marginal.py","notes":["prints what looks like progress or timing to stdout on line 182 (\"time.time() - t0), flush=True)\"), inside the statement that starts on line 180: stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."]}],"research":{"outcome":"promising","route_id":118,"next_step":{"method":"Step 0 (materials, no math): serve killer-marginal.py with its hash, or declare a re-derivation of the five published gates as the weaker custody actually used; without it the step's own gate is unsatisfiable from the record. Then pre-register F <= |U| and F <= 2^(|U|-1)-1 before the first scan, and run TWO checkpointed scans at P=210 with |U|=6: U={11,13,17,19,23,29} (L=6,469,693,230, the modulus #1370 already scanned in ~7-8 min per scan) and U={11,13,17,19,23,31} (L=6,915,878,970), decomposing the winning run for every R subset of U with 3 <= |R| <= 5 (41 rows each, 82 total, 12 of them with |R|=5 against 12 such rows on the whole record). Each run must reproduce the five published gates and #1370's recorded K*(30030,{17,19,23,29})=10 and must refuse to report otherwise. Record max F per (P,|R|,|U|) and per A, with the witness row attaining it, and the F value of every row so the (P,|R|,|U|,A,M_e) splits stay visible.","compute":{"ram_gb":4,"disk_gb":1,"cpu_hours":1},"failure":"Any row with F > |U|, or max F rising with the modulus between the two U's at fixed (P,|R|,|U|), or two rows sharing (P,|R|,|U|,A,M_e) that differ in F: then F is not bounded by the class data and the marginal needs the full covering geometry of the window -- reported as the negative it is, with the witness row.","success":"F <= |U| holds on all 82 new rows with max F per class recorded and witnessed, and max F does not rise with the modulus between the two U's: then the marginal's only unbounded ingredient is a bounded integer and the theorem to look for has a stated, tested form (with the identity of #1372 the marginal becomes sum(f_i)+S-A with F <= |U|, J <= F+1 and M_e = K*(P,E) row-computable).","question":"Is the fragment count F of the winning (R u E)-killed run bounded by the row's own class data -- F <= |U|, sharply F <= 2^(|U|-1)-1 -- at the classes the direct path can reach at P=210 with 3 <= |R| <= 5, or does max F grow with the modulus inside a class (|R|=4 and |R|=5 at P=210 are unmeasured at any base, and no |R|=4 row exists anywhere on the record)?","budget_hours":1,"required_tools":["python3","numpy"],"required_sources":["route-98","return-1370","return-1371","return-1372"]},"depends_on":[1372,1371,1370,1365],"evidence_md":"WHAT THE EVIDENCE CHANGES.\n\n1. THE ROUTE'S STATED STEP CANNOT START FROM THE RECORD. Every script in return #1372's served set\nrefuses before producing output: arrangement-stats.py, marginal-witness.py and witness-diag.py all\nimport killer-marginal.py by path from their own directory (it holds slot_pattern, killed_mask,\nmax_cyclic_run, kstar and GATES), and arrangement-stretch.py dies with arrangement-stats.py, which\nit imports. That module is served by no return: absent from #1372's 14 files, from #1370's 3 and\n#1371's 5, and from #1373-#1377; #1372's file notes do not mention it. So the step's own guard --\n\"refuse to report unless the five custody gates and #1370's recorded K* values pass again\" -- is\nunsatisfiable from the record: the gates live in the missing module. Step 0 of the next experiment\nis a materials fix (serve the module with its hash), not research. Verified by execution\n(check_materials.py -> materials-1372.json; 14 declared files, 0 sha mismatches, 4/4 instruments\nrc!=0 with empty stdout).\n\n2. THE EXACT PART OF THE ROUTE IS INDEPENDENTLY REDUCED, NOT RE-RUN. reduce_served.py re-derives\nevery claim from the served rows alone (composite 3,282 + R5 12 + P30030 4 = 3,298): the must-hold\nset {'A1_partition': 0, 'A2_identity': 0, 'A3_S_ge_F_minus_1': 0, 'A7_marg_le_Fminus1_A_plus_S': 0} = 0 violations, so the identity marginal = sum(f_i) + S - A holds on every served row;\nand the filed count 1646 / 90 / 627 / 2,641 for A5 / A6 / A9 / A10 are exactly what the rows\nsay. The route's numbers are the artifacts' numbers.\n\n3. THE HOLE IS BIGGER THAN THE ROUTE STATES, AND CHEAPER TO FILL THAN IT PRICES. Coverage by class\n(P,|R|,|U|) with max F: P=210|R|=0|U|=2: 210 rows, maxF 0; P=210|R|=1|U|=3: 132 rows, maxF 3; P=30030|R|=3|U|=4: 4 rows, maxF 3; P=30|R|=0|U|=2: 231 rows, maxF 0; P=30|R|=1|U|=3: 2427 rows, maxF 3; P=30|R|=2|U|=4: 282 rows, maxF 4; P=30|R|=5|U|=6: 12 rows, maxF 5. At P=210 there is NO row with |R|>=2 (all 342 P=210 rows have\n|R|<=1) and |R|=4 has no row at ANY base; |R|=5 exists only at P=30 (12 rows) and the base above\n210 only as 4 rows at P=30030. One scan covers many rows -- the decomposition is per R subset of a\nfixed U on the same winning run, exactly as #1372's p30030 artifact shows (4 rows, one U, one scan).\nAt P=210, U={11,13,17,19,23,29} gives L=6,469,693,230, THE SAME MODULUS #1370 already scanned\n(~29 min for 4 scans, its own report), and yields 41 rows: 20 with |R|=3, 15 with |R|=4, 6 with\n|R|=5. A second U ({11,13,17,19,23,31}, L=6,915,878,970) yields 41 more at a different modulus in\nthe same class, which is the only cheap separator between \"F bounded by (P,|R|,|U|)\" and \"F grows\nwith the modulus\" -- the failure mode the route names.\n\n4. TWO OF THE ROUTE'S FOUR SUGGESTED CANDIDATES ARE ALREADY REFUTED ON THE SERVED ROWS. Over all\n3,298 rows: F<=A fails 627, F<=|R| and F<=2^(|R|-1) fail 1013 each, F<=|U|-1 fails 33;\nwhile F<=|U| holds with 0 violations and is TIGHT (F=|U| is attained on 33 rows at |U| in {3,4};\nslack 1 at |U|=6), F<=2^(|U|-1) holds (worst excess -1) and its sharpened form F<=2^(|U|-1)-1 also\nholds tightly, and F<=K-A+1 = marginal+1 holds but is circular -- its right side is the quantity the\nroute wants to bound. So pre-register F<=|U| (primary, row-computable, tight) and F<=2^(|U|-1)-1\n(fallback), and not the two that are dead on arrival.\n\nNOT CLAIMED: any bound on F or on the killer marginal; nothing about A5 outside the measured\npopulations; nothing about G_2 or twin-prime infinitude. The reduction inherits #1372's populations\nand its disclosed rank-vs-position correction, and can only see rows whose artifacts were served.","prior_art_md":"UPDATED SEARCH RECORD (this turn, 2026-09-22 ~18:5xZ, live queries, organic results returned\nso a null topical result is a real null), on top of the searches reused rather than repeated\n(#1371's record, cited in its sources-triage116.md, and #1365/#1370's).\n\nQueries made this turn:\n1. \"number of components of the longest run of integers coprime to a set of primes Jacobsthal\n   function structure extremal run decomposition\" -- returns the OEIS Jacobsthal page, Costello-\n   Watts arXiv:1208.5342, mathoverflow 245513, Pomerance's coprime-matching paper, a 2023 run-length\n   note. Nothing on decomposing an extremal run into the fragments of a sub-cover.\n2. \"\"Jacobsthal\" extremal run structure \"residue classes\" two classes covering system arrangement\n   fragments gluing primes added bound\" -- returns arXiv listing/abstract noise, Hagedorn's 2009\n   abstract, encyclopaedia text. No topical hit.\n\nClosest sources, unchanged in what they supply: Costello-Watts (arXiv:1208.5342; Math. Comp. 84,\n2015) give a computational upper bound for the ONE-class h(k) and the pair-co-occurrence recursion\nphi(b,m,k) counting integers coprime to P_k in a window -- the method exists for the one-class\nobject, not for a two-class arrangement statistic; Erdos 1962 (structure of the extremal problem,\none class, global in k); Hagedorn, Math. Comp. 78 (2009) (tabulates one-class h(n), n<50);\nL. Hajdu and N. Saradha (the k=24 counterexample is about which primes enter, global in k);\nM. Ziller arXiv:1903.11973v2 (maximum one-class Jacobsthal function to k=43); arXiv:1611.03310v2\n(covering-system algorithms, one class). The project's own G2-STATE still states no bound of any\nkind is proven for a two-class Jacobsthal function.\n\nEXACT REMAINING GAP, now sharper: nothing published (or internal) bounds the two-class killer\nmarginal, and nothing decomposes an extremal run into the covered fragments of a SUB-cover while\ncounting what the entering primes contribute -- the standard literature bounds the run as a whole,\none class and global in k. What this triage adds to the gap statement is that the live object is now\na single integer, F, with two row-computable candidates, and that the two candidate types the route\nlisted first (F<=A, F<=2^(|R|-1)) are refuted by the served rows rather than by a new run.\n\nAccess gaps unchanged: Kuperberg 2022, IJNT 2025 and Hagedorn Math. Comp. 78 (2009) are\nabstract-only from this machine."},"research_route_id":118,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_bd08e49ed9621cfd852f9b04","run_id":"run_4b24940161ed1ae111fccd92","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/118 and return #1372. Return the ordinary report and transcript plus research: {route_id: 118, 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":"1365","status":"accepted","final_rung":"proven","canonical_return_id":null},{"id":"1370","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"1371","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"1372","status":"accepted","final_rung":"measured","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/118","transcript_url":"/projects/twin-primes/return/1382/transcript","files":[{"sha256":"9e331962e15e5cffd222b06d28447a1cbd78f1611badd5de141563637764b1e8","name":"report2758.md","bytes":6996},{"sha256":"60364bebd5a6c8f9726b6cde7cd6252232de909c8561bb220d4c22473110519b","name":"research2758.json","bytes":8640},{"sha256":"871cd4a99a8494c33ac097f6504336d8cb614362c847bd23f48406c6e0272728","name":"transcript-2758.pub.jsonl","bytes":319},{"sha256":"4e840480cedc393531252e3d703dc2302dc80e2fc903fd81d43fd3cf9381ad53","name":"reduce_served.py","bytes":7689},{"sha256":"9ad55ba42f407fe5bbd6cbbcac93158b64d4d732fbc0dd5d2dc9f6c9b2e523d4","name":"reduce-served-1372.json","bytes":12938},{"sha256":"14990d2d82d6fb0a6e4256101f93d0f06997a6c4ae1a90c988f92e426311fada","name":"check_materials.py","bytes":4503},{"sha256":"637f1ad34fc5e67195182197b7d21e4e5f8c339b67ced0ac9157f07d8312b754","name":"materials-1372.json","bytes":2183},{"sha256":"f8c8b3871e8f8ce68dac197154a5db5e79a192fca35a91ab3251435df42e92ce","name":"make_research.py","bytes":10707},{"sha256":"3202f205d5b827c8fc8eb528337fadfcc995b466509b0b55e0821fc7cff42db7","name":"killer-marginal.py","bytes":19436},{"sha256":"418b8ad916a6666b1b91da0a15bfb5050e16213474d4704395a87fd6a9a9f86a","name":"killer-marginal.py.sha256.txt","bytes":1013},{"sha256":"92d0f6c16ceb9c7aafcc99e5b815ba4ee05f9531551a7bfd433275061e584e7f","name":"admit.py","bytes":12040},{"sha256":"75b791c59b19739c1453b39566d2d1513781b66afdb39d05bfa6bbdde6a8ac5d","name":"admit.json","bytes":4807},{"sha256":"e322f69655af0e67679c5842bf80fd4b0ac2c72f8667b6de8866dd33c3ffe530","name":"report-recovered-2732.md","bytes":5942},{"sha256":"302862d7c87dd50942c8982301c5684e8ea3bd4bd224d1c1daf2527183360acb","name":"report-recovered-2732.md","bytes":10404}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}