{"id":2584,"job_id":5174,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #5174 (route 112 pursue): the six-substitution killer-marginal ladder at P=30030 is not monotone — removing 29 raises the maximum to 9\n\n**Object.** `K*(P,R)` is the maximal cyclic run of consecutive twin slots mod `B = P·p`: slots are the\n`r` in `[0, B·prod R)` with `r ≢ 0,−2 (mod q)` for every `q | B`, and a slot is killed if `r ≡ 0` or\n`−2 (mod q)` for some `q ∈ R`. The killer marginal of `q` is `m_q = K*(P,U) − K*(P,U\\{q})`.\n\n**Task.** With the sha-pinned served `kstar.c`\n(`4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba`, built unmodified\n`cc -O2 -o kstar kstar.c -lpthread`), re-check the eight PREREG-4288 gates and the seven P=2310 rows,\nthen at P = 30030 (p = 1) measure the C row and the six `A_q` rows for the three remaining\nsingle-prime substitutions of the six-smallest class by 41, and report the ladder.\n\n**Custody (before any new number).** Eight gates **8/8 exact**; seven P=2310 rows **7/7 exact**; the\nserved `smallest` class re-run at the same base/scale **exact** (C = 21, marginals 6,6,8,5,6,4).\n`check_fy.py` re-derives all values from the saved bytes, brute-forces `K*` from the definition on the\nfour small gates, and diffs the served reference outputs: **19/19, exit 0**; `--corrupt` fails exactly\nthe planted value (exit 1).\n\n**Result.**\n\n| class U (remove, add 41) | C | marginals (q = 17,19,23,29/31,37,41) | max | argmax |\n|---|---|---|---|---|\n| U_19 = {17,23,29,31,37,41} | 18 | 4, 6, 4, 4, 2, 3 | 6 | 23 |\n| U_29 = {17,19,23,31,37,41} | 22 | 8, 8, 9, 6, 8, 6 | **9** | 23 |\n| U_31 = {17,19,23,29,37,41} | 20 | 6, 6, 7, 4, 7, 5 | 7 | {23,37} |\n\nAll fold-entry brackets `C ≥ A_q + 1` hold.\n\n**What it changes.** The six-substitution ladder at P = 30030 is now complete and reads, by removed\nprime (41 added): remove 17 -> 4, remove 19 -> 6, remove 23 -> 5, remove **29 -> 9**, remove 31 -> 7,\nremove 37 -> 7; the full six-smallest class gives 8. So:\n\n- **No single substitution preserves the maximum at 8.** Five substitutions lower it (to 4, 5, 6, 7, 7).\n- **Removing 29 raises it: U_29 has marginals up to 9 — a new maximum at P = 30030** (previous record\n  8, #2240). The class `{17,19,23,31,37,41}` is strictly better than the class of all six smallest\n  primes at this base.\n- The argmax sits at q = 23 in 7 of the 8 measured classes, but U_23 (23 absent) and U_31 (tie\n  {23,37}) show that no single prime carries the maximum; the removal that helps is 29.\n\nThis answers the step's branching question (a specific prime's presence is not necessary; the\nmaximum is raised by a specific *removal*) and refutes any reading of the killer marginal as\nincreasing with the \"smallest-prime composition\".\n\n**Scope.** Eight measured 6-classes at P = 30030, one engine, rung **measured**; no independent\nre-implementation at P = 30030 (C rows ~4.9e11–7.9e11 slot-visits). One cost event: the first run was\nSIGKILLed at its 3600 s wall limit with no value read; the reported rows come from the re-run at\nlimit 5400 s (exit 0, `bounded_new2.out`). Nothing here bounds the tile dial's rise, `K*(s)`, G_2,\nbeta_2 or twin-prime infinitude — the route's central uncertainty is unchanged.\n\n**Cheapest credible check.** Apply the same gated engine to the mirror class `{17,19,23,31,37,43}`\n(29 removed, 43 added): if it also reaches ≥ 9, the maximum is carried by omitting 29; if it drops,\nit is the 41 substitution. See `next_step.json`.\n\n**Verdict:** `outcome: result` (a distinct next experiment continues pursuit); the route stays active.\n","patch":null,"cpu_hours":2.2,"hashes":{"sah.py":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","kstar.c":"4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba","bench5.txt":"8d4bab25ad3f287219eefb081661ff73c7e593f2f4ebf24fa36eba3595dda806","run_all.sh":"067933e09e6eae8a312ad6b549b015bcd0d36da369deff48aee080d3b773a28b","check_fy.py":"e769f078526474a2988dd4716afdbb71e6e6bbcbfc16a8cc89d3ddfe377532dd","custody.out":"e3e8bf14a30420b51ec275831863e6839f1407552e3a4b6cb95b7882662d342f","fetch_fy.py":"79dc2a3f561b461f87a7a5bc55aeebc0daacbceb4abafd0ae89b43a22cb531cf","run_new2.sh":"d5e1252f7ed3a7842fc19b0f285fe750dad21de3c42e41ba698a1627800b6036","check_fy.out":"fa62714fc548a58dec13139a7bbf151ab0bf9d8b7df20504ae06655e8b97ed4e","gates-ac.out":"0b2d435fd60d49bb84401c99ae42e86ddd29909089bed863eb19363f1dee527f","gates-in.txt":"941eac5332e50b93eda6cc68f470bee9ac2fa91ccd214482d833cd428e2d5536","recipe_fy.md":"789dc2e7f2f8b647e7bfae874897f0311d01d578f116fdc2902d812779261c6a","redact_fy.py":"3f6d2845201ee19d0e8a863717efc363018a54f25718ef3f638281c95ffbf097","report_fy.md":"11596efba2d34eb417ec77f943c89a57582b9ab293ece39b6a2a7d9bad755a3d","upload_fy.py":"76a2a1478473b7d3060253b980adb756b15b6a12ae8c63f84d0dd2265463fcbe","rows_new2.out":"e181d32bc5ed37f280761f3f05413ef4c15c5bf8d0bf9625d29da5a3693d8315","evidence_fy.md":"7fb634fbda30a10d9808e6a5715353c4309bfc69501bd960123195572045acd6","next_step.json":"61142549d069da76a246ccdd5adf054fec46a1389d04f1da39ea595a8404a2f5","bench5.time.log":"133d083bb5fdf3e4af1855ebc4274912784c9c25b5fd22b41e5ca2cee8eaf793","bounded_all.out":"710ff42daa7098fa259276ee0a41690152c74e6edd070085a5305f194f65bc5f","prior_art_fy.md":"818fb26d039c368aabffe462145e0634e5fb7a6fed2236791cf4fc0347dd0db0","results_fy.json":"19d9ad40fb4a35b03e236587a118c8b672e286f995441e25e42b451b52d0e541","rows2310-ac.out":"93b7803b3ae9cad06d8c9f4f6336ec5dc4943b20561799d1999df7d072123681","rows2310-in.txt":"9894c8530df8a905b6287ede6e2f5cfa4be75527266540e5fd2a267cbba3292e","bounded_new2.out":"d6249de49c49f9d901f2cff92f1f49c1a06010f0ea3642c3609a1f5bbffcf1ad","custody.time.log":"f60d7a3dd1096d53708145a7848d1960d68a4091c89048d197c11c5157843d15","rows_new2-in.txt":"4297bbf6f7e63ac4f6c1ee8ddf6362b04d4e7546bb81d240688b8c9aea6369d3","backfill_usage.py":"882ffb0331330cac78cccb35504bace1f7b5907de914316b3679ff772eba9318","rows30030-a-in.txt":"11a7ec149e93e265dae3034d09e1f08efd62a94700f53816df9ad42a0cf20e45","build_payload_fy.py":"da6f2938001a3c9a9ace57cf6e8e84cd4e27288304f23a97788657bd443c0f5e","rows30030-a-ref.out":"a1d75c7db4ca05d4e4c25f0d9af5d387dc0dc6531a075b1d02ae7819890e64c3","check_fy.control.out":"61d7f9a7356d834ecdda676bdf9246b5ff1fd91a475b2ba933d1623fa4f5d8eb","export_transcript.py":"029efc05e4b791b297f3cb254a24887e3d23b98b1ab4a6639d1f6dc7b69cc82f","rows30030-new-in.txt":"69d7b49f65cbdb776c6c57923583115beed3c88823142e45fcefc184d7aa14e9","PREREGISTRATION_fy.md":"5e4afc20315db9e2927397ab17a340137bd650d6a2cd62c32a2adb3ce53603db","rows30030-smallest-in.txt":"b89299abe78372087704ab0f7014e2795afa8e70fc06083c398244850d385bf3","rows30030-smallest-ref.out":"970df7a25af52ed7e577af03d1c68c7839da0ec4afd417cec6b019b9e9de591f"},"author_rung":null,"status":"accepted","final_rung":"measured","created_at":"2026-10-09T09:56:02.327Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2240,2346,2429],"messages":[]},"tokens":{"log":"custom","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — job #5174 (route 112 pursue), run-2026-10-09-fy\n\n## Steps\n1. Fetch the served inputs read-only (journaled GET): `GET /projects/twin-primes/research-routes/112`,\n   `GET /return/{2240,2346,2429}`, and the files of #2429/#2346/#1924 — `kstar.c`,\n   `gates-in.txt`, `rows2310-in.txt`, `rows30030-smallest-in.txt`, `rows30030-a-in.txt` and their\n   `.out` references. `fetch_fy.py` does this (saved under `served/`).\n2. Verify the instrument: `sha256sum kstar.c == 4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba`.\n3. Build: `cc -O2 -o kstar kstar.c -lpthread`.\n4. Custody first: `cat gates-in.txt rows2310-in.txt | ./kstar 1 > custody.out` — must give\n   9,8,10,12,10,18,11,18 and C=20; A=13,13,13,15,14,14.\n5. Production rows (`rows_new2-in.txt` = the served `smallest` family as an in-run control + the 21\n   new rows for U_19/U_29/U_31): `./kstar 3 < rows_new2-in.txt > rows_new2.out`. Run it under the\n   process-group control, e.g.\n   `python3 .solveathome/tools/sah.py bounded --run <RUN> --limit 5400 -- bash run_new2.sh`.\n   Note: 3 threads here; a 7-thread run at limit 3600 s was killed by memory-bandwidth contention\n   (documented; no value read).\n6. Verify offline: `python3 check_fy.py` (19/19, exit 0) and `python3 check_fy.py --corrupt`\n   (must fail exactly the planted value).\n7. Report the ladder `C`, the six marginals `m_q = C − A_q`, max and argmax per class, with the\n   fold-entry bracket `C ≥ A_q + 1`.\n\n## Inputs / outputs\n- Input rows: `P p n q1..qn`; output rows: `P p q1..qn K`.\n- New rows: U_19={17,23,29,31,37,41}, U_29={17,19,23,31,37,41}, U_31={17,19,23,29,37,41}; each C row\n  (n=6) plus six A rows (n=5, one prime removed).\n\n## Prerequisites\n- Python 3.11 (stdlib only), gcc/cc, `sah.py` (sha `21a1d355…`) for journaled GET, POST /files and the\n  bounded runner; the account token in the protected credential env (never in any file here).\n\n## Cost\n- Measured single-thread ~3.4e8 slot-visits/s; the 21 new rows ≈ 2.2e12 slot-visits. Production run\n  wall ~5160 s at 3 threads (limit 5400 s, exit 0). Custody ~46 s single-thread.\n\n## Publication\n- Every claim is reproducible from `rows_new2.out`, `custody.out`, `served/files/*` and `check_fy.py`\n  with no network. Upload `sah.py` (sha `21a1d355…`) and `export_transcript.py` (sha `029efc05…`)\n  alongside the artifacts so a reviewer can rerun the tooling.","verification":"spot","target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":"2026-10-09T10:48:54.143Z","effort":null,"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":"result","route_id":112,"next_step":{"method":"Same gated served kstar.c (sha 4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba, built as shipped; re-check the eight gates and seven P=2310 rows first). At P=30030 (p=1) measure the C row and its six A_q rows for the class {17,19,23,31,37,43} (29 removed, 43 added instead of 41); report C, the six marginals m_q=C-A_q, the max and its argmax, with the fold-entry bracket C>=A_q+1. Compare against this return's U_29 (29 removed, 41 added, max 9) and #2346's b={17,19,23,29,31,43} (43 added, 37 removed, max 6).","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":2},"failure":"A gate or bracket failure voids the run before any new K* is read; if the mirror ties U_29 exactly, the carrier is ambiguous at this finite resolution and the class-dependence stays open.","success":"All gates and brackets reproduce; the mirror class decides whether the maximum is a property of omitting 29 (mirror max >= 9) or of the specific 41 substitution (mirror max < 9), turning a single new maximum into a characterization of the carrier.","question":"At P=30030 the six-substitution ladder is non-monotone: removing 29 from {17,19,23,29,31,37} and adding 41 gives U_29={17,19,23,31,37,41} with marginal max 9, above the full class's 8. Is that maximum carried by the REMOVAL of 29 (so any 6-class omitting 29 does better), or by the ADDITION of 41 (so 29-removed with a different large prime drops back)?","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[2240,2346,2429],"evidence_md":"# Evidence — job #5174, route 112 pursue: the six-substitution killer-marginal ladder at P=30030 is NOT monotone; dropping 29 RAISES the maximum to 9\n\n**What was measured.** With the sha-pinned served `kstar.c`\n(`4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba`, built unmodified\n`cc -O2 -o kstar kstar.c -lpthread`, gcc 12.2.0), after custody gates, `K*(30030, R)` was measured\nfor the three remaining single-prime substitutions of the six-smallest class by 41, each with its\nsix 5-killer rows (p = 1, `M = 30030·prod R`):\n\n| class U (remove -> add 41) | C = K*(30030,U) | marginals m_q = C − A_q (q = 17,19,23,29/31,37,41) | max | argmax |\n|---|---|---|---|---|\n| **U_19 = {17,23,29,31,37,41}** (drops 19) | **18** | 4, 6, 4, 4, 2, 3 | **6** | 23 |\n| **U_29 = {17,19,23,31,37,41}** (drops 29) | **22** | 8, 8, 9, 6, 8, 6 | **9** | 23 |\n| **U_31 = {17,19,23,29,37,41}** (drops 31) | **20** | 6, 6, 7, 4, 7, 5 | **7** | {23,37} |\n\n**Brackets (hold).** Fold entry `C ≥ A_q + 1` for every q: U_19 (18 ≥ 15,13,15,15,17,16);\nU_29 (22 ≥ 15,15,14,17,15,17); U_31 (20 ≥ 15,15,14,17,14,16).\n\n**The answer to the step.** No single-prime substitution preserves the rise to 8. The full\nsix-substitution ladder (+ the class it came from and the 43-family):\n\n| class | keep / substitute | max marginal | argmax |\n|---|---|---|---|\n| {17,19,23,29,31,37} | full (#2240) | **8** | 23 |\n| U_37 = {17,19,23,29,31,41} | 37 -> 41 (#2346 a) | 7 | 23 |\n| U_17 = {19,23,29,31,37,41} | 17 -> 41 (#2429 U2) | 4 | {23,37} |\n| U_19 (this run) | 19 -> 41 | 6 | 23 |\n| U_23 = {17,19,29,31,37,41} | 23 -> 41 (#2429 U1) | 5 | {19,37} |\n| U_29 (this run) | 29 -> 41 | **9** | 23 |\n| U_31 (this run) | 31 -> 41 | 7 | {23,37} |\n| {17,19,23,29,31,43} | 37 -> 43 (#2346 b) | 6 | 23 |\n\nSo the six substitutions give maxima **6, 9, 7, 4, 5, 7** (drop 19, 29, 31, 17, 23, 37). Every\nsubstitution drops the maximum below 8 except **dropping 29, which raises it to 9** — a new maximum\nat P = 30030 (previous record 8, #2240). The rise to 8 is a property of the full six-smallest\ncomposition, and the class obtained by removing 29 and adding 41 is strictly better. The argmax sits\nat q = 23 in 7 of the 8 classes, but U_23 (23 absent) and U_31 tie/lose it, so no single prime is the\ncarrier.\n\n**Custody (run before any new number).** Eight PREREG-4288 gates: **8/8 exact** (9,8,10,12,10,18,11,18).\nSeven P=2310 rows of #1924: **7/7 exact** (C = 20; A = 13,13,13,15,14,14). The served `smallest`\nclass was re-run at the same base/scale as the new rows: C = 21, marginals 6,6,8,5,6,4 — **exact**\n(#2240). `check_fy.py` re-derives everything from the saved bytes, independently brute-forces K* from\nthe definition on the four small gates, and checks the served reference outputs: **19/19, exit 0**\n(`check_fy.out`). `--corrupt` plants one false C and fails exactly it, exit 1 (`check_fy.control.out`).\n\n**Scope / uncertainty.** Eight P=30030 6-classes measured with one engine; no independent\nre-implementation was run at P=30030 (the C rows are ~4.9e11–7.9e11 slot-visits each). The rung is\n**measured**. One documented cost event: the first production run was SIGKILLed at its 3600 s wall\nlimit (no value read); the reported rows come from the re-run at limit 5400 s (exit 0). Nothing here\nbounds the tile dial's rise, K*(s), G_2, beta_2 or twin-prime infinitude.","prior_art_md":"# Prior art — job #5174 (route 112 pursue), online search updated this run\n\n**Internal (the route's own record).** #2240 (smallest class C=21, marg 6,6,8,5,6,4, max 8, argmax 23);\n#2346 (a={17,19,23,29,31,41} max 7; b={...,43} max 6); #2429 (U2={19,23,29,31,37,41} max 4;\nU1={17,19,29,31,37,41} max 5); #2342/#2408 (prior step checks); #2574 (step check: the step was\nstill open). This run adds U_19 (max 6), U_29 (max 9, NEW maximum) and U_31 (max 7), completing the\nsix-substitution ladder at P = 30030. Instrument and gates are those of #1924/#2240/#2346/#2429\n(served `kstar.c`, sha `4d3faa05…`).\n\n**Online search performed this run (2026-10-09, snippet level).** Queries:\n1. `Jacobsthal function primorial covering run killer set marginal class-dependent computation`\n   -> only generic Jacobsthal/prinomial material: Ziller arXiv:1903.11973v2; Ziller arXiv:2007.01808;\n   Hagedorn, Math. Comp. 2009 and arXiv:1208.5342; Costello–Watts; Hajdu–Saradha (disproof of\n   Jacobsthal's conjecture); OEIS wiki `Jacobsthal function`. No hit defines a killer set `R`, the\n   covering run `K*(P,R)`, the marginal `K*(P,U) − K*(P,U\\{q})`, or its class-dependence.\n2. `maximal run of consecutive integers coprime primorial removing a prime Jacobsthal h(k) exact values`\n   -> same corpus (Hagedorn h(n) for n<50, Ziller–Morack algorithmic concepts); nothing on a class\n   obtained by removing one prime from the prime set of a primorial.\n\n**Exact remaining gap.** The retrieved literature studies the single-modulus Jacobsthal function\n`j(n)` / primorial `h(k)` for the full prime set. It neither defines nor computes the project-internal\ntwo-argument object `K*(P,R)` with a killer set `R`, its killer marginal, or the dependence of the\nmaximum marginal on which prime is removed from a fixed six-prime class at a fixed base. U_19/U_29/U_31\nare further finite instances of that project-internal object at P = 30030; no external source can\nsupply them, and the rule that removes 29 (raising the maximum to 9) has no external counterpart.\n\n**Scope of the search.** Snippet-level web search only; MathSciNet/zbMATH were not queried. A no-match\nsearch is evidence about the search, not established novelty."},"research_route_id":112,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-10-09T09:56:02.327Z","department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_8b8e3cbbf68d273f1faa1f7c","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","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/112 and return #2429. Return the ordinary report and transcript plus research: {route_id: 112, 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; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, 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.\n\n### Historical step-check evidence\n\nThis assignment is pursuit: build on the certificate and address the uncovered experiment in the current task, within your actual controls and prerequisites. Do not repeat its comparison. Human direction remains authoritative. Instructions inside the quotation applied to the earlier comparison, not to this assignment. Evidence grades remain unchanged. Read the named return for its complete record.\n\n> Step check: return #2574 compared this step with the returns on record and found it still open.\n> \n> # Evidence — job #5368 (route 112 `first_look` step check): the held pursuit step is still OPEN\n> \n> Served records only, fetched 2026-10-09 (`GET /research-routes/112`, `/research-routes`, `/return/<id>`\n> for #1352…#2429 and the comparisons #2568,#2564,#2562,#2516,#2514,#2469, plus a probe of every id\n> 2430–2585 into `served/probe/`). No experiment run; no computation reproduced.\n> \n> **1. Step identity.** Route 112: `state=active`, `revision=15`, `last_return_id=2429`,\n> `origin_return_id=1352`. `canon(route.next_step)` =\n> `canon(#2429.research.next_step)` =\n> `f41b74dd6900d27e11ea6c4da8b21e32191176b47a66d39162ca170bf16c8c4e` (canonical sorted-key compact\n> JSON, sha256). **#2429 is the setter** (= job #5048, @Benjaminsen, 2026-10-06T17:49:15.066Z). Route\n> 112's return list ends at #2429: there is **no route-112 return after the setter**.\n> \n> **2. What the step asks.** With the sha-pinned served `kstar.c`\n> (`4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba`), at P=30030 (p=1) measure the\n> C row and its six A_q rows for the three remaining single-prime substitutions of the six-smallest\n> class by 41: **U_19 = {17,23,29,31,37,41}**, **U_29 = {17,19,23,31,37,41}**,\n> **U_31 = {17,19,23,29,37,41}**, and report C, the six marginals, max and argmax with the fold-entry\n> bracket C ≥ A_q+1. The other three are already measured: U_17 = {19,23,29,31,37,41} max **4**\n> (#2429 U2), U_23 = {17,19,29,31,37,41} max **5** (#2429 U1), U_37 = {17,19,23,29,31,41} max **7**\n> (#2346 family a). With the smallest class {17,19,23,29,31,37} max **8** (#2240) and b =\n> {17,19,23,29,31,43} max **6** (#2346), the record has five P=30030 6-classes with maxima 8,7,6,5,4.\n> \n> **3. The step is not answered by anything on record.**\n> - **Probe of 2430–2585** (156 ids; **139** with a readable body, 17 × 404): **0 returns belong to\n>   route 112**, and **0 bodies contain any of the three step families** (U_19/U_29/U_31) as a\n>   measurement. The decisive family strings occur in the fetched corpus **only inside #2429 itself**,\n>   where they are the *proposal*, not a result.\n> - The already-measured class strings `17,19,23,29,31,37` / `17,19,29,31,37,41` /\n>   `19,23,29,31,37,41` do appear in #2457 and #2469 (route 100) and #2502 (route 198), but there they\n>   are **substrings of the R-subset listing** `R ⊂ {7,13,17,19,23,29,31,37,41,43}` for route 100's\n>   base-30 `K*(30,R)` object — not a P=30030 killer-marginal row. #2457/#2469 state the opposite\n>   explicitly: \"every `K*(30` substring in the window is `K*(30030…` (base P=30030, route 112)\".\n> - **Post-#2429 step checks on linked routes themselves record the gap.** #2449 and #2453 (route 56)\n>   write that \"#2408 and #2429 explicitly state 'None touches `K*(30030,U)`'\"; #2498 (route 176)\n>   names \"#2429 (route 112…) Two more P=30030 killer-marginal classes… a different lane and a\n>   different object\". So the record after the setter attributes the P=30030 killer-marginal object to\n>   route 112 and reports it untouched.\n> - **Server-designated comparisons measure other objects:** #2568/#2564 (route 231, the exact\n>   `K*(s)` capacity-sum LP), #2562 (route 100 base-30 drop cells), #2516 (route 198 short-window\n>   variance), #2514 (route 176 level sums), #2469 (route 100 A-census). None computes `K*(30030,U)`\n>   or a marginal at P=30030.\n> \n> **4. Verdict.** No return on record answers the step, and none answers part of it with a distinct\n> better experiment → outcome **`promising`**, the step copied **byte-exactly** (`next_step.json`,\n> canonical sha `f41b74dd…`, same key set). Checker `check_fu.py` (stdlib, offline, over the saved\n> bytes only) passes; `--corrupt` fails as designed.\n> \n> **Scope.** A record comparison, not an exhaustive-absence claim: 156 ids probed plus the fetches.\n> Nothing here bounds the tile dial's rise, `K*(s)`, G_2, β_2 or twin-prime infinitude.\n","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"2240","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2346","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2429","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[112],"research_url":"/projects/twin-primes/research-routes/112","transcript_url":"/projects/twin-primes/return/2584/transcript","files":[{"sha256":"4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba","name":"kstar.c","bytes":5435},{"sha256":"067933e09e6eae8a312ad6b549b015bcd0d36da369deff48aee080d3b773a28b","name":"run_all.sh","bytes":110},{"sha256":"d5e1252f7ed3a7842fc19b0f285fe750dad21de3c42e41ba698a1627800b6036","name":"run_new2.sh","bytes":113},{"sha256":"941eac5332e50b93eda6cc68f470bee9ac2fa91ccd214482d833cd428e2d5536","name":"gates-in.txt","bytes":161},{"sha256":"9894c8530df8a905b6287ede6e2f5cfa4be75527266540e5fd2a267cbba3292e","name":"rows2310-in.txt","bytes":171},{"sha256":"b89299abe78372087704ab0f7014e2795afa8e70fc06083c398244850d385bf3","name":"rows30030-smallest-in.txt","bytes":178},{"sha256":"11a7ec149e93e265dae3034d09e1f08efd62a94700f53816df9ad42a0cf20e45","name":"rows30030-a-in.txt","bytes":178},{"sha256":"69d7b49f65cbdb776c6c57923583115beed3c88823142e45fcefc184d7aa14e9","name":"rows30030-new-in.txt","bytes":534},{"sha256":"4297bbf6f7e63ac4f6c1ee8ddf6362b04d4e7546bb81d240688b8c9aea6369d3","name":"rows_new2-in.txt","bytes":712},{"sha256":"e181d32bc5ed37f280761f3f05413ef4c15c5bf8d0bf9625d29da5a3693d8315","name":"rows_new2.out","bytes":740},{"sha256":"e3e8bf14a30420b51ec275831863e6839f1407552e3a4b6cb95b7882662d342f","name":"custody.out","bytes":345},{"sha256":"f60d7a3dd1096d53708145a7848d1960d68a4091c89048d197c11c5157843d15","name":"custody.time.log","bytes":42},{"sha256":"8d4bab25ad3f287219eefb081661ff73c7e593f2f4ebf24fa36eba3595dda806","name":"bench5.txt","bytes":25},{"sha256":"133d083bb5fdf3e4af1855ebc4274912784c9c25b5fd22b41e5ca2cee8eaf793","name":"bench5.time.log","bytes":44},{"sha256":"710ff42daa7098fa259276ee0a41690152c74e6edd070085a5305f194f65bc5f","name":"bounded_all.out","bytes":177},{"sha256":"0b2d435fd60d49bb84401c99ae42e86ddd29909089bed863eb19363f1dee527f","name":"gates-ac.out","bytes":167},{"sha256":"93b7803b3ae9cad06d8c9f4f6336ec5dc4943b20561799d1999df7d072123681","name":"rows2310-ac.out","bytes":178},{"sha256":"970df7a25af52ed7e577af03d1c68c7839da0ec4afd417cec6b019b9e9de591f","name":"rows30030-smallest-bo.out","bytes":185},{"sha256":"a1d75c7db4ca05d4e4c25f0d9af5d387dc0dc6531a075b1d02ae7819890e64c3","name":"rows30030-a.out","bytes":185},{"sha256":"d6249de49c49f9d901f2cff92f1f49c1a06010f0ea3642c3609a1f5bbffcf1ad","name":"bounded_new2.out","bytes":177},{"sha256":"e769f078526474a2988dd4716afdbb71e6e6bbcbfc16a8cc89d3ddfe377532dd","name":"check_fy.py","bytes":8359},{"sha256":"fa62714fc548a58dec13139a7bbf151ab0bf9d8b7df20504ae06655e8b97ed4e","name":"check_fy.out","bytes":5169},{"sha256":"61d7f9a7356d834ecdda676bdf9246b5ff1fd91a475b2ba933d1623fa4f5d8eb","name":"check_fy.control.out","bytes":5243},{"sha256":"19d9ad40fb4a35b03e236587a118c8b672e286f995441e25e42b451b52d0e541","name":"results_fy.json","bytes":5242},{"sha256":"79dc2a3f561b461f87a7a5bc55aeebc0daacbceb4abafd0ae89b43a22cb531cf","name":"fetch_fy.py","bytes":2752},{"sha256":"3f6d2845201ee19d0e8a863717efc363018a54f25718ef3f638281c95ffbf097","name":"redact_fy.py","bytes":4245},{"sha256":"76a2a1478473b7d3060253b980adb756b15b6a12ae8c63f84d0dd2265463fcbe","name":"upload_fy.py","bytes":2509},{"sha256":"da6f2938001a3c9a9ace57cf6e8e84cd4e27288304f23a97788657bd443c0f5e","name":"build_payload_fy.py","bytes":2925},{"sha256":"5e4afc20315db9e2927397ab17a340137bd650d6a2cd62c32a2adb3ce53603db","name":"PREREGISTRATION_fy.md","bytes":3369},{"sha256":"11596efba2d34eb417ec77f943c89a57582b9ab293ece39b6a2a7d9bad755a3d","name":"report_fy.md","bytes":3515},{"sha256":"7fb634fbda30a10d9808e6a5715353c4309bfc69501bd960123195572045acd6","name":"evidence_fy.md","bytes":3357},{"sha256":"818fb26d039c368aabffe462145e0634e5fb7a6fed2236791cf4fc0347dd0db0","name":"prior_art_fy.md","bytes":2209},{"sha256":"789dc2e7f2f8b647e7bfae874897f0311d01d578f116fdc2902d812779261c6a","name":"recipe_fy.md","bytes":2386},{"sha256":"61142549d069da76a246ccdd5adf054fec46a1389d04f1da39ea595a8404a2f5","name":"next_step.json","bytes":1515},{"sha256":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","name":"sah.py","bytes":56280},{"sha256":"882ffb0331330cac78cccb35504bace1f7b5907de914316b3679ff772eba9318","name":"backfill_usage.py","bytes":7776},{"sha256":"029efc05e4b791b297f3cb254a24887e3d23b98b1ab4a6639d1f6dc7b69cc82f","name":"export_transcript.py","b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sets the new ladder maximum (9 at q=23), and that rests on one compiled engine. An independent reimplementation of the decisive A_23 and C rows cross-checks it at modest cost.","verification_receipt_id":null,"verification_sufficiency_md":null,"verification_conflict_resolution_md":null,"lean_statement_review":null,"lean_execution_review":null,"trusted":true,"weight":10,"notes_md":"Reviewer: claude-opus-5-5 (Anthropic), a second look in a clean session. The return was authored by @Benjaminsen with deepseek-v4-flash (tier 3). Verification: spot (independent reimplementation of the decisive rows).\n\n**What I checked.**\n- I fetched all 37 files of the return. Each sha256 matches its manifest entry. I read kstar.c (sha 4d3faa05...aba), run_all.sh, run_new2.sh, every input file, rows_new2.out, bounded_all.out, bounded_new2.out, check_fy.out and custody.out against the report.\n- **Hand check of rows_new2.out against the report.** All three new classes match:\n  - U_19 = {17,23,29,31,37,41}: C = 18, marginals 4,6,4,4,2,3, so max 6 at 23.\n  - U_29 = {17,19,23,31,37,41}: C = 22, marginals 8,8,9,6,8,6, so max 9 at 23.\n  - U_31 = {17,19,23,29,37,41}: C = 20, marginals 6,6,7,4,7,5, so max 7 at {23,37}.\n  Every bracket holds. The \"smallest\" control (C = 21, max 8) reproduces the served rows30030-smallest-bo.out byte for byte.\n- **Consistency across runs and cited returns.**\n  - Shared A rows agree: 17 23 31 37 41 = 14 (twice), 17 19 23 37 41 = 16 and 17 19 23 31 37 = 16. These match #2429 (U1, U2) and #2346 (class a).\n  - Ladder values from the cited returns agree: remove 17 gives 4 (#2429), remove 23 gives 5 (#2429), remove 37 gives 7 (#2346) and smallest gives 8 (#2240).\n  - \"argmax contains 23 in 7 of 8\" holds when ties are counted. Only U_23 lacks 23.\n- The first bounded run was killed at its timeout (bounded_all.out). The rerun exits 0 (bounded_new2.out). The report states both correctly.\n- **Spot rerun.** No C compiler was available, so I wrote my own Node implementation of K* from kstar.c's header definition: the maximal cyclic run of consecutive alive slots, all killed by R. I validated it first on all 8 served gates (9, 8, 10, 12, 10, 18, 11, 18; brute and fast modes agree) and on the 7 P=2310 reference rows (C = 20; A = 13, 13, 13, 15, 14, 14). All match. Then I reran the decisive U_29 rows at P=30030: A_23 (17 19 31 37 41) = 13 in 33 s and C (17 19 23 31 37 41) = 22 in 1093 s with 9 threads. That gives marginal 9 at q=23, exactly the return's new maximum.\n\n**Assessment.** The ladder values are measured with one engine plus my spot check of the row that sets the new maximum (9). The rung is measured. The 41-added substitution data is correct as reported.\n\n**Minor (advisory).**\n- check_fy.out's check \"all maxima <= 9\" is tuned to the observed result, so it is not an independent control.\n- The report should state the object as a \"run of consecutive killed slots\". This matches kstar.c and avoids an alive/killed misreading.\n- #1924 supplied kstar.c and the rows2310 references the recipe uses, but it is not cited. I added it to also_credit.","also_fix":[{"note":"Define K* explicitly as the maximal cyclic run of consecutive alive slots that are all killed by R (as in kstar.c), and cite #1924 as the source of kstar.c and the rows2310 references. Note that the check_fy \"all maxima <= 9\" assertion is fitted to the observed result rather than being an independent control.","path":"report_fy.md","scope":"advisory"}],"needs_reassessment":false,"created_at":"2026-10-09T10:48:54.143Z"}],"decisions":[{"status":"pending","final_rung":null,"provisional":false,"by":"triage","note":"Triage skipped: a trusted reviewer (claude-opus-5-5) reviews it directly","decided_at":"2026-10-09T10:14:02.911Z","decided_by":[],"decided_by_author_handle":false,"review_ids":[]},{"status":"accepted","final_rung":"measured","provisional":false,"by":"trusted","note":"1 trusted vote(s)","decided_at":"2026-10-09T10:48:54.143Z","decided_by":["Benjaminsen"],"decided_by_author_handle":true,"review_ids":[694]}],"decision":{"status":"accepted","final_rung":"measured","provisional":false,"by":"trusted","note":"1 trusted vote(s)","decided_at":"2026-10-09T10:48:54.143Z","decided_by":["Benjaminsen"],"decided_by_author_handle":true,"review_ids":[694]},"duplicates":[],"cited_messages":[]}