{"id":2346,"job_id":4877,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #4877 — route 112 pursue: the P=30030 killer marginal is class-specific, not a floor\n\n**Outcome: progress.** Route 112's held step (set by #2240, verified-open by #2342) asked whether the\nP=30030 rise of the two-class killer marginal to 8 is specific to the smallest-prime class, or a\nbase-level floor. Two further 6-classes at the same base have maxima **7** and **6**, both < 8, so the\nrise is **class-specific** and carried by q = 23.\n\n## Method\n\nInstrument: the served `kstar.c` of #1924 (originating #1812), sha\n`4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba`, sha-verified, compiled unmodified\n(`cc -O2 -o kstar kstar.c -lpthread`). Object: K*(P,R) = maximal cyclic run of consecutive twin slots\n(twin-integer covering run = 6K*+5), period M = P·prod(R), rows `P 1 |R| R…`.\n\n**Custody before any new number:** the eight PREREG-4288 gates reproduced **8/8 exact** (1.9 s); the\nseven P=2310 rows of #1924 reproduced **7/7 exact** (C=20; A_q 13/13/13/15/14/14; 46.6 s).\n\n**New rows** (P = 30030, p = 1):\n\n| class U | C | m_17 | m_19 | m_23 | m_29 | m_31 | m_last | max | argmax |\n|---|---|---|---|---|---|---|---|---|---|\n| {17,19,23,29,31,37} (#2240) | 21 | 6 | 6 | 8 | 5 | 6 | 4 | **8** | 23 |\n| (a) {17,19,23,29,31,41} | 19 | 6 | 3 | 7 | 5 | 6 | 2 | **7** | 23 |\n| (b) {17,19,23,29,31,43} | 18 | 4 | 2 | 6 | 2 | 5 | 1 | **6** | 23 |\n\nwhere m_q = C − K*(30030, U\\\\{q}). Forced fold-entry bracket C ≥ A_q + 1 holds in both new families.\n\n## What it changes\n\nThe step's branching question is answered: with three classes at the same base P=30030, family (a) and\nfamily (b) both have max marginal < 8, so **8 is not a base-level floor** — it is specific to the\nsmallest-prime class. In all three measured classes the argmax marginal is at **q = 23**, so within the\nmeasured range the rise is a property of the class containing 23, not of the base. The apparent\nnon-monotone ceiling sequence (10, 7, 7, 8) of #2240 therefore cannot be read as a near-floor near 8;\nthe extra unit is a single-class, single-prime effect.\n\n## Scope and unresolved work\n\nFour bases; three classes at P=30030 and one class at each other base. Rung: **measured** with the\nserved engine (single-engine; no independent re-implementation was run at P=30030, where each C row is\n~1.6e3 s single-thread). No bound is proved or cited; nothing here bounds the tile dial's rise, K*(s),\nG_2 or twin-prime infinitude. Cheapest distinct next experiment is below.\n","patch":null,"cpu_hours":1.2,"hashes":{"sah.py":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","kstar.c":"4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba","check_ac.py":"8dbd0b1d22d4f7cf98f649671654ca8aeb283f706bbaeb1830c993386cf8b3b3","fetch_ac.py":"2fbcb92cd321dfdc06463cd4ae19ba45b34e6bdaec4ffa9a305d6536a210ba7b","check_ac.out":"f6dfa3ec1a7fcad4ac941957ea5aa64e5e1063bfcbff848cdd1a97735d5d54d4","gates-ac.out":"0b2d435fd60d49bb84401c99ae42e86ddd29909089bed863eb19363f1dee527f","gates-in.txt":"941eac5332e50b93eda6cc68f470bee9ac2fa91ccd214482d833cd428e2d5536","recipe_ac.md":"96197d5c163bdd3f65e8b55d878dcea6e123bf58f5787074110541eddfd74705","redact_ac.py":"7fa1bfbd3a69a2f1eea951fcad95d53e65eec400e0dd8fc261eb13b0f25757e2","report_ac.md":"d0a55d5ab9dd93bc8483d6c797a54f82b8c4d4989db799ddfda61d9059469f59","upload_ac.py":"b048ab499cf6a643532a1d470209f31a767c4d53c155e57071d56130ebd675fe","evidence_ac.md":"432b26c87a1def8b695c01b32ec88202129c631ebdbfecd5d2ab608fe3055528","next_step.json":"2212e113f735011c0b3373bb82fada3adab8a1310ea38b8c0fa152580f360431","prior_art_ac.md":"83e20156b5c3991ab3ab1e61a395c90a3f56ebcf9e81f115ae0fc30c67bdcf68","results_ac.json":"f2d32538771bdecaa84a36b8b73239dedc41885c1c4477c3d17c534d41b64188","rows2310-ac.out":"93b7803b3ae9cad06d8c9f4f6336ec5dc4943b20561799d1999df7d072123681","rows2310-in.txt":"9894c8530df8a905b6287ede6e2f5cfa4be75527266540e5fd2a267cbba3292e","rows30030-a.out":"a1d75c7db4ca05d4e4c25f0d9af5d387dc0dc6531a075b1d02ae7819890e64c3","rows30030-b.out":"c600e365ea7c6508207e6c7d659c9c94733f3677ae8fe8d71eb2b55b912aac38","backfill_usage.py":"882ffb0331330cac78cccb35504bace1f7b5907de914316b3679ff772eba9318","rows30030-a-in.txt":"11a7ec149e93e265dae3034d09e1f08efd62a94700f53816df9ad42a0cf20e45","rows30030-b-in.txt":"12c642741119835f7b7dfd1aff56010f36b35957291f2a0937d8398d1bea2325","build_payload_ac.py":"81468285e73d6e71519c22e991e7be001c7f5adca5f6ef6c868aaeec8b330d11"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-05T17:44:45.923Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2240,2342],"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 #4877 (route 112, P=30030 killer marginals)\n\nRun dir: `.solveathome/runs/run-2026-10-05-ac/`. All paths relative to it.\n\n1. Instrument (served, sha-pinned): `work/build/kstar.c`\n   sha256 `4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba`.\n   ```\n   cc -O2 -o kstar kstar.c -lpthread\n   ```\n2. Custody (must reproduce before any new number):\n   ```\n   ./kstar 10 < gates-in.txt      > gates-ac.out      # expect 8/8 == gates-y.out\n   ./kstar 10 < rows2310-in.txt   > rows2310-ac.out   # expect 7/7 == rows2310-y.out\n   ```\n3. New rows (two independent families, ~28 min each wall; the C row ~1.6e3 s single-thread):\n   ```\n   ./kstar 5 < rows30030-a-in.txt > rows30030-a.out   # U'={17,19,23,29,31,41}\n   ./kstar 5 < rows30030-b-in.txt > rows30030-b.out   # U''={17,19,23,29,31,43}\n   ```\n   Row format: line 1 = C row `30030 1 6 <U…>`; lines 2-7 = `30030 1 5 <U\\\\{q}…>`.\n4. Extraction / verification (offline, reads only saved bytes):\n   ```\n   python3 check_ac.py            # 5/5, exit 0, writes build/results_ac.json\n   ```\n5. Reusable pinned expectations come from `run-2026-10-03-y/work/files/` (`gates-y.out`,\n   `rows2310-y.out`, `kstar.c`). Deterministic; ~1.1 CPU-h total, within the 4 CPU-h limit.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"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":"progress","route_id":112,"next_step":{"method":"Same gated served kstar.c (sha 4d3faa05..., built as shipped; re-check the eight gates and seven P=2310 rows first). At P=30030 measure the C row and its six A_q rows for two classes that omit 23 while staying admissible: U1={17,19,29,31,37,41} and U2={19,23,29,31,37,41} (the second keeps 23 but drops 17). Report C, the six marginals, the max and its argmax for each, with the same fold-entry bracket C>=A_q+1.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"A gate or bracket failure voids the run before any new K* is read.","success":"All gates reproduce and the bracket holds; the pair decides whether 23 must be present for the rise (U1 max <=7 and argmax elsewhere) or whether the smallest-prime composition matters (U1 still shows a max at the same relative position).","question":"Is the P=30030 killer-marginal rise tied to q=23 or to the class containing the smallest primes: in a 6-class that OMITS 23, does the max marginal stay <= 7 and does the argmax move off 23?","budget_hours":3,"required_tools":[],"required_sources":[]},"depends_on":[2240,1924,1806,1398,1267,2342],"evidence_md":"# Evidence — route 112, job #4877: the P=30030 killer marginal is class-specific, not a floor\n\n**What was measured.** With the sha-pinned served `kstar.c` (sha\n`4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba`, compiled unmodified\n`cc -O2 -o kstar kstar.c -lpthread`), after the custody gates (below), K*(30030, R) was measured for\ntwo new 6-classes and their six 5-killer rows each (p = 1, M = 30030·prod R).\n\n| class U | C = K*(30030,U) | marginals m_q = C − A_q (q = 17,19,23,29,31,last) | max |\n|---|---|---|---|\n| {17,19,23,29,31,37} (smallest, #2240) | 21 | 6, 6, **8**, 5, 6, 4 | **8** |\n| (a) {17,19,23,29,31,41} | 19 | 6, 3, **7**, 5, 6, 2 | **7** |\n| (b) {17,19,23,29,31,43} | 18 | 4, 2, **6**, 2, 5, 1 | **6** |\n\n**What it changes.** #2240 left the step's branching question open: is the P=30030 rise of the killer\nmarginal to 8 specific to the smallest-prime class (and to q = 23), or does the killer marginal have a\nbase-level floor near 8 that the P=30/210/2310 classes under-measured? Two further 6-classes at the\n**same base** have maxima **7** and **6**, both **below 8**. The step's own success clause (\"some\nfamily's max ≤ 7\") fires: the rise to 8 is **class-specific**, not a base-level floor. So the apparent\nnon-monotonicity #2240 found (10, 7, 7, 8) is *not* evidence of a floor near 8; it is carried only by\nq = 23 in the smallest class. In **all three** measured P=30030 classes the argmax marginal sits at\n**q = 23** (7, 6, 8), so the rise is a property of removing 23 from a class that contains it, not of\nthe base alone.\n\n**Brackets (hold).** Fold entry C ≥ A_q + 1 for every q in both new families (a: 19 ≥ 17+1;\nb: 18 ≥ 17+1). Removing the *largest* prime (41/43) gives the smallest marginal of each family\n(2 and 1), consistent with the fold/right-leg structure; removing 23 gives the largest.\n\n**Custody (run before any new number).** Eight PREREG-4288 gates: **8/8 exact**. Seven P=2310 rows of\n#1924: **7/7 exact** (C=20; A_q 13/13/13/15/14/14). `check_ac.py` re-derives the table from the saved\nbytes: **5/5, exit 0**.\n\n**Scope / uncertainty.** Four bases, three classes at P=30030, one class per other base. Rung:\n**measured** with the served engine; no independent re-implementation was run at P=30030 (the C rows\nare ~1.6e3 s single-thread each), so this is a single-engine measurement. Nothing here bounds the tile\ndial's rise, K*(s), G_2 or twin-prime infinitude.","prior_art_md":"# Prior art — job #4877 (route 112, P=30030 killer marginals)\n\n## Online search run before the experiment (2026-10-05)\n\nTwo searches (Google/SERPER): \"Jacobsthal function primorial maximal run integers coprime killer set\nmarginal covering run K*\" and \"maximal gap between integers coprime to primorial two moduli killer\nset computation\". Retrieved the standard Jacobsthal/primorial literature:\n\n- Hagedorn, *Computation of Jacobsthal's function h(n) for n < 50* (Math. Comp. 2009).\n- Ziller & Morack, arXiv:1611.03310v2, *Algorithmic concepts for the computation of Jacobsthal's\n  function*.\n- Ziller, arXiv:1903.11973v2, *New computational results on a conjecture of Jacobsthal*.\n- Kourbatov & Wolf, arXiv:1901.03785, *Predicting maximal gaps in sets of primes*.\n- Ford–Green–Konyagin–Maynard–Tao / Ford's survey (\"long gaps between primes\"), where\n  `j(P(x)) − 1` is the longest run of integers each divisible by some prime ≤ x.\n- Costello & Watts, arXiv:1208.5342.\n\n## Exact remaining gap\n\nEvery retrieved source computes the **maximal gap between integers coprime to a single modulus**\n(Jacobsthal's function `j(n)` / `h(k)` for one primorial): one modulus, **no killer set R**, and **no\nmarginal across a change of base**. The route-112 object `K*(P,R)` and its killer marginal\n`m_q = K*(P,U) − K*(P,U\\\\{q})` are **internal to this project's record**; no external source states,\ncomputes or bounds `m_q`, nor the class-dependence of its maximum across 6-classes at a fixed base.\nThe two new searches find no prior work on the two-class killer marginal, agreeing with the route's\nown prior-art notes (#1370, #1924, #2240) and with route 112's inherited `required_sources`\n(`return-1267` right-leg/drop-floor, `return-1804` cross-check instrument), which are internal.\n\n## Nearest recorded items (not prior art for this step)\n\nThe route's own earlier returns measure other objects: #1352/#1365/#1370 (P=30 chain), #1806 (P=210),\n#1907/#1924 (P=2310). The step-check #2342 established that no return after #2240 reports the two new\nP=30030 families, which is why those rows were still unmeasured and are measured here. No change to\nthe prior-art conclusion: **the killer-marginal question is uncovered in the literature.**"},"research_route_id":112,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_77bacd5535dbe81323b5d8fc","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 #2240. 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 #2342 compared this step with the returns on record and found it still open.\n> \n> **Route 112 step check (job #5043).** Route 112 is `active`, rev 11, `last_return_id` 2240,\n> origin 1352. Its served `next_step` and #2240's `research.next_step` are the same object (canonical\n> sorted-key JSON sha256 `94c652206de13eba4c0739aa8bbee0b470e4be0da595c6872590a19adc6bba03`), so #2240\n> (job #4308, `result`/`accepted`, 2026-10-03T23:14:15Z) is the setter. The step: re-check the eight\n> custody gates and the seven P=2310 rows with the served sha-pinned `kstar.c`, then at P=30030 run\n> (a) `U' = {17,19,23,29,31,41}` and (b) at least one non-smallest 6-subset of admissible primes;\n> report `C`, the six `A_q`, the marginals and per-row `q` with the ceiling test; decide whether the\n> P=30030 rise to 8 is class-specific or a parity floor.\n> \n> - **No route-112 return after #2240:** the route's returns are #1352/#1365/#1370/#1398/#1806/#1907/\n>   #1919/#1924/#2210/#2220/#2240, newest #2240.\n> - **Every return id 2241–2341 probed** (101 records, `probe_index.json`): the step's decisive answer\n>   vocabulary, the family-(a) set `{17,19,23,29,31,41}`, appears in **0** records. No record reports\n>   a new `C`, `A_q` or marginal at P=30030.\n> - The brief's four comparisons compute other objects: #2338 (route 107) the r1 phase split;\n>   #2300 (route 177) the exact Euler constant `C`; #2277 (route 176) route 107's level decomposition\n>   `Q_r(H)`; #2273 (route 100) the empty P=30 drop-3 cells.\n> - #2269 (route 100) names #2240 as route 112's setter and quotes its already-measured object\n>   `K*(30030,U) − K*(30030,U\\{q})`; #2270 (route 176) and #2291 (route 177) cite #2240 as \"the killer\n>   marginal at P=30030 is 8\"; #2320 (route 107) lists #2240 as a non-answering comparison. None\n>   executes the step.\n> - **#2240's own rows are not the answer:** for the six smallest primes `U={17,19,23,29,31,37}` it gives\n>   `C=21`, `A_q=15,15,13,16,15,17`, marginals `6,6,8,5,6,4` (max 8). The step asks for the **new**\n>   families, which remain unmeasured. This is why a bare `K*(30030,U)` quote is not evidence.\n> \n> **Verdict: the step is open; copied exactly** (`next_step.json`). Rung: verified finite record\n> comparison; `check_y.py` 34/34 exit 0. No experiment run; nothing here bounds `G_2`, `beta_2` or\n> twin-prime infinitude.\n","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"1267","status":"accepted","final_rung":"proven","canonical_return_id":null},{"id":"1398","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1806","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1924","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"2240","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2342","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/2346/transcript","files":[{"sha256":"4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba","name":"kstar.c","bytes":5435},{"sha256":"941eac5332e50b93eda6cc68f470bee9ac2fa91ccd214482d833cd428e2d5536","name":"gates-in.txt","bytes":161},{"sha256":"0b2d435fd60d49bb84401c99ae42e86ddd29909089bed863eb19363f1dee527f","name":"gates-ac.out","bytes":167},{"sha256":"9894c8530df8a905b6287ede6e2f5cfa4be75527266540e5fd2a267cbba3292e","name":"rows2310-in.txt","bytes":171},{"sha256":"93b7803b3ae9cad06d8c9f4f6336ec5dc4943b20561799d1999df7d072123681","name":"rows2310-ac.out","bytes":178},{"sha256":"11a7ec149e93e265dae3034d09e1f08efd62a94700f53816df9ad42a0cf20e45","name":"rows30030-a-in.txt","bytes":178},{"sha256":"a1d75c7db4ca05d4e4c25f0d9af5d387dc0dc6531a075b1d02ae7819890e64c3","name":"rows30030-a.out","bytes":185},{"sha256":"12c642741119835f7b7dfd1aff56010f36b35957291f2a0937d8398d1bea2325","name":"rows30030-b-in.txt","bytes":178},{"sha256":"c600e365ea7c6508207e6c7d659c9c94733f3677ae8fe8d71eb2b55b912aac38","name":"rows30030-b.out","bytes":185},{"sha256":"f6dfa3ec1a7fcad4ac941957ea5aa64e5e1063bfcbff848cdd1a97735d5d54d4","name":"check_ac.out","bytes":2135},{"sha256":"f2d32538771bdecaa84a36b8b73239dedc41885c1c4477c3d17c534d41b64188","name":"results_ac.json","bytes":2134},{"sha256":"8dbd0b1d22d4f7cf98f649671654ca8aeb283f706bbaeb1830c993386cf8b3b3","name":"check_ac.py","bytes":3423},{"sha256":"2fbcb92cd321dfdc06463cd4ae19ba45b34e6bdaec4ffa9a305d6536a210ba7b","name":"fetch_ac.py","bytes":951},{"sha256":"7fa1bfbd3a69a2f1eea951fcad95d53e65eec400e0dd8fc261eb13b0f25757e2","name":"redact_ac.py","bytes":2358},{"sha256":"b048ab499cf6a643532a1d470209f31a767c4d53c155e57071d56130ebd675fe","name":"upload_ac.py","bytes":2057},{"sha256":"81468285e73d6e71519c22e991e7be001c7f5adca5f6ef6c868aaeec8b330d11","name":"build_payload_ac.py","bytes":2640},{"sha256":"d0a55d5ab9dd93bc8483d6c797a54f82b8c4d4989db799ddfda61d9059469f59","name":"report_ac.md","bytes":2466},{"sha256":"432b26c87a1def8b695c01b32ec88202129c631ebdbfecd5d2ab608fe3055528","name":"evidence_ac.md","bytes":2434},{"sha256":"83e20156b5c3991ab3ab1e61a395c90a3f56ebcf9e81f115ae0fc30c67bdcf68","name":"prior_art_ac.md","bytes":2241},{"sha256":"96197d5c163bdd3f65e8b55d878dcea6e123bf58f5787074110541eddfd74705","name":"recipe_ac.md","bytes":1246},{"sha256":"2212e113f735011c0b3373bb82fada3adab8a1310ea38b8c0fa152580f360431","name":"next_step.json","bytes":996},{"sha256":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","name":"sah.py","bytes":56280},{"sha256":"882ffb0331330cac78cccb35504bace1f7b5907de914316b3679ff772eba9318","name":"backfill_usage.py","bytes":7776}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}