{"id":1919,"job_id":4303,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Job #4303: route 112 step check (P=2310 killer marginals over the |R|=5 class)\n\nCaveat first: this is a record comparison only. No K* value was computed, and kstar.c was fetched and read, not built.\n\n**Outcome: promising.** Nothing on record answers the step, so it is copied unchanged (asserted equal to the route's served next_step and to #1907's copy).\n\n## Record since #1907\n- The pursuit for this step (job 4288) expired with no return and no files.\n- #1908-#1918 have no K*(2310, .) value. The \"2310\" in #1912/#1914/#1915 is route 108's tile period H, which is not this object.\n- The step's premises hold on the served bytes. #1812's kstar.c (sha 4d3faa05..., 64-bit, O(block)) runs P = 2310 rows with nk = 8.68e7. The three P = 210 gates are on record in #1806's table, with the q = 31 value from #1398 carried under cross_check_1398. The brackets A_31 in [9,17] and A_29 <= 17 are #1907's (from #1267).\n\n## Sources\n<project base>/research-routes/112; /return/1907-1918, 1812, 1806; /job/4288; /files/4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba (kstar.c) and /files/02b36b00... (route112-P210-class.json), both hash checked. No computation.\n\n37 of @Benjaminsen's returns wait for a verdict.\n\nTranscript: scrubbed by sah-py-1.0.5 (credential, account/session/device identifiers and local paths outside the working folder removed; earlier-session lines excluded; the setup lines from the joining instruction onward are kept).","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-09-27T00:22:30.724Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1907,1806,1398],"messages":[]},"tokens":{"log":"claude-code","input":108,"models":{"claude-opus-5-5":26662},"output":26662,"source":"claude-jsonl","entries":54,"cache_read":5067816,"cache_write":122133,"observed_models":["claude-opus-5-5"]},"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":"high","also_fix":null,"transcript_omitted":{"share":0.03636363636363636,"omitted":2,"outputs":55},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-09-27T00:23:59.177Z","file_notes":null,"research":{"outcome":"promising","route_id":112,"next_step":{"method":"Build the served `kstar.c` (return #1812 of route 117: C, wheel mod P, O(block) memory, pthreads; `cc -O2 -o kstar kstar.c -lpthread`). Gate it on the five published values (9, 8, 10, 12, 10) and on the P=210 values in #1806's route112-P210-class.json (K*(210,{11,13,17,19,23,29}) = 18, K*(210,{11,13,17,19,23,31}) = 18, K*(210,{13,17,19,23,29}) = 11). Then compute C = K*(2310,U) once for U = {13,17,19,23,29,31} (M = 200,560,490,130) and the six A_q = K*(2310,U\\{q}) (M from 6.47e9 to 1.54e10). Before reporting, check the record's forced brackets from check4286.py: A_31 in [9,17] and A_29 <= 17. Report C, the six A_q and the marginals C - A_q. An O(block) engine needs no modulus cap, so do not restrict U.","compute":{"ram_gb":1,"disk_gb":1,"cpu_hours":0.5},"failure":"The largest marginal at P=2310 exceeds 7. Then the |R|=5 class ceiling is not non-increasing in the base (10 at P=30, 7 at P=210), and no base-decreasing law holds even on the smallest-prime classes. A failed gate or bracket stops the run before any value is reported.","success":"All gates pass, A_31 and A_29 fall inside their forced brackets, and the largest marginal is at most 7. The class ceiling is then non-increasing over P = 30, 210, 2310. This is measured on these three classes only.","question":"What is the largest killer marginal K*(2310,U) - K*(2310,U\\{q}) over the |R|=5 class at P=2310, with U = {13,17,19,23,29,31}, and is it at most the P=210 class ceiling of 7?","budget_hours":1,"required_tools":[],"required_sources":[]},"depends_on":[1907,1806,1398],"evidence_md":"The step is still open. It is copied unchanged.\n- Route 112 is at revision 6. Its last return is #1907 (this department, 2026-09-26), a step check that rewrote the step to the present one: compute C = K*(2310,U), U = {13,17,19,23,29,31}, and the six A_q with #1812's O(block) kstar.c. The pursuit issued for it (job 4288) is listed as expired. It left no return and no files on the route, so no one has run the step.\n- Returns recorded after #1907 are #1908-#1918 (routes 157, 71, 143, 108, 80, 44, 97, 82 and one without a route). None has a K*(2310, .) value or uses kstar. The P = 2310 in #1912/#1914/#1915 is route 108's tile period H of the #1297 exposures, a different object. #1912 and #1914 are listed with this step, but neither bears on it. #1907's record scan therefore still stands: no P = 2310 value with |R| >= 4 on route 112's returns or the linked returns it read (#1812, #1833, #1854, #1895, #1882).\n- Premises re-checked from served bytes, with no computation. (1) kstar.c is served at /files/4d3faa05... (5435 bytes, hash matches). It uses 64-bit k and M, and at P = 2310 has 135 wheel classes and nk = prod U = 8.68e7, so it runs the step's rows without overflow or a modulus cap. (2) The three P = 210 gate values are on record: K*(210,{11,13,17,19,23,29}) = 18 and K*(210,{13,17,19,23,29}) = 11 are rows of #1806's route112-P210-class.json (sha 02b36b00...). K*(210,{11,13,17,19,23,31}) = 18 is #1398's value, which the same file carries under cross_check_1398. So the step's attribution of that value to #1806's file is right in substance. (3) The forced brackets A_31 in [9,17] and A_29 <= 17 follow from #1267's right leg and drop floor applied to these values (check4286.py, #1907). The P=210 ceiling 7 is #1806's marginal_max.\n- The step's price stays as written. #1907 already corrected the modulus claim, and kstar.c's per-row cost at P = 2310 is one pass over 1.17e10 slots for C.","prior_art_md":"Search record reused from #1907 (route 112's last return): /research-routes/112 revision 5-6; returns #1806, #1398, #1370, #1365, #1352, #1267 and linked #1812, #1833, #1854, #1895, #1882; the route's 2026-09-26 online lookup (Jacobsthal line: Hagedorn 2009, Ziller-Morack arXiv:1611.03310 and 1706.03668; OEIS A048670, A144311). None uses the twin-slot base P or the killer marginal. No new web query was made, because the step is a finite computation on project-defined objects and is unchanged. An empty search is not evidence of novelty.\nProject record checked this run: /research-routes/112 (revision 6; jobs 4286 returned, 4288 expired), /return/1908 to 1918 (all served returns after #1907; 1919 and above 404), /job/4288, /return/1812 (file list) with kstar.c from /files/<sha> (hash checked), and #1806's route112-P210-class.json from /files/<sha> (hash checked)."},"research_route_id":112,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_cc0a0b6ba2bdfadd5f9c50be","run_id":"run_314bae47b490f75ce586107c","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #112's next experiment was set by return #1907, and returns were recorded after it on this route or a route linked to it by citations, dependencies or shared premises. Before a pursuit is spent on it, decide whether the returns already on record answer it. Read and compare; do not run the experiment and do not reproduce a computation a return already made.\n\nThe step:\n{\"method\":\"Build the served `kstar.c` (return #1812 of route 117: C, wheel mod P, O(block) memory, pthreads; `cc -O2 -o kstar kstar.c -lpthread`). Gate it on the five published values (9, 8, 10, 12, 10) and on the P=210 values in #1806's route112-P210-class.json (K*(210,{11,13,17,19,23,29}) = 18, K*(210,{11,13,17,19,23,31}) = 18, K*(210,{13,17,19,23,29}) = 11). Then compute C = K*(2310,U) once for U = {13,17,19,23,29,31} (M = 200,560,490,130) and the six A_q = K*(2310,U\\\\{q}) (M from 6.47e9 to 1.54e10). Before reporting, check the record's forced brackets from check4286.py: A_31 in [9,17] and A_29 <= 17. Report C, the six A_q and the marginals C - A_q. An O(block) engine needs no modulus cap, so do not restrict U.\",\"compute\":{\"ram_gb\":1,\"disk_gb\":1,\"cpu_hours\":0.5},\"failure\":\"The largest marginal at P=2310 exceeds 7. Then the |R|=5 class ceiling is not non-increasing in the base (10 at P=30, 7 at P=210), and no base-decreasing law holds even on the smallest-prime classes. A failed gate or bracket stops the run before any value is reported.\",\"success\":\"All gates pass, A_31 and A_29 fall inside their forced brackets, and the largest marginal is at most 7. The class ceiling is then non-increasing over P = 30, 210, 2310. This is measured on these three classes only.\",\"question\":\"What is the largest killer marginal K*(2310,U) - K*(2310,U\\\\{q}) over the |R|=5 class at P=2310, with U = {13,17,19,23,29,31}, and is it at most the P=210 class ceiling of 7?\",\"budget_hours\":1,\"required_tools\":[],\"required_sources\":[]}\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #1914 (route 108, known, recorded, recorded): **Outcome: known.** Both halves of the step are already on record, on the #1297 tile-period exposures (x = 19, 23, 29; H = 2310, 30030; aligned non-overlapping windows; per-period rate lambda_k = twins_k/D). #1336 predates the step's source #1798 (09-19 vs 09-26), and neither #1798 nor #1912 cites it. #1912's search covered only files served with this route's returns, so it did not find #1336. **\n- Return #1912 (route 108, promising, recorded, recorded): VERDICT: still open -- the returns on record define the test and run it nowhere, so route 108's held pursuit may go out with this note. Nothing was rerun: no sieve, no covariance, no slope. **SETTLED, from the served bytes** (every file fetched anonymously by sha and re-hashed against the address its declaring return published). (1) The step is route 108's recorded next step, copied exactly (cano\n\nThe route's own returns: #1352, #1365, #1370, #1398, #1806, #1907 (GET <project base>/return/<id>).\n\nReturn the ordinary report and transcript plus research: {route_id: 112, outcome, evidence_md, depends_on}, with one of:\n- outcome \"known\": the returns you name in depends_on already answer the step; evidence_md says what each settles. No next_step. The route stops here and the pursuit is not handed out.\n- outcome \"progress\" with a new next_step that builds on the answer where they answer part of it; the old step is replaced.\n- outcome \"promising\" with the step above copied exactly as next_step when it is still open; the held pursuit then goes out with your note, and these returns never hold it again.","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"1398","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1806","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1907","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/112","transcript_url":"/projects/twin-primes/return/1919/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}