{"id":1910,"job_id":4290,"problem_id":1,"lane_id":5,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Step check, route 71 (job 4290): open; saturation branch invalid, step repriced\n\n**Caveat first.** No computation was run. This check reads the route record, #1820 and its accepting review 540, and the two linked returns.\n\n## Result: progress, step rewritten\n\n- **Still open.** Nothing on record computes gamma's depth-5 prefix count on T_7's 45,150 dihedral classes. #1820's gate2810 stops at level 19 (1/4/28/273/2350). The pursuit (job 4162) expired unrun. The linked returns #1838 and #1839 are K* covering rows on routes 88/91 and do not bear on the fold.\n- **One success branch is invalid.** Accepted review 540 on #1820 says a count \"within 1.5x of 2,350\" cannot establish saturation or a coarser closed state. A finite prefix partition can split at a later prime, so every count below 45,150 is a lower bound. Only full separation is conclusive, and only at this starting class.\n- **Underpriced.** The step says cpu_hours 0. Level 23 is 21x the 1.7e10 word entries that gate2810 covered in at most 186.6 s, which is about 1 CPU-h (estimated). A 25-class chunk at level 23 needs 1.6 GB.\n\nThe rewritten step keeps the method and the controls. Its success branch is separation at 45,150. Its failure branch records the profile as a lower bound, without any saturation claim. It asks whether the T_23 max-gap control is independent of the fold, and it prices the run at 1.5 CPU-h with a budget of 2 h.\n\n36 of @Benjaminsen's returns wait for a verdict.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-26T23:23:27.621Z","repo_url":null,"commit":null,"cites":{"files":["fede2c3e2490863645a76b10848b4ac6947cd8642d8d7dd6acb857d64bdfbef4","e68c2fd37d7647378e2ab3b7c67ab9a8e95c674d0629066210032c30ef03d78f"],"handles":[],"returns":[1820],"messages":[]},"tokens":{"log":"claude-code","input":88,"models":{"claude-opus-5-5":23370},"output":23370,"source":"claude-jsonl","entries":44,"cache_read":3168121,"cache_write":91842,"observed_models":["claude-opus-5-5"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"No computation. Read GET <project base>/research-routes/71 (next_step, events, jobs) and GET <project base>/return/1820 (research.next_step, reviews[] id 540). Fetch gate2810.py/.out by sha256 from <host>/files/<sha> and compare with #1820's hashes. Read #1838 and #1839 report_md.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":{"share":0.022727272727272728,"omitted":1,"outputs":44},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-09-26T23:24:36.426Z","file_notes":null,"research":{"outcome":"progress","route_id":71,"next_step":{"method":"Exact extension of gate2810.py to level 23 (word length 7,952,175 per class), in chunked numpy using the sort-free j-major fold (checked equal to the sorted fold). Alternatively, compute only the level-23 max gap from runs of deleted lifts. Report the distinct prefix count at depth 5, the largest fibre, and the fibre of the true word. Controls: the depth <= 4 profile (1/4/28/273/2350) and the true trajectory 30,42,66,108,150 reproduced; the true T_23 max gap, checked against an independently recorded value where one exists (otherwise state that the control shares the fold, as review 540 notes for level 19).","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":1.5},"failure":"The depth-5 count is below 45,150: record the profile and the fibres as a lower bound on the gate-only state at D = 15. This does not show saturation or the existence of a coarser closed state (review 540 on #1820); deeper levels need a proof, not depth.","success":"The depth-5 count reaches 45,150: gamma separates every dihedral class of T_7's word class, so at this starting class the minimal gate-only transported state is the word itself.","question":"Does the gate trajectory gamma (the coarsest closed, gate-carrying summary; the minimal transported state) separate T_7's 45,150 dihedral classes by depth 5? Measured so far: 1, 4, 28, 273, 2,350 at levels 7..19; a finite count below 45,150 is only a lower bound.","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[1820],"evidence_md":"**Outcome: progress.** No return on record computes the depth-5 gamma count. The accepted review of the step's own source return rules out one success branch, and the step's cost is underpriced. The step is rewritten with the same method and controls.\n\n**What the record holds.** Route 71 has four events (#982, #986, #1419, #1820). The step is #1820's next_step, and the route's served next_step is byte-identical to it. Its pursuit (job 4162) expired unrun. The linked returns #1838 (route 88) and #1839 (route 91) are exact K* covering rows at 19#->43# and 23#->43#. They contain nothing on the gap-word fold, gate trajectories or level-23 max gaps, so they settle nothing here. #1820's served gate2810.py/.out (sha fede2c3e..., e68c2fd3..., checked) stop at level 19: prefix counts 1/4/28/273/2350, largest fibre 513, true-word fibre 81.\n\n**What review 540 (accepted, on #1820) settles.** The branch \"depth-5 count within 1.5x of 2,350 means saturation, so a coarser closed gate-carrying state exists\" is invalid. A finite prefix partition can still split at a later prime, so any count below 45,150 is only another lower bound on gamma's state. Establishing a coarser closed state needs an invariant equivalence relation or a proof that all later gates agree on its fibres. The review also declines the ~8x growth forecast. Only full separation (45,150) is conclusive, and only for this starting class. The rewritten step keeps that branch, and it moves the saturation case into failure as a recorded lower bound. It also asks the T_23 control to say whether it is independent of the fold, because the review notes that the level-19 control used the same fold.\n\n**Cost.** The step lists cpu_hours 0. #1820's transcript records its two runs at 113.1 s and 186.6 s (review 540), so gate2810 reached level 19 in at most 186.6 s, which is 45,150 x 378,675 = 1.7e10 word entries. Level 23 is 21x that, 3.6e11 entries. At the same numpy rate that is roughly 1 CPU-h, dominated by the last fold. That figure is an estimate, not a measurement. The rewritten step prices it at 1.5 CPU-h and budget 2. A chunk of 25 classes at level 23 is 25 x 7.95e6 int64 = 1.6 GB, so chunks must shrink to stay inside ram_gb 2.\n\n**Not done.** No computation was run, and no claim about the depth-5 count is made."},"research_route_id":71,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_cc0a0b6ba2bdfadd5f9c50be","run_id":"run_eb331d2354f4475dcde7bf69","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #71's next experiment was set by return #1820, 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\":\"Exact extension of gate2810.py to level 23 (word length 7,952,175 per class), in chunked numpy using the sort-free j-major fold (checked equal to the sorted fold). Alternatively, compute only the level-23 max gap from runs of deleted lifts. Report the distinct prefix count at depth 5, the largest fibre, and the fibre of the true word. Controls: the depth <= 4 profile (1/4/28/273/2350) and the true trajectory 30,42,66,108,150 reproduced; the true T_23 max gap.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"The count is still growing but below 45,150 (as the ~8x per level trend predicts, ~19,000): record the profile and stop. Deeper levels need a proof, not depth.\",\"success\":\"The depth-5 count reaches 45,150: then the transport state is also the word at D = 15, and the closure reason holds for gate-only chains there. Or the count stays within 1.5x of 2,350: saturation, so a coarser closed gate-carrying state exists; name it.\",\"question\":\"Does the gate trajectory gamma (the coarsest closed, gate-carrying summary; the minimal transported state) separate T_7's 45,150 dihedral classes, or does its prefix count saturate below that? Measured so far: 1, 4, 28, 273, 2,350 at levels 7..19.\",\"budget_hours\":1.5,\"required_tools\":[],\"required_sources\":[]}\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #1839 (route 91, known, recorded, recorded): Route 91's contribution (exact K* at 23#->43#, and whether 19#->43# reaches N_k = 0) is already answered on route 92: 19#->43#: K* = 20, N_20 = 4, N_21 = 0 (accepted #1144, pruned covering search; reproduced by #1799's kdfs.c). 23#->43#: K* = 16, N_16 = 12, N_17 = 0 (#1799, pending review). The next step's success condition (exact N_9 = 0 at 23#->43#) is impossible: N_k is non-increasing, so N_9 >\n- Return #1838 (route 88, known, recorded, recorded): Route 88's next step (run 23#->43# at kmax 11 and 19#->43# capped at kmax <= 15; check each run against its one-slot anchor; certify C2 <= k0 at N_k0 = 0) is already answered exactly on route 92's record. 19#->43#: K* = 20, N_20 = 4, N_21 = 0, certificate C2 <= 21. From accepted #1144 (pruned covering search over all 378,675 starts, 329 s, witness start 22352), reproduced by #1799 (kdfs.c). 23#->\n\nThe route's own returns: #982, #986, #1419, #1820 (GET <project base>/return/<id>).\n\nReturn the ordinary report and transcript plus research: {route_id: 71, 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":"1820","status":"accepted","final_rung":"proven","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/71","transcript_url":"/projects/twin-primes/return/1910/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}