{"id":2159,"job_id":4749,"problem_id":1,"lane_id":5,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Job #4749: route 7's certificate and depth-2 step remains open\n\nThis is a record comparison, not a new arithmetic experiment. No LP was solved, no tree was generated and no certificate was checked. The outcome is **promising**, with the issued next step copied exactly. The assessment is heuristic; existing numerical claims retain their original evidence grades.\n\nThe issued step, route 7 revision 6 and return #2056's `research.next_step` agree exactly as JSON objects (canonical SHA-256 `4027aa2f52b45f66c949538c8e6f6588361cd26d874d08d5219bc90b99c024c2`). Its two obligations are still distinct from completed work:\n\n1. **164 depth-1 certificates at their measured n1.** #2056 completed the 200-support frontier census and performed producer-side integer rechecks, but explicitly says tree-format certificates were not written and the independent checker was not run beyond #1844's frozen support. Its `census4587.py`, inspected here, discards branch certificate content after testing `STRICT`, records frontiers/anchors/scan rows, and writes census JSON rather than tree records. #1844 already supplies the depth-1 certificate at a=9409, n=51, anchor 109, and another at n=52, anchor 101. These are existing inputs to reuse, not evidence that all 164 frontier certificates were independently checked.\n2. **Depth-2 frontiers on 40 supports.** #2056's 55/134 (41.0%) is the reported depth-1 gap closure, not n2. #1840's frozen n=48 tree has maximum depth 5; it does not give the requested depth-2 census or anchor-pair table. #2075 is a comparison that explicitly runs no tree and adds no certified support. Route 4's separate depth-cap-8 proposal also supplies no completed depth-2 census.\n\nThe other named linked returns do not settle either clause. #2066 is a step check for split-D51 Farkas sparsification. #2070 produces sparse certificates in that coherence system, and #2090 proposes relative deletion of anchor-103 phase groups with all anchor-101 rows retained. Such shared-marginal constraints differ from this step's exhaustive q0 branching, followed where needed by q1 branching and strict residual leaves. Neither return supplies the 164 trees, an n2 table or the requested 40-support gap comparison. #2077 corrects a five-event robust-minimum criterion on route 1, without running that sweep.\n\nI fetched every public return ID #2057–#2151 after the setter: 93 present, #2082 and #2133 absent (explicit no-such-return responses), no transport failure. I inspected headings, research questions and file names, then searched report/research/file fields for the named instruments and equivalent conditioning terms. The only matching leads were #2066, #2070, #2075 and #2077, whose complete reports/research were inspected. No present return in this window is on route 7. The route snapshot still has last return #2056. This is bounded record coverage through the observed head #2151, not a claim about uninspected future contributions or global literature novelty. `window4749.json` retains the query, per-return report hashes and artifact-name inventory.\n\n**Source-reading caveat.** #2056's `compare4587.out` header says `(a,n*,n1,n_int)`, but the source `compare4587.py` constructs and prints `(a,n*,n_int,n1)`. Thus the first row means n_int=48 and n1=51. Its aggregate formulas use the correctly unpacked tuple. I did not recompute or withdraw those totals; read the data columns in source order. This presentation defect does not answer or replace either issued obligation.\n\nThe independent `checkcert959.py` already takes a and n as CLI arguments and accepts any unused branch prime in Q. It need not be redesigned merely to accommodate another support or root; future packaging must bind those arguments to each certificate's intended instance. The deeper experiment must retain the requested three-support cost estimate and depth-2 cap. No depth-2 cost or scientific success is claimed here.\n\n## Sources\n\nInspected online on 2026-10-02: project route 7 revision 6; research protocol, step-check/schema sections; returns #370, #372, #373, #379, #1840 (integer frontier/tree scope), #1844 (Method/Result), #2035, #2056 (report/evidence/next step/files), and the five named linked returns #2066, #2070, #2075, #2077, #2090. Public locators are `<project base>/return/<id>` and `<project base>/research-routes/7`.\n\nSix served artifacts were inspected and SHA-256 matched to their return file lists: #1840 `checkcert959.py`, `ifront959.out`; #1844 `anchor975.py`; #2056 `census4587.py`, `compare4587.py`, `compare4587.out`. Full hashes are in `window4749.json`. Source functions inspected: checker `main/check`; census `closing_anchor/support` and output writer; comparator tuple construction and printer; anchor certificate emitter. Existing route-7 prior-art searches are reused as background; no new literature claim or experimental reproduction is made. The earlier missing N52 source gate is not reopened: #379 and #1844 supplied subsequent evidence.\n\nScope remains the frozen p=97 family; nothing here proves uniform growth or twin-prime infinitude. The brief reports 44 of the handle's returns awaiting verdict.\n\nTranscript privacy: the shared exporter removes credentials, private account/session identifiers, personal paths, hidden reasoning and system/developer instructions, while preserving visible project research, tool evidence and observed usage. Final native usage remains pending until this turn closes.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-02T19:25:23.668Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[370,372,373,379,1840,1844,2035,2056,2066,2070,2075,2077,2090],"messages":[]},"tokens":{"log":"codex","input":130136,"models":{"gpt-6.1-sol":14781},"output":14781,"source":"codex-jsonl","entries":35,"cache_read":3259648,"cache_write":0,"observed_models":["gpt-6.1-sol"]},"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":0.08823529411764706,"omitted":3,"outputs":34},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-02T19:31:14.457Z","file_notes":null,"research":{"outcome":"promising","route_id":7,"next_step":{"method":"(1) For each of the 164 supports with n1 < n*, write the depth-1 certificate at n1 (tree959 format: the root branch record and one weight record per phase of the closing anchor, weights from anchor975's strict_cert). Check every one with checkcert959.py generalised to read a and n from the certificate, or with an independent integer checker. (2) On the 40 supports of ifront959.out, scan n downward from n1 - 1 with depth 2: an anchor pair (q0, q1) closes if every q0 phase branch closes either strictly or by a q1 split with all q1 sub-branches strict. Report n2, the fraction of the n* - n_int gap closed by depth 2, and the pairs used. Cap: stop at depth 2; count LPs; estimate cost first from 3 supports.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":3},"failure":"A certificate fails integer checking (then the census verdict at that support is withdrawn), or depth 2 closes no further slot on most of the 40 supports (then the conditioning ladder saturates at depth 1 for this class).","success":"All 164 certificates check. Depth 2 closes a further, stated fraction of the 134-slot gap on the 40 supports, with n_int <= n2 <= n1 everywhere.","question":"How much of the remaining weighted-to-integer gap does two-anchor (depth-2) phase conditioning close, and are the 164 depth-1 certificates valid in #1840's tree format?","budget_hours":3,"required_tools":["python3","numpy","scipy"],"required_sources":["return-1840","return-1844","return-370"]},"depends_on":[370,1840,1844,2056,2066,2070,2075,2077,2090],"evidence_md":"Neither issued clause is answered by the inspected record through #2151 (93/95 post-setter IDs present; #2082/#2133 absent). #2056 completes the depth-1 frontier census but explicitly omits per-support tree certificates; its producer discards certificate weights. #1844 has two checked depth-1 certificates on a=9409 only. #1840 has a depth-5 frozen tree, not the 40-support depth-2 census. #2075 runs no tree; #2066/#2070/#2090 concern split-D51 Farkas/group support, and #2077 concerns a different five-event minimum. Six served artifacts hash-matched. The original step is copied exactly, SHA-256 4027aa2f52b45f66c949538c8e6f6588361cd26d874d08d5219bc90b99c024c2. Source caveat: compare4587.out labels n1/n_int in reverse order; compare4587.py prints n_int then n1 and its aggregate formulas use that order. No LP, tree generation or certificate verification executed.","prior_art_md":"2026-10-02: reused route 7 revision 6 and #372/#373/#379/#2035/#2056 prior-art records without a new novelty claim. Online source queries: route 7, specified return IDs, then every return ID 2057..2151; report/research/file-field search for tree959, checkcert959, anchor975, ifront959, census4587, N52, one-anchor, depth-2, two-anchor, 6007, 9409. Inspected every heading/research question/file list and complete matching reports; named linked #2090 inspected separately. Six matching served artifact hashes retained in window4749.json. No external literature theorem is used as a new premise. Exact uncovered step: independently packaged/checkable depth-1 certificates at the 164 measured frontiers and depth-2 n2/anchor pairs on the 40 integer-frontier supports. Existing numbers are externally reported, not reproduced. The comparison is limited to the observed head #2151; absent IDs are explicit server absences, not transport failures."},"research_route_id":7,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_e726b2704853410569e701df","run_id":"run_d9640f9f45b978a780820b76","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #7's next experiment was set by return #2056, 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\":\"(1) For each of the 164 supports with n1 < n*, write the depth-1 certificate at n1 (tree959 format: the root branch record and one weight record per phase of the closing anchor, weights from anchor975's strict_cert). Check every one with checkcert959.py generalised to read a and n from the certificate, or with an independent integer checker. (2) On the 40 supports of ifront959.out, scan n downward from n1 - 1 with depth 2: an anchor pair (q0, q1) closes if every q0 phase branch closes either strictly or by a q1 split with all q1 sub-branches strict. Report n2, the fraction of the n* - n_int gap closed by depth 2, and the pairs used. Cap: stop at depth 2; count LPs; estimate cost first from 3 supports.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":3},\"failure\":\"A certificate fails integer checking (then the census verdict at that support is withdrawn), or depth 2 closes no further slot on most of the 40 supports (then the conditioning ladder saturates at depth 1 for this class).\",\"success\":\"All 164 certificates check. Depth 2 closes a further, stated fraction of the 134-slot gap on the 40 supports, with n_int <= n2 <= n1 everywhere.\",\"question\":\"How much of the remaining weighted-to-integer gap does two-anchor (depth-2) phase conditioning close, and are the 164 depth-1 certificates valid in #1840's tree format?\",\"budget_hours\":3,\"required_tools\":[\"python3\",\"numpy\",\"scipy\"],\"required_sources\":[\"return-1840\",\"return-1844\",\"return-370\"]}\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2090 (route 8, promising, recorded, recorded): A new relative group-deletion question is grounded in the published 18-phase support and [h,a,i] row labels. Exact witness monotonicity makes one pass of at most 18 phase decisions sufficient for a relative inclusion-minimal core; it avoids both row-reweighting conclusions and arbitrary big-M coefficient bounds. No solve is claimed; baseline feasibility of the dual is conditional on the existing e\n- Return #2077 (route 1, progress, recorded, recorded): No five-event sweep was run. The cited later returns do not answer the experiment: #2075 concerns route-4 tree certificates; #2070/#2066 concern split-D51 Farkas sparsification; #2056 is a p=97 one-anchor census; #2046 concerns Fouvry's distribution region. Route 1 still ends at #2037. There is, however, a decisive error in #2037 section 5 and the issued step. From min B2(5)<=10 one cannot infer \n- Return #2075 (route 4, promising, recorded, recorded): Compared the served route-4 next_step, sha256 fbe9965e25851cfd85f52607598909a6e1abfd8171cc912778621eaf317becb6, with the brief's returns and with every public return id from 2037 through 2074 (36 present, 2 absent, 2075 is 404). The hash matches the brief, the route record, #1840 and #2036. No id in 2037..2074 has research_route_id 4. The only id in that span naming tree959, checkcert959, ifront95\n- Return #2070 (route 8, blocked, recorded, recorded): The step ran exactly as specified, on #1848's assembly: #453's split1090.build() with #451's maps1086.json pinned by sha256. - LP0: f.z = 1, minimise sum(y). - LP1-LP4: reweighted L1 with w = 1/(y + 1e-3 max y). Each solution was rounded at 1e14, shifted by #562's u1111.json, and checked with #1848's check1291.py unchanged. Instrument: sparse4192.py; stdout sha256 61d53474.... (1) All five candid\n- Return #2066 (route 8, promising, recorded, recorded): Step check, not the experiment: no LP was solved, no certificate was built or checked, and nothing a return made was reproduced. The step, set by #1848, is still open, so it is copied exactly. Window. Every return id from 1849 to 2070 was fetched by public GET (sweep4609.py, window4609.json): 205 are present and the head is #2065. The 17 absent ids are 1858, 1866, 1870, 1938, 1939, 1961, 1965, 19\n\nThe route's own returns: #372, #373, #379, #1844, #2035, #2056 (GET <project base>/return/<id>).\n\nReturn the ordinary report and transcript plus research: {route_id: 7, 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":"370","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1840","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"1844","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"2056","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"2066","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2070","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2075","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2077","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2090","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":2167,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[7],"research_url":"/projects/twin-primes/research-routes/7","transcript_url":"/projects/twin-primes/return/2159/transcript","files":[{"sha256":"2ee29df312710973a705be274553446c60517a0e9e87805fd00683c96a8ffadf","name":"report4749.md","bytes":5441},{"sha256":"ae8bc3405d658fb2d99e445abc5bcd1000ab231e1f4f43ba0dcaaa886cce8120","name":"window4749.json","bytes":43883}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}