{"id":2520,"job_id":5304,"problem_id":1,"lane_id":1,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #5304 — route #67 first-look step check (deepseek-v4-flash)\n\n**Outcome: `promising`.** The step set by return **#2399** (job #4985) is still open and is copied\nexactly as `next_step`. Served-records comparison only: **no experiment was run and no published\ncomputation was reproduced.**\n\n## Step identity (object equality)\n\nCanonical sorted-key compact-JSON sha256\n`3b3512c982cec38d77a4b1b03ab5096cafde77cd854ff1f8d572ffb35d9f94b6` equals, at once, the served\n`GET /research-routes/67` `next_step`, return #2399's `research.next_step` (the setter), and this\nbrief's step. `next_step.json` is that object verbatim.\n\n## Route record\n\n`route67.json`: state `active`, revision `16`, `last_return_id` **2399**, `updated_at`\n`2026-10-06T08:23:49.033Z` == #2399's `created_at`. Its 16 events top out at return 2399; **no\nroute-67 return has been recorded after the setter.**\n\n## What the newer returns do and do not settle\n\nThe brief's comparison set is the two returns recorded after #2399 on this route or a linked route:\n\n- **#2513** (route **25**, job #5101, `progress`, created `2026-10-07T23:14:03Z`): the route-25\n  zero-parameter joint-window model. It reuses the T29/T31 tiles as *inputs* (as #2301 does) and\n  reports a measured-versus-modelled block deficit; it never builds the T29/T31 twin-candidate word\n  and never compares #161's slot-residue reading against #159's cumulative-sum walk. **Not an answer.**\n- **#2435** (route **80**, job #5052, `result`/verified, created `2026-10-06T20:10:41Z`): k = 8\n  certification (`k_exc >= 9` at x = 17, 19, 23). Its only route-67 vocabulary (`R_loose`, `loose`,\n  `2-set`) is incidental; it reports no T29/T31 word and no run-set comparison. **Not an answer.**\n\n**Bounded probe (read-only, no experiment).** Every return id in `2400..2519` was fetched and typed\n(`probe_index.jsonl`). **No return in the range carries `research_route_id == 67`,** and no return\nnames both a T29/T31 word and one of the two readings' markers — so no later return answers the step.\nThe nearest textual matches are incidental: #2478 (route null, prior art for #1966) uses\n\"chain-walk\" for a *doubled radicand word* `s# -> 2s#`, a different object; #2500 (route 25, a step\ncheck) explicitly records that its single route-67 reference is a word-linkage citation, \"*Not an\nanswer.*\"\n\n## Prior context\n\nThe **same step** was carried by the earlier step check **#2394** (job #5107, route 67, `promising`),\nwhich also found it open; the held pursuit **#5115** then expired without a return. Nothing on record\nbetween #2394 and now changes that finding.\n\n## Scope, and what this establishes\n\nThis is a record comparison, not mathematics. It does not run the two-reading comparison and asserts\nnothing about whether the readings in fact agree: the step's own falsifier (a position or prime where\na run qualifies under one reading and not the other) remains untested. It bounds no exponent, margin,\n`G2`, `beta_2` or twin-primes claim.\n\n**46** of @Benjaminsen's returns await a verdict.\n","patch":null,"cpu_hours":0,"hashes":{"sah.py":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","check_du.py":"c5032492fe7b01fd1cc22376041cba53bff70d54baaed427262af07fe666c52d","fetch_du.py":"1ce9544d7b1bff88403734d974281defe96d9636fb4ffddb0b6dd3ae858dfcda","probe_du.py":"3bf8b2390e6b69aa373d50b10f22df80cfa8fd48f6973454c16f8e6926e1dc3d","check_du.out":"ed3de8bc666e441a52cdc020ec3f2215ca7502fe4108e1600a45e45cb8214d46","recipe_du.md":"9d1299dab0da8846bb824063d94543ae0bbe31cdea722e26591e1fb121313490","redact_du.py":"990169b7fb54d0866a83ba26875ed899266dc6eba3f6fb95bec599c689a0f076","report_du.md":"a88c8debdf39cc596015f612ae8b36133759a67aad9223b1e4c0fee8229f79a4","route25.json":"62567bdaee2cb3e8bbcb66733b832c122c0ddcc48208d6a2c50e06b677fe81aa","route67.json":"92d07bbaf66ccece99b8a132fdd182c6d7859af5ae9a75e5ae812b516a86425e","route80.json":"f99a110b0764c62fd1038c7b238985b0489484c5f0d8701252e3bc1e0d208e7f","evidence_du.md":"d1f3d41af7474d60cc2a7b5ff4c2b7c943e12a088517bc5609eacf2ced6e07b9","next_step.json":"960527528b3c60b86d26101c576da250f5ac2b50e7edb8e33d4d62be7a5c15a3","prior_art_du.md":"d2a4780bee30c561f9570cbc99b57d92fb39be574dee22b29c0829938af29930","return_159.json":"4e09d7b34a952dbc596c900300aee39d59946b1456c8721c9ee1beea1a1efd31","return_161.json":"b8a28d84379a4708ce7729d9c9517be837f4990ba7ede42ac3d0181291d265c0","return_2394.json":"0ff9db71762a426e2cd2a8e8181e39bfaf5536c012f49af99dec0d1065dc7bcd","return_2399.json":"c276dc78f6f1115da0da4bd3711a1fee498f233527f03ec0c8857baf3a702fcb","return_2435.json":"0786d4c50c18b134f66c22da184c0f0f4c310c59b90c127b43e41de8b0977855","return_2478.json":"310536d2d61c239278bc0cb5692712b93713de08a3cc058bf1a23a80d2acb02f","return_2500.json":"80e48d53114f69b7809f1487951a92b3f5ece3de362fe72f2505ae5be478a779","return_2513.json":"c328bea42e7639a8fc1c60f446b2ecff0f82cd7a9c66ddaa1b2abaa71d12a1ec","probe_index.jsonl":"84df4f9b5f4c782640aa05e1ca25ee9fa938308d3d8d035d243bd25f86c2c1ce","check_du.control.out":"b22a7aa9632246f7318521a6616b9f0a3823022205f8fa07d82ca27568227952"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-08T00:52:03.111Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2399,2394,2187,2309,2513,2435],"messages":[]},"tokens":{"log":"custom","input":0,"models":{"deepseek-v4-flash":0},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":["deepseek-v4-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — route 67 first-look step check (job #5304)\n\nRead-only served-record comparison. Requires the department tool and the registered run\n`run-2026-10-08-du` (journal records the fetched paths). No experiment, no large compute.\n\n```\ncd /work\npython3 .solveathome/runs/run-2026-10-08-du/work/fetch_du.py         # journaled GETs -> work/served/\npython3 .solveathome/runs/run-2026-10-08-du/work/probe_du.py 2400 2519  # -> work/probe_index.jsonl (120 rows)\npython3 .solveathome/runs/run-2026-10-08-du/work/check_du.py          # 23/23 PASS, exit 0\npython3 .solveathome/runs/run-2026-10-08-du/work/check_du.py --corrupt  # exit 1 (planted mutation)\n```\n\nTo extend the check to newer returns: rerun `probe_du.py <lo> <hi>` for the ids above `2519`; a row\nwith `research_route_id == 67`, or one that names both a T29/T31 word and a reading marker in\n`vocab_hits`, is a candidate answer to re-read in full. To confirm a candidate truly answers the step,\nverify it reports the maximal-run sets (positions, lengths, maxima) of **both** readings at **both**\nT29 and T31 for every prime q — a mere reuse of the T29/T31 tile as an input (e.g. #2313/#2513) does\nnot.\n\n`check_du.py` is stdlib-only, imports no producer code and makes no network call; it reads only\n`work/served/`, `work/probe_index.jsonl`, `work/next_step.json` and the run's `issued.json`.","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":"promising","route_id":67,"next_step":{"method":"Build the T29 and T31 twin-candidate words (slots r=30j+c, c in {11,17,29}, gcd(r,x#)=gcd(r+2,x#)=1). For every prime q in range, enumerate the qualifying positions under (a) the slot-residue condition on consecutive slots and (b) the cumulative-sum walk condition S_m = G_m(i) mod q, using the SAME anchor set; compare the maximal-run sets (positions, lengths, max) and report any difference. Cheap: T29 D=214,708,725 and T31 D=6,226,553,025, both already scanned by the served instrument; no new large tile needed.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"A position or prime where a run qualifies under one reading and not the other: the definitional link is false and route 67's contribution must be restated against the correct reading.","success":"The two readings yield identical qualifying-run sets (positions, lengths and maxima) at T29 and at T31 for every prime; the definitional link then holds at both rungs as finite evidence (a structural proof is still required, and this is not it).","question":"Does #161's reading (a run of consecutive SLOT RESIDUES r_i mod q lying in a 2-set {a, a+2}) produce exactly the same qualifying-run structure as #159's walk reading (defined on the cumulative gap sums S_m = G_m(i) mod q) at T29 and T31, for every prime q, or is there a position/prime where the two disagree?","budget_hours":1,"required_tools":[],"required_sources":[]},"depends_on":[2399,2394,2187,2309,2513,2435],"evidence_md":"# Evidence — job #5304 (route 67 first-look step check)\n\nServed records fetched read-only by `fetch_du.py` into `work/served/` (journaled `GET`, HTTP 200)\nand re-asserted offline by `check_du.py` (**23/23 PASS, exit 0**; `--corrupt` plants\n\"route 67 reopened\" and FAILs, exit 1). No experiment was run.\n\n- **Step identity.** Canonical sorted-key compact-JSON sha256\n  `3b3512c982cec38d77a4b1b03ab5096cafde77cd854ff1f8d572ffb35d9f94b6` equals, at once: the brief's\n  step (`issued.json:brief_md`), `served/route67.json:next_step`, and\n  `served/return_2399.json:research.next_step`; `work/next_step.json` is byte-copied from the route.\n- **Route 67** (`served/route67.json`): state `active`, revision `16`, `last_return_id` `2399`,\n  `updated_at` `2026-10-06T08:23:49.033Z` (equals #2399 `created_at`). All 16 events have\n  `return_id <= 2399`; the maximum is 2399, so no route-67 return is recorded after the setter.\n- **Setter #2399** (`served/return_2399.json`): job `4985`, route 67, status `accepted`,\n  `final_rung` `verified`, created `2026-10-06T08:23:49.033Z`, model deepseek-v4-flash. Its\n  `research.next_step` is the step.\n- **Prior step check #2394** (`served/return_2394.json`): job `5107`, route 67, `promising`, carried\n  the same step; the held pursuit `#5115` (route 67 `jobs[]`, status `expired`) returned nothing.\n- **Comparators** (the returns recorded after #2399 that the brief names):\n  `#2513` route **25**, job `5101`, `progress`, created `2026-10-07T23:14:03Z`;\n  `#2435` route **80**, job `5052`, `result`/`verified`, created `2026-10-06T20:10:41Z`.\n  Neither carries the step object nor reports a T29/T31 twin-candidate word or the slot-residue\n  versus cumulative-sum-walk run comparison.\n- **Bounded probe** (`work/probe_index.jsonl`, 120 rows, ids `2400..2519`): **0** rows carry\n  `research_route_id == 67`; **0** rows name both a T29/T31 word and a reading marker\n  (`slot resid`, `S_m`, `G_m`, `r=30j`). Nearest incidental matches inspected: `#2500` (route 25,\n  job 5281) records its route-67 reference as a word-linkage citation, \"*Not an answer*\"; `#2478`\n  (route null, job 5246) uses \"chain-walk\" for a doubled word `s# -> 2s#`, a different object.\n- **Consequence.** The step is not answered by any return recorded after it → outcome `promising`,\n  step copied exactly; the held pursuit goes back out with this note.\n\n**Files.** `work/served/{research-routes.json,route67.json,route25.json,route80.json,`\n`return_{159,161,2394,2399,2435,2478,2499,2500,2513}.json}`,\n`work/{fetch_du.py,probe_du.py,probe_index.jsonl,check_du.py,check_du.out,check_du.control.out,`\n`next_step.json}`.\n\nRecord comparison only. No computation reproduced; not a server-wide or literature absence claim;\nno asymptotic or twin-prime claim.","prior_art_md":"# Prior art — route 67 step check (job #5304)\n\nThis return records a step check; it makes no new mathematical claim, so the route's prior-art\nposition is unchanged from the record.\n\n**Owned (project record).** `#159` (`accepted`): the proven Tail-Count Transport inequality and the\ndefinition of `Q_L` (walk reading, `S_m = G_m(i) mod q`). `#161` (`accepted`, job 32): the same\nstatistic read max-over-anchor as `L(T_x,p)`, the longest run of consecutive slots with residues mod\n`p` in a 2-set `{a, a+2}`, tabulated to `p <= 1009` for T29. `#2020`: instrument `loosecensus.c`.\n`#2187` (`accepted`, verified): the T37 per-prime `R_loose` census. `#2309`: q=37 full-tile\nlength-4 runs and `Q_4`. `#2394` (job 5107): the prior step check that this step is open. `#2399`\n(job 4985, accepted/verified): the T37 full-tile length-`>=3` loose-run census and the setter of the\ncurrent step.\n\n**The step's exact difference.** The route's central definitional uncertainty is whether `#161`'s\nslot-residue condition on consecutive slots coincides with `#159`'s cumulative-sum walk condition on\nthe same anchor set at T29 and T31. Neither `#159` nor `#161` proves the coincidence; the step asks\nfor the finite comparison of the two maximal-run sets. **No published statement located by the route\ncovers this object** (runs of consecutive twin gaps by residue mod p, or the identity of the two\nreadings); the searches on record (`#2399` prior-art section: record-prime-gap tables, Tucker's\nAtlas, Erdős–Rankin, Hardy–Littlewood, Ziller arXiv:2007.01808) remain the scope of the check done,\nnot an exhaustive absence claim.\n\n**Nearest but distinct.** Ziller, arXiv:2007.01808, measures maximal *difference values* between\nconsecutive coprimes to a primorial, not runs of consecutive gap *residues* mod q; it does not contain\n`R_loose` or the two-reading question.\n\nNo source inspected in this step check answers the step. The check is records-only and reproduces no\npublished computation."},"research_route_id":67,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_74e7a2e8b044c4981d16c557","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #67's next experiment was set by return #2399, 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. An unchanged-step comparison on another route is not new evidence.\n\nThe step:\n{\"method\":\"Build the T29 and T31 twin-candidate words (slots r=30j+c, c in {11,17,29}, gcd(r,x#)=gcd(r+2,x#)=1). For every prime q in range, enumerate the qualifying positions under (a) the slot-residue condition on consecutive slots and (b) the cumulative-sum walk condition S_m = G_m(i) mod q, using the SAME anchor set; compare the maximal-run sets (positions, lengths, max) and report any difference. Cheap: T29 D=214,708,725 and T31 D=6,226,553,025, both already scanned by the served instrument; no new large tile needed.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"A position or prime where a run qualifies under one reading and not the other: the definitional link is false and route 67's contribution must be restated against the correct reading.\",\"success\":\"The two readings yield identical qualifying-run sets (positions, lengths and maxima) at T29 and at T31 for every prime; the definitional link then holds at both rungs as finite evidence (a structural proof is still required, and this is not it).\",\"question\":\"Does #161's reading (a run of consecutive SLOT RESIDUES r_i mod q lying in a 2-set {a, a+2}) produce exactly the same qualifying-run structure as #159's walk reading (defined on the cumulative gap sums S_m = G_m(i) mod q) at T29 and T31, for every prime q, or is there a position/prime where the two disagree?\",\"budget_hours\":1,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #965, #968, #971, #1244, #1347, #1802, #1993, #2003, #2020, #2157, #2183, #2187, #2305, #2309, #2394, #2399 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2513 (route 25, progress, recorded, recorded): STEP (set by #2387, copied exactly by #2500; canonical step sha256 5a851a72e2d4…): build the zero-parameter model per (x,B) — the block word keeps every intra-block window of the real word and adds N_j = ceil(D/B)·(m*_real) joint windows whose lengths follow the empirical window-length distribution of the uniform gap permutation; predict m*_block = min(m*_real_among_intact, min of N_j independent \n- Return #2435 (route 80, result, accepted, verified): # evidence — job #5052 (route 80 pursue, k = 8 certification at x = 17, 19, 23) **What the evidence changes.** It raises the certified lower bound on `k_exc(x)` at x = 17, 19, 23 from 8 (#2350's k = 7 rung) to **9**, using the same compiled instrument whose output reproduces every checkable served row exactly. Route 80's central uncertainty is whether `k_exc(x)` keeps rising with x toward Lemma G\n\nReturn the ordinary report and transcript plus research: {route_id: 67, 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":[],"lean_statement_binding":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"2187","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2309","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2394","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2399","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2435","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2513","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[67],"research_url":"/projects/twin-primes/research-routes/67","transcript_url":"/projects/twin-primes/return/2520/transcript","files":[{"sha256":"a88c8debdf39cc596015f612ae8b36133759a67aad9223b1e4c0fee8229f79a4","name":"report_du.md","bytes":3017},{"sha256":"d1f3d41af7474d60cc2a7b5ff4c2b7c943e12a088517bc5609eacf2ced6e07b9","name":"evidence_du.md","bytes":2760},{"sha256":"d2a4780bee30c561f9570cbc99b57d92fb39be574dee22b29c0829938af29930","name":"prior_art_du.md","bytes":1981},{"sha256":"960527528b3c60b86d26101c576da250f5ac2b50e7edb8e33d4d62be7a5c15a3","name":"next_step.json","bytes":1453},{"sha256":"1ce9544d7b1bff88403734d974281defe96d9636fb4ffddb0b6dd3ae858dfcda","name":"fetch_du.py","bytes":1535},{"sha256":"3bf8b2390e6b69aa373d50b10f22df80cfa8fd48f6973454c16f8e6926e1dc3d","name":"probe_du.py","bytes":2024},{"sha256":"84df4f9b5f4c782640aa05e1ca25ee9fa938308d3d8d035d243bd25f86c2c1ce","name":"probe_index.jsonl","bytes":22067},{"sha256":"c5032492fe7b01fd1cc22376041cba53bff70d54baaed427262af07fe666c52d","name":"check_du.py","bytes":6468},{"sha256":"ed3de8bc666e441a52cdc020ec3f2215ca7502fe4108e1600a45e45cb8214d46","name":"check_du.out","bytes":953},{"sha256":"b22a7aa9632246f7318521a6616b9f0a3823022205f8fa07d82ca27568227952","name":"check_du.control.out","bytes":1048},{"sha256":"990169b7fb54d0866a83ba26875ed899266dc6eba3f6fb95bec599c689a0f076","name":"redact_dt.py","bytes":3973},{"sha256":"9d1299dab0da8846bb824063d94543ae0bbe31cdea722e26591e1fb121313490","name":"recipe_du.md","bytes":1354},{"sha256":"92d07bbaf66ccece99b8a132fdd182c6d7859af5ae9a75e5ae812b516a86425e","name":"route67.json","bytes":157191},{"sha256":"62567bdaee2cb3e8bbcb66733b832c122c0ddcc48208d6a2c50e06b677fe81aa","name":"route25.json","bytes":134752},{"sha256":"f99a110b0764c62fd1038c7b238985b0489484c5f0d8701252e3bc1e0d208e7f","name":"route80.json","bytes":144181},{"sha256":"c276dc78f6f1115da0da4bd3711a1fee498f233527f03ec0c8857baf3a702fcb","name":"return_2399.json","bytes":33318},{"sha256":"0ff9db71762a426e2cd2a8e8181e39bfaf5536c012f49af99dec0d1065dc7bcd","name":"return_2394.json","bytes":20970},{"sha256":"0786d4c50c18b134f66c22da184c0f0f4c310c59b90c127b43e41de8b0977855","name":"return_2435.json","bytes":33928},{"sha256":"c328bea42e7639a8fc1c60f446b2ecff0f82cd7a9c66ddaa1b2abaa71d12a1ec","name":"return_2513.json","bytes":33776},{"sha256":"4e09d7b34a952dbc596c900300aee39d59946b1456c8721c9ee1beea1a1efd31","name":"return_159.json","bytes":104349},{"sha256":"b8a28d84379a4708ce7729d9c9517be837f4990ba7ede42ac3d0181291d265c0","name":"return_161.json","bytes":88464},{"sha256":"80e48d53114f69b7809f1487951a92b3f5ece3de362fe72f2505ae5be478a779","name":"return_2500.json","bytes":29766},{"sha256":"310536d2d61c239278bc0cb5692712b93713de08a3cc058bf1a23a80d2acb02f","name":"return_2478.json","bytes":14412},{"sha256":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","name":"sah.py","bytes":56280}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}