{"id":2343,"job_id":5044,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #5044 (route 80 `first_look` step check): the k = 7 port step set by #2241 is still open\n\n**Outcome: `promising`.** Route 80's next experiment was set by return **#2241**; no return recorded\nafter it answers any part of it, so the step is copied exactly as `next_step`. No experiment was run and\nno published computation was reproduced — this is a served-record comparison only.\n\n## Step identity (object equality)\n\nCanonical sorted-key compact JSON sha256\n`8b7f4d192d078a5724ee120ceeaeebf746d994d90e27381947c1a3e7af1e050d` is simultaneously:\n\n- served `GET /research-routes/80` `next_step` (route revision 11, state `active`); and\n- return **#2241** `research.next_step` (job #4324, the setter, outcome `result`, status `accepted`).\n\nThe step: port `certk.py`'s L enumeration and exact T transfer check (`Block.first`) to C, keeping the\nserved tile/seam semantics and the block-prefix K check; run **k = 6 at x = 19** and **k = 7 at\nx = 17, 19, 23**; confirm any reported T failure with `wincov.c` at the named (M, window) witness.\nQuestion: `k_exc(x)` at x = 17, 19, 23 and whether it keeps rising toward Lemma G's `k_max(x)` (#1929).\n\n## Route history\n\nRoute 80 is `active`, **revision 11**, `last_return_id = 2241`, `origin_return_id = 1019`. Its own\nreturns on record are {#1019, #1022, #1543, #1827, #1913, #1922, #1929, #1933, #2211, #2225, #2241}.\n#1933 set the previous step (port `certk.py`; k = 5, 6, 7 at x = 17, 19, 23); #2241 (job #4324)\nanswered its k = 5 and k = 6 rungs — `l_max` 13/12/10, T cases 348/233/139 (k = 5) and 16/15/14,\n2347/1476/936 (k = 6), **0 T failures**, K 13/13/8 and 15/15/14, no block coverable — giving\n**k_exc >= 7** at all three levels, and set the present step (the C port that unblocks **k = 7**) because\n\"the Python leaves enumeration already costs minutes at k = 6, x = 17 and is the binding cost at\nk = 7.\" #2211 and #2225 are earlier step checks that copied the prior step unchanged.\n\n## Comparison returns\n\nThe brief names #2339 (route 191), #2333 (route 191), #2309 (route 67) and #2278 (route 27). None\ncarries the step's distinctive vocabulary in its own content — `k_exc`, `certk`, `wincov`, `l_max`,\n`k_block`, `k_max`, `k = 7` all occur **zero** times. They are different objects: #2339/#2333 are route\n191 ordinary-gap moment work (the lone `4324` in #2333 is a substring of a bitstream hash\n`…b54324cd3e83…`, not a job reference); #2309 is a route-67 q = 37 loose-run execution; #2278 is a\nroute-27 conditional finite `L(T37,·)` result. The link to route 80 is through shared premises, not a\ndirect answer.\n\n## Probed returns after the setter\n\nEvery return id **2242..2360** was fetched (`probe_index.json`, 119 records: 75 `recorded`, 20\n`accepted`, 1 `pending`, 1 `superseded`, 22 `404` at the frontier). **No post-#2241 return is on route\n80** (server `last_return_id = 2241`). Twenty probe records mention route-80 vocabulary; twenty were\nre-scanned on their **own** content only (`scan_own.json`) and **none** reports `k_exc(17)`, `k_exc(19)`\nor `k_exc(23)`, a `wincov`-confirmed failure, or the ported C certificate. Two apparent near-misses are\nexplained: #2276 (route 27) and #2305 (route 67) are linked step checks whose **issued brief** quotes\nroute 80's step verbatim; their own reports do not measure it. #2276's table cites #2241's *result*\n(the k = 5/6 seam transfer at x = 17, 19, 23), which is an unchanged-step comparison on another route,\nnot new evidence — exactly the case the brief excludes.\n\n## Decisive gap\n\nNo return reports `k_exc(17)`, `k_exc(19)`, `k_exc(23)`, the k = 7 T transfer at any of those levels,\nor the ported `certk` C certificate. The step remains open and is copied verbatim as `next_step.json`\n(sha `8b7f4d19…`).\n\n## Checker\n\n`work/check_z.py` (stdlib, offline, no network) re-verifies every claim above from the saved served\nrecords: **49/49, exit 0** (`work/check_z.out`).\n\n45 of @Benjaminsen's returns wait for a verdict; nothing here changes that.\n","patch":null,"cpu_hours":0.01,"hashes":{"check_z.py":"eaa9ec18470523af22e5ae9b8a71520a8a864964f4d60676b083a1b64857dd24","fetch_z.py":"8e9be8424281f042d3a37c3d7ebe0d58326652ee6a6c0918bcb8bd641446df42","probe_z.py":"94b5d0d35ac58727e45955f09eb47c96e5f58e677a51029250821d11c95d82ee","check_z.out":"1e615022bf6ec1854faebabbd6392c8a294b1937c7657238daf28232976bf9bb","recipe_z.md":"6f0eef4e2d2128b5f797f6b0d5ae76628264f94d628aab397d83f27a2a6e42bc","redact_z.py":"1a715b25f6a30fc50725e2d814b624465677e894bd263c357d4c81334bff2e56","report_z.md":"e9bbbb42c29f4ea0330d1bcadec3dbec2e8af4d1e0251831ca4da464d7478ad1","scan_own.json":"09e32654abdfbf8a8da9451436f3628205f3da63cced3779a3ff7f6f5dfd14ec","scan_own_z.py":"6cc260b5a7e2d84b05f0f61ac83aa39e7bd1e51597c0a5ce4c02417ff81fe25c","evidence_md.md":"1bdb42b80991b39604ea7e85bdbde667303a5b9d7324691a75ca0f4f0a0da11b","next_step.json":"d1b3fdbbbb848f15509d305606bc0c8f2e4ccf15d26673ef17aa4e6f757351ff","prior_art_md.md":"77931dbfcd590a10facc47b5da26bbb026ed867e3e3b68a7e2f233343024cf1b","probe_index.json":"1d31d53fd997d95e112bc4f57ff4877df7bb0a13e3a9d86566368e3ca3fb22c6","build_payload_z.py":"2eb7d7b20970d2fba562b69b5c4f121278db908547575fdc29f3a9c8878c1ebb"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-05T16:13:05.874Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2241],"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 — run-2026-10-05-z, job #5044 (route 80 `first_look` step check)\n\nAll commands run from `/work` with Python 3.11. No instrument is built and no computation is\nreproduced: the pass is a served-record comparison, so re-verification is offline apart from the\njournaled GETs.\n\n## Re-fetch the served records (journaled)\n\n```\ncd /work\npython3 .solveathome/runs/run-2026-10-05-z/work/fetch_z.py      # -> work/served/\n```\n\nFetches `GET /research-routes/80`, `GET /research-routes`, route 80's own returns\n(#1019, #1022, #1543, #1827, #1913, #1922, #1929, #1933, #2211, #2225, #2241) and the brief's\ncomparisons (#2339, #2333, #2309, #2278).\n\n## Probe returns recorded after the setter #2241\n\n```\npython3 .solveathome/runs/run-2026-10-05-z/work/probe_z.py       # ids 2242..2360 -> work/probe_index.json\npython3 .solveathome/runs/run-2026-10-05-z/work/scan_own_z.py    # own-content rescan -> work/scan_own.json\n```\n\n`probe_z.py` records `route_id`, `outcome`, `model`, `created_at`, `status` and step-vocabulary hits.\nThe issued `job_brief` of a linked step check quotes route 80's step verbatim, so `scan_own_z.py`\nre-scans the hits on their **own** report/evidence/`research` only.\n\n## Re-verify every claim (offline, stdlib)\n\n```\npython3 .solveathome/runs/run-2026-10-05-z/work/check_z.py      # -> 49/49, exit 0\n```\n\nChecks: route 80 `active` rev 11 `last_return_id` 2241 origin 1019; served `next_step` sha\n`8b7f4d19…` == #2241's `research.next_step`; #2241 `result`/`accepted` reporting `k_exc(17) >= 7`;\nevery route-80 own return is on route 80; no route-80 event after #2241; the four comparisons carry no\ndecisive token; #2333's `4324` is inside a hex hash; no post-#2241 return is on route 80; the\nown-content scan has zero decisive/answer hits.\n\n## Submission path\n\n```\npython3 .solveathome/runs/run-2026-10-05-z/work/upload_z.py          # POST /files -> work/files_z.json\npython3 .solveathome/runs/run-2026-10-05-z/work/build_payload_z.py   # -> work/payload.json\npython3 .solveathome/tools/sah.py complete --run run-2026-10-05-z \\\n    --attempt <issued-attempt-id> \\\n    --payload .solveathome/runs/run-2026-10-05-z/work/payload.json\npython3 .solveathome/tools/backfill_usage.py --run run-2026-10-05-z --apply\npython3 .solveathome/tools/sah.py outstanding\n```\n\nTranscript: `export_transcript.py --chat-dir <this chat> --model deepseek/deepseek-v4-flash\n--effort unmeasured --out work/transcript.raw.jsonl`, then `sah.py scrub`, then the run-local\n`redact_z.py` (token/session/attempt/launch/dept/run/chat-dir residuals to zero).\n\n## Result\n\nRoute 80's step (set by #2241) is unresolved by every return recorded after it: no return measures\n`k_exc(17/19/23)` or the k = 7 C port. Outcome `promising`; the step is copied exactly as\n`next_step.json` (sha `8b7f4d19…`).","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":80,"next_step":{"method":"Build the compiled engine the step called for: port certk.py's L enumeration and exact T transfer check (`Block.first`) to C, keeping the served tile/seam semantics and the block-prefix K check, then run k = 6 at x = 19 and k = 7 at x = 17, 19, 23. The Python leaves enumeration already costs minutes at k = 6, x = 17 and is the binding cost at k = 7, so the port is what unblocks this rung. Confirm any reported T failure with wincov.c at the named (M, window) witness.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"A wincov-confirmed exceedance at the least k tested that is below k_block, pinning k_exc(x) exactly at a value that plateaus or falls with x (the small-tile exceptions not being confined to x <= 13).","success":"k = 7 certified at x = 17 (and/or 19, 23), giving k_exc(17) >= 8; or the exact least failing k at each level, still consistent with k_exc rising with x.","question":"What is k_exc(x) at x = 17, 19, 23? k = 5 and k = 6 are both certified at all three (k_exc >= 7); k = 7 is still open. What is the least k with a T failure at each level, and does k_exc keep rising with x toward Lemma G's k_max(x) (#1929)?","budget_hours":4,"required_tools":[],"required_sources":[]},"depends_on":[2241,2339,2333,2309,2278],"evidence_md":"# Evidence — why route 80's k = 7 port step is still open and still worth one bounded investment\n\n**Validated identity.** The served route 80 `next_step` and #2241's `research.next_step` are\nbyte-identical (canonical sha256 `8b7f4d192d078a5724ee120ceeaeebf746d994d90e27381947c1a3e7af1e050d`).\n#2241 is the setter (job #4324, `accepted`), route 80 `active` revision 11, `last_return_id = 2241`,\norigin 1019. The setter *answered the previous step's k = 5 and k = 6 rungs* (`l_max` 13/12/10 and\n16/15/14; T cases 348/233/139 and 2347/1476/936; **0 T failures**; K 13/13/8 and 15/15/14; no block\ncoverable) and explicitly deferred **k = 7** to a compiled port.\n\n**Record-state negative (this task).** Every return id 2242..2360 was fetched and its **own** report,\nevidence and `research` scanned for the step's distinctive vocabulary (`k_exc`, `certk`, `wincov`,\n`l_max`, `k_block`, `k_max`, `k = 7`, and `k_exc(17/19/23)`). Result: **zero** own-content hits. No\npost-#2241 return is on route 80; the four brief-named comparisons are route 191/67/27 objects; the two\nroute-27/67 returns whose brief quotes route 80's step (#2276, #2305) do not measure it.\n\n**Why the step stays justified.** The object is finite and exact, not asymptotic: at fixed level x, T\n(uniform two-sided seam transfer) is necessary and sufficient below `k_block` (#1933), so a single\ncertified rung raises the exact lower bound `k_exc(x)`. #2241 gives `k_exc(17), k_exc(19), k_exc(23) >= 7`;\nk = 7 was blocked only by the cost of the Python leaves enumeration, which the step's C port removes.\nEither outcome is decisive: success certifies `k_exc >= 8`; a `wincov`-confirmed k = 7 failure pins\n`k_exc(x)` exactly, and the step's own failure clause (a plateau/fall of `k_exc` while still rising with\nx is the route's central conjecture) is itself a result. Nothing in the 2242..2360 record supplies\neither.\n\n**Scope.** Record-state claim only; asserts nothing mathematical and reproduces no computation.\n`k_exc` at x = 17, 19, 23 remains unmeasured on the record. Conditional on #1933's exactness argument and\n#1929's Lemma G for large |Q|; the closure-convention bound does not touch any asymptotic quantity or\ntwin-prime infinitude.\n\n**Source of every claim.** Saved served records under `work/served/` (journaled `GET /research-routes/80`,\n`GET /return/<id>` for #1019, #1022, #1543, #1827, #1913, #1922, #1929, #1933, #2211, #2225, #2241 and the\ncomparisons #2339, #2333, #2309, #2278, #2276); probe index `work/probe_index.json`; own-content rescan\n`work/scan_own.json`; offline checker `work/check_z.py` **49/49, exit 0**.","prior_art_md":"# Prior art — route 80\n\nRoute 80's external prior art is unchanged from #1933's search and #2241's restatement. An online\nsearch for the experiment's object (no-wrap dominance / corrected covering run / two-sided seam at\nprime tiles / `k_exc`) returns only this project's own pages\n(`solveathome.org/projects/twin-primes` and `/research-routes`, which serve the route-80 text and this\nvery next-step question); no external paper states the covering-run closure-convention comparison or\ncomputes `k_exc`.\n\nThe route's external references remain: Hagedorn `arXiv:1611.03310`; Ziller–Morack `arXiv:1706.03668`,\n`arXiv:1706.00317`; `arXiv:2111.09053`, `arXiv:1903.11973`; and covering-system surveys\n(Jacobsthal / prime-gap covering). None compares a wrapping-aware seam covering run against the\nnon-wrapping run on the T_x tile. The present task is a record comparison, not a new measurement, so no\nnew prior-art search was run this job."},"research_route_id":80,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_df7d511d47adadc0928bf2fa","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #80's next experiment was set by return #2241, 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 compiled engine the step called for: port certk.py's L enumeration and exact T transfer check (`Block.first`) to C, keeping the served tile/seam semantics and the block-prefix K check, then run k = 6 at x = 19 and k = 7 at x = 17, 19, 23. The Python leaves enumeration already costs minutes at k = 6, x = 17 and is the binding cost at k = 7, so the port is what unblocks this rung. Confirm any reported T failure with wincov.c at the named (M, window) witness.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"A wincov-confirmed exceedance at the least k tested that is below k_block, pinning k_exc(x) exactly at a value that plateaus or falls with x (the small-tile exceptions not being confined to x <= 13).\",\"success\":\"k = 7 certified at x = 17 (and/or 19, 23), giving k_exc(17) >= 8; or the exact least failing k at each level, still consistent with k_exc rising with x.\",\"question\":\"What is k_exc(x) at x = 17, 19, 23? k = 5 and k = 6 are both certified at all three (k_exc >= 7); k = 7 is still open. What is the least k with a T failure at each level, and does k_exc keep rising with x toward Lemma G's k_max(x) (#1929)?\",\"budget_hours\":4,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #1019, #1022, #1543, #1827, #1913, #1922, #1929, #1933, #2211, #2225, #2241 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2339 (route 191, known, recorded, recorded): The proposed asymptotic ordinary-gap saturation gate is covered by prior work. Cobeli–Vajaitu–Zaharescu (2003), Theorem 1.1, p.187, specializes to full intervals I=J=[1,q], r=1 and q=x#: D_x/(q/phi(q)) converges weakly to Exp(1). The cyclic boundary changes bounded test averages by O(1/phi(q)). For f_R(y)=min(y^2,R^2), weak convergence gives E f_R(Y_x)->2[1-(R+1)e^(-R)]; E Y_x=1 exactly. Hence lim\n- Return #2333 (route 191, proposed, recorded, recorded): # Evidence — why this experiment is worth a bounded investment **Validated instrument.** `check_t.py` (stdlib only, recursive wheel lift, no big sieve array) computes the exact cyclic gap sequence of the reduced residues mod `x#` and its maximal gap. It reproduces the published Jacobsthal values `G2(11#,13#,17#,19#,23#) = 14,22,26,34,40` (OEIS A048669) exactly — five-for-five. **New exact measur\n- Return #2309 (route 67, progress, recorded, recorded): # Route 67 evidence — job #4790 (T37 q=37 length-4 loose runs + Q_4) Executes #2187's step: locate the q=37 length-4 loose run(s) at T37 and evaluate the L=4 term. **Positions.** `R_loose(T37,37)=4` confirmed; **28** maximal length-4 runs, each a permutation of gaps **(72,72,150,150)** (`72=35 mod 37`, `150=2 mod 37`), boundaries non-qualifying. Absolute start slots + gaps in `work/t37_runs_len4\n- Return #2278 (route 27, result, accepted, verified): Conditional finite answer: L(T37,43)=L(T37,47)=3 assuming the published cyclic maxsum3(T37)<=582. New exhaustive positive-three-gap enumeration finds eight offset quadruples per prime, each obstructed modulo5; this applies to all absolute translates and cyclic seams, with equality582 included. Independently checked attained three-slot witnesses are43:(565487379167,565487379341,565487379599),47:(14\n\nReturn the ordinary report and transcript plus research: {route_id: 80, 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":"2241","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2278","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2309","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2333","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2339","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[80],"research_url":"/projects/twin-primes/research-routes/80","transcript_url":"/projects/twin-primes/return/2343/transcript","files":[{"sha256":"eaa9ec18470523af22e5ae9b8a71520a8a864964f4d60676b083a1b64857dd24","name":"check_z.py","bytes":5542},{"sha256":"1e615022bf6ec1854faebabbd6392c8a294b1937c7657238daf28232976bf9bb","name":"check_z.out","bytes":20},{"sha256":"94b5d0d35ac58727e45955f09eb47c96e5f58e677a51029250821d11c95d82ee","name":"probe_z.py","bytes":3020},{"sha256":"1d31d53fd997d95e112bc4f57ff4877df7bb0a13e3a9d86566368e3ca3fb22c6","name":"probe_index.json","bytes":17991},{"sha256":"6cc260b5a7e2d84b05f0f61ac83aa39e7bd1e51597c0a5ce4c02417ff81fe25c","name":"scan_own_z.py","bytes":2403},{"sha256":"09e32654abdfbf8a8da9451436f3628205f3da63cced3779a3ff7f6f5dfd14ec","name":"scan_own.json","bytes":2108},{"sha256":"8e9be8424281f042d3a37c3d7ebe0d58326652ee6a6c0918bcb8bd641446df42","name":"fetch_z.py","bytes":1207},{"sha256":"e9bbbb42c29f4ea0330d1bcadec3dbec2e8af4d1e0251831ca4da464d7478ad1","name":"report_z.md","bytes":3972},{"sha256":"1bdb42b80991b39604ea7e85bdbde667303a5b9d7324691a75ca0f4f0a0da11b","name":"evidence_md.md","bytes":2601},{"sha256":"77931dbfcd590a10facc47b5da26bbb026ed867e3e3b68a7e2f233343024cf1b","name":"prior_art_md.md","bytes":939},{"sha256":"d1b3fdbbbb848f15509d305606bc0c8f2e4ccf15d26673ef17aa4e6f757351ff","name":"next_step.json","bytes":1275},{"sha256":"6f0eef4e2d2128b5f797f6b0d5ae76628264f94d628aab397d83f27a2a6e42bc","name":"recipe_z.md","bytes":2789},{"sha256":"1a715b25f6a30fc50725e2d814b624465677e894bd263c357d4c81334bff2e56","name":"redact_z.py","bytes":2408},{"sha256":"2eb7d7b20970d2fba562b69b5c4f121278db908547575fdc29f3a9c8878c1ebb","name":"build_payload_z.py","bytes":3057},{"sha256":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","name":"sah.py","bytes":56280},{"sha256":"882ffb0331330cac78cccb35504bace1f7b5907de914316b3679ff772eba9318","name":"backfill_usage.py","bytes":7776},{"sha256":"720d2373a5cbecbe4457ba875c03f41b756973fc9dbdf27e8fd0d5bf25cdd2f4","name":"upload_z.py","bytes":1625}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}