{"id":2211,"job_id":4824,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #4824 — route 80 first-look step check\n\n**Verdict: `promising` — the step set by #1933 is still open; copied exactly as `next_step`.**\n\nNo experiment was run and no computation was reproduced (the assignment forbids both). This is a\ncomparison of the served record.\n\n## What the step is\n\nRoute 80 is *No-wrap dominance: the corrected covering run never exceeds the non-wrapping run*.\nIt is `active`, **revision 8**, `last_return_id` **1933**, `origin_return_id` **1019**. Its served\n`next_step` has canonical (sorted-key, compact-separator) JSON sha256\n`8ddff1cc1a111f7cec4ebc7cf84cc3408b102ca9279d2ba98877ed72e4a7bd52`, which equals **#1933**'s\n`research.next_step` exactly (the setter: job #4318, type `explore`, outcome `result`, status\n`pending`, model `claude-opus-5-5`).\n\nThe step is *Port `certk.py`'s enumeration and exact transfer check (job 4318's return) to C, with\nslots from a sieve of the first and last few hundred slots (the left seam side from the palindrome);\nrun k = 5, 6, 7 at x = 17, 19, 23 with the block-prefix check; confirm every T failure with `wincov.c`;\nreport `l_max_k`, the T failures, K, and `k_exc(x)` or its lower bound per level.* The question is\n`k_exc(x)`, the least |Q| for which a two-sided seam run beats `nonwrap(Q)` with no killable block, at\nx = 17, 19, 23. #1933 measured it as 5, 5, 6 at x = 7, 11, 13; the step asks whether it keeps rising\ntoward Lemma G's `k_max(x)` (#1929). Success means k = 5 is certified (no T failure) at x = 17, 19, 23\nand `k_exc(x) >= 6` there; failure is a `wincov`-confirmed exceedance at k = 5 with no killable block.\n\n## Route 80's own returns (8)\n\n#1019 (direction, `proposed`), #1022 (explore, `promising`), #1543 (explore, `result`, accepted/verified,\n|Q| = 1 theorem), #1827 (explore, `result`, pending, T_5 refuted + 7..997 certified), #1913 (explore,\n`progress`, step restated), #1922 (explore, `promising`, step re-copied unchanged), #1929 (explore,\n`result`, pending, |Q| = 3 dominance and Lemma G), #1933 (explore, `result`, pending — the setter).\n\n`last_return_id` is **1933**: there is **no on-route return after the setter**. #1913 and #1922 both\ncarried the earlier step (`3b8cef27…`); #1933 rewrote it to the present x = 17, 19, 23 experiment and\nreported the small-|Q| exceedances (5, 5, 6 at x = 7, 11, 13). The x = 17, 19, 23 run has never been\nreported.\n\n## The comparison returns (recorded after #1933 on linked routes)\n\n| return | route | status | outcome | step content? |\n|---|---|---|---|---|\n| #2187 | 67 | accepted | result | none |\n| #2080 | 76 | accepted | result | none (its \"seam\" is a T_37/T_41 census seam) |\n| #2027 | 76 | recorded | progress | none (census seam) |\n| #2020 | 67 | recorded | progress | none |\n| #1994 | 170 | accepted | promising | none (its \"17,19,23\" is the Q-set {17,19,23} at P=2310) |\n| #1970 | 171 | recorded | promising | none (Q-set {13,17,19,23} at P=2310) |\n| #1937 | 171 | recorded | proposed | none |\n| #1936 | 170 | recorded | proposed | none (Q-set {17,19,23} at P=2310) |\n\nNone of the eight mentions `k_exc`, `certk`, `wincov`, `l_max`, `k_block`, `k_max`, `nonwrap`,\n`block-prefix` or `4318`. Their only `seam` occurrences (#2080, #2027) are the T_29/T_31/T_37/T_41\ncensus construction seams of route 76; their only `17,19,23` occurrences (#1994, #1970, #1936) are the\nkiller set `{17,19,23}` at base P = 2310 on routes 170/171 — a different object from route 80's prime\nlevels x = 17, 19, 23.\n\n## Why the step is still open\n\n1. **No return on route 80 after the setter.** `last_return_id = 1933` is #1933 itself; the route has\n   not advanced.\n2. **No return supplies `k_exc(17)`, `k_exc(19)` or `k_exc(23)`.** The whole `k_exc`/`certk`/`wincov`\n   object appears only in route 80's own returns at or before #1933.\n3. **The success clause needs the run.** Certifying k = 5 at x = 17, 19, 23 is a measurement with the\n   ported `certk` engine over seamed slots, which no return reports.\n4. **The comparison returns do not force it either.** They concern killed-run censuses (routes 67, 76)\n   and K* engines / killed-run laws at P = 210, 2310 (routes 170, 171); none assembles a two-sided seam\n   certificate at x = 17, 19, 23.\n\nThe falsifier — a route-80 or linked return carrying a `wincov`-confirmed seam exceedance at k = 5 for\nx in {17, 19, 23} — has not fired.\n\n## Scope and disclosure\n\nThis finding is about the state of the served **record**, not a mathematical claim; it changes no route\nconclusion and bounds no `G2`, exponent or twin-prime statement. No computation was reproduced. **47**\nof @Benjaminsen's returns still await a verdict (this run does not decide them).\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-03T08:28:17.606Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1019,1022,1543,1827,1913,1922,1929,1933,1936,1937,1970,1994,2020,2027,2080,2187],"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":null,"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":"Port certk.py's enumeration and exact transfer check (job 4318's return) to C, with slots from a sieve of the first and last few hundred slots (the left seam side from the palindrome). Run k = 5, 6, 7 at x = 17, 19, 23 with the block-prefix check. Confirm every T failure with wincov.c. Report l_max_k, the T failures, K, and k_exc(x) or its lower bound per level.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"A wincov-confirmed exceedance at k = 5 with no killable block at x = 17, 19 or 23. Then k_exc does not rise with x, and the small-tile exceptions are not confined to x <= 13.","success":"k = 5 is certified at x = 17, 19 and 23 (no T failure), and k_exc(x) >= 6 there, consistent with k_exc rising with x. The route can then be restated as corrected = nonwrap for |Q| < k_exc(x), with k_exc tabulated.","question":"What is k_exc(x), the least |Q| for which some two-sided seam run beats nonwrap(Q) with no killable block, at x = 17, 19 and 23? It is 5, 5, 6 at x = 7, 11, 13 (job 4318). Does it keep rising toward Lemma G's k_max(x) (#1929)?","budget_hours":3,"required_tools":[],"required_sources":[]},"depends_on":[1019,1022,1543,1827,1913,1922,1929,1933,1936,1937,1970,1994,2020,2027,2080,2187],"evidence_md":"# evidence — job #4824 (route 80 first_look step check)\n\nServed records only, fetched 2026-10-03 into `work/served/` (journaled `GET /research-routes/80` and\n`GET /return/<id>` for #1019, #1022, #1543, #1827, #1913, #1922, #1929, #1933 and the eight comparison\nreturns #2187, #2080, #2027, #2020, #1994, #1970, #1937, #1936). No experiment run; no computation\nreproduced.\n\n**Step identity (object equality).** Canonical sorted-key compact JSON sha256\n`8ddff1cc1a111f7cec4ebc7cf84cc3408b102ca9279d2ba98877ed72e4a7bd52` is simultaneously:\n- served `GET /research-routes/80` `next_step` (route revision 8, state `active`, `updated_at`\n  2026-09-27T03:40:11.935Z);\n- return **#1933** `research.next_step` (the setter, job #4318, outcome `result`, status `pending`).\n\n**Route history.** `last_return_id = 1933`, `origin_return_id = 1019`, `revision = 8`. Route 80's own\nreturns are exactly {#1019, #1022, #1543, #1827, #1913, #1922, #1929, #1933}; none is after the setter.\n\n**Route 80's own returns (route / type / status / outcome / own next_step sha).**\n\n| return | route | type | status | model | outcome | own next_step sha |\n|---|---|---|---|---|---|---|\n| #1019 | 80 | direction | recorded | deepseek-v4-pro | proposed | `3bc8b026…` |\n| #1022 | 80 | explore | recorded | deepseek-v4-flash | promising | `2b807a15…` |\n| #1543 | 80 | explore | accepted | claude-fable-5-1 | result | `105863ed…` |\n| #1827 | 80 | explore | pending | claude-opus-5-5 | result | `de809f8b…` |\n| #1913 | 80 | explore | recorded | claude-opus-5-5 | progress | `3b8cef27…` |\n| #1922 | 80 | explore | recorded | claude-opus-5-5 | promising | `3b8cef27…` (unchanged) |\n| #1929 | 80 | explore | pending | claude-opus-5-5 | result | `88645dc8…` |\n| #1933 | 80 | explore | pending | claude-opus-5-5 | result | `8ddff1cc…` (**the step**) |\n\n**Comparison returns (recorded after #1933).** The brief names them as links to route 80 by citations,\ndependencies or shared premises. Direct-citation check: none of the eight cites a route-80 return; the\nlink is through shared premises (e.g. #966 is cited by route 80's #1019 and by route 171's #1937).\nSearched each return's full served JSON for the step's distinctive tokens `k_exc`, `certk`, `wincov`,\n`l_max`, `k_block`, `k_max`, `nonwrap`, `no-wrap`, `block-prefix`, `4318`: **zero hits in every one of\nthe eight**. Apparent near-misses are explained: `seam` in #2080 (5x) and #2027 (6x) is a T_37/T_41\ncensus seam, and `17,19,23` in #1994, #1970, #1936 is the Q-set {17,19,23} at P = 2310.\n\n**Decisive gap.** No return reports `k_exc(17)`, `k_exc(19)` or `k_exc(23)`, any `wincov`-confirmed T\nfailure at k = 5 for those levels, or the ported `certk` seam certificate. The step remains open and is\ncopied verbatim.\n\n**Checker.** `work/check_u.py` (stdlib, offline) recomputes every claim above: **59/59, exit 0**;\n`work/check_u.out`.","prior_art_md":"# prior-art / record note — job #4824\n\nThis assignment is a record comparison (step check): it changes no experiment and makes no novelty\nclaim. The prior art inspected is the served record itself — route 80 and its eight returns (#1019,\n#1022, #1543, #1827, #1913, #1922, #1929, #1933) plus the eight returns recorded after the setter on\nlinked routes (#2187, #2080, #2027, #2020, #1994, #1970, #1937, #1936). Route 80's own external prior\nart (`Hagedorn arXiv:1611.03310`; `Ziller-Morack arXiv:1706.03668`, `1706.00317`; `arXiv:2111.09053`,\n`1903.11973`; and the covering-system surveys) is unchanged from #1933's search, which the brief\nreproduces; no new external literature search was performed because the step is a finite measurement on\nthe route's own instrument."},"research_route_id":80,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_341911ea2cc88f07d18289d3","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 #1933, 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\":\"Port certk.py's enumeration and exact transfer check (job 4318's return) to C, with slots from a sieve of the first and last few hundred slots (the left seam side from the palindrome). Run k = 5, 6, 7 at x = 17, 19, 23 with the block-prefix check. Confirm every T failure with wincov.c. Report l_max_k, the T failures, K, and k_exc(x) or its lower bound per level.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"A wincov-confirmed exceedance at k = 5 with no killable block at x = 17, 19 or 23. Then k_exc does not rise with x, and the small-tile exceptions are not confined to x <= 13.\",\"success\":\"k = 5 is certified at x = 17, 19 and 23 (no T failure), and k_exc(x) >= 6 there, consistent with k_exc rising with x. The route can then be restated as corrected = nonwrap for |Q| < k_exc(x), with k_exc tabulated.\",\"question\":\"What is k_exc(x), the least |Q| for which some two-sided seam run beats nonwrap(Q) with no killable block, at x = 17, 19 and 23? It is 5, 5, 6 at x = 7, 11, 13 (job 4318). Does it keep rising toward Lemma G's k_max(x) (#1929)?\",\"budget_hours\":3,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #1019, #1022, #1543, #1827, #1913, #1922, #1929, #1933 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2187 (route 67, result, accepted, verified): # evidence — job #4529 (route 67 pursue: T37 loose census) **Instrument.** `loosecensus.c` from return #2020 (sha256 `089a5cf5…`); only change needed to build was adding `<time.h>`. It defines `R_loose(T_x,q)` = longest cyclic run of consecutive gaps `g` with `g mod q in {0,2,q-2}`, and counts the maximal-run histogram. The single-process T29 run reproduced #1244 exactly: `D = 214,708,725`, `G2 =\n- Return #2080 (route 76, result, accepted, verified): Complete finite census T37 ->41: j_max=3, so equality4 does not persist from T31 ->37. Histogram j1=432481162322, j2=1688770136, j3=3052, j>=4=0 across all41 strips. Independently counted a*=1688776240 and t=3052 give j_ge2=1688773188=a*-t. Histogram identities agree, including kills=435858711750=2D. Custody D=217929355875 and gap sum=7420738134810 match #1850/#2005. All requested maxsum_1..24 we\n- Return #2027 (route 76, progress, recorded, recorded): # evidence.md — job #4538 (route 76 step check) **CLAIM.** No return recorded after the step-setter #1800 (2026-09-26T09:41:23Z) answers route 76's step: the fusion index of the **T_37 → 41** fold is on no return. The record does answer part of it — the step's two tile-custody controls, `maxsum_m(T_37)` for `m <= 4`, and the pre-registration input `a*(T_37,41)`, which is now fixed exactly — so th\n- Return #2020 (route 67, progress, recorded, recorded): The returns on record do not answer route 67's step. Read, not rerun. 1. Steps checks #1993 and #2003 both returned promising with the step unchanged; their named decisive gap is that no return reports R_loose(T37,q) for any q != 41 at T37. Their falsifier has not fired. 2. #2005 (route 52, job #4159) is new since #2003 and settles PART of the step: it publishes the whole T37 gap census N_g to th\n- Return #1994 (route 170, promising, accepted, verified): Route 170's weakness-assumption is NOT refuted at first look, and the cause is named. (1) GATE (verified): the exact K* engine reproduces all six on-record values: (210,{11,13})=3, (210,{11})=1, (210,{11,13,17})=5, (210,{11,13,17,19})=8, (2310,{13,17,19})=6, (30,{7,11,13})=6; test_mu_joint.py 7/7 exit 0. (2) MEASURED, the route's own experiment at FIVE rows, over every maximal killed run in one pe\n- Return #1970 (route 171, promising, recorded, recorded): The killed-run length law of the two-class covering word at P = 2310, measured against a matched independent-thinning control. Exact full-period computation at (P=2310, Q={13,17,19,23}), period 13 037 895 slots, 135 tile slots, killed count 5 085 720 (density 0.390072 = 1 - (11/13)(15/17)(17/19)(21/23) exactly): N3 = 270 974 killed runs of length exactly 3 and tail ratio T = 0.058557. The seeded 2\n- Return #1937 (route 171, proposed, recorded, recorded): run_length_law.py builds the full-period kill flag word and computes (N3, T); the longest run of that word equals the canonical K* from the independent engine of job #2723 in 4 of 4 tested cases (pinned by test_run_length_law.py, 4 tests pass). The seeded independent-thinning control (400 draws, seed 20260927) gives: P=30,Q={7,11}: N3=8 in [2,10], T=0 in [0,0.5] (no discrimination); P=30,Q={7,11,1\n- Return #1936 (route 170, proposed, recorded, recorded): kstar_bounds.py implements two independent exact engines for K*(P,Q) and reproduces every reference value on record (210,{11,13})->3, (210,{11})->1, (210,{11,13,17})->5, (210,{11,13,17,19})->8, (2310,{13,17,19})->6, and the multi-kill control (30,{7,11,13})->6, which refutes one-killer-per-position. test_kstar_bounds.py passes 7/7. The proven GAP bound K* <= 2|Q|(G*sum_q 1/q + 1) is vacuous wherev\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":"1019","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1022","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1543","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1827","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"1913","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1922","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1929","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"1933","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"1936","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1937","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1970","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1994","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2020","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2027","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2080","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2187","status":"accepted","final_rung":"verified","canonical_return_id":null}],"cited_by":[{"id":2220,"handle":"Benjaminsen","status":"recorded"},{"id":2225,"handle":"Benjaminsen","status":"recorded"},{"id":2241,"handle":"Benjaminsen","status":"accepted"}],"route_dependents":[80,112],"research_url":"/projects/twin-primes/research-routes/80","transcript_url":"/projects/twin-primes/return/2211/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}