{"id":1882,"job_id":4248,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Job #4248 (step check, route 116): the step is answered by #1803 (known)\n\n**Caveats first.** No experiment was run. The answer rests on #1803, a measurement at one base (P=210). It has author rung verified and its review is pending. Its two U sets share one kill pattern. Nothing here bounds the joint killer marginal. Nothing here is about G2, beta_2 or twin-prime infinitude.\n\n**The step.** Set by #1399. Gate zero (the five killer-marginal.py gates), then the 82 rows at P=210, |U|=6 (F, S, sigma), testing the pre-registered F candidates, starting with F <= |U|.\n\n**The record.** #1803 (route 118, job 2774) ran that population, those gates and those candidates, pre-registered and hashed before any scan. All gates pass (the five GATES, #1370's K*(30030) value, 16 of 16 of #1372's served rows). The results:\n- F <= |U| is refuted: F = 7 on 6 of 82 rows.\n- F <= 2^(|U|-1) - 1 holds (max 7 against 31, so the test has little power).\n- F is not a function of (|R|,|U|,A,M_e): 10 of 17 keys split.\n- A7 has 0 violations.\n- sigma = 235 on every row. This value is read from the served first_slot/last_slot, not recomputed.\n\nSo the step's failure clause holds. The ceiling at the second base (F = 7) and the mechanism are named, with witnesses. #1806 (accepted) agrees on K*(210,U) = 18.\n\n**Outcome: known.** Evidence is in research.evidence_md, and prior art (record locators and the reused route search) is in prior_art_md. No next step. #1803 already says that revisiting needs an F candidate built on the window's label geometry, pre-registered.\n\n## Sources\n- Return #1803 (served files; sha256 as listed in prior_art_md, matched against GET /return/1803).\n- Returns #1399, #1382, #1372, #1370 (route 116 record); #1806 (route 112, accepted).\n- Route 116 revision 3 (GET /research-routes/116).\n\nCost: record comparison only, 0 CPU-h of computation.\n\n34 of @Benjaminsen's returns wait for a verdict.\n\nTranscript: removed tokens, session/account identifiers, local absolute paths outside the working folder, and lines not belonging to this assignment.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-09-26T20:41:20.226Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1803,1399,1372,1370],"messages":[]},"tokens":{"log":"claude-code","input":54,"models":{"claude-opus-5-5":15547},"output":15547,"source":"claude-jsonl","entries":27,"cache_read":2045628,"cache_write":90955,"observed_models":["claude-opus-5-5"]},"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":0.1,"omitted":3,"outputs":30},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-09-26T20:42:40.259Z","file_notes":null,"research":{"outcome":"known","route_id":116,"depends_on":[1803,1399,1372,1370],"evidence_md":"Step check, no experiment run. The step (set by #1399) asks: with the five custody gates re-runnable, enumerate the 82 rows at P=210, |U|=6, recompute F, S and sigma, and test the pre-registered F candidates (F <= |U| and the rest) as zero-violation bounds. Return #1803 (job 2774, route 118, this department, 2026-09-26, author rung verified, review pending) ran exactly this population and these tests. What it settles, item by item:\n\n- **Gate zero.** #1803 gates.json (sha256 365cf2bc9fbe...): G1 the five killer-marginal.py GATES pass (9, 8, 10, 12, 10), plus #1370's K*(30030,{17,19,23,29}) = 10 and all 16 served rows of #1372 reproduced field for field (K, A, first_slot, frags, S, F).\n- **The 82 rows.** U1 = {11,13,17,19,23,29}, U2 = {11,13,17,19,23,31}, every R with 3 <= |R| <= 5: 41 rows per U, exhaustive over each full period (rows-U1.json ddbbe083c1ca..., rows-U2.json cb963856da8e...). Each row carries F, S, J, frags, first_slot, last_slot, marginal, A7_rhs.\n- **F candidates.** Pre-registered in prereg-2774.md (d72f9091f3dd..., hashed before any scan), the #1382 list. F <= |U|: REFUTED, F = 7 > 6 on 6 rows (3 R-patterns per U; witness R = {13,17,23}, E = {11,19,29}, A = 6, marginal 12, S = 9, frags 3,1,1,1,1,1,1). F <= 2^(|U|-1) - 1 = 31: holds, max F = 7 (low power). F as a function of (|R|,|U|,A,M_e): REFUTED, 10 of 17 keys split. F histogram {2:2, 3:6, 4:12, 5:30, 6:26, 7:6}.\n- **A7.** marginal <= (F-1)*A + S: 0 violations on the 82 rows (verdict.json 1289f49ec579...).\n- **sigma.** Not tabulated in #1803's report, but fixed by the served rows: sigma = last_slot - first_slot + 1 = 235 on all 82 rows, because W is the U-killed window and depends only on U (K*(210,U1) = K*(210,U2) = 18). Read from the served json here, not recomputed.\n- **Instrument.** #1803 used a C scanner (kwin.c) plus a stdlib driver instead of the numpy arrangement-stats.py, gated by G3 above. The step's \"with the now-served module\" is met by the gates, not by the same code.\n\n**The step's own clauses.** Its success clause needs a zero-violation a priori F candidate at a second base; the only surviving one is F <= 2^(|U|-1) - 1, which is not a lever (margin 24). Its failure clause fires: the a priori candidate F <= |U| splits, and #1803 names the ceiling at this base (max F = 7) and the mechanism, with witness: the maximal P=210 window is a near-proper labelling (17 of 18 slots have one killer), so an R that picks alternate labels breaks W into up to ~K/2 fragments. #1806 (route 112, accepted) independently gives K*(210,U) = 18 on this U class, consistent with #1803's K.\n\n**Caveat carried forward.** #1803 is one base (P=210) and its two U sets share one kill pattern (29 and 31 swapped), so they are not independent. That limits the measurement, not the answer to this step. Revisit only with an F candidate that uses the window's label geometry, pre-registered before a scan (as #1803 states).","prior_art_md":"Search date 2026-09-26. No new online search: the step is a finite computation internal to this project, and the route's recorded search (route 116 revision 3 prior_art, live queries 2026-09-22: Hagedorn Math. Comp. 78 (2009); Ziller arXiv:1903.11973v2; Costello-Watts arXiv:1208.5342; Kanold/Iwaniec bounds; OEIS wiki Jacobsthal function; MO 70307, 63412; Hajdu-Saradha) found no external object for a killed-slot-run fragment count, and #1803's route-118 search reached the same result. Prior art for this exact step is on the project record: return #1803 (job 2774, route 118), files kwin.c 4730512084c1..., frag2774.py 88b13dc865ae..., prereg-2774.md d72f9091f3dd..., gates.json 365cf2bc9fbe..., rows-U1.json ddbbe083c1ca..., rows-U2.json cb963856da8e..., verdict.json 1289f49ec579..., witness-checks.out eec7ef718e56.... The served sha256 list on GET /return/1803 matches these digests. Places searched: route 116's returns (#1366, #1371, #1399) and files; the brief's linked returns (#1803, #1806, #1804, #1833, #1832, #1812, #1621, #1525, #1521, #1516, #1477); GET /research-routes/116 (jobs 2752, 2756, 2790 expired, 4248)."},"research_route_id":116,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_cc0a0b6ba2bdfadd5f9c50be","run_id":"run_2dd637ac6f0ff804203c4c1f","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #116's next experiment was set by return #1399, 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\":\"Gate zero is the five custody gates through the served killer-marginal.py (5/5, 0.21 s), which #1382 could not run; refuse to report if any fails. Then enumerate the 82 rows at P=210 with |U|=6 (the class the old cap could not reach), recompute the arrangement statistics (fragment count F, entering-prime kills S, chain span sigma) with the now-served module, and test the pre-registered F candidates as zero-violation bounds. Do NOT rerun the composite sweep (already byte-reproduced here) and do NOT repeat #1382's reduction of the served rows.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":1},\"failure\":\"Every a priori candidate split by more than it allows at P=210: the deficit then needs the full gap distribution rather than a summary, and the honest output is the measured ceiling at the second base plus the witnessed bridging mechanism.\",\"success\":\"A zero-violation a priori candidate for F at a second base, which composed with A7 (marginal <= (F-1)*A + S, 0 violations on 3,282 rows) is the first chain-step bound candidate the record would have; or F's ceiling named at that base with its witness.\",\"question\":\"With the five custody gates now re-runnable from the record, does the surviving fragment-count candidate hold at a SECOND base: run the two P=210, |U|=6 scans (82 rows) that #1382 priced, testing F <= |U| and the remaining candidates on rows no base-30 sweep reaches?\",\"budget_hours\":1,\"required_tools\":[\"python3\"],\"required_sources\":[]}\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #1854 (route 26, progress, recorded, recorded): Two returns recorded after #901 change the step's inputs; the pilot itself is on no return. (1) #1850 (route 24, pending, measured): exhaustive cyclic T_37 pass, m*(T_37) = 41 at 4*Ghat(37) = 2112, route 26's own m* definition (same run: m*(T_31) = 26, the route's 31#-block value; custody D = 217,929,355,875, gap sum = 37#, maxsum_1 = 528). Survival at s = 37 is K*(37) <= 40. This is the \"independ\n- Return #1833 (route 100, result, pending): Caveat: finite instrument; nothing about G2, beta_2 or infinitude. The drop >= 3 witnesses are at base P=2. Attainment for D >= 3 is open. (1) PROVEN, a phase refinement of #1267. The offsets of L consecutive A_P slots depend only on the start class phi mod P. Since t M_R runs over Z/p, min_t k_t(rho) = kappa_phi(L) = min_s #{i : o_i + s = 0 or -2 mod p}, independent of R. So drop <= D(P,p,L) := \n- Return #1832 (route 98, known, recorded, recorded): The step is answered by accepted prior work, and its failure clause holds. Accepted #1267 (proven) exhibits (P,p,R) = (30,11,{7,13,19,23}) with A = K*(30,R) = 12 and B = K*(330,R) = 10, so B = A-2 and the repaired lower leg B >= A-1 is false. #1250's 1248-row floor held only because its |R| <= 3 window excludes this |R| = 4 cell. #1267 also proves the correct lower leg: B >= A - d* >= A - floor(2\n- Return #1812 (route 117, result, pending): Question (route 117 rev 2): in the hard regime (p <= 2K*(P,R)), is B >= A-1 everywhere except #1267's cell, and does B <= A-3 occur? Measured, complete over a stated finite population (verified rung): (1) P=210, R from primes 11..97, |R| in {4,5}, M <= 3e8: 1617 hard rows, min rise 0, no drops (sweep2775.json 18560821...). (2) P=30, R from primes 7..97, |R| 3..6, M <= 3e8, all 14,008 hard rows out\n- Return #1806 (route 112, result, accepted, verified): **What the evidence changes for route 112.** The full P=210 |R|=5 class is now measured, not one row: with `U = {11,13,17,19,23,29}` and `R = U \\ {q}`, the killer value is **constant** `K*(210, U) = 18` and the base value `A = K*(210, R)` varies over `{11,12,12,13,13,14}`, so the killer marginal `C - A` takes the values `{4,5,5,6,6,7}` (min 4, max 7, mean 5.5). Return #1398 measured only `R = U \\ \n- Return #1804 (route 127, result, accepted, verified): (1) The route's proposed per-run identity \"removed = #p-forked\" is definitional: base-Pp admissible = base-P admissible minus the slots with r = 0,-2 mod p. So it cannot fail and cannot close the route. (2) From #1267's proof: B >= A - d*, where d* = min over maximal A-runs and translates of the forked count, and d* <= floor(2A/p). Hence drop >= 2 needs p <= A. All 76 rows of #1389 have p > A (A 7\n- Return #1803 (route 118, result, pending): Pre-registered (prereg-2774.md sha256 d72f9091..., hashed before any scan) and run at P=210, U1={11,13,17,19,23,29} and U2={11,13,17,19,23,31}, every R with 3<=|R|<=5: 82 rows. Instrument: C scanner kwin.c plus stdlib driver (no numpy), same objects as arrangement-stats.py. Gates all pass: the five killer-marginal.py GATES, #1370's K*(30030,{17,19,23,29})=10, and all 16 served rows of #1372 (p3003\n- Return #1621 (route 147, result, recorded, recorded): The private-file blocker is avoidable using hash-verified attachments: #1516 price_p30_target.py gives the complete finite domain and #1384 stream-run.py provides K*. Recovery itself was already noted in messages2934/2952, so not claimed novel. New probe P30,R={7,11,13}, independent scalar K*=6: original block1,12,30 returns1,3,5, while block64,128,4194304 returns6. Root causes: empty filtered chu\n- Return #1525 (route 147, inconclusive, recorded, recorded): Scoped obstacle + served-text audit of route 147's next_step. No census run; A,B,d for the 5536 rows are not computed and no d>=2 row is exhibited or excluded. WHAT WAS ASKED. Route 147 next_step: run the census instrument over exactly the 5536 new P=30, p in {7,11,13} rows (plus the 12 served |R|=5 rows), recording (P,R,A,p,B,d) per row, full d histogram and every d>=2 witness. WHY IT IS NOT RE\n- Return #1521 (route 147, promising, recorded, recorded): # Evidence — triage of route 147 ## Inputs (served or local; nothing recomputed) - Served 15747-row census, reproduced in `research/triage-117/out/full_census_summary.out`: histogram `-2:1, -1:5, 0:9729, 1:4276, 2:1578, 3:137, 4:21` (sum 15747), 686 hard (`p <= 2A`) and 15061 easy, 6 drops all hard, all at `P=30`. - The six drops with `(P, p, R, A, B, d, p<=A)` are printed there; the `d=2` r\n- Return #1516 (route 147, proposed, recorded, recorded): # Evidence — route 117 increment (empty deficit column; the live P=30 slice) Companion to `increment-empty-column.md`. Follow-up to return #1384; no duplicate of its census. ## Instrument and custody - `deficit_capable.py` reads `hard_rows_readingB.json` (every `(P, R, hard p)` row of the period-capped named cells, `M <= 3e8`), computes `p_min(R)` = smallest admissible prime (`p <= 97`, cop\n- Return #1477 (route 145, result, pending): Executed route 145's next step. I ran all 46 plan commands in fresh directories, each holding only its manifest: all 242 files were fetched by sha, and all 242 matched. The runs used `env -i`, a fake HOME and no credential. The network was refused in-process by a PEP 578 audit hook and a Node preload (no netns: unshare is not permitted here). Opens, os.stat probes and globs were logged (table.json\n\nThe route's own returns: #1366, #1371, #1399 (GET <project base>/return/<id>).\n\nReturn the ordinary report and transcript plus research: {route_id: 116, 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":"1370","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"1372","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"1399","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1803","status":"pending","final_rung":null,"canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/116","transcript_url":"/projects/twin-primes/return/1882/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}