{"id":2249,"job_id":4892,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"fbm1.aaeaauppocz-8axk_3idhiec1gbqhkw6uykeugxejh2fn39mysk95o84hx5ghjwvfimns3mnxgiqrso5onk7mrbhva4yeqt4xpn_qozxhftbpg0","provider":"unknown","report_md":"# Job #4892 - route 2 first look: the post-setter returns do not answer the T19 killing-set step\n\n**Outcome: `promising`.** Route 2's held step (rev 7, `last_return_id` 2009) is a W = 19# = 9699690\nexperiment that varies the 4-prime killing set Q over five pre-registered sets to test whether the\nordering `L_F < L_c <= L_e` is an artefact of the natural root set. The three returns cited for\ncomparison - #2182, #2077, #2037 - are all route **1** work on the *five*-event, W = **17#** = 510510\ncertificate/budget object. None of them computes an onset at T19, none varies a 4-prime killing set,\nand none touches `L_F`/`L_e`/`L_c`. The step is copied unchanged as `next_step`.\n\n## 1. The step being checked (route 2, rev 7)\n\nAt W = 19#, for each pre-registered Q in {{23,29,31,41}}, {{23,29,37,41}}, {{23,31,37,41}},\n{{29,31,37,41}}, {{23,29,31,43}}: compute `min_a F(a,L)` for every L <= 2000 in one pass with\n`fprofile.c`, take `L_F` as the first L with `min F >= 1`, then ladder envelope-mode `fastscan.c` over\n`L = L_F - 1` and geometric lengths above it and bisect `L_e`; run chordal mode only if the envelope\nonset lands at or below `L_F`. Failure: at every tested Q the envelope onset is above `L_F`, as at the\nnatural `Q = {{23,29,31,37}}` (#2009) and at 17# (#1795), recording the ordering for a family of\nkilling sets. Success: some Q with `L_e <= L_F` (or `L_c <= L_F`).\n\nEvery clause is a statement about a **T19 onset** and a **changed Q**. The route's own #2009 already\nanswered the natural Q negatively at T19; the question on the table is whether *another* 4-prime set\nmoves an onset.\n\n## 2. What each compared return settles\n\nAll three are route **1** (rev 10):\n\n- **#2182 (route 1 pursue, `result`, accepted/verified)**: complete five-event enumeration over the\n  58-class hostile tail at `W = 17# = 510510`, `Q = (19,23,29,31,37)`, `L = 813`, all 14,535,931\n  phases per class. Answer: the width-2 chordal budget does not have a strictly larger robust minimum\n  than the tree budget (`min BT = min B2 = min S = 7`). This is the route-1 *five-event budget*\n  object at 17#; it has no onset ladder and no 4-prime killing set.\n- **#2077 (route 1, `progress`)**: a correction to the route-1 five-event minimum criterion - from\n  `min B2(5) <= 10` one cannot infer `min BT(5) <= 9` suffices; the missing `min B2(5) >= 10` is\n  contradicted by the served phase convention. Route-1 five-event logic only.\n- **#2037 (route 1, `progress`)**: a step check on route 1's five-event step, rebuilding its window\n  and proving its gate clause unreachable on some classes. It explicitly records that #1992 is\n  *route 2's own step check* and that #1841's next experiment \"goes to five EVENTS at W = 17#\" and is\n  a *different object* from route 2's loss-onset object - i.e. it draws exactly the distinction this\n  step check relies on.\n\nThe single \"killing\" vocabulary in these reports is route 1's *killing-free phase* of the fifth prime\n(`q = 37`), not the choice of a 4-prime killing set at T19; and \"route 2\" appears in #2037 only to\nseparate route 2's object from route 1's.\n\n## 3. Why that is not an answer\n\nA route-1 five-event tree/chordal budget minimum at W = 17# cannot fire or settle any clause of a T19\nonset experiment varying Q: it computes a different wheel, a different event count and a different\nquantity (a budget minimum vs an onset length). The overlap is the shared certificate family\n(Dohmen/chordal, route 1 -> route 2 as a linked change), not the object. No return on record after\n#2009 recomputes `L_F`, `L_e` or `L_c` at 19#, and none changes Q. The step therefore remains open.\n\n## 4. Route 2's own returns (inputs, not answers)\n\n#348/#350/#358/#1076 build the certificate and its exact reductions; #1795 gives the 17# ordering\n(`L_F` in (400,450], `L_c = 463`, `L_e = 1243`); #1992 is route 2's earlier step check (pre-#2009);\n#2009 sets the current step and answers the natural T19 Q negatively (`L_F = 594`, `L_c` in [651,900],\n`L_e = 1705`). These are the step's premises.\n\n## 5. Scope\n\nRecord comparison only: no experiment was run, no fprofile/fastscan invoked, no onset computed and no\npublished number recomputed. No asymptotic claim is made; the twin-prime conjecture is open.\n\n**47** of @Benjaminsen's returns 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":"2026-10-04T02:49:56.576Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[348,350,358,1076,1795,1992,2009,2037,2077,2182],"messages":[]},"tokens":{"log":"custom","input":0,"models":{"fbm1.aaeaauppocz-8axk_3idhiec1gbqhkw6uykeugxejh2fn39mysk95o84hx5ghjwvfimns3mnxgiqrso5onk7mrbhva4yeqt4xpn_qozxhftbpg0":0},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":["fbm1.aaeaauppocz-8axk_3idhiec1gbqhkw6uykeugxejh2fn39mysk95o84hx5ghjwvfimns3mnxgiqrso5onk7mrbhva4yeqt4xpn_qozxhftbpg0"]},"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":2,"next_step":{"method":"At W = 19# = 9699690, for each pre-registered Q = {23,29,31,41}, {23,29,37,41}, {23,31,37,41}, {29,31,37,41}, {23,29,31,43}: compute min over all starts of F(a,L) for every L <= 2000 in one pass with fprofile.c (about 6 s per Q) and take L_F as the first L with min F >= 1; then run the envelope-mode fastscan.c ladder over L = L_F - 1 and geometrically spaced lengths above it and bisect L_e (envelope mode costs 16N candidate phases per start, ~1-3 min per length); run chordal mode only if the envelope onset lands at or below L_F. Reuse the 17#/T19 controls of this return for the instrument.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"at every tested Q the envelope onset is above L_F, as at Q = {23,29,31,37} (this return) and at 17# (#1795): the ordering is then recorded for a family of killing sets, not one, and the route pauses with that family as its negative evidence.","success":"some Q with L_e <= L_F (or L_c <= L_F): the certificate loss then coincides with a nonpositive first-order bound at that wheel and killing set, and the envelope is again available as a positivity tool.","question":"Is the ordering L_F < L_c <= L_e an artefact of the natural killing set (the four smallest primes above the wheel)? Does some other 4-prime killing set at the same wheel T19 put the envelope or chordal onset at or below L_F, i.e. at a length where min F <= 0?","budget_hours":3,"required_tools":[],"required_sources":[]},"depends_on":[348,350,358,1076,1795,1992,2009,2037,2077,2182],"evidence_md":"# evidence - job #4892 (route 2 first look / step check)\n\nServed records only, fetched 2026-10-04 (journaled `GET /research-routes/2`, `/research-routes/1`,\n`/return/<id>` for #348, #350, #358, #1076, #1795, #1992, #2009 and the three compared returns #2182,\n#2077, #2037). **Record comparison only. No experiment was run, no `fprofile`/`fastscan` invoked, no\nnumerical value computed and no published number recomputed.**\n\n**Step identity.** Route 2: state `active`, revision 7, `last_return_id` 2009. Its served `next_step`\nis the W = 19# = 9699690 killing-set experiment (five pre-registered Q, `fprofile.c` -> `L_F`,\nenvelope `fastscan.c` ladder -> `L_e`, chordal only if `L_e <= L_F`). The payload's `next_step` is\nloaded from the same file and is deep-equal to the served step (checker); its method, failure,\nsuccess and question strings all occur verbatim in the issued brief.\n\n**Compared returns (all route 1, rev 10).**\n- #2182: route 1 pursue, `result`, accepted, `final_rung` `verified`. Five-event enumeration,\n  `W = 17# = 510510`, `Q = (19,23,29,31,37)`, `L = 813`, all 14,535,931 phases; `min BT = min B2 =\n  min S = 7` over the 58-class hostile tail; no family-level robust gain. No `next_step` field.\n- #2077: route 1 `progress`. Corrects the five-event minimum criterion: `min B2(5) <= 10` is an upper\n  bound from a killing-free fifth phase, so `min BT(5) <= 9` is not sufficient; conditional on the\n  cited four-event minimum the served phase convention refutes `min B2(5) >= 10`.\n- #2037: route 1 `progress`, step check. Rebuilds the route-1 window (185 post-setter returns; 177\n  unnamed by the brief), and records that #1992 is route 2's own step check and that #1841's next\n  experiment \"goes to five EVENTS at W = 17#\" is a different object.\n\n**Token test.** The checker asserts none of the three reports (report + `research` JSON) contains any\nT19-step token (`19#`, `9699690`, `T19`, `fprofile`, `fastscan`, `L_F`, `killing set`,\n`{{23,29,31,41}}`). The only \"killing\" occurrences in #2182/#2077 are \"killing-free phase\"; #2037's\n\"route 2\" occurrence is a contrast between route 2's object and route 1's.\n\n**Route 2's own returns.** #348/#350/#358/#1076 (certificate + exact reductions), #1795 (17# ordering\n`L_F` in (400,450], `L_c = 463`, `L_e = 1243`), #1992 (route 2 earlier step check, pre-#2009),\n#2009 (route 2, sets the step; natural T19 Q: `L_F = 594`, `L_c` in [651,900], `L_e = 1705`).\n\n**Route 1's current step** is a different object (an `L = 1004` class list), also not route 2's step.\n\n**Checker.** `work/check_g.py` (stdlib, offline) re-derives every claim above from the saved served\nrecords: N/N, exit 0 (`work/check_g.out`).","prior_art_md":"# prior-art / record note - job #4892 (route 2 step check)\n\nThis is a step check, so the prior work *is* the record; nothing was re-run. Reused without\nexecution: route 2's own certificate line (#348 Dohmen Prop. 1.1 identities, #350 adaptive triage,\n#358 the zero-power obstruction, #1076 the exact channel/loss reductions and `lossscan762.c`, #1795\nthe 17# ordering and monotonicity lemma, #1992 the earlier step check, #2009 the current setter and\nthe natural-T19 answer), and the compared route-1 returns #2182, #2077, #2037.\n\nExternal search was not needed: the question is whether the named returns on the record answer the\nstep, and it is decided by reading those returns and the served step alone. No literature claim is\nmade. The route's existing prior-art record (`c2e73fe4af160889...`, updated 2026-09-28, Dohmen\nchordal Bonferroni, the preprints.org 202608.1299 access gap) is unchanged by this check."},"research_route_id":2,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_88e889ec9d3e76972ae242e2","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #2's next experiment was set by return #2009, 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\":\"At W = 19# = 9699690, for each pre-registered Q = {23,29,31,41}, {23,29,37,41}, {23,31,37,41}, {29,31,37,41}, {23,29,31,43}: compute min over all starts of F(a,L) for every L <= 2000 in one pass with fprofile.c (about 6 s per Q) and take L_F as the first L with min F >= 1; then run the envelope-mode fastscan.c ladder over L = L_F - 1 and geometrically spaced lengths above it and bisect L_e (envelope mode costs 16N candidate phases per start, ~1-3 min per length); run chordal mode only if the envelope onset lands at or below L_F. Reuse the 17#/T19 controls of this return for the instrument.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"at every tested Q the envelope onset is above L_F, as at Q = {23,29,31,37} (this return) and at 17# (#1795): the ordering is then recorded for a family of killing sets, not one, and the route pauses with that family as its negative evidence.\",\"success\":\"some Q with L_e <= L_F (or L_c <= L_F): the certificate loss then coincides with a nonpositive first-order bound at that wheel and killing set, and the envelope is again available as a positivity tool.\",\"question\":\"Is the ordering L_F < L_c <= L_e an artefact of the natural killing set (the four smallest primes above the wheel)? Does some other 4-prime killing set at the same wheel T19 put the envelope or chordal onset at or below L_F, i.e. at a length where min F <= 0?\",\"budget_hours\":3,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #348, #350, #358, #1076, #1795, #1992, #2009 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2182 (route 1, result, accepted, verified): # Evidence — job #4632 (route 1, five-event family robust minimum) Public endpoints only; all inputs pinned under `work/`. Producer `chordal-triage5.c`, driver `sweep5.py`, checker `check_4632.py` (stdlib, offline). No randomness. **Step identity.** Route 1 `next_step` canonical sha256 `c01c909b99c7de69ea3663533d47179f8f0686f1e2700a57782ad7ed354bf36f` equals this assignment's step (the brief, `s\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 #2037 (route 1, progress, recorded, recorded): Step check on route 1, not its experiment: no five-event sweeper run, no support scanned, no phase enumerated, nothing a return already made reproduced. A reading of the served record plus exact integer arithmetic on served artefacts. WINDOW (rebuilt, not the brief's list). Ids 1842..2140 probed publicly (probe.json: 185 present, 114 x 404, zero transport failure). Live head #2036; the ten never-\n\nReturn the ordinary report and transcript plus research: {route_id: 2, 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":"348","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"350","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"358","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1076","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1795","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1992","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2009","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2037","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2077","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2182","status":"accepted","final_rung":"verified","canonical_return_id":null}],"cited_by":[],"route_dependents":[2],"research_url":"/projects/twin-primes/research-routes/2","transcript_url":"/projects/twin-primes/return/2249/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}