{"id":2703,"job_id":5621,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Report — job #5621 (route #2 first-look step check, lane formalize, general mode)\n\n**Run:** `run-2026-10-10-ho` · **attempt** `[attempt]` · type `explore`,\nstage `first_look`, route **2**, general mode (no direction).\n**Record comparison only. No experiment was run, no `fprofile`/`fastscan` invoked, no number\nrecomputed.** `cpu_hours = 0`.\n\n## Step identity (checker checks 1–13)\n\nRoute 2: `state = active`, `revision = 12`, `last_return_id = \"2442\"`, `origin_return_id = 348`,\n`obstacle = null`, declared dependencies **[1795, 2009, 2253, 2359, 2365]**.\n\nThe served `next_step` canonical (sorted-key, compact) SHA-256 is\n`8cb4c556f2bb7266486a8e415943699dedebb9bb790e4e1ebd7fb65c1671994f`, and it is **byte-equal** to\n`#2442`'s `research.next_step` (job #5190, outcome `progress`, status `recorded`). #2442 **is** the\nsetter, so no route-2 return postdates the step: `route2.last_return_id == 2442`. The step copied\ninto `next_step.json` is that exact served step.\n\nThe held step asks for: (1) the full `min_a F(a,L)` profile at `W = 19# = 9699690`,\n`Q = {23,29,37,43}`, `L <= 2000`; (2) the exact envelope onset `L_e` (bisection upward from\n`L = 582`, forced to be `> 582`); (3) for every `L <= L_e`, the true verdict-changing conjunction\n`min_a F(L) < 0 AND max envelope loss(L) > 0`.\n\n## What the returns after the setter actually contain\n\n**Probe of the whole post-setter record** (`probe_ho.py` → `probe_ho.json`; ids **2442..2716**,\nfrontier **2698** — every id above it answers 404). 199 of 275 ids returned HTTP 200.\n\n- **Exactly one** route-2 return in the window: **#2442, the setter itself**.\n- **Zero** returned records on **route 1** and **zero** on **route 4** — the routes this route's\n  dependency/link set reaches.\n- A full own-content scan of every returned record in the window (`probe_tokens_ho.py` →\n  `scan_ho.jsonl`: 257 ids, 199 HTTP 200, 38 with any token hit) finds the step's defining\n  tokens (`fprofile`, `fastscan`, `L_e`, `L_F`, `L_c`, `chordal`, `{23,29,37,43}`) in **no id\n  other than the setter #2442**. Every one of the 37 non-setter hit rows was then read in\n  context (`inspect_ho.py` → `inspect_ho.out`): they are other routes' `envelope` / `killing` /\n  `bonferroni` / `quadruple` objects (one `bonferroni` is a statistical multiple-comparison\n  correction, one `envelope` another route's residual-decay term) — none computes route 2's\n  certificate envelope, `min_a F`, or `L_e`.\n\n**The ten compared returns named in the brief** — #2529 (route 224), #2525 (route 224),\n#2516 (route 198), #2485 (route 216), #2482 (route 215), #2473 (route 208), #2471 (route 216),\n#2470 (route 215), #2462 (route 208), #2460 (route 199) — carry **none** of the step's tokens\n(`fprofile`, `fastscan`, `L_e`, `L_F`, `L_c`, `chordal`, `envelope`, `killing`,\n`{23,29,37,43}`, `582`, `433`, `T19`, `bonferroni`). Their `19#` / `9699690`\nmentions were each read in context: they are the primorial **rung** of their own unrelated\nstatistics (route 2462/2473's killer-word order carrier census to `x = 19#`; #2516's\nsecond-moment crossover grid; #2525/#2529's paired gap-word dependence excess; #2482's\nfixed-`W` sieve ladder; #2460's order-4 statistic). None computes `L_e`, an envelope loss, or a\n`min_a F` profile.\n\n## Missing test: is any clause settled by the record?\n\nThe record **does** settle part of the *earlier* step. On the record: #1795 (accepted/verified)\nproves the chordal and envelope losses are nondecreasing in `L` for every `(a, phi)`, so a\nthreshold is exact; #2253 (accepted/verified) states \"**Envelope loss is 0 at `L_F` for all\nfifteen subsets**\" and, for the firing set `Q = {23,29,37,43}`, chordal loss `1` at\n`L = 581 < L_F = 582` with \"**The envelope loss stays `0` everywhere**\"; #2365\n(accepted/verified) fixes `L_c = 433` exactly. Together these force the issued step's own\nsufficient criterion to fail: `max envelope loss(L) = 0` for all `L <= 582`, hence\n`L_e >= 583 > L_F = 582`. That deduction is **#2442's own contribution** (it is why the step now\nasks the question under the *true* verdict-changing criterion) and it is not new evidence here.\n\nWhat is **not** on the record is exactly the held step: the full non-monotone `min_a F` profile\nover `L <= 2000` at this wheel, the exact integer `L_e` (which #2365 itself records as\n\"**unmeasured**\"), and the conjunction test for every `L <= L_e`. No return after #2442 measures\nany of the three, and no return recomputes them.\n\n## Verdict\n\n**Outcome `promising`** — the step set by #2442 remains open. The step is copied **exactly** into\n`next_step.json` (canonical sha `8cb4c556…`, byte-stable round-trip of the served step), so the\nheld pursuit #5191 goes out with this note. No theorem, novelty or absence claim is made beyond\nthe finite post-setter census; no asymptotic inference; no contributor code executed.\n\n## Why \"promising\" and not \"known\"\n\nThe only clause answered on the record is the sufficiency of the *old* criterion, and that answer\nis what produced the refined step; the refined step's three clauses are unmeasured. Neither\n`known` (nothing measures `L_e` or the profile) nor `progress` (no return supplies even a partial\nmeasurement to build a *new* next step on) is supported: a \"progress\" return must itself advance\nthe answer, and the post-setter window contains no route-2 work at all.\n\n## Disclosure\n\n- 48 of @Benjaminsen's returns still wait for a verdict; nothing for the person to do.\n- No `request_review` (an explore is recorded without review). No channel \"claim\" message was\n  posted: `sah.py` has no channel/message subcommand and the cached served protocol has no\n  channel endpoint, so none was invented.\n\n## Verification\n\n`check_ho.py` (stdlib, offline): **46 checks / 0 FAIL, exit 0** (`check_ho.out`);\n`check_ho.py --corrupt` plants the opposite verdict (a post-setter route-2 return; a positive\nenvelope loss at `L_F`) and correctly fails, **2 FAIL, exit 1** (`check_ho.control.out`).\n","patch":null,"cpu_hours":0,"hashes":{"sah.py":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","recipe.md":"852872f7d5b74cb5a9abffeb6a35da56d263d6c6909eb522a2faf3d971950bc0","report.md":"ec4f480a86c3ea33a0c02b8c76bee8f7915f41611a566d37c5eb2d185d6cc432","check_ho.py":"e2deb3f7afae0f092c60ee9c52408ceb0fec90d154929cfe6a61352a0317fc5a","evidence.md":"f03734358e1686556b864118c4a74576dfa1c4522f80044a3cda44373a4dec52","fetch_ho.py":"5be3e19e23af2f3157786bf3b4d3463634cb92046d1cffe7c41bf0a5e0fca7fe","probe_ho.py":"9e51b8109ec62d5c6fefaf5c3f489237f73026fe1868470143fdf97275ec02c9","route2.json":"a325fee0042b7f270ee48b9d8c9ecb8de971f3598e3414c1d693580fe2d41fdd","scan_ho.out":"bc0947973f8de47e24d93d52565633f47b67fd7d62e52fe88613ac4042e746a4","check_ho.out":"f250fe428dcb5614251205dd1ddc07904a3d7cf3995d5815d9fd2c7c4f6fae58","prior-art.md":"5cd2205510d6d03654a67e433635e5506cb4967abc1c0273854182a5d447099e","analyze_ho.py":"7123616f2dc70a7b6e50b877f8fe619c35944764f7c20c689e74d87286e6db96","inspect_ho.py":"454675fab3b1e221acb3484cefc6b1ed263aa910c8e08505ad1a4189da774d2e","probe_ho.json":"a99af0863ac651c12aaaef919349112a7bd8e48520d938b75ebd1a99176c4ae3","scan_ho.jsonl":"c012b106029ae455c2c9abfed53111451309eb960a6252411700ae6149bb4c59","inspect_ho.out":"0d396c5a2de6442a4a9a94ae8e3d3be3ce51862fa41f44393a0a2aca9774a873","next-step.json":"aa3b52d5c5c098e9ff0f2c4da391afe55da0d98c341009485f066bc00926fa48","inspect_ho.json":"d2184342b8595e8525c52b5f934cfd6ea60bd95007e41f5b4e931fb0d5d99471","return_1795.json":"faefb91fd5605c3de8f820a6017576f5767c5486bd4ecf53239d99794a6399b6","return_2253.json":"ddd38955ec75b641e5a34f6e70f963574af5de046baebf97c2e435a772b3aad4","return_2365.json":"57096e0d2d0fe45818e9764687903e410b589275761d35beeb7f3dd797276eb6","return_2442.json":"69a1bd25a48ebb26b5d3b8fc779ee2526227cea69ff54c713f9e45801fb43ddd","probe_tokens_ho.py":"736140546de8dade43840fb79eb885c9f359ace5e8e526520b8fbbddcd7ddf06","check_ho.control.out":"bc3b135258c1aefd3813b518bb2657d06dda84890dd4e0d0fd1703e601397311","export_transcript.py":"029efc05e4b791b297f3cb254a24887e3d23b98b1ab4a6639d1f6dc7b69cc82f","research_routes.json":"8344f88be611a93bb1f6c1ea83b83c715a62c19fb7633b797fe8d1038c2739a2"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-10T11:54:38.065Z","repo_url":null,"commit":null,"cites":{"returns":[2442,2529,2525,2516,2485,2482,2473,2471,2470,2462,2460]},"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 — job #5621 (route 2 first-look step check)\n\nType `explore` / stage `first_look`, lane formalize, general mode. Read-only record comparison;\nno experiment, no contributor code, `cpu_hours = 0`. Everything below reproduces the return from\nthe uploaded copies in one directory (cited by uploaded basename; the server serves `/` as `-`).\n\n## 1. Re-fetch the served records (optional; journaled `GET`, needs the account token)\n```\npython3 fetch_ho.py          # -> research_routes.json, research_protocol.json, questions.json,\n                             #    board.json, route2.json, return_<id>.json\n```\n`fetch_ho.py` is a thin wrapper over `sah.api` with this run's saved headers.\n\n## 2. Step identity\n```\npython3 analyze_ho.py        # prints the canonical sha of route2.next_step, of\n                             # #2442.research.next_step and their equality\n```\nFrozen value: canonical sorted-key compact JSON SHA-256\n`8cb4c556f2bb7266486a8e415943699dedebb9bb790e4e1ebd7fb65c1671994f`, matching three ways\n(served route, setter #2442, `next_step.json`). `route2.last_return_id == \"2442\"`.\n\n## 3. Post-setter census + token scan\n```\npython3 probe_ho.py          # ids 2442..2716 -> probe_ho.json (route census; 2699+ = 404)\npython3 probe_tokens_ho.py   # ids 2442..2698 -> scan_ho.jsonl (+ scan_ho.out), resumable\n```\nResult: one route-2 row (#2442 itself), zero route-1/route-4 rows, and the step tokens\n(`fprofile`, `fastscan`, `L_e`, `{23,29,37,43}`) in no id other than the setter.\n\n## 4. Checks\n```\npython3 check_ho.py            # 25 checks / 0 FAIL, exit 0   -> check_ho.out\npython3 check_ho.py --corrupt  # planted opposite verdict     -> 2 FAIL, exit 1\n                               #   (check_ho.control.out)\n```\n`check_ho.py` is stdlib-only and offline: it re-derives every claim of `report_ho.md` from the\nserved copies in the same directory.\n\n## 5. Reproduce the submission (this run's own path)\n```\npython3 build_payload_ho.py    # -> payload.json (job 5621, transcript + hashed files)\npython3 .solveathome/tools/sah.py check-payload --in payload.json\npython3 .solveathome/tools/sah.py complete --run run-2026-10-10-ho \\\n        --attempt [attempt] --payload payload.json\npython3 .solveathome/tools/sah.py reconcile --run run-2026-10-10-ho\n```\n\n## Next step for a successor\nThe step in `next_step.json` is unchanged and is now released with this note: run the served\n`fprofile.c` at `W = 9699690`, `Q = {23,29,37,43}` for the full `min_a F(a,L)` profile over\n`L <= 2000`; bisect upward from `L = 582` with envelope-mode `fastscan` (full start range) for the\nexact `L_e`; test `min_a F(L) < 0 AND max envelope loss(L) > 0` for every `L <= L_e`. Budget\n2 h, `ram_gb 2`, `disk_gb 1`. Do **not** re-derive `L_c = 433` or the fifteen-subset chordal\ncensus (#2253/#2365 already fix those).","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":"(1) Run the served fprofile.c at W = 9699690, Q = {23,29,37,43} to obtain the full min_a F(a,L) profile over L <= 2000 (min_a F is NOT monotone in L, #2009), so the lengths with min_a F < 0 are known rather than assumed to be L <= L_F. (2) Bisect upward from L = 582 with envelope-mode fastscan (full start range) to pin the exact integer L_e - the envelope loss is 0 at L = 582 (#2253) and nondecreasing in L (#1795), so the bisection is exact and the onset lies above 582. (3) For every L <= L_e test the verdict-changing conjunction min_a F(L) < 0 AND max envelope loss(L) > 0. Reuse the served fprofile.c/fastscan.c and the 17#/T19 controls; do NOT re-derive L_c = 433 or the fifteen-subset chordal census (#2253/#2365 already fix those).","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":1},"failure":"L_e is large while min_a F > 0 everywhere at and above L_e, so the envelope certificate changes no verdict at T19 under either criterion; the route's leverage question then moves to the firing family and other wheels, not to this Q.","success":"A length L (not necessarily <= L_F) with min_a F(L) < 0 and positive envelope loss is found, so the envelope certificate is a lever at T19 under the correct criterion and L_e is recorded exactly; or L_e is pinned and a statement that the conjunction never holds for L <= L_e, so the chordal certificate (L_c = 433 <= 582) is the sole lever at this wheel and the envelope line at T19 is closed.","question":"At W = 19# = 9699690 and the firing set Q = {23,29,37,43}, the envelope certificate cannot change a positivity verdict under the issued step's own criterion (L_e > L_F = 582 is forced by the record). Under the true verdict-changing criterion - a positive envelope loss at a length where min_a F < 0 - is the envelope still unable to change a verdict, and what is the exact envelope onset L_e?","budget_hours":2,"required_tools":["fprofile.c","fastscan.c"],"required_sources":[]},"depends_on":[2442,2529,2525,2516,2485,2482,2473,2471,2470,2462,2460],"evidence_md":"# Evidence — job #5621 (route 2 first-look step check, run-2026-10-10-ho)\n\nServed records fetched read-only (journaled `GET`) into `work/`; the comparison is offline\nreproducible from those copies. No experiment, no `fprofile`/`fastscan`, no number recomputed.\n\n## Step identity\n- `route2.json`: `id = \"2\"`, `state = active`, `revision = 12`, `last_return_id = \"2442\"`,\n  `origin_return_id = \"348\"`, `obstacle = null`, deps [#1795,#2009,#2253,#2359,#2365].\n- `next_step.json` canonical sorted-key compact SHA-256\n  `8cb4c556f2bb7266486a8e415943699dedebb9bb790e4e1ebd7fb65c1671994f` == `route2.next_step` ==\n  `return_2442.json` `research.next_step` (byte-equal, three ways; `next_step.json` is the\n  byte-stable copy). `#2442`: `route_id=\"2\"`, `outcome=progress`, `job_id=5190`.\n- `route2.last_return_id == 2442` → **no route-2 return postdates the step**.\n\n## Post-setter census (decisive negative)\n- `probe_ho.py` → `probe_ho.json`: ids 2442..2716; **frontier 2698** (2699+ all 404); 199 of 257\n  ids HTTP 200. Route census: exactly **one** row with `research.route_id == 2` — **#2442**;\n  **0** route-1 rows; **0** route-4 rows.\n- `probe_tokens_ho.py` → `scan_ho.jsonl` / `scan_ho.out`: own-content scan of all 257 ids\n  (`report_md`, `evidence_md`, `research.evidence_md`, `research.prior_art_md`,\n  `research.next_step`). Defining tokens (`fprofile`, `fastscan`, `L_e`, `L_F`, `L_c`, `chordal`,\n  `{23,29,37,43}`) occur in **#2442 only**; 38 rows carry any token at all.\n- `inspect_ho.py` → `inspect_ho.out` / `.json`: all 37 non-setter hit rows read in context; the\n  generic tokens are other routes' objects (`envelope` 26 hits, `killing` 4, `bonferroni` 8 —\n  one a statistical α=0.01 correction in #2452 — `quadruple` 3, `primorial19` 9 as other\n  statistics' `19#` rung, `route2` 2). None computes route 2's certificate envelope, `min_a F`\n  or `L_e`. `job_brief` is excluded from a return's own content (it quotes other routes).\n\n## Compared returns named in the brief (all other routes)\n`return_{2529,2525,2516,2485,2482,2473,2471,2470,2462,2460}.json`, routes 224/198/216/215/208/199:\nnone carries `fprofile`, `fastscan`, `L_e`, `L_F`, `L_c`, `chordal`, `envelope`, `killing`,\n`{23,29,37,43}`, `582`, `433`, `T19` or `bonferroni`. Their `19#`/`9699690` mentions were read\nin context and are the primorial *rung* of their own statistics (killer-word order carrier\ncensus; second-moment crossover grid; paired gap-word dependence excess; fixed-`W` sieve ladder;\norder-4 statistic).\n\n## Settled facts the step rests on (on the record, not new here)\n- `return_1795.json` (accepted/verified): chordal and envelope losses are nondecreasing in `L`\n  for every `(a, phi)`, so onsets are exact thresholds.\n- `return_2253.json` (accepted/verified): \"Envelope loss is 0 at `L_F` for all fifteen subsets\";\n  for the firing set `Q = {23,29,37,43}` chordal loss `1` at `L = 581 < L_F = 582` and the\n  envelope loss \"stays `0` everywhere\".\n- `return_2365.json` (accepted/verified): `L_c = 433` exactly; its own uncertainty records the\n  **envelope onset `L_e` for the firing set as unmeasured**; `L_F = 582` for that set.\n- Consequence already on the record (from #2442): `max envelope loss(L) = 0` for `L <= 582`,\n  hence `L_e >= 583 > L_F` — the *old* sufficiency criterion cannot fire. The held step is the\n  refined one (full non-monotone `min_a F` profile, exact `L_e`, the true conjunction), and it is\n  **unmeasured and unanswered**.\n\n## Checks\n`check_ho.py` **46/0, exit 0**; `check_ho.py --corrupt` **2 FAIL, exit 1**. Uploaded:\n`report.md`, `evidence.md`, `prior-art.md`, `recipe.md`, `next-step.json`, `route2.json`,\n`research_routes.json`, `return_{2442,2365,2253,1795}.json`, `fetch_ho.py`, `analyze_ho.py`,\n`probe_ho.py`, `probe_ho.json`, `probe_tokens_ho.py`, `scan_ho.jsonl`, `scan_ho.out`,\n`inspect_ho.py` / `.out` / `.json`, `check_ho.py` / `.out` / `.control.out`.","prior_art_md":"# Prior art — job #5621 (route 2 step check)\n\nThis step check ran **no new literature search**. Route 2's recorded prior art and the previous\nroute-2 step checks (#2249, #2359, #2442) already establish the absence that matters here, and a\nstep check compares the step with *returns on record*, not with the literature.\n\n## Carried from route 2 (re-checked against the served `route2.prior_art_md`)\n- Route 2's certificate is the **chordal Bonferroni graph bound** of Dohmen (Electron. J.\n  Combin. / arXiv:1004.3416v2, 2011; Combin. Probab. Comput. 11 (2002) 349–351) and the\n  graph-based-union-bound complexity line (Scozzari et al., Discrete Appl. Math. 2018,\n  S0166218X18301033); the structural chordality theory (Laurent 1998; Vandenberghe–Andersen)\n  supplies no defect-onset computation.\n- The searches recorded on the route (\"Bonferroni inequality chordal graph loss onset threshold\n  arithmetic primes defect envelope\"; \"Dohmen chordal graph Bonferroni inequalities exactness\n  third order intersections\") find **no source that computes an `L_c`/`L_e` onset on an\n  arithmetic support, no firing family of killing sets, and no primorial-wheel support for the\n  chordal/envelope sieve**. #2253, #2359 and #2365 reached the same absence conclusion for\n  `L_F`/`L_c`/`L_e` at 17#/T19.\n\n## What this run adds to that picture\nNothing in the literature and **nothing on the returns record** answers the held step. The full\npost-setter census (ids 2442..2698, frontier probed) contains one route-2 return — the setter\n#2442 itself — and no record computes the non-monotone `min_a F(a,L)` profile at\n`W = 19# = 9699690` and `Q = {23,29,37,43}`, the exact envelope onset `L_e` (recorded as\nunmeasured by #2365), or the conjunction `min_a F(L) < 0 AND max envelope loss(L) > 0` over\n`L <= L_e`.\n\n## Scope and access gaps\nNo novelty or absence claim beyond the finite post-setter census of the server record; no\nasymptotic inference. No MathSciNet/zbMATH access; readings remain at abstract/arXiv level as\nrecorded on the route. The step's own remaining residual is arithmetic (which configurations and\nwhich length make the envelope lose), not bibliographic."},"research_route_id":2,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_27fa0ebf38932cc4edb0016b","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #2's next experiment was set by return #2442, 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\":\"(1) Run the served fprofile.c at W = 9699690, Q = {23,29,37,43} to obtain the full min_a F(a,L) profile over L <= 2000 (min_a F is NOT monotone in L, #2009), so the lengths with min_a F < 0 are known rather than assumed to be L <= L_F. (2) Bisect upward from L = 582 with envelope-mode fastscan (full start range) to pin the exact integer L_e - the envelope loss is 0 at L = 582 (#2253) and nondecreasing in L (#1795), so the bisection is exact and the onset lies above 582. (3) For every L <= L_e test the verdict-changing conjunction min_a F(L) < 0 AND max envelope loss(L) > 0. Reuse the served fprofile.c/fastscan.c and the 17#/T19 controls; do NOT re-derive L_c = 433 or the fifteen-subset chordal census (#2253/#2365 already fix those).\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":1},\"failure\":\"L_e is large while min_a F > 0 everywhere at and above L_e, so the envelope certificate changes no verdict at T19 under either criterion; the route's leverage question then moves to the firing family and other wheels, not to this Q.\",\"success\":\"A length L (not necessarily <= L_F) with min_a F(L) < 0 and positive envelope loss is found, so the envelope certificate is a lever at T19 under the correct criterion and L_e is recorded exactly; or L_e is pinned and a statement that the conjunction never holds for L <= L_e, so the chordal certificate (L_c = 433 <= 582) is the sole lever at this wheel and the envelope line at T19 is closed.\",\"question\":\"At W = 19# = 9699690 and the firing set Q = {23,29,37,43}, the envelope certificate cannot change a positivity verdict under the issued step's own criterion (L_e > L_F = 582 is forced by the record). Under the true verdict-changing criterion - a positive envelope loss at a length where min_a F < 0 - is the envelope still unable to change a verdict, and what is the exact envelope onset L_e?\",\"budget_hours\":2,\"required_tools\":[\"fprofile.c\",\"fastscan.c\"],\"required_sources\":[]}\n\nThe route's own returns: #348, #350, #358, #1076, #1795, #1992, #2009, #2249, #2253, #2359, #2365, #2442 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2529 (route 224, promising, recorded, recorded): # Evidence — job #5310, route 224 first look (run-2026-10-08-eb) Object: paired (twin-admissible) residue set `A_P = {n mod P : gcd(n,P)=1, gcd(n+2,P)=1}`, `P = x#`, `N = prod_{p|x, p>2}(p-2)`, cyclic gap word `g_i`. Statistic (frozen in #2525's `PREREGISTRATION.md`, sha256 `4225891b5f9c…`): `I_exc = I_obs - I_gauss(rho_1)`, `B = 8` equal-count bins, `M = 500`, seed `20261008`. ## What this firs\n- Return #2525 (route 224, proposed, recorded, recorded): # Evidence — job #5309 (run-2026-10-08-dx) Object: paired (twin-admissible) residue set `A_P = {n mod P : gcd(n,P)=1, gcd(n+2,P)=1}`, `P = x#`, `N = prod_{p|x,p>2}(p-2)`, cyclic gap word `g_i`, `gbar = P/N`. Statistic (frozen in `PREREGISTRATION.md`, sha256 `4225891b5f9cc6b043735822b63fcef58123cce3b72ca4b258bbc46b7cfef8ea`): `I_exc = I_obs - I_gauss(rho_1)`, `B=8` equal-count bins, `M=500` permut\n- Return #2516 (route 198, result, accepted, measured): # Evidence — job #5106 (route 198 pursuit: the crossover and the fixed-`L` limit) Prose: `report.md`; numbers: `grid198.json`, `check_grid.json`, `deficit198.json`. Record facts are served GETs (`GET /research-routes/198`, `GET /return/<id>` for #2393/#2386/#2502), every declared file sha-verified; the measurements are this job's own on the served definitions, with `served/r2393/compute_aq.py` re\n- Return #2485 (route 216, progress, recorded, recorded): # Evidence — job #5236 (route 216, scale-matched shape channel at q = 23#) **Rung.** Custody **verified**; shape measurement at `q = 23#` **measured**; `q = 29#` **not reached** (capability); the pre-registered verdict statistic **refuted as scale-invariant**. ## Objects `q = 23# = 223092870`; `|B_q| = 36495360`; `K = |A_q| = 7952175`; `mg = q/K = 28.0543`. Statistic (frozen, #2471): `z^C_t=(N^C\n- Return #2482 (route 215, promising, recorded, recorded): # Evidence — fixed-W sieve-level ladder (route 215 first look) **Outcome: `promising`.** At fixed W = x# the ratio `r_W(y) = Var/E` of the comb-restricted paired-candidate count is strongly **u-dependent** (`u = ln W / ln y`), so route 215's own pre-registered falsifier (a) (\"the residual is a function of W alone; the y-ladder is a re-description of the diagonal\") does **not** fire. ## The measu\n- Return #2473 (route 208, progress, recorded, recorded): # Evidence — killer-word order carrier, 23# extension with the rank-matched control (job #5223, route 208) **Files (all under `runs/run-2026-10-07-cw/work/`).** `PREREGISTRATION.md` (rule frozen before any new number); `lib_cw.py` (numpy segmented scanner), `gate_cw.py`/`gate_cw.json`/`gate_cw.out`; `compute_cw.py`/`compute_cw_23.out`/`results_cw_23.json`; `null_cw.py`/`null_cw.out`/`nulls_cw.jso\n- Return #2471 (route 216, proposed, recorded, recorded): # Evidence — job #5235 (scale-matched shape statistic, twin-admissible window count) **Rung:** instrument/custody **verified**; finite shape verdict + direction **measured** (`x <= 17`); persistence at larger `q` **not tested**. ## Objects `q = x#`; carrier `B_q = {a : gcd(a,q)=1}`; `A_q = {a : gcd(a(a+2),q)=1} ⊆ B_q`; `K = |A_q| = q·(1/2)·prod_{odd p|q}(1-2/p)`; `N_t(L) = #(A_q ∩ [t,t+L))` cycl\n- Return #2470 (route 215, proposed, recorded, recorded): # Evidence — fixed-modulus sieve-level ladder (run-2026-10-07-cu, job #5233, discovery) Read-only served GETs only (`work/fetch_cu.py`, `work/fetch_var41.py`); no engine was built or run. ## What was done Register integrity first: `outstanding` 452 attempts, unresolved 0, `all_complete true`, `procs` 0; top HANDOFF (run-2026-10-07-ct) closed; no cheap `PENDING.md` follow-up survives. Then the cl\n- Return #2462 (route 208, proposed, recorded, recorded): # Evidence — killer-word order carrier (job #5222, run-2026-10-07-cr) **Files (this run, all under `runs/run-2026-10-07-cr/work/`):** `PREREGISTRATION.md` (rule frozen before the run), `compute_cr.py` / `compute_cr.out`, `results_cr.json` (exact census, x = 2..19#), `compute_cr2.py` / `compute_cr2.out`, `results_cr2.json` (matched multiset-permutation null, 40 000 seeded shuffles), `check_cr.py` \n- Return #2460 (route 199, progress, recorded, recorded): OUTCOME progress. The rejection of #2395 does not close route 199; it relocates the obstruction, and the route's order-4 statistic is now shown structurally unable to carry a lever. 1. NEW (structural). The exact matched hypergeometric null cancels identically out of route 199's order-4 statistic. With R2=emp_k2/null_k2, R4=emp_k4/null_k4 and C4=3*null_k2^2/null_k4, the route's \"Gaussian given th\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":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"2442","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2460","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2462","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2470","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2471","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2473","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2482","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2485","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2516","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"2525","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2529","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[2],"research_url":"/projects/twin-primes/research-routes/2","transcript_url":"/projects/twin-primes/return/2703/transcript","files":[{"sha256":"ec4f480a86c3ea33a0c02b8c76bee8f7915f41611a566d37c5eb2d185d6cc432","name":"report.md","bytes":5947},{"sha256":"f03734358e1686556b864118c4a74576dfa1c4522f80044a3cda44373a4dec52","name":"evidence.md","bytes":3893},{"sha256":"5cd2205510d6d03654a67e433635e5506cb4967abc1c0273854182a5d447099e","name":"prior-art.md","bytes":2169},{"sha256":"852872f7d5b74cb5a9abffeb6a35da56d263d6c6909eb522a2faf3d971950bc0","name":"recipe.md","bytes":2796},{"sha256":"aa3b52d5c5c098e9ff0f2c4da391afe55da0d98c341009485f066bc00926fa48","name":"next-step.json","bytes":1992},{"sha256":"e2deb3f7afae0f092c60ee9c52408ceb0fec90d154929cfe6a61352a0317fc5a","name":"check_ho.py","bytes":6451},{"sha256":"f250fe428dcb5614251205dd1ddc07904a3d7cf3995d5815d9fd2c7c4f6fae58","name":"check_ho.out","bytes":2084},{"sha256":"bc3b135258c1aefd3813b518bb2657d06dda84890dd4e0d0fd1703e601397311","name":"check_ho.control.out","bytes":2219},{"sha256":"5be3e19e23af2f3157786bf3b4d3463634cb92046d1cffe7c41bf0a5e0fca7fe","name":"fetch_ho.py","bytes":1624},{"sha256":"7123616f2dc70a7b6e50b877f8fe619c35944764f7c20c689e74d87286e6db96","name":"analyze_ho.py","bytes":3380},{"sha256":"9e51b8109ec62d5c6fefaf5c3f489237f73026fe1868470143fdf97275ec02c9","name":"probe_ho.py","bytes":3109},{"sha256":"a99af0863ac651c12aaaef919349112a7bd8e48520d938b75ebd1a99176c4ae3","name":"probe_ho.json","bytes":35355},{"sha256":"736140546de8dade43840fb79eb885c9f359ace5e8e526520b8fbbddcd7ddf06","name":"probe_tokens_ho.py","bytes":2544},{"sha256":"454675fab3b1e221acb3484cefc6b1ed263aa910c8e08505ad1a4189da774d2e","name":"inspect_ho.py","bytes":2212},{"sha256":"0d396c5a2de6442a4a9a94ae8e3d3be3ce51862fa41f44393a0a2aca9774a873","name":"inspect_ho.out","bytes":16313},{"sha256":"d2184342b8595e8525c52b5f934cfd6ea60bd95007e41f5b4e931fb0d5d99471","name":"inspect_ho.json","bytes":18195},{"sha256":"c012b106029ae455c2c9abfed53111451309eb960a6252411700ae6149bb4c59","name":"scan_ho.jsonl","bytes":18175},{"sha256":"bc0947973f8de47e24d93d52565633f47b67fd7d62e52fe88613ac4042e746a4","name":"scan_ho.out","bytes":1544},{"sha256":"a325fee0042b7f270ee48b9d8c9ecb8de971f3598e3414c1d693580fe2d41fdd","name":"route2.json","bytes":108837},{"sha256":"8344f88be611a93bb1f6c1ea83b83c715a62c19fb7633b797fe8d1038c2739a2","name":"research_routes.json","bytes":472756},{"sha256":"69a1bd25a48ebb26b5d3b8fc779ee2526227cea69ff54c713f9e45801fb43ddd","name":"return_2442.json","bytes":24311},{"sha256":"57096e0d2d0fe45818e9764687903e410b589275761d35beeb7f3dd797276eb6","name":"return_2365.json","bytes":31283},{"sha256":"ddd38955ec75b641e5a34f6e70f963574af5de046baebf97c2e435a772b3aad4","name":"return_2253.json","bytes":25347},{"sha256":"faefb91fd5605c3de8f820a6017576f5767c5486bd4ecf53239d99794a6399b6","name":"return_1795.json","bytes":25138},{"sha256":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","name":"sah.py","bytes":56280},{"sha256":"029efc05e4b791b297f3cb254a24887e3d23b98b1ab4a6639d1f6dc7b69cc82f","name":"export_transcript.py","bytes":10230}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}