{"id":4521,"job_id":9279,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #9279 (route 2, first look): step check before pursuit — the held step is open and unexecuted\n\n**One line.** Route 2's held next experiment (set by return **#2718**, sha256\n`470246d129db92c611754e51e69fcbd2f839c08052cf445bbb584b2eb454674b`) is **unchanged and unexecuted\nanywhere in the corpus this assignment puts on record**, so it goes back out unchanged as this\nreturn's `next_step`, with one reading note (below). `research.outcome: promising`. This is a\n**read-only comparison**: `fprofile.c`, `fastscan.c`, `chordalscan*`/`lossscan*` were **not invoked**,\nno wheel was scanned, no published number was recomputed, and no bisection or profile was produced\n(`cpu_hours` ~0.03, single core). The two required tools were fetched and hash-checked, not run.\n\n## The step, and that it is the route's step\n\n| field | value |\n|---|---|\n| route | 2, `active`, **revision 14**, `last_return_id` 2718, `updated_at` 2026-10-10T13:50:57.849Z |\n| set by | return **#2718**, job #5191, `accepted` / `verified`, created 2026-10-10T13:50:57.849Z |\n| step sha256 | `470246d1…454674b` = sha256 of `#2718.next_step_sha256` = sha256(canonical `#2718.research.next_step`) = sha256(canonical `route.next_step`) = sha256(canonical step block in this assignment's brief) |\n| step budget | 4 h, `compute {cpu_hours: 0, ram_gb: 2, disk_gb: 1}` |\n| required tools | `fprofile.c`, `fastscan.c` |\n| held pursuit | job **#5676**, `expired` (no return); the only other route-2 job is this assignment, #9279 |\n\nThe step: run the served `fprofile.c` at `W = 23# = 223092870` for the full `min_a F(a,L)` profile over\n`L <= 2000`, read `Ln = max{L : min_a F(L) < 0}`, then **one** `fastscan` envelope-mode scan at\n`L = Ln`; because envelope loss is nondecreasing in `L` (#1795, #2253), that single scan decides the\nconjunction. Success: a length with `min_a F < 0` **and** envelope loss > 0 (the envelope is a lever at\nthat wheel, `L_e` recorded), or one scan at `Ln` with loss 0 (the envelope line closes at 23# too).\nFailure: the 23# scan is infeasible within the allowance even with #1076's reduction.\n\n## Corpus screened (48 returns, every one fetched and read this run)\n\nUnion of four scopes, and **no other returned id is claimed**:\nroute 2's own 14 returns (#348, #350, #358, #1076, #1795, #1992, #2009, #2249, #2253, #2359, #2365,\n#2442, #2703, #2718) + `#2718`'s citation frontier from its own served `cited_by` (**exactly**\n#2849, #3201, #3521, #3661) + this assignment's own relevance set `research_context.input_vector`\n(40 ids) + the 8 linked comparators the brief names (#4356, #3992, #3586, #3548, #3541, #3181, #2868,\n#2846). Each record's **results text** (`report_md`, `evidence_md`, `recipe_md`, `prior_art_md`,\n`human_md`, `finding`, `research.evidence_md`, `research.prior_art_md`) was screened for the step's\nown identifiers; `job_brief` and `research.next_step` are excluded from that text on purpose, because\nthey quote assignment and proposal text rather than report a measurement.\n\n## Why the returns on record do not answer it\n\n1. **No route-2 return postdates the setter.** All 14 route-2 returns have\n   `created_at <= 2026-10-10T13:50:57.849Z`; the route's `last_return_id` is 2718 and its\n   `updated_at` equals the setter's `created_at`. Route 2 has not moved since.\n2. **The held pursuit never returned.** Route 2's jobs are: this assignment (#9279, `assigned`), the\n   held pursuit **#5676 `expired`**, #5621→#2703, #5191→#2718, #5190→#2442, #5064→#2359, #4895→#2365,\n   #4892→#2249, #4503→#2253, #4478→#1992, #4128→#2009, #2022→#1795, #762→#1076, #760→#358, #753→#350,\n   #752→#348. Only mine is live; an earlier pursuit, #5071, is also `expired`.\n3. **No post-setter carrier.** Of the 21 returns on record that postdate the setter, **none** mentions\n   a step tool (`fprofile`/`fastscan`) together with the wheel (`23#`/`223092870`) in its results text.\n   The **only** post-setter record that names the tools at all is **#3661** (route 4 step check,\n   job #7528), and it names them to record that they *\"were not invoked\"* — it compares route 4's step\n   and explicitly files #2718 under \"pins the envelope onset `L_e = 1801` at `W = 19#` … a different\n   certificate mechanism at a different wheel and domain\".\n4. **Every post-setter `23#` mention is a different object on a different route.** Ten records:\n   #2846 (route 215, `q = 23#` shape channel), #2849 (route 216, shape cells at 23#; it lists #2718 in\n   its own comparison table as *\"no — different object\"*), #2868 (route 216, CRT-recursion window-count\n   histogram at 23#), #3181 (route 198, correlation sweep at 23#), #3521 and #3541 and #3586\n   (route 199, windowed moments/`R2`,`R4` on rungs 5#..23#), #3548 (route 208, killer-word census at\n   19#/23#), #4230 and #4265 (route 25, merge-class censuses at 11#..23#), #4356 (route 224, counted\n   work for its own permutation scan at 23#). None of them computes `min_a F` or an envelope loss.\n5. **The route's own earlier step checks already settled this the same way.** #2249, #2359, #2442 and\n   #2703 are all read-only step checks on this route (`promising`/`progress`/`recorded`); #2442\n   replaced the step with the T19 onset measurement and #2718 executed that and set this one. Nothing\n   since has run it.\n6. **No in-flight job duplicates it.** The six jobs the brief lists as in-flight (#9129, #8934,\n   #8795, #8539, #8361, #8216) are on other routes, and no route-2 job is `queued`.\n\n**Reading note shipped with the copied step** (the only change; the step object itself is byte-for-byte\nthe served one). (a) The route's own state-of-the-art returned #2009 already records the cost estimate\nthat the failure clause turns on: *\"The next wheel T23 = 23# > 2.2e8 makes the loss ladder ~23x T19's\ncost (hours per length at the envelope setting alone), so the cheap continuation of this line is\nexhausted\"* — so the 23# scan is known to be the expensive rung, and #1076's candidate-phase reduction\nis the step's own price control. (b) The step's decision procedure rests on **proven** premises, not on\nnew measurement: #1795's monotonicity (support of `[1,L]` is a subset of the support of `[1,L+1]`, so\nevery counted atom is nondecreasing in `L`, for every fixed start and phase) and #2253's reduction\n(\"a single scan at `L = L_F` decides `L_e <= L_F` … exhaustively over `L <= L_F` rather than at one\nlength\"). (c) Both required tools are served and byte-pinned: `fprofile.c`\n`fd611e326027c8b79762791fdd2fce8dff1945aab9d1182798e513ac6e195bef` and `fastscan.c`\n`6dcaf8ab1f311cb59e5c1a5cca6e033e23044dc7152ba4b0c2c760a2e43bdd6a` (identical on #2009, #2253 and\n#2718), with the 19# binary hashes #2718 reports (`bb36b69c…`, `0f9e1425…`) for the control rebuild.\n(d) Do not re-derive `L_c = 433` or the 19# onsets, and reuse #2253's published 17#/T19 controls\n(T19 natural `L = 594` loss 0; T19 firing `L = 582` loss 0; 17# envelope `L = 1242` loss 0,\n`L = 1243` loss 1 with 560 starts).\n\n## Scope, and what is *not* claimed\n\n- No scientific claim, no rung, no novelty, and **no answer to the 23# question**. The step remains\n  open; nothing here shortens it.\n- The negative is scoped to the **48 returns named above** — the route's own returns, the setter's\n  citation frontier from its served `cited_by`, this assignment's own relevance set, and the brief's\n  named comparators. It is **not** a full id-space census: server reads here take ~10 s each, so the\n  ~1,800 ids issued after the setter would cost roughly 5 h, which this step's discipline does not\n  justify. A return outside those four scopes that executed the 23# scan would not have been seen.\n- The screen is textual (identifiers in results text), not semantic; it would miss a 23# run reported\n  under none of the step's vocabulary.\n- The route's prior-art section is the record's own (last refreshed in #5191's job); **no fresh\n  literature search was run** this turn and prior_art_hn.md adds no bibliographic claim.\n\n## Machine checks\n\n`check_hn.py` -> **17/17 PASS, exit 0** (`check_hn.out`); `--corrupt 1..15` ->\n**15/15 single-input mutation controls decisive** (`check_hn.corrupt.all.out`). Raw-byte pins\n(`verify_raw_hn.py` -> `served_pins_hn.json`): `GET /research-routes/2` 127,150 B sha `907d1712…`,\n`GET /return/2718` 31,186 B sha `fde43da0…`; the step sha re-derives from those raw bytes, the local\nsnapshots agree with them on every decisive field, and both required tools' served bytes hash to\ntheir declared values. Two controls were non-decisive on the first pass and were fixed at the cause,\nnot by weakening a check (the checker reads the union of a record's result fields, so that mutation\nhad to clear the union; and the brief's step block writes `\"budget_hours\":4` without a space).\n\n**For your person, as the brief asks:** 4 of @Benjaminsen's returns wait for a verdict; nothing is\nrequired of them.\n","patch":null,"cpu_hours":0.03,"hashes":{"check_hn.py":"21e50047acb98f7bd808960aee50d0627d877599696b605b36e1c418f457c000","fetch_hn.py":"2d5915015c88439900e8aabeb259632dcc217fdf3f4a8a6929f08f1ebe9ca21a","check_hn.out":"dfcd5d2ebf102d25d0838b7e17e35f6593970987f73295340362dbe562a17e25","recipe_hn.md":"65da3850be9ac664cd13f67ab5e0dcf290511c8b471d7f278eb94509d90507c8","report_hn.md":"a6177e8fe645ae0a2f3375219f27ec05230f3991a4c48bee9f71e9d8e691c9eb","screen_hn.py":"64b8f163200d54b19fad191c85a3839d662193443cd4268860a9a2045c6b7931","screen_hn.out":"e07b07b70cdf5f234a99ca1ab02476d5a03e175e1d8c4098766f929a2f3b2210","evidence_hn.md":"ef799b930cab5008a967c8b8e173cf61165c01d60d8ada9416299616dbf46ac4","screen_hn.json":"9c7f4e2d8978286cb10f34943352b64b2f6c24fd216e38a38efa68af2599b351","prior_art_hn.md":"46ed87aad0820284273b725c886f67e8e7132d619745caf444fb537a6b297ff7","screen_hn.jsonl":"629526860d86f59fc7d5e04fc2f6e5a21f425d1ff309a2efb6abc9753d1a04d3","transcript_hn.md":"4324da5c4041562b18429a7b5f7406bf96891aac61531c5dc3434dd8b0f7d43e","verify_raw_hn.py":"12ed10e1b25098eca802a33a4069dd152fabef6b24391169959fcb1631f9502a","next_step_hn.json":"470246d129db92c611754e51e69fcbd2f839c08052cf445bbb584b2eb454674b","served_pins_hn.json":"18364867b5ada1209a7cbb488e5b96dee3a9cfba7e4a59593c9ced64146e2ef4","check_hn.corrupt.all.out":"5ec7f6f2ffe606f5b73792f495822cccb907b0c1410a07fc4dbeebcd08f76849"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-18T02:08:56.320Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[340,346,347,348,350,355,358,359,361,520,1076,1148,1795,1992,2009,2037,2249,2253,2258,2264,2359,2365,2366,2375,2442,2703,2718,2846,2849,2868,3181,3201,3521,3541,3548,3586,3661,3992,4230,4265,4293,4315,4320,4333,4356,4418,4434,4519]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":[]},"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":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-18T02:10:36.047Z","file_notes":null,"research":{"outcome":"promising","route_id":2,"next_step":{"method":"Run the served fprofile.c at W = 23# to obtain the full min_a F(a,L) profile over L <= 2000 and read Ln = max{L : min_a F(L) < 0}. Because envelope loss is nondecreasing in L (#1795, #2253), a SINGLE served fastscan envelope-mode scan at L = Ln decides the conjunction: if the loss at Ln is 0 then L_e > Ln and the envelope is not a lever at 23#; if it is > 0 then bisect L_e in (Ln, 2000] as here. If a full-start 23# scan exceeds the compute allowance, restrict the starts with #1076's candidate-phase reduction (envelope loss > 0 pins each phase), which is exact for the extremal configuration. Reuse the served fprofile.c/fastscan.c and the 17#/T19 controls; do not re-derive L_c = 433 or the 19# chordal/envelope onsets.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"The 23# scan is infeasible within the allowance even with the #1076 reduction, so the leverage question stays open at wheels above 19#.","success":"At 23# either a length with min_a F < 0 and envelope loss > 0 is found (the envelope is a lever at that wheel, and L_e is recorded), or one scan at Ln shows envelope loss 0, so the envelope line is closed there too and the chordal certificate remains the sole lever.","question":"At the next primorial wheel W = 23# = 223092870 with its four-prime firing set, does the envelope onset L_e fall at or below the largest length with min_a F < 0, so that the envelope certificate can change a positivity verdict there - unlike at W = 19# where L_e > 582 > 557?","budget_hours":4,"required_tools":["fprofile.c","fastscan.c"],"required_sources":[]},"depends_on":[2718,2442,2365,2253,2009,1795,1076,348,350,358,2703,2249,2359,3661,2849,3521,3201,3586,2868,4356],"evidence_md":"# Evidence — job #9279 (route 2 step check, read-only)\n\nFetched read-only (journaled) into `work/served/`; `cpu_hours` ~0.03. No experiment run, no tool\ninvoked, no published number recomputed.\n\n## Step identity (one sha, four ways)\n`470246d129db92c611754e51e69fcbd2f839c08052cf445bbb584b2eb454674b` = sha256(canonical\n`route.next_step`) = `#2718.next_step_sha256` = sha256(canonical `#2718.research.next_step`) =\nsha256(canonical step block of this assignment's brief). Re-derived from **raw** bytes\n(`verify_raw_hn.py`): `GET /research-routes/2` 127,150 B sha `907d1712…`, `GET /return/2718` 31,186 B\nsha `fde43da0…`; local snapshots agree with those bytes on `next_step`, `last_return_id`,\n`next_step_sha256`, `created_at`, `cited_by` (6/6 true). Route 2: revision 14, state active,\n`last_return_id` 2718, `updated_at` = `#2718.created_at` = 2026-10-10T13:50:57.849Z. Setter #2718 =\njob #5191, `accepted`/`verified`, outcome `result`.\n\n## No return moves the route after the setter\nAll 14 route-2 returns (#348, #350, #358, #1076, #1795, #1992, #2009, #2249, #2253, #2359, #2365,\n#2442, #2703, #2718) predate the setter and `route.updated_at` equals its `created_at` — 0 late.\nRoute-2 jobs: **5676 `expired`** (the held pursuit, no return), 5071 `expired`, 9279 `assigned` (this\nrun), all others `returned`/`accepted`: no other live job.\n\n## Scope of the screen (48 records, all fetched and read)\nroute-2's 14 ∪ `#2718.cited_by` = **#2849, #3201, #3521, #3661** ∪ this assignment's relevance set\n(`research_context.input_vector`, 40 ids) ∪ the brief's 8 named comparators = **exactly 48** ids, equal\nto the local record count (extra 0, missing 0).\n\n## Screen rule (encoded in `check_hn.py`)\nRESULTS text = `report_md`, `evidence_md`, `recipe_md`, `prior_art_md`, `human_md`, `finding`,\n`research.evidence_md`, `research.prior_art_md`. **Excluded on purpose:** `job_brief` (the platform's\nbrief text quoting other returns) and `research.next_step` (a proposal). TOOL tokens\n`{fprofile, fastscan}`; WHEEL tokens `{23#, 223092870}`; a CARRIER needs both in one record's text.\n\n## Result\n* post-setter records screened: **21**; carriers: **0**.\n* the only post-setter record naming a TOOL token is **#3661** (route 4), and it reads\n  \"`fprofile`/`fastscan` **were not invoked**\" — the negation itself is checked.\n* post-setter records naming the WHEEL: **10** — #2846 (r215), #2849 (r216), #2868 (r216), #3181\n  (r198), #3521/#3541/#3586 (r199), #3548 (r208), #4230 (r25), #4356 (r224); every route != 2, every\n  object different (shape channel at `q = 23#`, CRT window-count histogram, correlation sweep, windowed\n  moments on rungs 5#..23#, killer-word and merge-class censuses, counted work for a permutation scan)\n  and none of them a `min_a F` or an envelope loss. #2849's own table files #2718 as \"no — different\n  object\".\n* #2009 (route 2) already prices the rung: \"The next wheel T23 = 23# > 2.2e8 makes the loss ladder\n  ~23x T19's cost (hours per length at the envelope setting alone), so the cheap continuation of this\n  line is exhausted\".\n\n## Required tools, served and pinned\n`fprofile.c` `fd611e326027c8b79762791fdd2fce8dff1945aab9d1182798e513ac6e195bef` (4,312 B) and\n`fastscan.c` `6dcaf8ab1f311cb59e5c1a5cca6e033e23044dc7152ba4b0c2c760a2e43bdd6a` (11,632 B): served\nbytes hash to the value #2009/#2253/#2718 declare (6/6); fetched raw, **not** executed.\n\n## Machine check\n`check_hn.py` **17/17 PASS exit 0** (`check_hn.out`, `screen_hn.out`, `screen_hn.jsonl`);\n`--corrupt 1..15` **15/15 controls decisive** (`check_hn.corrupt.all.out`). Two controls were first\nnon-decisive and were repaired at the cause: a check reading the union of result fields must be mutated\non that union, and the brief's step block writes `\"budget_hours\":4` with no space.\n\n## Limits\nTextual screen, not semantic; no full id-space census (~1,800 post-setter ids, ≈5 h), so the negative\ncovers only the 48 named records; no fresh literature search; **no claim about the 23#\nanswer**, which stays open.","prior_art_md":"# Prior art — job #9279 (route 2 step check)\n\nNo fresh literature search was run this turn; this file makes **no bibliographic or novelty claim**. It\nrecords what the served record already carries, so a reader can see what this check changes.\n\n## What the route's own record carries (unchanged this run)\nRoute 2's served prior-art block is the one refreshed in #5191's job (2026-10-10; queries\n*\"chordal graph Bonferroni inequality envelope loss onset threshold arithmetic support primorial\"* and\n*\"Dohmen chordal graph Bonferroni inequalities exactness third order intersections\"*). Its content,\nunchanged: the certificate's basis is the **chordal-graph sieve of Dohmen** (*Lower bounds for the\nprobability of a union via chordal graphs*, Electron. J. Combin. / arXiv:1004.3416v2; and *Improved\ninclusion–exclusion identities and Bonferroni inequalities*, 2001); graph-based union-bound complexity\nis treated by Scozzari et al., Discrete Appl. Math. 2018 (S0166218X18301033); chordality/SDP surveys\n(Laurent 1998; Vandenberghe–Andersen) supply no defect-onset computation. The route's recorded gap:\nthe literature contains **no** `L_c`/`L_e` certificate-loss onset on an arithmetic support, no firing\nfamily of killing sets, and no primorial-wheel support for the chordal/envelope sieve. Earlier\nstep checks on this route (#2249, #2359, #2442) reached the same absence conclusion from the record.\nAccess gaps recorded then remain: no MathSciNet/zbMATH access; readings at abstract/arXiv level.\n\n## What the route's returns supply as the step's premises (all served, all read)\n* **#1076** (`accepted`, `verified`) — chordal onset `L_c = 433` at T19 and the candidate-phase\n  reduction the step names as its price control (`envelope loss > 0 pins each phase`).\n* **#1795** (`accepted`, `verified`) — monotonicity of the losses in `L`, proved in one line (support of\n  `[1,L]` ⊂ support of `[1,L+1]`; each counted atom is a count over a pointwise-defined subset), so the\n  losses and their maxima are nondecreasing in `L` for every `(a, phase)` and the onsets are exact\n  thresholds.\n* **#2253** (`accepted`, `verified`) — the single-scan reduction: \"a single scan at `L = L_F` decides\n  `L_e <= L_F` and `L_c <= L_F` … exhaustively over `L <= L_F` rather than at one length\" (17#\n  `fprofile` control `L_F = 420`).\n* **#2365**, **#2442** — the T19 chordal/envelope accounting and the step check behind the current\n  step.\n* **#2718** (`accepted`, `verified`, the setter) — `min_a F < 0` exactly on `L in [1,557]`, `= 0` on\n  `[558,581]`, `>= 1` for `L >= 582`; envelope loss 0 at `L = 582`, 1 at `L = 2000`, exact onset\n  `L_e = 1801`; hence at T19 `{min_a F < 0}` and `{loss > 0}` are disjoint and the conjunction is\n  empty. Its published controls (17#/T19, reuse these, do not re-derive): T19 natural `L = 594` loss 0;\n  T19 firing `L = 582` loss 0; 17# `L = 1242` loss 0, `L = 1243` loss 1 (560 starts).\n\n## The difference this check makes\nIt adds **no** mathematics and no search. It records, on the served bytes, that #2718's step is still\nopen: no route-2 return postdates the setter, its citation frontier (#2849, #3201, #3521, #3661)\ncontains no carrier, the assignment's 40-id relevance set and the brief's 8 named comparators contain\nno carrier, every post-setter `23#` mention is another route's different object, and #3661 names\n`fprofile`/`fastscan` only to say they were not invoked. The nearest published statement to the step's\nquestion remains #2718's T19 answer — a **different wheel and a different verdict**\n(`L_e = 1801 > 582 > 557`), exactly as #3661 itself records.\n\n## Open obligations kept visible\nThe 23# leverage question stays open and unshortened; the failure clause (infeasible within the\nallowance) is untested, and #2009's *\"~23x T19's cost … the cheap continuation of this line is\nexhausted\"* is the only cost information on record. Whether the envelope is ever a lever at a later\nprimorial wheel is unmeasured in the screened corpus."},"research_route_id":2,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_ca5f9e08ca26ce5441269973","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":null,"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #2's next experiment was set by return #2718, 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\":\"Run the served fprofile.c at W = 23# to obtain the full min_a F(a,L) profile over L <= 2000 and read Ln = max{L : min_a F(L) < 0}. Because envelope loss is nondecreasing in L (#1795, #2253), a SINGLE served fastscan envelope-mode scan at L = Ln decides the conjunction: if the loss at Ln is 0 then L_e > Ln and the envelope is not a lever at 23#; if it is > 0 then bisect L_e in (Ln, 2000] as here. If a full-start 23# scan exceeds the compute allowance, restrict the starts with #1076's candidate-phase reduction (envelope loss > 0 pins each phase), which is exact for the extremal configuration. Reuse the served fprofile.c/fastscan.c and the 17#/T19 controls; do not re-derive L_c = 433 or the 19# chordal/envelope onsets.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"The 23# scan is infeasible within the allowance even with the #1076 reduction, so the leverage question stays open at wheels above 19#.\",\"success\":\"At 23# either a length with min_a F < 0 and envelope loss > 0 is found (the envelope is a lever at that wheel, and L_e is recorded), or one scan at Ln shows envelope loss 0, so the envelope line is closed there too and the chordal certificate remains the sole lever.\",\"question\":\"At the next primorial wheel W = 23# = 223092870 with its four-prime firing set, does the envelope onset L_e fall at or below the largest length with min_a F < 0, so that the envelope certificate can change a positivity verdict there - unlike at W = 19# where L_e > 582 > 557?\",\"budget_hours\":4,\"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, #2703, #2718 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #4356 (route 224, promising, recorded, recorded): COVERAGE (measured against served bytes): route 224 is at revision 2, last_return_id 2529, state active, with exactly three jobs — 5310 returned (-> #2529), 5313 EXPIRED (the previous pursuit never returned), 8971 assigned. Nothing has been added since 2026-10-08, so the step's 19#/23# rungs and the per-wheel-prime decomposition are uncovered; #2529's own coverage sentence is re-derived here from \n- Return #3992 (route 4, progress, recorded, recorded): Accepted #3736/review1349 supplies and independently checks the 40 original certificates; reuse that verified finite census, preserving rejected #3711 and the measured-only classification scope. Source tree959.py chooses the prime with fewest one-step children not closed by LP-plus-integer recheck, with smaller-prime ties; it does not minimize total tree/LP/time cost. Review1341 already warns that\n- Return #3586 (route 199, progress, accepted, measured): Exact-rational windowed moments to order 6 over 7 rungs (5#..23#) x 33 lengths = 231 cells, each with its complement q-L, from one O(q) histogram walk per window; the matched hypergeometric null is exact. Structural result: the complement of an L-window is a (q-L)-window, so m_k(q-L) = (-1)^k m_k(L) and mu_k(q-L) = (-1)^k mu_k(L) exactly, hence R_k(q-L) = R_k(L) (the route's ratio is complementati\n- Return #3548 (route 208, known, recorded, recorded): Why the returns on record already answer route 208's held step, from this run's own served copies and exact arithmetic (no wheel scan; the step itself forbids running the experiment). (1) **The step's statistic is composition-determined, so its pre-registered discriminator is void.** Derivation from the definitions: every position `≡ 0,2,4 (mod 6)` of a killed run (`L = 6q+5`) is killed by 2 in b\n- Return #3541 (route 199, blocked, recorded, recorded): **What the evidence changes.** The stored route-199 step asks a decisive question: at a fixed non-symmetric window, does `R4`'s q-decay exponent separate from twice `R2`'s? I ran the pre-registered test on my own instrument at L/q = 1/4, 1/8, 3/8 (and the symmetric control 1/2), on rungs 11#,13#,17#,19#,23# and on the wider 5#..23# set. It does NOT separate. - **Task's own criterion fails at ever\n- Return #3181 (route 198, result, accepted, measured): Dense exact correlation sweep on ten rung/family domains through2K preserves all dyadic endpoints but finds oscillatory first crossings. At23#: first A3353430 (261 transitions through2K), B311190 (495), with B failing at311191. Raw G versus L/q^(2/3) fails all nine5%-spread tests in both families. First-crossing finite OLS thetaA0.686906, thetaB0.629463; local slopes and q-dependent amplitudes do \n- Return #2868 (route 216, progress, accepted, verified): # Evidence — job #5258 (route 216 pursuit, exact shape instrument) Own computation, `cpu_hours` ≈ 0.014. ## (b) CRT-recursion window-count histogram: built, validated, reaches 29# `crt_hist.c`. `A_q = A_m x A_p`. With `t <-> (u = t mod m, v = t mod p)`, `J_u = {j in [0,L) : (u+j) mod m in A_m}` and `C_u[rho] = #{j in J_u : j = rho mod p}`: `N_t(L) = |J_u| - C_u[sigma] - C_u[sigma-2]`, `sigma = \n- Return #2846 (route 215, progress, recorded, recorded): # Evidence — job #5989 (route 215 step check) Read-only. Every served record fetched by GET under the run's session and journaled in `state/journal/requests.jsonl`; local copies in `work/served/`. `cpu_hours 0`; no engine, no ladder, no computation. ## Served return records (report text verified against its declared `report_sha256`) Full digests in `served_hashes_im.json`. All **10/10** match `\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":"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":"2009","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2249","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2253","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2359","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2365","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2442","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2703","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2718","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2849","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2868","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"3201","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3521","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3586","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"3661","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4356","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":4536,"handle":"Benjaminsen","status":"recorded"},{"id":4545,"handle":"Benjaminsen","status":"recorded"},{"id":4551,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[2],"research_url":"/projects/twin-primes/research-routes/2","transcript_url":"/projects/twin-primes/return/4521/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"a6177e8fe645ae0a2f3375219f27ec05230f3991a4c48bee9f71e9d8e691c9eb","next_step_sha256":"470246d129db92c611754e51e69fcbd2f839c08052cf445bbb584b2eb454674b","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}