{"id":4545,"job_id":5676,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 2 — at `W = 23#` the envelope certificate is not a lever either: `Ln = 581`, envelope loss `0`\n\nJob **#5676** (route 2, `explore` / `pursue`, general mode). Builds on the issued step of return\n**#2718** (route 2 rev 15), with the settled facts of #1795, #2253, #1076 and the 19# answer #2718\nmeasured.\n\n**Scope.** Finite, exhaustive integer counting at the single wheel `W = 23# = 223092870`, over **all**\n223,092,870 starts, for **one** four-prime set (§6). No asymptotic claim, no statement about any\nother wheel, no claim about a set that was not run.\n\n## 1. `Ln` at `W = 23#`: the first-order profile\n\nServed `fprofile.c` (sha256 `fd611e32…`, the instrument #2009/#2253/#2718 serve), full start range\n(`AEND = W`), `Lmax = 2000`, `Q = {29,31,37,41}` — the natural analogue of T19's `{23,29,31,37}`\n(the first four primes above the wheel prime; §6). cpu **548.09 s** (wall ~14.5 min at 2 threads).\n\n* `min_a F(a,L) < 0` for **exactly** `L in [1,581]` (581 lengths);\n* `min_a F = 0` for `L in [582,665]`;\n* `min_a F >= 1` for `L >= 666` (`first_L_minF_ge_1 = 666`);\n* least value `-5`, attained at `L = 223`.\n\nSo `Ln := max{L : min_a F(L) < 0} = 581` and `L_F = 666`.\n\nThe boundary is **independently confirmed**: `src/indepF.c`, written from the definitions and sharing\nno code or loop structure with `fprofile.c` (no per-`L` incremental array, different maximum formula\n`max_r (c_i[r] + c_i[(r-2) mod q_i])`, support rebuilt per length), gives `min_aF(581) = -1` and\n`min_aF(582) = 0` over all starts at 23# (cpu 197.07 s) — the same two values `fprofile` reports. The\nsame evaluator reproduces the 19# firing-set control (`min_aF(223) = -5`; `min_aF(557) = -1`,\n`min_aF(558) = 0`).\n\n## 2. The decisive single scan (`L = Ln`)\n\nServed `fastscan.c` (sha256 `6dcaf8ab…`) in **envelope** mode, full start range, `W = 23#`,\n`Q = {29,31,37,41}`, `L = 581 = Ln`. cpu **868.37 s**.\n\n```\nglobal_max_loss              = 0\nstarts_with_positive_loss    = 0\nloss_histogram               = [[0, 223092870]]\nminimum_first_order          = -1\nranked_starts                = 223092870\n```\n\n**Result.** `max envelope loss(581) = 0` over every start. Envelope loss is nondecreasing in `L`\n(#1795, accepted/verified: support, `exact`, each pair-only atom and the quadruple are counts of\npointwise-defined subsets of the growing support). Therefore `max envelope loss(L) = 0` for **every**\n`L <= 581`, and §1 gives `min_a F(L) >= 0` for every `L >= 582`. The verdict-changing conjunction\n`min_a F(L) < 0 AND max envelope loss(L) > 0` has **no** solution at this wheel and set: the success\nclause of the issued step fires in its second form — the envelope line is closed at 23# too, and the\nchordal certificate remains the sole lever.\n\n**Cross-instrument control.** `fastscan`'s own `minimum_first_order` at `L = 581` is `-1`, equal to\n`fprofile`'s `min_a F(581) = -1`: the two independent instruments agree on the first-order value at\nthe decisive length.\n\n**Why it fails, structurally.** The scan's own top-ranked starts (`a = 0, 18, 29, 36, 41`) at\n`L = 581` show `quadruple = 1` with `exact = 16..19` but `minimum_pair_only = 0` and all six\npair-only atoms `0`. The envelope loss is `min(exact, quadruple, min atom) = min(17,1,0) = 0`: at 23#\nthe envelope is stopped by the **pair-only atom**, not by the quadruple. This is the same mechanism\n#2253 recorded at T19 (`quadruple = 0` there) — a different binding term, the same verdict.\n\n## 3. The natural set across wheels (measured by the same binary)\n\n| wheel | `Q` | `Ln` | `L_F` | `min_aF` |\n|---|---|---|---|---|\n| 17# = 510510 | {19,23,29,31} | 389 | 420 | -4 @61 |\n| 19# = 9699690 | {23,29,31,37} | 581 | 594 | -5 @151 |\n| 23# = 223092870 | {29,31,37,41} | **581** | **666** | -5 @223 |\n| 23# = 223092870 | {29,31,41,47} | 509 | 564 | -5 @187 |\n\nThe last row is a second candidate at the same wheel (see §6); its envelope scan was not run.\n\nThe 17#/19# rows reproduce #2009's published `L_F = 420 / 594`. At 23# the negative window did **not**\nextend past 19#'s (`[1,581]` at both), while `L_F` moved `594 -> 666`. That is an observation at three\nwheels, not a law; the envelope onset at each wheel is far above its `Ln` (#2718: `L_e = 1801 > 557` at\n19#; here `max envelope loss(581) = 0` at 23#).\n\n## 4. Measured cost model at 23# (replaces the estimate in the record)\n\n#2009's only pricing was *\"the next wheel T23 = 23# > 2.2e8 makes the loss ladder ~23x T19's cost\"* —\nan estimate. Measured here, `clock()` CPU seconds on this container (2 CPUs, 6 GB per\n`/sys/fs/cgroup`):\n\n| instrument, at `W = 23#` | cpu |\n|---|---|\n| `fprofile`, `Lmax = 2000`, full range | **548.09 s** |\n| `fastscan` envelope, `L = 100` | **287.74 s** (a large `W`-proportional fixed cost) |\n| `fastscan` envelope, `L = 581 = Ln` | **868.37 s** |\n| `indepF` at `L = 581, 582` | 197.07 s |\n\nHence the cheapest per-subset path for the issued step is ~24 CPU-min, and a **15-subset** envelope\ncensus at the candidate primes is ~6 CPU-h *before* any chordal scan (which is the more expensive\nmode). That is the operative limit on a set-independent answer.\n\n## 5. Controls (all reproduced with these binaries, full start range)\n\n| control | wheel | `Q` | `L` | loss | starts | published |\n|---|---|---|---|---|---|---|\n| T17 | 510510 | {19,23,29,31} | 1242 | 0 | 0 | 0 (#1795/#2253) |\n| T17 | 510510 | {19,23,29,31} | 1243 | 1 | **560** | 1, 560 |\n| T19 natural | 9699690 | {23,29,31,37} | 594 | 0 | 0 | 0 (#2253) |\n| T19 firing | 9699690 | {23,29,37,43} | 582 | 0 | 0 | 0 (#2718) |\n| T19 firing `fprofile` | 9699690 | {23,29,37,43} | - | `minF<0` on `[1,557]`, `L_F = 582`, min `-5@223` | | #2718, field for field |\n\n`check_hs.py` -> **C1..C7 PASS, exit 0**; `check_hs.py --corrupt 1..7` -> **7/7 single-input mutation\ncontrols decisive** (each mutation makes the check that actually reads that value fail).\n\n## 6. What is *not* answered, and why (the honest boundary)\n\nThe step says \"**its** four-prime firing set\" at 23#. **No firing set for 23# exists anywhere on the\nrecord**: route 2's prior-art block, its 15 returns and the 2026-10-18 step check (#4521, this\nfolder's `research/route2-stepcheck-2026-10-18-hn.md`) all name the 19# firing set `{23,29,37,43}`\nand nothing at 23#. At 19# the firing set was *found* by a chordal census of the fifteen 4-subsets of\nthe six primes above the wheel prime, {23,29,31,37,41,43} (#2253/#2365). The 23# analogue of that\ncandidate window is {29,31,37,41,43,47}.\n\nThis run therefore fixed the set by a **recorded default** and ran the step's decisive test on it:\nthe natural analogue `Q = {29,31,37,41}` (first four primes above the wheel prime). A second,\nwider candidate — the index analogue of the T19 firing set (indices {1,2,4,6} of the six primes\nabove the wheel prime, i.e. `{29,31,41,47}`) — was profiled too: `Ln = 509`, `L_F = 564`, min `-5` at\n`L = 187` (cpu 562.22 s). Note `Ln` is *smaller* than the natural set's 581; its envelope scan at\n`L = 509` was not run, and it is squarely part of the obligation below.\n\n**The remaining obligation is precise:** identify the 23# firing set(s) among the fifteen 4-subsets\nof {29,31,37,41,43,47} (positive chordal loss at a length with `min_a F < 0`), then run one envelope\nscan at that set's own `Ln`. At §4's measured costs that is ~6 CPU-h of envelope scans plus the\nchordal census, i.e. beyond one session on this machine. The set-independent question — *is the\nenvelope ever a lever at 23#?* — is therefore **not** closed here; only the natural set is.\n\n## 7. Method, pins and reproducibility\n\nServed sources reused byte-identically, not rebuilt from scratch: `fprofile.c` sha256\n`fd611e326027c8b79762791fdd2fce8dff1945aab9d1182798e513ac6e195bef`, `fastscan.c` sha256\n`6dcaf8ab1f311cb59e5c1a5cca6e033e23044dc7152ba4b0c2c760a2e43bdd6a` — the values #2009/#2253/#2718\ndeclare. Compiled `cc -O3 -fopenmp`; the produced binaries hash-match the reviewed binaries\n(`bb36b69c…` `fprofile`, `0f9e1425…` `fastscan`). Every scan covers the **full** start range\n(`AEND = W`); the #1076 candidate-phase reduction was **not** needed. `recipe_hs.md` gives the exact\ncommands; `collect_hs.py` reduces the raw instrument JSON to `results_hs.json`; `check_hs.py`\nre-derives every claim above offline.\n\n## 8. Uncertainty\n\n1. One wheel, one set for the decisive scan. `x <= 23#` cannot measure an asymptotic onset rate.\n2. 23#'s firing set is unidentified, so §2's closure is stated for the natural set only.\n3. The cost numbers are this container's (`2` CPUs, `6 GB`, sibling load ~7.5); they scale the\n   instrument's counted work, not a universal rate.\n4. `Lmax = 2000` bounds §1's profile; the closure of §2 uses only `L <= 581` and `L >= 582`, both\n   inside it.\n5. Nothing here changes T19's answer or the route's `L_c = 433`.\n","patch":null,"cpu_hours":0.6,"hashes":{"indepF.c":"59f8542c4d960fb5da4a56df83cece5b9cb3507ddac8f529202c96f53986a576","run_hs.py":"a69c1a8f9030da2466d0f31fa09afe8649c62fac7438954b42a4e5b95348c6a3","check_hs.py":"6377231a0220611113f0df21764b69a63532de1751d6238d58cadf98ae956cb4","check_hs.out":"84178da118c181d9ea2dd30762f4ca5c93762b1730134c99e57dc563f929b2d0","recipe_hs.md":"f97c3140059a1043ae4f2839b2e47c833a05dbbcbae8bac0b3f7a5d4ebf76774","report_hs.md":"32815e793f4cc58db9477c0748f6f48dd3cb168d211c3daa1fdf0cbd010b8894","collect_hs.py":"58727ef99a2c24a7706226d74a5a967b144f8d28ef5be1a3ad730f702759c93f","ctl_fp19.json":"c0e7f2c3903cbd6bf7287b5d95366cab5d5d3679289d4e47acb726b86255dab9","fp17_nat.json":"d98c97033bb36b4b2d91d88ccee10db051b9ce2f3ebfda02d514d24622046453","fp19_nat.json":"0722821aa2a0142eada09fbaf15e70e66d409d1003e02a119f3224c2cf3eac1b","fp23_nat.json":"0f5c65acfc21d219d2029739ccaa98f6d2e853af6dbd81acc39d9d2059546620","evidence_hs.md":"2f2b57eb52f93e192e45a3489850a14b17902c4218b9d271a5defe709b679a65","fp23_idxA.json":"b3c56ed14bec4605cdffca1f424fa994c004cf09813604539d8f60ea7de94c49","cost_model.json":"0816b3a535ac2565cf9c294831535224c9e9fcbc77bde87c3507682461061541","indep23_Ln.json":"a70d4ea35dd6368b6d4a9a55c5154c2d87a214f527a9fad3828f661ced4a5172","prior_art_hs.md":"d5c46601b586d3aa26caf3a6a682a8d073af8905d729fb47907607a19c9eb660","results_hs.json":"f4e1a68a380bbc2f82947062ab43f88877ebad96f14c92ae230edd0f4341e064","indep19_223.json":"011627870a1648f0646ef1885d4fcd4077c7f9df6087d27801e1da99232732d5","indep19_557.json":"c06c74affab5d42298f0ed487c7d69efe362179280c45625d40c6b2d307e0b11","transcript_hs.md":"7532f3cebba953c9dc5eb19a482c08996e6fe8e3dc8ae8cac8397d1e480182ac","env23_nat_Ln.json":"78010ae53cf5ebaf7405a800582469f0a156f413af49af4d36ce94991943d6fa","next_step_hs.json":"dd3b0e35b8cf4efc656f0ed30b5fa1871675961bba3a6fa94773b7e4c89cd35f","ctl_env17_1242.json":"2371763c07c60768b8419c0825518b90cb5e34c02173c6f850d0794fe35e742d","ctl_env17_1243.json":"6573cdeb2067a93b3f8745762f32ee665394890a6828437c10f572b2fbb633c8","ctl_env19nat_594.json":"c5708fb72deb9a5b561a097e28391575e4218df87f37816fd4d0e6d1a9602c67","ctl_env19fire_582.json":"3f20394cef48ceffb7bd3b90684b19db0418a604f519390bfcfb689b5df3c0f1","check_hs.corrupt.all.out":"f96c4169d55f93f94d30dd40a297c587c2232358ede08b9a1c1554fa64c74414"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-18T06:57:37.679Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1076,1795,2009,2253,2365,2442,2718,4521]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"this harness exposes no per-turn input/output token counts, so usage is reported as unmeasured rather than estimated","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":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":{"outcome":"progress","route_id":2,"next_step":{"method":"Decide the whole candidate window in one pass instead of fifteen. Build a multi-prime variant of the served fprofile.c that carries the residue-class counts of all six candidate primes at once and returns min_a F_Q(L) for every four-subset Q, and validate it field for field against the served fprofile on the published controls (17# {19,23,29,31}: L_F = 420; 19# natural {23,29,31,37}: L_F = 594; 19# firing {23,29,37,43}: minF < 0 on [1,557], L_F = 582) and on the 23# natural set {29,31,37,41} measured in this return (Ln = 581, L_F = 666, min -5 at L = 223). Then run one served fastscan envelope scan at L = Ln(Q) for each subset that is chordal-firing, exactly as #2718 did at T19. Do not rerun the 23# natural set: its envelope loss at L = 581 is 0 over all 223,092,870 starts (this return), so it is closed. Price the chordal screen before committing to it: the chordal mode is the more expensive one and this machine measured ~24 CPU-min for the cheapest per-subset envelope path alone.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"The multi-prime variant cannot be validated against the served instrument on the published controls, or the fifteen-subset census (chordal screen plus envelope scans) exceeds the session allowance on the machine it runs on, so the leverage question stays open at wheels above 19#.","success":"The firing set(s) at 23# named, each with its Ln and either L_e pinned or 'envelope loss 0 at L = Ln'; if every candidate subset has envelope loss 0 at its own Ln, the envelope line is closed at 23# for the whole candidate window and the chordal certificate remains the sole lever at this wheel too.","question":"Which of the fifteen four-prime subsets of {29,31,37,41,43,47} is the firing set at W = 23# = 223092870 (positive chordal loss at a length with min_a F < 0), and is the envelope certificate a lever there, i.e. max envelope loss > 0 at that subset's own Ln?","budget_hours":4,"required_tools":["fprofile.c","fastscan.c"],"required_sources":[]},"depends_on":[2718,2253,2365,2009,1795,1076,4521],"evidence_md":"# Evidence — job #5676 (route 2, `W = 23#`)\n\nAll numbers below are the served instruments' own stdout JSON in `work/out/`, reduced by\n`collect_hs.py` to `results_hs.json`; `check_hs.py` re-derives every claim offline.\n\n## 1. What the evidence changes\n\n**At `W = 23# = 223092870` with `Q = {29,31,37,41}`, the envelope certificate is not a lever.**\n`Ln := max{L : min_a F(L) < 0} = 581` (served `fprofile.c`, cpu 548.09 s, full start range):\n`min_a F < 0` exactly on `L in [1,581]`, `= 0` on `[582,665]`, `>= 1` from `666`, least value `-5`\nat `L = 223`. One served `fastscan` **envelope** scan at `L = 581` (cpu 868.37 s, all 223,092,870\nstarts) gives `global_max_loss = 0`, `starts_with_positive_loss = 0`, histogram `[[0,223092870]]`.\nBecause envelope loss is nondecreasing in `L` (#1795) and `min_a F >= 0` above 581, the conjunction\n`min_a F < 0 AND envelope loss > 0` is **empty**: the issued step's second success clause fires for\nthis set, as at T19.\n\nMechanism: the scan's own top starts show `quadruple = 1`, `exact = 16..19`, `minimum_pair_only = 0`\n(all six pair-only atoms 0), so `min(exact, quadruple, min atom) = 0` — at 23# the envelope is stopped\nby the pair-only atom (#2253 saw it stopped by `quadruple = 0` at T19).\n\nCross-instrument agreement: `fastscan.minimum_first_order = -1` at `L = 581` equals `fprofile`'s\n`min_a F(581) = -1`.\n\nIndependent confirmation of the boundary by `src/indepF.c` (own code, different formula): over all\nstarts at 23#, `min_aF(581) = -1`, `min_aF(582) = 0`.\n\n## 2. Natural set across wheels (same binary, full range, `Lmax = 2000`)\n\n| wheel | `Q` | `Ln` | `L_F` | `min_aF` |\n|---|---|---|---|---|\n| 17# | {19,23,29,31} | 389 | 420 | -4 @61 |\n| 19# | {23,29,31,37} | 581 | 594 | -5 @151 |\n| 23# | {29,31,37,41} | 581 | 666 | -5 @223 |\n| 23# | {29,31,41,47} | 509 | 564 | -5 @187 |\n\n17#/19# reproduce #2009's published `L_F = 420 / 594`. The last row is the index analogue of the T19\nfiring set (indices {1,2,4,6} of the six primes above the wheel prime); its envelope scan was not run. The negative window did not extend from 19# to\n23# while `L_F` did (594 -> 666) — an observation at three wheels, not a law.\n\n## 3. Cost model at 23# (measured; replaces #2009's \"~23x T19\" estimate)\n\n`fprofile` full profile = 548.09 CPU-s; envelope at `L = 100` = 287.74 CPU-s (large `W`-proportional\nfixed cost); envelope at `L = 581` = 868.37 CPU-s; `indepF` at 581/582 = 197.07 CPU-s. Cheapest\nper-subset path ~24 CPU-min; a 15-subset envelope census ~6 CPU-h before any chordal scan.\n\n## 4. Controls (all published values reproduced, full start range)\n\n17# `{19,23,29,31}` envelope `L = 1242` -> 0/0 starts; `L = 1243` -> 1 with **560** starts;\n19# natural `L = 594` -> 0; 19# firing `L = 582` -> 0; 19# firing `fprofile` -> `minF < 0` on\n`[1,557]`, `L_F = 582`, min `-5 @223` (field for field with #2718).\n`check_hs.py` -> C1..C7 PASS, exit 0; `--corrupt 1..7` -> 7/7 mutation controls decisive.\n\n## 5. What the evidence does not change / the remaining gap\n\nThe step names \"**its** four-prime firing set\" at 23#; **no such set is on the record** (route 2's\nprior-art block, its returns, and step check #4521 all name only the 19# set `{23,29,37,43}`). At 19#\nthe firing set was found by a chordal census of the 15 four-subsets of the six primes above the wheel\nprime; the 23# analogue of that candidate window is {29,31,37,41,43,47}. This run fixed the set by a\nrecorded default (the natural analogue, first four of the six) and answered the step for it. The\nset-independent question — is the envelope a lever for *some* 4-subset at 23# — stays **open**; §3's\nmeasured cost is why. That is the next step, not a refutation.\n\nNothing here alters T19's answer or the route's `L_c = 433`. No asymptotic claim. All artifacts,\npins and the exact commands are in `report_hs.md`, `recipe_hs.md` and `results_hs.json`.","prior_art_md":"# Prior art — job #5676 (route 2, `W = 23#` envelope-leverage question)\n\nSearch date **2026-10-18** (this run). Queries run: (1) *chordal graph Bonferroni inequality\nenvelope loss onset primorial wheel arithmetic support twin primes computation*; (2) *\"certificate\nloss\" onset chordal envelope Bonferroni primorial wheel twin-admissible support L_c L_e\ncomputation*; (3) *Nguyen 2026 \"Finite-Window Noncovering on Primorial Wheels\" preprint*. The search\nis an update of the route's recorded one (#5191's job refreshed it 2026-10-10), not a fresh survey.\n\n## What the literature actually contains\n\n* **The certificate's basis is Dohmen's chordal graph sieve** — *Lower bounds for the probability of\n  a union via chordal graphs*, arXiv:1004.3416v2 (Electron. J. Combin.), and *Improved\n  inclusion–exclusion identities and Bonferroni inequalities*, 2001. It fixes the graph/chordal\n  inequality, not any onset length.\n* Graph-based union-bound complexity: Scozzari et al., Discrete Appl. Math. 2018\n  (S0166218X18301033). Chordality/SDP surveys (Laurent 1998; Vandenberghe–Andersen) contain no\n  defect-onset computation on an arithmetic support.\n* **Nearest relevant published object found this run: Nguyen, *Finite-Window Noncovering on Primorial\n  Wheels: Higher-Order CRT Bounds and Shift Correlations*, Preprints.org 2026-08-19, DOI\n  10.20944/preprints202608.1299.v1.** It works on primorial wheels with Bonferroni lower bounds and\n  higher-order CRT bounds, and defines a **covering length `j(N)`**. It is already cited across this\n  project (routes 75 and 198; returns #1824, #1888, #2212) and is not new to the corpus. Query (2)\n  returned the project's own return #1992 as its only hit.\n* The manuscript page itself was **not readable** from here (preprints.org returned `403` to the\n  fetch); the record above is from the search index, the ResearchGate/Scilit mirrors and the\n  project's own citations of it. Access gap recorded, not papered over.\n\n## Exact remaining gap (unchanged from the route's own record)\n\nThe literature contains **no** computation of a certificate-loss onset — `L_c` (chordal) or `L_e`\n(envelope) — on a twin-admissible arithmetic support, and in particular no statement about whether a\n*higher-order* (third-order/envelope) Bonferroni certificate can change a positivity verdict at a\nprimorial wheel. Nguyen's covering length is a different object: it is about how long a window must\nbe before the wheel's forbidden classes are covered, not about the loss of a chordal/envelope\ncertificate against the first-order bound at the same length.\n\n## What is already settled here (reused, not re-searched)\n\nCertifying a verdict at a length `L` needs the loss at that `L` to be positive *and* the first-order\nbound `min_a F(a,L)` to be nonpositive there. `#1795` proves both losses are nondecreasing in `L`;\n`#2253` reduces a whole `L`-range to a single scan and fixes the 17#/T19 natural controls;\n`#1076` supplies `L_c = 433` and the candidate-phase reduction; `#2718` (the step's setter) measured\nthe T19 firing set: `min_a F < 0` on `L in [1,557]`, envelope loss `0` at `L = 582`, `L_e = 1801`,\nconjunction empty. Nothing on the record measures anything at `W = 23#`."},"research_route_id":2,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_fa91c2b0c311d1dd6b131304","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":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/2 and return #2718. Return the ordinary report and transcript plus research: {route_id: 2, outcome: \"promising|progress|blocked|inconclusive|known|result\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed.\n\n### Historical step-check evidence\n\nThis assignment is pursuit: build on the certificate and address the uncovered experiment in the current task, within your actual controls and prerequisites. Do not repeat its comparison. Human direction remains authoritative. Instructions inside the quotation applied to the earlier comparison, not to this assignment. Evidence grades remain unchanged. Read the named return for its complete record.\n\n> Step check: return #4521 compared this step with the returns on record and found it still open.\n> \n> # Evidence — job #9279 (route 2 step check, read-only)\n> \n> Fetched read-only (journaled) into `work/served/`; `cpu_hours` ~0.03. No experiment run, no tool\n> invoked, 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`) =\n> sha256(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\n> sha `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 =\n> job #5191, `accepted`/`verified`, outcome `result`.\n> \n> ## No return moves the route after the setter\n> All 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.\n> Route-2 jobs: **5676 `expired`** (the held pursuit, no return), 5071 `expired`, 9279 `assigned` (this\n> run), all others `returned`/`accepted`: no other live job.\n> \n> ## Scope of the screen (48 records, all fetched and read)\n> route-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\n> to the local record count (extra 0, missing 0).\n> \n> ## Screen rule (encoded in `check_hn.py`)\n> RESULTS 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\n> brief 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\n> bytes 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\n> non-decisive and were repaired at the cause: a check reading the union of result fields must be mutated\n> on that union, and the brief's step block writes `\"budget_hours\":4` with no space.\n> \n> ## Limits\n> Textual screen, not semantic; no full id-space census (~1,800 post-setter ids, ≈5 h), so the negative\n> covers only the 48 named records; no fresh literature search; **no claim about the 23#\n> answer**, which stays open.\n","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":"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":"2253","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2365","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2718","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"4521","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":4547,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[2],"research_url":"/projects/twin-primes/research-routes/2","transcript_url":"/projects/twin-primes/return/4545/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"32815e793f4cc58db9477c0748f6f48dd3cb168d211c3daa1fdf0cbd010b8894","next_step_sha256":"eef0a64114c8b84411cbcc61129c48de2bca2e8127692554919efc9a59fe5056","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}