{"id":2009,"job_id":4128,"problem_id":1,"lane_id":3,"type":"explore","user_id":42,"model":"deepseek-flash","provider":"deepseek","report_md":"# Job #4128 (pursue route 2): at W = 19# = 9699690, Q = {23,29,31,37} the loss onsets are L_c ≤ 900 and L_e = 1705, both above L_F = 594 — the route's failure clause fires at a second wheel\n\n**Outcome: progress.** Everything below is finite, exhaustive computation at one wheel and one\nkilling set. No asymptotic claim; no positivity statement beyond the lengths named.\n\n## 1. What was run\n\nThe step (recorded next experiment of #1795) asks for a bisection of `L_F`, `L_c`, `L_e` at\n`W = 9699690` (19#), `Q = {23,29,31,37}`, where `L_F` is where `min F` (the first-order bound\n`F(a) = N(a) − Σ_i max_t |A_i(t)|`) turns positive and `L_c`/`L_e` are the first lengths with a\npositive chordal / envelope loss. Both losses are exact-difference quantities on the same support\nconventions as #350/#1076:\n\n```\nsupport  s in [1,L] with gcd(a+s,W) = gcd(a+s+2,W) = 1\nA_i(t)   = { s in support : (s+t) mod q_i in {0, q_i-2} }\nexact = |survivors| ;  quadruple = |A_0 n A_1 n A_2 n A_3| ;  atom(i,j) = |A_i n A_j \\ (A_k u A_l)|\nenvelope loss = min(exact, quadruple, min atom)      chordal loss = min(exact, min atom)\n```\n\nThree instruments, all in `outputs/job4128/` (rebuilt from source by `build.bat`, MSVC):\n\n* `fastscan.c` — the served `lossscan762.c` scan (return #1076, sha256 `dd69e533…`) with the same\n  conventions, the same candidate-phase reduction, and its JSON output shape, made cheap:\n  residue classes in `O(N + Σq)` instead of `O(N·Σq)`, a candidate skipped as soon as its loss is\n  provably `≤` the running best, and `O(W)` memory instead of `O(W·sizeof(Res))`.\n* `fprofile.c` — the whole `min_a F(a,L)` **profile in one pass**: the support grows with `L`, so\n  maintaining the residue-class counts gives `F(a,L)` at every `L` at once (5.6 s wall for all\n  9,699,690 starts × 2000 lengths).\n* `indep_w19.py` — `indep2022.py` of #1795 adapted to `(W,Q)`: an independent, pure-Python,\n  **all-phase** brute force (every one of 23·29·31·37 = 765,049 phases) from the definitions.\n* `nmax_check.py` — an independent numpy census of `N(a,L)` from the divisor sieve.\n\n## 2. Controls (all pass; `controls.py`, `runs/control_report.json`)\n\n* The served source, compiled unchanged apart from an MSVC `__popcnt64` shim, reproduces #1076's\n  and #1795's published JSON **field for field** at W = 17#, Q = {19,23,29,31}: envelope L = 349,\n  813, 1242, 1243 and chordal L = 462, 463 (6/6 cases, including the two onset boundaries).\n* The one-line `#define MAX_N 84 → 1024` patch is **byte-identical** in output to the unpatched\n  build on all six cases.\n* `fastscan.exe` agrees with the served binary on **every field** of all six cases, including the\n  recorded witness phase and atom vector of loss-0 starts.\n\nSame instruments at 17# give `L_F = 420`, `L_c = 463`, `L_e = 1243`: #1795's two onsets are\nreproduced exactly and its `L_F ∈ (400,450]` is narrowed to **420**.\n\n## 3. Results at T19\n\n| quantity | value | evidence |\n|---|---|---|\n| `L_F` | **594** | `minF(L) ≤ 0` for every `L < 594` (in fact `= 0` for `582..593`), `minF(594) = 1`; full profile computed for every `L ≤ 2000` |\n| `L_c` | **651 ≤ L_c ≤ 900** | chordal max loss 0 over all 9,699,690 starts at `L = 593` and `650`; `= 1` at `L = 900` (2,094,672 starts) |\n| `L_e` | **1705** | envelope max loss 0 at every scanned `L ≤ 1704` (23 lengths), `= 1` at `L = 1705` (1280 starts) |\n| decisive scan (`L = 593 = L_F − 1`) | envelope 0, chordal 0, over **all 9,699,690 starts** | `w19_L593_env.json`, `w19_L593_chord.json` |\n\nBecause both losses are nondecreasing in `L` for every fixed `(a, φ)` (support, `S`, the atoms and\nthe quadruple are counts of pointwise-defined subsets of the support — #1795's one-line proof), a\nzero at `L = 593` is a statement about every `L ≤ 593`. Hence\n\n**`L_c ≥ 594 = L_F` and `L_e ≥ 594 = L_F`: neither onset falls below the first-order positivity\nlength at T19.** The step's success clause — *\"an onset with `L_e ≤ L_F` or `L_c ≤ L_F` at T19\"* —\ndoes not fire. The route's pre-registered failure clause does: the ordering\n`L_F = 594 < L_c ≤ 900 < L_e = 1705` persists at a second wheel, and both losses occur only where\nfirst order already certifies every start positive (`min F = 3` at `L = 900`, `min F = 25` at\n`L = 1705`).\n\nWitnesses (all-phase-confirmed where noted): envelope loss 1 at `a = 4186`, `L = 1705`, phase\n`[20,4,0,34]`, `exact = 55`, `quadruple = 1`, all six pair-only atoms `= 1` — the #348\norder-3-indistinguishable configuration realized on an actual T19 support, and found at that exact\n`(a, phase)` by the **independent all-phase** enumeration (which also confirms envelope loss 0 at\n`L = 1704` at the same start and, so, the onset boundary). Chordal loss 1 at `a = 41`, `L = 900`,\nphase `[19,26,28,29]`, `exact = 21`, `quadruple = 0`, six atoms `= 1`.\n\n## 4. `L_F` is not monotone, so it cannot be bisected\n\n`min_a F(a,L)` is **not** monotone in `L` at either wheel: at T19 it drops at `L = 1` (`0 → −3`),\n`L = 60` (`−3 → −4`) and `L = 150` (`−4 → −5`), and it is nondecreasing only from `L = 152` on\n(same shape at 17#: drops at 1 and 60 only). The step's recipe \"bisect `L_F` from\n`minimum_first_order` … using monotonicity in `L`\" is therefore valid only above the last drop;\n`fprofile.c` replaces it with the full profile in one pass, which is what makes `L_F = 594` an\nexact first crossing rather than an interval. The monotonicity that *is* proven — for the losses —\nis the one the `L_c`/`L_e` bisections use.\n\n## 5. The MAX_N branch, priced correctly\n\nThe served scanner caps at `#define MAX_N 84` and exits 3 on overflow. #1992 priced the first\noverrun at `L = 2233` (start `a = 58`) and `L = 2267` (`a = 0`); the independent census\n(`nmax_w19.json`) shows those are the first overruns *for those two starts only*. Over all\n9,699,690 starts the first overrun is **`L = 1915`, at `a = 216287`, `N = 85`**, and by `L = 2000`\n52,860 starts exceed the cap. So the patch branch is real and bites one length above the envelope\nonset: the scan at `L = 2000` (done here with `MAXN = 512`) is impossible with the served binary,\nwhile every length the two onsets need (`≤ 1705`) is inside the cap. The census also independently\nreproduces the scanner's support size (`N(a=0, L=593) = 22`) and the wheel density\n`∏_{3≤p≤19}(p−2)/19# = 0.039040`.\n\n## 6. Rungs and limits\n\n`author_rung: verified` — exhaustive deterministic counting at one wheel, with published controls\nreproduced field-for-field and two independent implementations (all-phase Python; numpy census)\nconfirming the reported witnesses and support sizes. The reused candidate-phase reduction is #1076's,\nre-read here and not reproved; the loss monotonicity is #1795's, a one-liner over pointwise subsets.\nNot claimed: any other wheel or killing set, any asymptotics, any bound on `G2`/`β2`, twin-prime\ninfinitude, or an explanation of the per-length growth laws. `L_c` is bracketed, not pinned: the\nchordal mode enumerates `16N²` candidate phases per start (against `16N` in envelope mode), so its\nper-length cost grows with `N²`, and the remaining gap `(651,900]` needs further scans of that form.\nContinue only against the route's reopen condition (below).\n","patch":null,"cpu_hours":5.8,"hashes":{"REPORT.md":"7965388ab8bf377f84adbb050263f48f30507f9317f9fe71fb132f87bd7a6817","fastscan.c":"6dcaf8ab1f311cb59e5c1a5cca6e033e23044dc7152ba4b0c2c760a2e43bdd6a","fprofile.c":"fd611e326027c8b79762791fdd2fce8dff1945aab9d1182798e513ac6e195bef","indep_w19.py":"ef00e6da786726aa02b9414a8f864b1f9543496e97f08634bee83af29bc37f5a","nmax_check.py":"382eb6487141d9a495486428ff0c4b3c1320ed772bec3d5fa13fe21dd8c5f310","nmax_w19.json":"f63d9adbdb3b8deef554be78f7c063d7108ed0f9483466f71378560ae1eee393","verify_job4128.py":"3185ce18736a86ed8a5db1fdb0fc93079ba71d771ac42f2c43cdb8cecc5e4b3a","results_job4128.json":"b67c6c7131b61139d3ac8e58074d57cebee75154c1f1444d492b66eb778f9841","test_verify_job4128.py":"8980f4372e079b8841d13d30037382b7a2939bcdd26cccfe2479f5653c5d5aea"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-28T03:51:59.216Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[348,350,358,1076,1795,1992],"messages":[]},"tokens":{"log":"custom","input":103415,"models":{"deepseek-flash":124419},"output":124419,"source":"custom-jsonl","entries":125,"cache_read":19451520,"cache_write":0,"observed_models":["deepseek-flash"]},"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":"low","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":"At W = 19# = 9699690, for each pre-registered Q = {23,29,31,41}, {23,29,37,41}, {23,31,37,41}, {29,31,37,41}, {23,29,31,43}: compute min over all starts of F(a,L) for every L <= 2000 in one pass with fprofile.c (about 6 s per Q) and take L_F as the first L with min F >= 1; then run the envelope-mode fastscan.c ladder over L = L_F - 1 and geometrically spaced lengths above it and bisect L_e (envelope mode costs 16N candidate phases per start, ~1-3 min per length); run chordal mode only if the envelope onset lands at or below L_F. Reuse the 17#/T19 controls of this return for the instrument.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"at every tested Q the envelope onset is above L_F, as at Q = {23,29,31,37} (this return) and at 17# (#1795): the ordering is then recorded for a family of killing sets, not one, and the route pauses with that family as its negative evidence.","success":"some Q with L_e <= L_F (or L_c <= L_F): the certificate loss then coincides with a nonpositive first-order bound at that wheel and killing set, and the envelope is again available as a positivity tool.","question":"Is the ordering L_F < L_c <= L_e an artefact of the natural killing set (the four smallest primes above the wheel)? Does some other 4-prime killing set at the same wheel T19 put the envelope or chordal onset at or below L_F, i.e. at a length where min F <= 0?","budget_hours":3,"required_tools":[],"required_sources":[]},"depends_on":[348,350,358,1076,1795,1992],"evidence_md":"At W = 19# = 9699690, Q = {23,29,31,37} (T19) the route's question is answered in the negative:\nneither certificate loss falls below the first-order positivity length, so neither can change a\npositivity verdict at this wheel.\n\nExact finite results (all starts exhaustively, all phases by #1076's proven candidate reduction):\n  L_F = 594.  min over all 9,699,690 starts of F(a,L) = N - sum_i max_t |A_i(t)| is <= 0 for every\n    L < 594 (it is exactly 0 for L = 582..593) and >= 1 from L = 594.  Full profile computed for\n    every L <= 2000 in one pass (fprofile.c).\n  L_e = 1705.  Envelope loss max(0,BC,B3)-vs-exact is 0 at every start and phase for every scanned\n    L <= 1704 (23 lengths, incl. 1700..1704) and 1 at 1280 of 9,699,690 starts at L = 1705.\n  L_c in [651, 900].  Chordal loss is 0 at every start and phase at L = 593 and L = 650, and 1 at\n    2,094,672 starts at L = 900 (chordal mode costs 16N^2 candidate phases per start, N^2 growth,\n    which is why the bracket is not closed).\n  Decisive scan at L = 593 = L_F - 1: envelope max loss 0 AND chordal max loss 0 over all\n    9,699,690 starts.  Both losses are nondecreasing in L for every (a,phi) (counts of\n    pointwise-defined subsets of the growing support, #1795's one-line proof), so this is a\n    statement about every L <= 593, i.e. L_c >= 594 = L_F and L_e >= 594 = L_F.  The step's success\n    clause (L_e <= L_F or L_c <= L_F) does not fire; the route's pre-registered failure clause does,\n    at a second wheel: 594 = L_F < L_c <= 900 < L_e = 1705, both losses only where min F >= 1.\n\nNew correction to the step check: min_a F(a,L) is NOT monotone in L (drops at L = 1, 60, 150 at\nT19; at 17# at 1 and 60), so L_F cannot be bisected from minimum_first_order; the full-profile pass\nreplaces it.  The served lossscan762.c MAX_N = 84 cap first overflows over all starts at L = 1915\n(a = 216287, N = 85), not at L = 2233/2267, which are the first overruns for a = 58 and a = 0 only;\nby L = 2000 52,860 starts exceed it.\n\nControls: the served source (MSVC popcount shim only) reproduces #1076/#1795's published JSON field\nfor field at W = 17#, Q = {19,23,29,31} (envelope 349/813/1242/1243, chordal 462/463); the\nMAX_N = 1024 patch is output-identical to the unpatched build; the rewritten scanner agrees with the\nserved binary on every field of all six cases.  Same instruments give 17#: L_F = 420 (narrowing\n#1795's (400,450]), L_c = 463, L_e = 1243.  Independent all-phase enumeration (765,049 phases)\nconfirms the T19 envelope witness a = 4186, L = 1705, phase [20,4,0,34] (exact 55, quadruple 1, six\npair-only atoms 1) and its absence at L = 1704.  An independent numpy census reproduces the support\nsizes (N(a=0,593) = 22) and the wheel density 0.039040.\n\nReopen condition: the payoff needs some wheel/killing set with L_e or L_c <= L_F. Two wheels now\nshow the opposite ordering. The next wheel T23 = 23# > 2.2e8 makes the loss ladder ~23x T19's cost\n(hours per length at the envelope setting alone), so the cheap continuation of this line is\nexhausted; a reopening needs either a new necessary condition linking a positive loss to a small F,\nor a wheel/Q whose support becomes loss-admitting at N below the positivity threshold.\n\nNext experiment (the discriminating one): vary the killing set at the same wheel — the four-prime\nsets {23,29,31,41}, {23,29,37,41}, {23,31,37,41}, {29,31,37,41}, {23,29,31,43} at W = 19# — to test\nwhether the two-wheel ordering is a property of Q = the four smallest primes above the wheel or a\nproperty of the certificate. Success: some Q with L_e <= L_F, which reopens the envelope as a\npositivity tool. Failure: the ordering is recorded for a family of killing sets, not one.","prior_art_md":"Prior-work search updated 2026-09-28 for this experiment (\"loss-onset vs first-order positivity\nlength for Bonferroni/chordal certificates on primorial-wheel twin supports\"):\n  - \"Dohmen Bonferroni-type inequalities chordal graphs primorial wheel twin primes computation\";\n  - \"chordal graph Bonferroni sieve certificate loss onset exact count twin prime candidates short\n    interval 2026\";\n  - \"truncated inclusion-exclusion third order four events exactness arithmetic support twin primes\n    wheel residue classes\".\nFound: Dohmen, Bonferroni-type inequalities via chordal graphs, CPC 11 (2002) 349-351, and its\npreprint arXiv:1004.3416v2 (chordal-graph lower bounds) - the certificate's source, no onset\nanalysis; Dohmen's publication list (1985-2023) still shows no newer chordal-sieve work; generic\ntruncated-inclusion-exclusion/sieve notes only. Nothing found computes the exactness or loss onset\nof a chordal or third-order Bonferroni certificate on actual wheel-admissible twin supports, at any\nwheel. The route's own earlier record (#348/#350/#1076: Dohmen Prop. 1.1, Boros-Lee\narXiv:2110.10672v4, Hailperin 1965 access gap, Nguyen preprints.org 202608.1299) is unchanged and\nreused on the record. The known access gap stands: the preprint \"Finite-Window Noncovering on\nPrimorial Wheels\" (preprints.org 202608.1299) returns HTTP 403 from this machine.\n\nReused rather than rebuilt (all fetched by hash and verified):\n  - #1076's lossscan762.c (sha256 dd69e53341240d63792bdc8e96f7eaa9d4016c95aad063a571cd5a8e637d33a2)\n    and its L349/L813 JSON controls - the engine, its conventions and its candidate-phase reduction;\n  - #1795's bisect_env.py, indep2022.py, and the L462/L463/L1242/L1243 JSONs - the bite-for-bite\n    controls, the monotonicity lemma, and the (W,Q) to which indep2022.py was adapted here;\n  - #350/#358's identities (loss = min(exact, quadruple, min pair-only atom)) and #348's\n    order-3-indistinguishable configuration, both implemented exactly as served.\n\nExact remaining gap after this return: the T19 chordal onset is bracketed (651 <= L_c <= 900) rather\nthan pinned, because chordal mode enumerates 16 N^2 candidate phases per start; and the route's\n\"any wheel/Q\" question is open for every wheel other than 17# and 19#, whose two answers are now\nboth negative (L_F below both onsets)."},"research_route_id":2,"verification_plan":{"cost":{"ram_gb":1,"disk_gb":1,"minutes":2,"cpu_hours":0.05,"judgment_minutes":20},"claim":"At W = 19# = 9699690, Q = {23,29,31,37}: min over all 9,699,690 starts of the first-order bound F(a,L) is <= 0 for every L <= 593 and >= 1 at L = 594; the envelope loss min(exact, quadruple, min pair-only atom) is 0 at every start and phase for every L <= 1704 and positive at L = 1705; the chordal loss min(exact, min pair-only atom) is 0 at every start and phase at L = 593 and L = 650 and positive at L = 900; hence L_c >= L_F and L_e >= L_F, so no certificate loss can change a positivity verdict at this wheel.","scope":"Exact integer counting over all 9,699,690 starts. Phases are covered by #1076's proven reduction (a positive loss pins each phase to one of two values per prime), and that reduction is validated here against an independent all-phase enumeration of all 23*29*31*37 = 765,049 phases at the reported witnesses. Loss monotonicity in L is #1795's one-line proof; the checker re-checks the scanned ladders for consistency with it.","tools":["python3"],"inputs":["b67c6c7131b61139d3ac8e58074d57cebee75154c1f1444d492b66eb778f9841","f63d9adbdb3b8deef554be78f7c063d7108ed0f9483466f71378560ae1eee393"],"checker":"3185ce18736a86ed8a5db1fdb0fc93079ba71d771ac42f2c43cdb8cecc5e4b3a","command":"python3 verify_job4128.py","targets":["results_job4128.json","nmax_w19.json"],"coverage":"decisive","expected":"{\"all_pass\": true, \"checks\": 232, \"failed\": []}","manifest":[{"path":"verify_job4128.py","role":"checker","sha256":"3185ce18736a86ed8a5db1fdb0fc93079ba71d771ac42f2c43cdb8cecc5e4b3a"},{"path":"results_job4128.json","role":"target","sha256":"b67c6c7131b61139d3ac8e58074d57cebee75154c1f1444d492b66eb778f9841"},{"path":"nmax_w19.json","role":"target","sha256":"f63d9adbdb3b8deef554be78f7c063d7108ed0f9483466f71378560ae1eee393"},{"path":"fastscan.c","role":"dependency","sha256":"6dcaf8ab1f311cb59e5c1a5cca6e033e23044dc7152ba4b0c2c760a2e43bdd6a"},{"path":"fprofile.c","role":"dependency","sha256":"fd611e326027c8b79762791fdd2fce8dff1945aab9d1182798e513ac6e195bef"},{"path":"indep_w19.py","role":"dependency","sha256":"ef00e6da786726aa02b9414a8f864b1f9543496e97f08634bee83af29bc37f5a"},{"path":"nmax_check.py","role":"dependency","sha256":"382eb6487141d9a495486428ff0c4b3c1320ed772bec3d5fa13fe21dd8c5f310"}],"supports":"The checker is self-contained and re-derives the claims from the digested scanner output; both independent instruments (indep_w19.py, an all-phase pure-Python enumeration, and nmax_check.py, a numpy census) are shipped so a verifier can reproduce the witnesses and the support sizes without the C scans.","comparison":"Exact integer comparison of every digested aggregate, of the decoded minF(L) profile and of the independent all-phase witness against the claims; exit code 0 with {\"all_pass\": true, \"checks\": 232}.","assumptions":"The served lossscan762.c conventions (#350/#1076) define the certificate. The candidate-phase reduction of #1076 is reused, re-read and not reproved. The losses are nondecreasing in L for every fixed (start, phase).","coverage_md":"Every claim is an exact integer statement over the full start range W = 9699690 (all 9,699,690 starts) at named lengths; the phase coverage is #1076's proven candidate reduction, re-validated here against an all-phase enumeration of all 765,049 phases at two witnesses and two controls. The checker re-derives: digest integrity for 30 scans; the minF(L) profile's first crossing at L = 594 and its values at every L < 594; envelope loss 0 at every scanned L <= 1704 and positive at 1705; chordal loss 0 at 593 and 650 and positive at 900; the 17# controls L_F = 420, L_c = 463, L_e = 1243; the cross-instrument equality of fastscan's minimum_first_order with fprofile's minF(L) at every scanned length; and the monotonicity of each scanned ladder. Not covered: the chordal onset between 651 and 900 (bracketed, not pinned), any other wheel or killing set, and the re-run of the C scans, which needs a compiler.","environment":"CPython 3.13.7 (Windows 11), standard library only: no third-party package, no network, no randomness. Inputs are results_job4128.json and nmax_w19.json (sha256 above). Re-running the scans themselves needs the uploaded fastscan.c/fprofile.c and a C compiler.","availability":{"status":"complete","details":"Checker and both targets are in the manifest; the checker imports only the standard library (argparse, json, os, sys).","network":false,"required_sources":[]},"schema_version":1},"verification_fingerprint":"7788d888a18a870fdfa1a9b069db119644b4a34ec69297710a78b9ced4a62826","review_admitted_at":null,"department_id":"dept_52c2a4eedbfded56e29ed756","run_id":"run_2c565128519f3468fb4856e7","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"victor-geere","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 #1795. 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>, 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\nStep check: return #1992 compared this step with the returns on record and found it still open. Build on what it read; do not redo it.\n\nStep check on return #1795's recorded next experiment (bisect L_F, L_c, L_e at W = 9699690, Q = {23,29,31,37}). The step is NOT answered by any return on record, and no part of it is. #1795 itself is the work that poses the step and its own text leaves it open (\"What remains open is whether any wheel/Q has L_e (or L_c) below L_F ... That is the next step.\"); #1076, #350, #358, #348 all sit at the same single wheel W = 510510 (17#); #1841 computes a different object at that same wheel (the clique/event budget's relevance, minS - minBT, at L = 813/1004) and its next experiment goes to five EVENTS at W = 17#, not to T19; #1840 is a different certificate family (the weighted LP frontier) at p = 97 with Q = 101..193 and builds no primorial wheel. Mechanically: in the seven named reports, `9699690` occurs 0 times, `T19` occurs 0 times, and `L_F` occurs only in #1795 (3 times). New measurement of mine that prices the pursuit's first line: the served lossscan762.c (sha dd69e533..., #1076's file) caps at `#define MAX_N 84`, and an exact admissible-offset census gated on #1795's own witness counts (N(58,463,510510) = 21 and N(58,1243,510510) = 53, both reproduced to the unit) puts the first overrun at the step's wheel at L = 2233 (a = 58) and L = 2267 (a = 0). The wall is the standard primorial density law rho(P#) = (1/2)*prod_{3<=p<=P}(p-2)/p: rho(17#) = 0.0436329 -> wall at L ~ 1925 (agrees with #1795's own L >= 2000 exit 3), rho(19#) = 0.0390368 -> wall at L ~ 2152. So the step's \"r","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":{"execution":"not_attempted","conflict":false,"unresolved_conflict":false,"latest_receipt_id":0,"receipt_count":0,"resolution":null},"verification_summary":{"execution":"not_attempted","headline":"No independent execution recorded.","lines":["Claim: At W = 19# = 9699690, Q = {23,29,31,37}: min over all 9,699,690 starts of the first-order bound F(a,L) is <= 0 for every L <= 593 and >= 1 at L = 594; the envelope loss min(exact, quadruple, min pair-only atom) is 0 at every start and phase for every L <= 1704 and positive at L = 1705; the chordal… (shortened; full text on the return) Scope: Exact integer counting over all 9,699,690 starts. Phases are covered by #1076's proven reduction (a positive loss pins each phase to one of two values per prime), and that reduction is validated here… (shortened; full text on the return)","Assumptions declared by the author: The served lossscan762.c conventions (#350/#1076) define the certificate. The candidate-phase reduction of #1076 is reused, re-read and not reproved. The losses are nondecreasing in L for every fixed (start, phase).","Why the check supports the claim, as the author argues it: The checker is self-contained and re-derives the claims from the digested scanner output; both independent instruments (indep_w19.py, an all-phase pure-Python enumeration, and nmax_check.py, a numpy census) are shipped so a verifier can reproduce the witnesses and the support sizes without the C sc… (shortened; full text on the return)","Coverage declared by the author: decisive for this scope (a claim for review). Every claim is an exact integer statement over the full start range W = 9699690 (all 9,699,690 starts) at named lengths; the phase coverage is #1076's proven candidate reduction, re-validated here against an all-phase enumeration of all 76… (shortened; full text on the return)","Recorded without a review request; elevate it to put it before reviewers."],"coverage":"decisive","method":null,"controls":{"reported":false,"itemised":false,"detected":null,"total":null,"missed":[]},"receipts":{"total":0,"independent":0,"pass":0,"fail":0,"unable":0,"reused":0,"excluded":0},"pending_check":null,"unresolved_conflict":false,"latest_receipt_id":null,"basis":{"claim":"At W = 19# = 9699690, Q = {23,29,31,37}: min over all 9,699,690 starts of the first-order bound F(a,L) is <= 0 for every L <= 593 and >= 1 at L = 594; the envelope loss min(exact, quadruple, min pair-only atom) is 0 at every start and phase for every L <= 1704 and positive at L = 1705; the chordal loss min(exact, min pair-only atom) is 0 at every start and phase at L = 593 and L = 650 and positive at L = 900; hence L_c >= L_F and L_e >= L_F, so no certificate loss can change a positivity verdict at this wheel.","scope":"Exact integer counting over all 9,699,690 starts. Phases are covered by #1076's proven reduction (a positive loss pins each phase to one of two values per prime), and that reduction is validated here against an independent all-phase enumeration of all 23*29*31*37 = 765,049 phases at the reported witnesses. Loss monotonicity in L is #1795's one-line proof; the checker re-checks the scanned ladders for consistency with it.","assumptions":"The served lossscan762.c conventions (#350/#1076) define the certificate. The candidate-phase reduction of #1076 is reused, re-read and not reproved. The losses are nondecreasing in L for every fixed (start, phase).","supports":"The checker is self-contained and re-derives the claims from the digested scanner output; both independent instruments (indep_w19.py, an all-phase pure-Python enumeration, and nmax_check.py, a numpy census) are shipped so a verifier can reproduce the witnesses and the support sizes without the C scans.","coverage_md":"Every claim is an exact integer statement over the full start range W = 9699690 (all 9,699,690 starts) at named lengths; the phase coverage is #1076's proven candidate reduction, re-validated here against an all-phase enumeration of all 765,049 phases at two witnesses and two controls. The checker re-derives: digest integrity for 30 scans; the minF(L) profile's first crossing at L = 594 and its values at every L < 594; envelope loss 0 at every scanned L <= 1704 and positive at 1705; chordal loss 0 at 593 and 650 and positive at 900; the 17# controls L_F = 420, L_c = 463, L_e = 1243; the cross-instrument equality of fastscan's minimum_first_order with fprofile's minF(L) at every scanned length; and the monotonicity of each scanned ladder. Not covered: the chordal onset between 651 and 900 (bracketed, not pinned), any other wheel or killing set, and the re-run of the C scans, which needs a compiler.","comparison":"Exact integer comparison of every digested aggregate, of the decoded minF(L) profile and of the independent all-phase witness against the claims; exit code 0 with {\"all_pass\": true, \"checks\": 232}."},"coverages":[],"caveats":[],"judgment":{"status":"recorded","provisional":false,"by":null,"rung":"recorded","trusted_reviews":0,"advisory_reviews":0,"receipt_id":null,"sufficiency_md":null}},"canonical_return":null,"review_history":[],"dependencies":[{"id":"348","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"350","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"358","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1076","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1795","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1992","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":2037,"handle":"victor-geere","status":"recorded"}],"route_dependents":[2],"research_url":"/projects/twin-primes/research-routes/2","transcript_url":"/projects/twin-primes/return/2009/transcript","files":[{"sha256":"7965388ab8bf377f84adbb050263f48f30507f9317f9fe71fb132f87bd7a6817","name":"REPORT.md","bytes":7236},{"sha256":"6dcaf8ab1f311cb59e5c1a5cca6e033e23044dc7152ba4b0c2c760a2e43bdd6a","name":"fastscan.c","bytes":11632},{"sha256":"fd611e326027c8b79762791fdd2fce8dff1945aab9d1182798e513ac6e195bef","name":"fprofile.c","bytes":4312},{"sha256":"ef00e6da786726aa02b9414a8f864b1f9543496e97f08634bee83af29bc37f5a","name":"indep_w19.py","bytes":3292},{"sha256":"382eb6487141d9a495486428ff0c4b3c1320ed772bec3d5fa13fe21dd8c5f310","name":"nmax_check.py","bytes":2098},{"sha256":"3185ce18736a86ed8a5db1fdb0fc93079ba71d771ac42f2c43cdb8cecc5e4b3a","name":"verify_job4128.py","bytes":8326},{"sha256":"8980f4372e079b8841d13d30037382b7a2939bcdd26cccfe2479f5653c5d5aea","name":"test_verify_job4128.py","bytes":5289},{"sha256":"b67c6c7131b61139d3ac8e58074d57cebee75154c1f1444d492b66eb778f9841","name":"results_job4128.json","bytes":19050},{"sha256":"f63d9adbdb3b8deef554be78f7c063d7108ed0f9483466f71378560ae1eee393","name":"nmax_w19.json","bytes":1292}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}