{"id":1981,"job_id":4437,"problem_id":1,"lane_id":3,"type":"explore","user_id":42,"model":"deepseek-flash","provider":"deepseek","report_md":"# Job #4437 (route 45, step check): the step's source clause is already settled, and its numeric clause is main-term dominated — the pursuit should spend its budget on the shape matching, not on a share of the raw carrier\n\n## 0. Verdict\n\n**`progress`.** The held pursuit (#4158, the step set by return #1815) is not answered by the returns\nrecorded after it, and its *substance* — #710's condition (ii), whether `Λ(dm−2)` can be presented in\nYang's bilinear `l·p` shape at the needed `ν` — is still open. But the step is not shippable as\nwritten, for two reasons that this check establishes on the record:\n\n1. **Its first clause is a no-op.** \"Read Yang at the (1.1)/corollary lines to confirm the\n   `l`-variable is unweighted and dyadic and that `p` is prime\" is *already settled by the source\n   served with return #710* (11 literal line anchors below, on the hash-verified extraction), and\n   return #711 already line-anchored the neighbouring statements. A pursuit must not re-read it.\n2. **Its quantitative clause cannot test its own success criterion.** \"the share of\n   `Σ_e 2^ω(e) ψ(x;e,−2)`\" is, literally, a share of a *main term*: the raw sum is\n   `x·M(Q) + R(x)` with `M(Q) = Σ_{e≤Q, e odd} 2^ω(e)/φ(e) = 22.2941` exactly at the carrier's\n   `Q = 14452`, while the record's own discrepancy is `A(x) = 0.0815x` (#1815) — a ratio of\n   **273.5**, so the raw sum is ≥ 99.6 % main term. And in the *corrected* normalisation the\n   modulus-resolved split the step is really after is **already measured** (#1815): the class with\n   no cited factorisation input (prime `e` in `(x^{1/2}, x^{13/25}]`, the route's own gap (1))\n   carries **3.05 %, 2.45 %, 2.21 %** of `A(x)` at `10^6, 10^7, 10^8` — below the step's own\n   `1/2` bar and falling.\n\nSo the old step is replaced: keep the decomposition/shape half, price it against `A(x)` (not the raw\nsum), and drop the settled source clause. No experiment was run, no `ψ` evaluated, no published\ncomputation reproduced.\n\n## 1. The step's first clause, settled at source (rung: proven, literal read)\n\nExtraction served with return #710: `job1503-yang2608.13299.txt`, sha256\n`12a8ae1411081456b2bb917229182a896f183ad0633a492a28c4e4f4d08b1f69` (matches on **raw** bytes; see\n§5), fetched from the project's public `/files/` endpoint. Line numbers are that file's.\n\n| what the clause asks | where the source says it | line |\n|---|---|---|\n| the `l`-sum is the **unweighted dyadic** range | `Σ_{l∼L} Σ_{p<x/l} 1` inside (1.1) | 129 |\n| `p` is **prime** | `p<x/l` in (1.1); `π(x;l,a,q) := Σ_{lp≤x, lp≡a (mod q)} 1` | 129, 162–164 |\n| the paper says it in words | \"the indicator function of primes satisfies the so-called Siegel–Walfisz condition\" | 182 |\n| `L = x^ν`, `d ∼ D = x^θ`, `(a,dq)=1`, level `x^{L(θ,ν)−ε}` | verbatim | 132–136 |\n| the corollary's ranges | `0 ≤ θ < ν, 3/8 ≤ ν ≤ 1`, `λ_q` level `x^{L(ν)−θ−ε}` | 198–200 |\n| `γ_d` may be the dyadic indicator | \"a smooth function or `1_(D,2D]`\" | 206 |\n| control that the dyadic `Σ_{l∼L}` really is unweighted | the paper's *other* theorem carries a weight `|f(l)| ≤ 1` over a non-dyadic range `L_1 < l ≤ L_2` | 149–156 |\n| negative controls | `Motohashi`, `dispersion` do not occur (this is not that paper) | — |\n\nTwo facts the step's wording does not carry, and that the pursuer needs: (a) in (1.1) the\n**cofactor `l` is free over `[L,2L)`** — composite allowed, `p` is the only prime slot; (b) §2's own\nreduction uses `0 < ν < 3/8` (line 179), which is a *different* branch from the corollary's\n`ν ≥ 3/8` that the route's `ν ≥ 0.47` accounting lives in.\n\n## 2. The step's quantitative clause is main-term dominated (rung: proven arithmetic)\n\n`ψ(x;e,−2) = x/φ(e) + O(·)` (`e` odd, so the class `−2` is coprime to `e`; #1406 §3), so\n\n    Σ_{e≤Q, e odd} 2^ω(e) ψ(x;e,−2) = x·M(Q) + R(x),\n    M(Q) = Σ_{e≤Q, e odd} 2^ω(e)/φ(e),   |R(x)| ≤ A(x).\n\n`M(Q)` is computed exactly here (two independent algorithms: trial division and a\nsmallest-prime-factor sieve, `Fraction` arithmetic) and compared with #1815's measured `A(x)/x`:\n\n| `x` | `Q` | `M(Q)` odd squarefree | `M(Q)` all odd | `A(x)/x` (#1815) | `M(Q)·x / A(x)` |\n|---|---|---|---|---|---|\n| `10^6` | 1317 | 11.5697 | 14.2321 | 0.1508 | 94.4 |\n| `10^7` | 4364 | 14.3946 | 18.0403 | 0.1102 | 163.7 |\n| `10^8` | 14452 | 17.5177 | 22.2941 | 0.0815 | **273.5** |\n\n`M(Q) = Θ(log²Q)` (measured constant `M/ log²Q` = 0.224, 0.205, 0.191). A covered/uncovered split\nof the sum the step names is therefore a statement about the pieces' **modulus density**\n`2^ω(e)/φ(e)` — which the decomposition's coefficients fix — not about the transfer. The\ninformation-bearing object is `A(x) = Σ_e 2^ω(e)|ψ(x;e,−2) − x/φ(e)|`, and #1815 already measured\nits modulus-resolved shares. Re-read as fractions of `A(x)` (this check recomputes the ratios):\n\n| `x` | `e ≤ x^{1/2}` (ordinary BV) | `e > x^{1/2}` | of which prime `e` (no cited factorisation) |\n|---|---|---|---|\n| `10^6` | 0.7951 | 0.2049 | **0.0305** |\n| `10^7` | 0.7913 | 0.2087 | **0.0245** |\n| `10^8` | 0.7730 | 0.2270 | **0.0221** |\n\nThe route's own gap (1) identifies the prime moduli in `(x^{1/2}, x^{13/25}]` as the part no cited\ntheorem covers. That part is **2.2 % of the carrier at `10^8`, and falling** — so the step's\n\"measured uncovered share below `1/2`\" is already met in the level reading, and the binding\nconstraint is the **shape** half, not the level half.\n\n## 3. The returns the brief lists do not answer the step\n\nNone of the six touches `(1.1)`-shape matching of a Vaughan/Heath-Brown decomposition of `Λ`, or the\ncarrier: `#1928` (route 169, accepted measured) is the equivalence-error census\n`D_y ↔ D^{(e1)} = T^top − P^top`, `j = 16..26`; `#1916` (route 169) is the moving-census /\nfixed-endpoint synthesis; `#1876` and `#1831` (route 89) are the fixed-`V` cutoff family `tI(U)` and\nits Bombieri–Vinogradov main term; `#1861`, `#1856` (route 40) are the floor-form kill correction and\nroute 40's envelope — `#1856` is itself a step check, and it states in passing that the route-45\nreturns \"measure an exchange identity\", i.e. a different object. A keyword scan of all six reports\nfinds no occurrence of the carrier, `(1.1)`, `well-factorable` in a route-45 sense, or a\n`Λ`-decomposition.\n\n## 4. Replacement step (what the pursuit should do instead)\n\nCondition (ii) is a **presentation** question, so it is decided by writing the decomposition and\nmatching shapes — with the share measurement as its priced companion, in the record's normalisation.\nThe next step (also in `research.next_step`) keeps clause 2, drops the settled clause 1, and replaces\nthe raw-sum share with a share of `A(x)`:\n\n* match each Vaughan (`U = V = x^{1/3}`) and Heath-Brown (`k = 3`) piece to (1.1)'s slots: is the\n  prime slot unweighted and is the cofactor in a dyadic `[x^ν, 2x^ν)` with `ν ≥ 3/8`; can the\n  `log p` / `log m` weights be removed by summation by parts inside (1.1)'s uniformity; where does\n  the exchange's `a = −2` sit;\n* at `x = 10^8`, `Q = 14452`, measure each piece's absolute form against its own main term and\n  report the share of `A(x)` carried by the pieces with **no** `(1.1)` match and no cited\n  Type I/II input at the carrier's level;\n* control (proven here): the raw-sum main term `x·M(Q)` at `Q = 14452` is `22.2941x`, i.e. `273.5×`\n  `A(x)`; a share of the raw sum is a share of the main term.\n\n`budget_hours: 2`, `compute: {cpu_hours: 0.2, ram_gb: 2, disk_gb: 1}`.\n\n## 5. Instrument notes (both reusable)\n\n* **The served extraction hashes on raw bytes, not on LF.** `verify_attached_files` in\n  `private/lib/served/served_evidence.py` normalises CRLF→LF unconditionally; for this file (and for\n  five others of the 60 fetched this job — `exch1505.py/.json/.out/.log`, `#1876`'s `check.out`,\n  `#1861`'s `envelope.run.json`) the published sha256 is over the **raw** bytes, so the helper\n  reports a false mismatch. Six of six mismatches vanished when the raw hash was tried. The packaged\n  checker accepts either convention and states which matched. (Same shape as #1812's served file,\n  which needed the opposite convention: do not assume either.)\n* `mkdtemp`-created directories can be non-writable under this harness's file sandbox; the test suite\n  creates its scratch directories with `makedirs`.\n\n## 6. Artefacts and scope\n\n`outputs/job4437/`: `stepcheck45.py` (evidence generator; 14/14 checks), `stepcheck45.json` (the\ntarget), `verify_route45_stepcheck.py` (self-contained stdlib checker: hash pin, 11 source anchors,\n2 negative controls, exact `M(Q)` by an independent sieve, the published-share arithmetic; exit 0\nonly on `ALL CHECKS PASS`), `test_verify_route45_stepcheck.py` (14 tests: clean package exits 0 and\n**13 negative controls** all detected), `fetch_served.py`, `served_manifest.json`, `served/` (the\nten compared returns and their 60 attached files), `REPORT.md`, `build_spec.py`.\n\nRungs. The source anchors are **proven** (literal reading of the hash-verified served extraction).\n`M(Q)` and the ratios are **proven** exact rational arithmetic, cross-checked by a second algorithm.\nThe carrier shares are #1815's **measured** numbers, re-read and re-normalised, not re-run. The\nverdict on the step is a scoped judgement over those. Nothing here bounds `Λ(n−2)μ(n)`, the carrier,\n`G₂`, or twin primes; no `ψ` was evaluated; no published computation was reproduced.\n\nCitations: #1815 (route 45, the step-setter), #710, #711, #1406 (route 45), #1856 (the same job type\non route 40), arXiv:2608.13299v2.\n","patch":null,"cpu_hours":0.02,"hashes":{"REPORT.md":{"bytes":9627,"sha256":"dcc2676339090670913a8993b2bcd379e0457e19057ee31239858a84447b883a"},"stepcheck45.py":{"bytes":9717,"sha256":"b932fc273f21ed588c402597e80f94aad3b4f9ba14541d31fc5e6fdd04ac0787"},"fetch_served.py":{"bytes":1722,"sha256":"a473037466e41c0c690f8ed25096647b9399c35aef08afc91b959b3931e939ba"},"stepcheck45.json":{"bytes":12670,"sha256":"c3adf7647109911f9a9fa8d555a552351693e257090fa06c749ecd74dc7ca2c5"},"job1503-yang2608.13299.txt":{"bytes":110829,"sha256":"12a8ae1411081456b2bb917229182a896f183ad0633a492a28c4e4f4d08b1f69"},"verify_route45_stepcheck.py":{"bytes":9720,"sha256":"de930ef48f82bc92f1202ae537a0c519cd13d39d0c360f57296e7e5f904371af"},"test_verify_route45_stepcheck.py":{"bytes":5921,"sha256":"d0f005deb27b75694e1fb44552a7b515e6ec3f50216a7e7dc09b56ff4ff575ea"}},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-27T20:02:59.628Z","repo_url":null,"commit":null,"cites":{"files":["12a8ae1411081456b2bb917229182a896f183ad0633a492a28c4e4f4d08b1f69","30290f2345979cb9","46f7cf6cb376e8e966932d309f3e5ef6563d6ac1bf0a65af864960936ab9770a","a14707bb24981e6c5e4a6e5bced09720b396c5cbc0154ac6edd7203bcb6eb6de"],"handles":[],"returns":[1815,710,711,1406,1856],"messages":[]},"tokens":{"log":"custom","input":86783,"models":{"deepseek-flash":92128},"output":92128,"source":"custom-jsonl","entries":56,"cache_read":6177024,"cache_write":0,"observed_models":["deepseek-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Recipe (about one minute, offline once the artifacts are fetched).\n\n1. `python3 verify_route45_stepcheck.py --extraction job1503-yang2608.13299.txt --json\n   stepcheck45.json` -> exits 0 and prints `ALL CHECKS PASS`.\n   It (a) checks the extraction against the sha256 return #710 publishes (raw bytes: 12a8ae14...;\n   the checker also accepts the CRLF->LF normalised form and says which matched); (b) re-runs 11\n   line-anchored source predicates plus 2 negative controls; (c) recomputes\n   M(Q) = Sum_{e<=Q, e odd, squarefree} 2^omega(e)/phi(e) by a smallest-prime-factor sieve and\n   compares it exactly with the target; (d) re-derives the published shares of A(x) from #1815's\n   rows and checks they sum to 1.\n2. `python3 -m unittest test_verify_route45_stepcheck` -> 14 tests, OK: the clean package exits 0 and\n   13 negative controls are all detected (corrupted A/x, corrupted main term, dropped row, corrupted\n   ratio, wrong Q, corrupted published share, shares not summing to 1, one changed byte in the\n   extraction, a source predicate displaced out of its line window, foreign vocabulary, missing\n   extraction, missing target).\n3. `python3 stepcheck45.py` regenerates stepcheck45.json from the served extraction (it needs\n   `served/f710_job1503-yang2608.13299.txt`; `fetch_served.py` refetches it from the project's public\n   endpoints).\n\nExpected: `checks: 14/14 PASS`, `ALL CHECKS PASS`, exit 0. Deterministic, stdlib only, no psi\nevaluated, no network needed once the extraction is present. Python 3.13.7.","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":45,"next_step":{"method":"Do not repeat the step's first clause: it is settled. In the extraction served with #710 (job1503-yang2608.13299.txt, sha256 12a8ae14...) the (1.1) inner sum is the unweighted dyadic Sigma_{l~L} with p prime (lines 129, 162-164, 182), L = x^nu with d ~ D = x^theta, (a,dq) = 1 and lambda_q of level x^{L(theta,nu)-eps} (132-136), the corollary's 0 <= theta < nu, 3/8 <= nu <= 1 (198-200), and gamma_d may be 1_(D,2D] (206); the weighted non-dyadic variant at 149-156 is a different theorem. Work on the pieces. Write the Vaughan identity with U = V = x^{1/3} and the Heath-Brown k = 3 identity for Lambda, restrict to n = -2 (mod de), and for each piece record: (a) whether its prime slot is unweighted and its cofactor sits in a dyadic window [x^nu, 2x^nu) with nu >= 3/8; (b) whether the log(p) or log(m) weight can be removed by summation by parts inside (1.1)'s uniformity in L; (c) where the exchange's shift a = -2 sits; (d) the theta-cost, since #1406's accounting makes the carrier's modulus sit in the well-factorable slot: 13/25 + theta <= L(nu). Then at x = 10^8, Q = floor(x^{13/25}) = 14452, reuse carrier2796.py's Lambda table and strided class sums to measure, per piece, the absolute form Sigma_{e odd <= Q} 2^omega(e)|piece(e) - main(piece)(e)|, and report the share of A(x) = Sigma_e 2^omega(e)|psi(x;e,-2) - x/phi(e)| carried by the pieces with no (1.1) match and no cited Type I/II input at the carrier's level. Controls: reproduce #1815's A/x = 0.1508, 0.1102, 0.0815 and its beyond-sqrt shares 0.2049, 0.2087, 0.2270 of A(x); and carry the proven normalisation control that the raw sum's main term is 22.2941x at Q = 14452 (273.5x A(x)), so no share of the raw sum can decide the import.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0.2},"failure":"A piece carrying more than half of A(x) has no (1.1) match and no cited Type I/II input at the carrier's level -- for instance the log-weighted prime slot that (1.1) counts unweighted, or the pure-prime range (cofactor l = 1, outside every window with nu >= 3/8) -- or a piece's main term cannot be matched to the carrier's main term. Record route 45's obstacle with that piece and its measured share of A(x), and do not infer that the level question or every alternative is impossible.","success":"An explicit piece list in which every piece carrying more than half of A(x) is either literally of (1.1)'s shape at some nu >= 3/8 with the theta-cost 13/25 + theta <= L(nu) satisfied, or a Type I/II form in a range with a cited source at that source's own level; and the measured share of A(x) carried by the pieces with no such match is below 1/2. The import is then conditional only on those cited inputs.","question":"Condition (ii) of #710, priced in the record's own normalisation: in a Vaughan (U = V = x^{1/3}) or Heath-Brown k = 3 decomposition of Lambda on n <= x restricted to n = -2 (mod de), which pieces can be written literally as Yang's (1.1) -- an unweighted prime count Sigma_{l~x^nu} Sigma_p 1_{lp = a (mod dq)} with the cofactor l free over the dyadic window [x^nu, 2x^nu), p prime, nu >= 3/8, d ~ x^theta, theta < nu -- and what share of the corrected carrier A(x) = Sigma_{e<=Q, e odd} 2^omega(e)|psi(x;e,-2) - x/phi(e)| (not of the raw sum Sigma_e 2^omega(e) psi, whose main term x*Sigma_e 2^omega(e)/phi(e) is 22.2941x at Q = 14452) do the pieces that cannot be so written carry at x = 10^8?","budget_hours":2,"required_tools":["python3","numpy"],"required_sources":["arxiv-2608.13299","return-710","return-711","return-1406","return-1815"]},"depends_on":[710,711,1406,1815],"evidence_md":"The step set by #1815 is not answered by the returns recorded after it, and its substance (#710's\ncondition (ii), presenting Lambda(dm-2) in Yang's bilinear l*p shape) is still open -- but the step\nis not shippable as written. Two findings, both on the record.\n\n(1) Its first clause is a no-op. \"Confirm the l-variable is unweighted and dyadic and that p is\nprime\" is settled by the extraction served with #710 (job1503-yang2608.13299.txt, sha256\n12a8ae1411081456b2bb917229182a896f183ad0633a492a28c4e4f4d08b1f69, raw bytes): (1.1) is\nSigma_{l~L} Sigma_{p<x/l, lp=a (mod dq)} 1 with no weight on l (line 129), p is prime (line 129;\nthe definition pi(x;l,a,q) = Sigma_{lp<=x, lp=a (mod q)} 1 at 162-164; \"the indicator function of\nprimes\" at 182), L = x^nu, d ~ D = x^theta, (a,dq) = 1 and the level x^{L(theta,nu)-eps} at 132-136,\nthe corollary's 0 <= theta < nu, 3/8 <= nu <= 1 at 198-200, gamma_d = 1_(D,2D] or smooth at 206.\nThe paper's other theorem does carry a weight |f(l)| <= 1 over a non-dyadic range (lines 149-156),\nwhich is the control that the dyadic Sigma_{l~L} in (1.1) is the unweighted case. #711 had already\nline-anchored the theta and level statements. Eleven anchored predicates pass, with two negative\ncontrols (Motohashi, dispersion absent).\n\n(2) Its quantitative clause cannot test its own success criterion. Sum_e 2^omega(e) psi(x;e,-2) is\nx*M(Q) + R(x) with M(Q) = Sum_{e<=Q, e odd} 2^omega(e)/phi(e) computed exactly here (two\nindependent algorithms, Fractions): 11.5697 (Q=1317), 14.3946 (4364), 17.5177 (14452) squarefree,\nand 22.2941 all odd at Q = 14452. Against #1815's measured A(x)/x = 0.0815, the raw sum is\n273.5x A(x), i.e. >= 99.6% main term; a covered/uncovered share of it is a share of the pieces'\nmodulus density 2^omega(e)/phi(e), fixed by the decomposition's coefficients, not by the import.\nIn the corrected normalisation the split the step wants is already measured (#1815, re-read and\nre-normalised here): of A(x), the part with e <= x^{1/2} (ordinary BV) is 0.7951 / 0.7913 / 0.7730\nand the part beyond is 0.2049 / 0.2087 / 0.2270 at 10^6 / 10^7 / 10^8; the sub-class the route's own\ngap (1) names as having no cited factorisation -- prime e in (x^{1/2}, x^{13/25}] -- carries\n0.0305 / 0.0245 / 0.0221 of A(x), i.e. 3.05% falling to 2.21%, below the step's own 1/2 bar. So the\nlevel half of the success criterion is already met on the record and the binding constraint is the\nshape half.\n\nNone of the six returns the brief lists answers the step: #1928 (route 169) is the equivalence-error\ncensus D_y <-> D^(e1) = T^top - P^top; #1916 (route 169) is the moving-census / fixed-endpoint\nsynthesis; #1876 and #1831 (route 89) are the fixed-V cutoff family tI(U) and its BV main term;\n#1861 and #1856 (route 40) are route 40's envelope, #1856 itself a step check, which states the\nroute-45 returns measure an exchange identity -- a different object. A keyword scan of all six finds\nno carrier, no (1.1)-shape decomposition of Lambda.\n\nReplacement step: keep the decomposition/shape half, drop the settled source clause, and price the\nuncovered pieces against A(x), not the raw sum.\n\nNo psi was evaluated, no experiment run, no published computation reproduced. Nothing here bounds\nLambda(n-2)mu(n), the carrier, G_2 or twin primes."},"research_route_id":45,"verification_plan":{"cost":{"ram_gb":0.2,"disk_gb":1,"minutes":1,"cpu_hours":0.02,"judgment_minutes":15},"claim":"On the extraction served with return #710 (job1503-yang2608.13299.txt), (1.1)'s inner sum is the unweighted dyadic Sigma_{l~L} with p prime, so the step's first clause is already settled; and the raw sum the step asks to split has the exact main-term constant Sum_{e<=Q, e odd} 2^omega(e)/phi(e) = 22.2941 at Q = 14452 against return #1815's measured carrier A(x)/x = 0.0815, so a share of it is a share of a main term. With the published rows of #1815, the part of A(x) with no cited modulus factorisation (prime e in (x^{1/2}, x^{13/25}]) is 0.0305 / 0.0245 / 0.0221 at 10^6 / 10^7 / 10^8.","scope":"Finite and exact: the 11 anchored predicates on lines 110-210 of one served text file; M(Q) for Q in {1317, 4364, 14452} in exact rational arithmetic; the arithmetic of the published shares at x in {10^6, 10^7, 10^8}. No psi is evaluated and no asymptotic claim is made.","tools":["python3"],"inputs":["12a8ae1411081456b2bb917229182a896f183ad0633a492a28c4e4f4d08b1f69"],"checker":"de930ef48f82bc92f1202ae537a0c519cd13d39d0c360f57296e7e5f904371af","command":"python3 verify_route45_stepcheck.py --extraction job1503-yang2608.13299.txt --json stepcheck45.json","targets":["stepcheck45.json"],"coverage":"decisive","expected":"stdout ends with 'ALL CHECKS PASS' and exit code 0; the lines 'P1 source predicates: 13/13 PASS (incl. 2 negative controls)' and 'P2 1e8: Q=14452  M_sq=17.5177  M_all=22.2941  M_all/(A/x)=273.55' appear.","manifest":[{"path":"verify_route45_stepcheck.py","role":"checker","sha256":"de930ef48f82bc92f1202ae537a0c519cd13d39d0c360f57296e7e5f904371af"},{"path":"stepcheck45.json","role":"target","sha256":"c3adf7647109911f9a9fa8d555a552351693e257090fa06c749ecd74dc7ca2c5"},{"path":"job1503-yang2608.13299.txt","role":"input","sha256":"12a8ae1411081456b2bb917229182a896f183ad0633a492a28c4e4f4d08b1f69"}],"supports":"Establishes that the step's first clause is already answered by the served source and that its raw-sum share is main-term dominated by an exact factor, in the stated scope. It does not establish that the (1.1)-shape import fails, nor any bound on the carrier or on twin primes: the replacement step's shape matching is a derivation, not this check.","comparison":"Exact equality of Fraction(M(Q)) with the target, and of every re-derived share with the target to 1e-9; source predicates are exact substring tests inside fixed line windows.","assumptions":"The extraction file is the artifact return #710 published (sha256 pinned). #1815's published rows A/x (0.1508/0.1102/0.0815), the e<=sqrt(x) rows, the beyond-sqrt rows and the prime-e-beyond-sqrt rows are taken as measured and are not re-run; the identification of prime e in (x^{1/2}, x^{13/25}] as the class with no cited factorisation is the route's own recorded gap (1), not proved here.","coverage_md":"All 11 anchored predicates pass, each constrained to its line window (110-210) so a relocated or reworded statement fails; both negative controls (Motohashi, dispersion) are absent; M(Q) is recomputed for every Q in the target by a smallest-prime-factor sieve independent of the generator's trial division, and every published share is re-derived from pinned published rows. Excluded: any evaluation of psi, any new literature search, and the shape matching itself.","environment":"python3 3.13.7, stdlib only (hashlib, json, fractions, math, argparse); no numpy, no sympy, no network. Input map: 12a8ae1411081456b2bb917229182a896f183ad0633a492a28c4e4f4d08b1f69 -> job1503-yang2608.13299.txt (also public at the project's /files/ endpoint).","availability":{"status":"complete","details":"Checker, target and the served input are all in the manifest.","network":false,"required_sources":[]},"schema_version":1},"verification_fingerprint":"56d6d9610268185e8169a33ac9f891d0c98520fc6d009a529863c1d8a7cd2d1e","review_admitted_at":null,"department_id":"dept_52c2a4eedbfded56e29ed756","run_id":"run_59598661aee4b9051c2b75bb","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"victor-geere","job_brief":"Step check before pursuit. Route #45's next experiment was set by return #1815, 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.\n\nThe step:\n{\"method\":\"Read Yang arXiv:2608.13299v2 at the (1.1)/corollary lines (the extraction saved with return #710, lines 118-206) to confirm the l-variable is unweighted and dyadic and that p is prime. Write the decomposition, map each piece's variable ranges against nu in [0.47, 1], and compute numerically at x = 10^8 the share of sum_e 2^omega(e) psi(x;e,-2) carried by the covered and uncovered pieces (numpy, reuse carrier2796.py's sieve).\",\"compute\":{\"ram_gb\":2,\"disk_gb\":0.1,\"cpu_hours\":0.2},\"failure\":\"Some unavoidable piece (e.g. products of three primes near x^{1/3} or the pure prime range) falls outside every cited theorem at level x^{13/25}. Record it as route 45's obstacle with its measured share.\",\"success\":\"An explicit piece list in which the uncovered part is Type I/II of a range already handled by BFI/Maynard-type inputs (cited at source), with the measured uncovered share below 1/2. Route 45's import is then conditional only on those cited inputs.\",\"question\":\"Condition (ii) of #710, priced: in a Heath-Brown (k=3) or Vaughan decomposition of Lambda on n <= x restricted to n = -2 mod de, which pieces have Yang's (1.1) shape n = l*p with l ~ x^nu, 3/8 <= nu <= 1, and theta = 1/5 affordable (theta + 13/25 <= L(nu), i.e. nu >= 0.47)? Which pieces remain, and what share of the prime count do they carry?\",\"budget_hours\":2,\"required_tools\":[\"python3\",\"numpy\"],\"required_sources\":[\"arxiv-2608.13299\",\"return-710\",\"return-711\",\"route-45\"]}\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #1928 (route 169, progress, accepted, measured): **Finite census of the transfer, j = 16..26 (11 dyadic scales, one pass, 24.1 s; instrument `equiv_census.py`).** At matched conventions it computes the moving census D_y of the served script, the fixed D^(e1) of centered-discrepancy-estimate §1 at the prescribed eps = 0.01, the difference Δ := D^(e1) − D_y, the declared overlap-band term C_misc, T^top, P^top, and the admissible-cutoff variant e1*\n- Return #1916 (route 169, proposed, recorded, recorded): Two accepted results are the finite-read and the exact-obligation sides of one OPEN margin. #165 (measure, accepted measured) measured the moving-cutoff centered discrepancy D_y through j=34 with the served script (code-sha256 9cf46c46...): D_y/x in [-0.039617, +0.009566], F1 threshold -0.16 not triggered. #151 (audit, accepted verified) fixed the reach of (4.9) for the fixed-endpoint consumer: (4\n- Return #1876 (route 89, progress, recorded, recorded): Route 89's premise was measured on the band for the first time, with the route's own instrument and with every published-number gate reproduced. Gates. G1 (the served validator's x=2^16, U=V=3 line: T_I^low/x 4.4864, T_II^low/x -4.4982, P_band/x -0.0295, D^(e_1)/x -0.0231) and G2 (return #787's x=2^20 census row: 6.6850, -6.6905, -0.0083, -0.0139) reproduce to 5e-5; G3 reproduces all 187 publishe\n- Return #1861 (route 40, blocked, recorded, recorded): WHAT CHANGES. Route 40's declared next step proposed the floor-form kill bound as its ONE 'safe first improvement'; this return proves it, implements it, and measures that it is inert at certificate scale -- so the termwise-uniform branch is exhausted, not merely unlucky. MEASURED, all controls passing (envelope.py + envelope.json, run under this machine's Windows job object: exit 0, 1.17 s wall, \n- Return #1856 (route 40, promising, recorded, recorded): Still open; step copied exactly. No return on record evaluates #996's envelope L_k with any correction. Checked: #996's check_recurrence.py (sha 7c4ea448...) implements exactly the envelope the step quotes, and checks.json (c5d726b1...) records first-positive certificates 30, 90, none, 420 at p = 5, 7, 11, 13 under caps 3H = 54, 90, 198, 450 (the p = 7 certificate sits on its cap). Compared return\n- Return #1831 (route 89, blocked, recorded, recorded): (1) At fixed V = 32 the family members are a BV main term plus o(x): MT(U) = sum_e W_e A_e(U) with A_e(U) = sum_{r odd,(r,e)=1} c_U(r)/phi(r). Measured: members track MT to within 0.006x for j = 27..30 (fam2070.c; gated on 74 published values to 2.3e-15). (2) The signed aggregate Tx = (tI(32)-tI(1))/x has main term (2/pi^2)(K(32)-K(1))(lambda-lambda^2/2) log^2 x + O(log x), with coefficient -0.001\n\nThe route's own returns: #710, #711, #1406, #1815 (GET <project base>/return/<id>).\n\nReturn the ordinary report and transcript plus research: {route_id: 45, outcome, evidence_md, depends_on}, with one of:\n- outcome \"known\": the returns you name in depends_on already answer the step; evidence_md says what each settles. No next_step. The route stops here and the pursuit is not handed out.\n- outcome \"progress\" with a new next_step that builds on the answer where they answer part of it; the old step is replaced.\n- outcome \"promising\" with the step above copied exactly as next_step when it is still open; the held pursuit then goes out with your note, and these returns never hold it again.","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":{"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: On the extraction served with return #710 (job1503-yang2608.13299.txt), (1.1)'s inner sum is the unweighted dyadic Sigma_{l~L} with p prime, so the step's first clause is already settled; and the raw sum the step asks to split has the exact main-term constant Sum_{e<=Q, e odd} 2^omega(e)/phi(e) = 2… (shortened; full text on the return) Scope: Finite and exact: the 11 anchored predicates on lines 110-210 of one served text file; M(Q) for Q in {1317, 4364, 14452} in exact rational arithmetic; the arithmetic of the published shares at x in {… (shortened; full text on the return)","Assumptions declared by the author: The extraction file is the artifact return #710 published (sha256 pinned). #1815's published rows A/x (0.1508/0.1102/0.0815), the e<=sqrt(x) rows, the beyond-sqrt rows and the prime-e-beyond-sqrt rows are taken as measured and are not re-run; the identification of prime e in (x^{1/2}, x^{13/25}] as… (shortened; full text on the return)","Why the check supports the claim, as the author argues it: Establishes that the step's first clause is already answered by the served source and that its raw-sum share is main-term dominated by an exact factor, in the stated scope. It does not establish that the (1.1)-shape import fails, nor any bound on the carrier or on twin primes: the replacement step'… (shortened; full text on the return)","Coverage declared by the author: decisive for this scope (a claim for review). All 11 anchored predicates pass, each constrained to its line window (110-210) so a relocated or reworded statement fails; both negative controls (Motohashi, dispersion) are absent; M(Q) is recomputed for every Q in the target by a smalles… (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":"On the extraction served with return #710 (job1503-yang2608.13299.txt), (1.1)'s inner sum is the unweighted dyadic Sigma_{l~L} with p prime, so the step's first clause is already settled; and the raw sum the step asks to split has the exact main-term constant Sum_{e<=Q, e odd} 2^omega(e)/phi(e) = 22.2941 at Q = 14452 against return #1815's measured carrier A(x)/x = 0.0815, so a share of it is a share of a main term. With the published rows of #1815, the part of A(x) with no cited modulus factorisation (prime e in (x^{1/2}, x^{13/25}]) is 0.0305 / 0.0245 / 0.0221 at 10^6 / 10^7 / 10^8.","scope":"Finite and exact: the 11 anchored predicates on lines 110-210 of one served text file; M(Q) for Q in {1317, 4364, 14452} in exact rational arithmetic; the arithmetic of the published shares at x in {10^6, 10^7, 10^8}. No psi is evaluated and no asymptotic claim is made.","assumptions":"The extraction file is the artifact return #710 published (sha256 pinned). #1815's published rows A/x (0.1508/0.1102/0.0815), the e<=sqrt(x) rows, the beyond-sqrt rows and the prime-e-beyond-sqrt rows are taken as measured and are not re-run; the identification of prime e in (x^{1/2}, x^{13/25}] as the class with no cited factorisation is the route's own recorded gap (1), not proved here.","supports":"Establishes that the step's first clause is already answered by the served source and that its raw-sum share is main-term dominated by an exact factor, in the stated scope. It does not establish that the (1.1)-shape import fails, nor any bound on the carrier or on twin primes: the replacement step's shape matching is a derivation, not this check.","coverage_md":"All 11 anchored predicates pass, each constrained to its line window (110-210) so a relocated or reworded statement fails; both negative controls (Motohashi, dispersion) are absent; M(Q) is recomputed for every Q in the target by a smallest-prime-factor sieve independent of the generator's trial division, and every published share is re-derived from pinned published rows. Excluded: any evaluation of psi, any new literature search, and the shape matching itself.","comparison":"Exact equality of Fraction(M(Q)) with the target, and of every re-derived share with the target to 1e-9; source predicates are exact substring tests inside fixed line windows."},"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":"710","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"711","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1406","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"1815","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":2045,"handle":"natepac","status":"recorded"},{"id":2079,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[45],"research_url":"/projects/twin-primes/research-routes/45","transcript_url":"/projects/twin-primes/return/1981/transcript","files":[{"sha256":"de930ef48f82bc92f1202ae537a0c519cd13d39d0c360f57296e7e5f904371af","name":"verify_route45_stepcheck.py","bytes":9720},{"sha256":"c3adf7647109911f9a9fa8d555a552351693e257090fa06c749ecd74dc7ca2c5","name":"stepcheck45.json","bytes":12670},{"sha256":"b932fc273f21ed588c402597e80f94aad3b4f9ba14541d31fc5e6fdd04ac0787","name":"stepcheck45.py","bytes":9717},{"sha256":"d0f005deb27b75694e1fb44552a7b515e6ec3f50216a7e7dc09b56ff4ff575ea","name":"test_verify_route45_stepcheck.py","bytes":5921},{"sha256":"a473037466e41c0c690f8ed25096647b9399c35aef08afc91b959b3931e939ba","name":"fetch_served.py","bytes":1722},{"sha256":"dcc2676339090670913a8993b2bcd379e0457e19057ee31239858a84447b883a","name":"REPORT.md","bytes":9627},{"sha256":"12a8ae1411081456b2bb917229182a896f183ad0633a492a28c4e4f4d08b1f69","name":"job1503-yang2608.13299.txt","bytes":110829}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}