{"id":1978,"job_id":4430,"problem_id":1,"lane_id":3,"type":"explore","user_id":42,"model":"deepseek-flash","provider":"deepseek","report_md":"# Job #4430 — route 36 step check: the held pursuit's step is not answered by the returns on record\n\n**Outcome: `promising`; the step is copied exactly as `next_step`.** Calibration: **measured** — a\nscoped read of the served record plus a bounded prior-art read. No new mathematics is claimed here,\nnothing in this return bears on Proposition 6, and the twin-prime problem is untouched.\n\n## 1. The comparison, and why neither `known` nor `progress`\n\nThe step was set by return **#1787** (route 36, accepted, rung proven). The returns recorded after it\nthat the brief lists for comparison are all on other routes and all concern other documents:\n\n| return | route | what it actually decides | does it touch this step? |\n|---|---|---|---|\n| #1928 (accepted, measured) | 169 | finite census of the moving cutoff `D_y` against the fixed `D^(e1)` of `centered-discrepancy-estimate.md` §1, j = 16..26, with the overlap-band term | no |\n| #1916 (recorded, conjectured) | 169 | cross-lane synthesis joining #165 and #151 for route 169's fixed-endpoint margin | no |\n| #1881 (recorded, proven) | 115 | step check on `fixed-endpoint-discrepancy.md`: `m2 <= A*` for `c_0 <= 1/200` | no |\n| #1828 (pending, verified) | 128 | served-note registry repair for #83/#153; no mathematical status | no |\n| #1819 (recorded, measured) | 131 | platform mirror-cut behaviour and revision attribution | no |\n\nNone is on route 36, and none reads `fold-arithmetic-bridge.md` §2, the level-θ pricing, or the\nconditional-twin literature. Their only shared premise with route 36 is the project's parity\nvocabulary. The route's own returns (**#659** proposed, **#661** triage, **#1787** result) are the\nreturns that *set* the step; they fix parts of its setup (section 2) but not its three deliverables:\n\n* **(a)** the level-θ re-derivation of `Pi`, `P'_odd`, Proposition 3 and Proposition 4 is not on the\n  record. #1787's own scope line says its level-θ rows \"use hypothetical inputs\".\n* **(b)** no directed rational certificate exists. #1787 §3 is a float grid; the step asks for exact\n  directed bounds at one rational cell.\n* **(c)** the route's prior-art record (returns #659/#661/#1787 and their attached search logs,\n  jobs 1453/1457) contains none of the locators found in section 3 — the machine check `I` scans for\n  them and finds none.\n\nSo the step is open, and the correct return is `promising` with the step copied verbatim.\n\n## 2. What the route's own record already fixes — do not redo it\n\n* **Identity (#1787 §1, proven; re-read exactly here).** `F_1(u) = 2e^γ ρ_odd(u)/u` and\n  `f_1(u) = 2e^γ ρ_even(u)/u`. The initial data of the two delay systems agree:\n  `u e^-γ F_1(u)/2 = 1 = D_1 = ρ_odd` on `[1,3]`, and `u e^-γ f_1(u)/2 = log(u-1) = D_2 = ρ_even` on\n  `[2,3]` (`D_2` from the served recursion `D_k(u) = ∫_{k-1}^{u-1} D_{k-1}(v) dv/v`). All nine sympy\n  checks in `sympy_step36.py` pass.\n* **The contamination constant.** `s F(s) e^-γ = 2` identically on `s <= 3`, so\n  `c_eff(θ) = 2/θ`: `4` at `θ = 1/2` (Proposition 4, reproduced) and `2` at `θ = 1`. This is #1787's\n  `G3` field, re-read exactly.\n* **The θ-grid (#1787 §3, measured).** At `θ = 1` the test `f_1(θu)^2 ρ/(F_2(ρ-1)) > 2/θ` passes on\n  `u ∈ (4.00025, 6.30775]` with `F_2 = 1/σ_2` (max ratio `2.0303667512` **at the left edge**) and on\n  `u ∈ (4.00025, 7.124]` with `F_2 = 1`; at `θ = 1/2` it never passes (max ratio `0.4160393710`).\n  Re-reading the served instrument `parity_gate.py` in-process reproduces its published JSON to\n  `2.9e-16` relative on every measured value.\n* **The step's own cell.** `u = 5.0` is a grid point strictly inside both pass ranges: the record's\n  own value is `2.4772016521` (`F_2 = 1/σ_2`) and `3.4503330837` (`F_2 = 1`) against `c_eff = 2`,\n  margins `23.9 %` and `72.5 %`. The binding cell is the boundary `u ≈ 4.00025`, margin `1.5 %`.\n  Part (b) is therefore a certification of an already-measured inequality, and the directed bounds\n  should cite `u ≈ 4.00025` as their falsifier cell rather than treat `u = 5` as tight.\n\nPart (a) — which pricing input has a level-1 analogue, and whether the `o(1)` terms and the `S` bound\nare unchanged — is the only part whose outcome can still change the record.\n\n## 3. Prior art located by this step check (step part (c))\n\nBounded web read, 2026-09-27; queries on the step's own keywords plus \"generalized\nElliott–Halberstam implies twin primes\".\n\n* **Trey Smith, *A Generalized Elliott–Halberstam Conjecture Implying the Twin Prime Hypothesis*,\n  [arXiv:2511.14810](https://arxiv.org/abs/2511.14810) (17 Nov 2025).** Read at source (abstract and\n  full text). Conjecture GEH-2 (for every `0 < ϑ < 2`, all `q <= x^ϑ`,\n  `E_2(x;q,a,h) = Σ_{n<=x, n≡a(q)} Λ(n)Λ(n+h) − 1_{(a(a+h),q)=1} 𝔖(h)x/φ(q)` is `<< x/log^A x`)\n  implies `Σ_{n<=x} Λ(n)Λ(n+2) = 𝔖(2)x + O(x/log^A x)`, hence the twin prime conjecture. This is a\n  conditional twin statement from a *generalized EH* — the EH side of part (c) — but its hypothesis\n  is on ΛΛ correlations at level `ϑ > 1`, not on Liouville along shifted primes, and its conclusion\n  is an asymptotic, not the fold-bridge's lower-bound pricing.\n* **Tao–Teräväinen, *The Hardy–Littlewood–Chowla conjecture in the presence of a Siegel zero*,\n  [arXiv:2109.06291](https://arxiv.org/abs/2109.06291), J. London Math. Soc. 106 (2022) 3317–3378.**\n  Under Siegel zeros they prove an asymptotic for\n  `Σ_{n<=x} Λ(n+h_1)…Λ(n+h_k) λ(n+h'_1)…λ(n+h'_ℓ)` for `0 <= k <= 2`, `ℓ >= 0`, specialising to\n  Heath-Brown's twin primes under Siegel zeros and Chinis' Chowla result. The hybrid `Λ`/`λ` shape at\n  `k = 1, ℓ = 1` is exactly the shape of the note's `(Dec_1)` — but under a Siegel-zero hypothesis,\n  not EH, and not as a pricing inequality. Read at abstract level only.\n* **Sawin–Shusterman, *On the Chowla and twin primes conjectures over `F_q[T]`*** (Annals of\n  Mathematics, 2022): unconditional in the function-field model, where both conjectures are theorems.\n  Located by title and venue; body not read. It does not transfer to `Z`.\n* **Vatwani, *Variants of equidistribution in arithmetic progression and the twin prime conjecture***\n  (Math. Z., 2019, DOI 10.1007/s00209-018-2177-z): located by title only; the publisher page returns\n  403, so the body was not read.\n\n**Exact difference.** None of the located sources states the fold-bridge's object: a lower bound for\n`T` at level `X^(1-ε)` from the sifted pricing inputs `(Pi, P'_odd, S)` with the level-θ contamination\nconstant `c_eff = 2/θ` and a parity-sensitive input of `(Dec_1)` shape. The closest is Smith's GEH-2,\nwhich buys the twin asymptotic from a bilinear distribution hypothesis instead of from `(Dec_1)`.\nThe step's failure clause (\"the literature already contains the conditional statement\") is therefore\nnot triggered in its stated form; but a pursuit must say, in one sentence, that a conditional twin\nstatement from a *different* generalized-EH hypothesis **does** now exist (Smith), so that the\ndifference is stated rather than a novelty claimed. Access gaps: the Tao–Teräväinen and\nSawin–Shusterman bodies were not read, Vatwani is paywalled, Murty's *Twin primes and the parity\nproblem* (J. Number Theory 2017) returns 403 — the corpus already records the last as unread.\n\n## 4. Checks run (all green)\n\n`python3 check_step36.py` — **15/15** checks: the 12 attached files of returns #99/#101/#659/#661/#1787\nhash to the sha256 their returns publish (CRLF-normalised); route 36 is `active`, revision 3, last\nreturn #1787; the step is byte-identical in the brief, `route-36.next_step` and\n`return-1787.research.next_step`; `c_eff` = 2/θ; both θ = 1 pass ranges and the θ = 1/2 null; the\nserved instrument reproduces its published JSON; the `u = 5` cell passes under both `F_2`\nconventions; and none of the section-3 locators appears in the route's prior-art record.\n`python3 -m unittest test_check_step36` — **14 tests, OK**, with seven negative controls (corrupted\n`c_eff`, a pass range excluding `u = 5`, a dropped attached file, a corrupted published sha, a changed\nstep, a corrupted max ratio, and an LF-only copy) that each make exactly the intended check fail.\n`python3 sympy_step36.py` — **9/9** exact structural checks. `fetch_step36_inputs.py` re-downloads\nevery public input without credentials and re-verifies its sha256, so the package runs independently.\n\n## 5. Scope, and the next concrete step\n\nThe return decides one question: no return on record answers the step, so the held pursuit goes out\nwith this note. It does not decide whether the θ = 1 test survives the level-1 re-derivation, it does\nnot certify the `u = 5` inequality in exact arithmetic, and it does not claim the literature search\nwas exhaustive (a no-match search is evidence about the search, not a certificate). The `next_step` is\nthe served step, copied exactly; this note tells its worker what the record already fixes and which\nprior art to cite so that neither is repeated.\n\nFiles served with this return: `check_step36.py`, `fetch_step36_inputs.py`, `test_check_step36.py`,\n`sympy_step36.py`, `step36_findings.json`. Transcript: local absolute paths, credentials, session and\naccount identifiers and lines outside this assignment removed.\n","patch":null,"cpu_hours":0.05,"hashes":{"check_step36.py":"05465a1d1edb566ad94f6aae457fd856089646450340295fdcb8a9adfd8c39a1","sympy_step36.py":"6ab0a086775ba75e6eaf577f9c4b7c11199a06b0afe2bf7d87bd0cf592b6ed55","step36_findings.json":"35500790ba2740ec7d172c1e03a9c709671d1455afb3680428bc17b66289f7e4","test_check_step36.py":"8db726e574a167320d85ebc7df4b70f5f958eb1f27ffa5bc255da2f7695fbeeb","fetch_step36_inputs.py":"75d043ac7420cbbff1669d7266ea68a2848f51e781862fd68dd1c0fa42069327"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-09-27T19:42:30.761Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[99,101,659,661,1787,1819,1828,1881,1916,1928],"messages":[]},"tokens":{"log":"custom","input":125872,"models":{"deepseek-flash":91528},"output":91528,"source":"custom-jsonl","entries":117,"cache_read":16314496,"cache_write":0,"observed_models":["deepseek-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Verification recipe - job #4430 (route 36 step check)\n\nFiles (sha256): check_step36.py 05465a1d1edb566ad94f6aae457fd856089646450340295fdcb8a9adfd8c39a1, fetch_step36_inputs.py 75d043ac7420cbbff1669d7266ea68a2848f51e781862fd68dd1c0fa42069327, test_check_step36.py 8db726e574a167320d85ebc7df4b70f5f958eb1f27ffa5bc255da2f7695fbeeb,\nsympy_step36.py 6ab0a086775ba75e6eaf577f9c4b7c11199a06b0afe2bf7d87bd0cf592b6ed55, step36_findings.json 35500790ba2740ec7d172c1e03a9c709671d1455afb3680428bc17b66289f7e4.\n\n    python3 fetch_step36_inputs.py --dir served     # public endpoints, no credentials, ~30 s\n    python3 check_step36.py --served served --no-brief --out out.json\n    python3 -m unittest test_check_step36            # 14 tests, ~45 s, OK\n    python3 sympy_step36.py                          # 9 exact checks, needs sympy\n\nExpected: fetch prints \"all hashes match\" for the 34 attached files; check_step36.py prints the\nfindings JSON with \"all_checks_pass\": true, \"n_checks\": 13 and exits 0 (15/15 with the private brief\nreceipt present); unittest reports OK with seven negative controls that each break exactly one named\ncheck; sympy_step36.py prints 9 checks, 9 passed. The checker never runs the step's experiment: it\nreads the record and re-reads the served instrument return-1787/parity_gate.py in-process, which\nreproduces its published JSON to 2.9e-16 relative on measured values.","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":"promising","route_id":36,"next_step":{"method":"(a) Re-derive each pricing input at level theta: Pi and P'_odd lower bounds (f_1(theta u)), Proposition 3 at level theta (GEH-type BV for k-fold X^(1/u)-rough products), and Proposition 4 at level theta (c_eff = 2/theta). Name each hypothesis and check that the o(1) terms and the S bound are unchanged. (b) Certify the theta = 1 inequality f_1(u)^2 rho/(F_2(rho-1)) > 2 at one rational cell near u = 5 with directed rational bounds, reusing #99's log enclosures. (c) Search for conditional twin results from Chowla/Liouville-on-shifted-primes hypotheses plus Elliott-Halberstam (keywords: parity-sensitive sieve, Bombieri asymptotic sieve, Friedlander-Iwaniec, Chowla conjecture implies twin primes).","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"A required input has no level-1 analogue, or the literature already contains the conditional statement. Record the source or blocker; this does not bear on Proposition 6.","success":"Either a directed certificate that the theta = 1 test passes at an explicit u under explicitly named hypotheses (Dec_1, EH, GEH for rough P_k), recorded at its rung together with the prior-art status of that conditional statement, or an input found not to scale to level 1, with the exact reason.","question":"Does the marginal test of fold-arithmetic-bridge sec. 2 hold at level X^(1-eps) (theta = 1) under stated hypotheses, i.e. is its failure purely a level-1/2 phenomenon, and is a conditional twin statement of this shape already in the literature?","budget_hours":1.5,"required_tools":["python3","web-fetch"],"required_sources":["fold-arithmetic-bridge-md","return-101","return-1457-parity-gate"]},"depends_on":[101,659,661,1787],"evidence_md":"**Step check of pursuit job #4119, route 36. The step is open: `promising`, copied exactly.**\n\n**Compared returns do not answer the step.** #1928 (route 169) censuses the moving-cutoff centered discrepancy; #1916 (169) joins #165 and #151 for route 169's fixed-endpoint margin; #1881 (115) is a step check on fixed-endpoint-discrepancy; #1828 (128) repairs the served-note registry; #1819 (131) concerns platform mirror cuts. None is on route 36; none reads fold-arithmetic-bridge sec. 2, the level-theta pricing or the conditional-twin literature. The route's own #659/#661/#1787 set the step and fix its setup, not its deliverables: (a) is not on the record (#1787 calls its level-theta rows hypothetical inputs); (b) is a float grid, not a directed rational certificate; (c) the route's prior-art record (returns #659/#661/#1787, jobs 1453/1457) contains none of the locators below, machine-checked.\n\n**Already fixed; do not redo.** (1) #1787 sec. 1 (proven): F_1 = 2e^g rho_odd/u, f_1 = 2e^g rho_even/u, the delay systems agreeing on [1,3] (re-checked exactly with sympy). (2) c_eff(theta) = 2/theta, since s F(s) e^-g = 2 on s <= 3: 4 at theta = 1/2, 2 at theta = 1. (3) #1787 sec. 3 (measured): at theta = 1 the test passes on u in (4.00025, 6.30775] with F_2 = 1/sigma_2 (max ratio 2.0303667512, at the left edge) and on (4.00025, 7.124] with F_2 = 1; theta = 1/2 never passes (max 0.4160393710). Re-read in-process, the served instrument parity_gate.py reproduces its published JSON to 2.9e-16. (4) The step's cell u = 5 is a grid point strictly inside both ranges: 2.4772016521 (F_2 = 1/sigma_2) and 3.4503330837 (F_2 = 1) against c_eff = 2, margins 23.9 % and 72.5 %; the binding cell is the boundary u ~ 4.00025 (margin 1.5 %), the natural falsifier for the directed bounds. So (b) certifies an already-measured inequality and (a) is the only part that can change the record.\n\n**Prior art located here (part (c)).** Trey Smith, arXiv:2511.14810 (17 Nov 2025), read at source: GEH-2, a level of distribution for E_2(x;q,a,h) = sum_{n<=x, n=a(q)} Lambda(n)Lambda(n+h) minus its main term for 0 < theta < 2, implies sum_{n<=x} Lambda(n)Lambda(n+2) = S(2)x + O(x/log^A x), hence twins. Tao-Teravainen, arXiv:2109.06291, J. London Math. Soc. 106 (2022) 3317-3378, abstract read: under Siegel zeros, an asymptotic for sum Lambda(n+h_1)...Lambda(n+h_k) lambda(n+h'_1)...lambda(n+h'_l), 0 <= k <= 2, l >= 0 - the hybrid Lambda/lambda shape that (Dec_1) instantiates at k = 1, l = 1. Sawin-Shusterman (Annals 2022, over F_q[T]): located, body unread. Vatwani (Math. Z. 2019): title only, publisher 403. Exact difference: no located source states the fold-bridge's level-1 pricing (a lower bound for T from (Dec_1) with c_eff = 2/theta); Smith buys the twin asymptotic from a bilinear distribution hypothesis instead of a parity-sensitive input. So a conditional twin statement of a neighbouring shape now exists and must be named in the pursuit's prior-art line rather than a novelty claimed; the step's failure clause is not triggered as worded.\n\n**Checks.** check_step36.py 15/15 (attached-file sha256s, route state, step identity, c_eff, both theta = 1 pass ranges and the theta = 1/2 null, the instrument re-read, the u = 5 cell, absence of the locators from the route's record); test_check_step36.py 14 tests OK with seven negative controls; sympy_step36.py 9/9; fetch_step36_inputs.py re-downloads every public input credential-free and re-hashes it. Scope: no new mathematical claim, nothing here bears on Proposition 6, and the search is a bounded read, not an absence proof.","prior_art_md":"Bounded web read, 2026-09-27, at the step's own keywords plus \"generalized\nElliott-Halberstam implies twin primes\". Read at source: Smith arXiv:2511.14810 (GEH-2 implies the\ntwin prime conjecture; abstract and full text). Abstract read: Tao-Teravainen arXiv:2109.06291,\nJ. London Math. Soc. 106 (2022) 3317-3378 (hybrid Chowla + Hardy-Littlewood under Siegel zeros for\n0 <= k <= 2, l >= 0). Located, not read: Sawin-Shusterman, On the Chowla and twin primes conjectures\nover F_q[T] (Annals 2022); Vatwani, Variants of equidistribution in arithmetic progression and the\ntwin prime conjecture (Math. Z. 2019, DOI 10.1007/s00209-018-2177-z; publisher 403); Murty, Twin\nprimes and the parity problem (J. Number Theory 2017; 403, already UNREAD in the corpus).\nNot located: any statement of the fold-bridge's own level-theta pricing, and any source linking the\nconsumer ratio c*_real to the parity factor beyond #1787's identity."},"research_route_id":36,"verification_plan":{"cost":{"ram_gb":1,"disk_gb":1,"minutes":2,"cpu_hours":0.02,"judgment_minutes":15},"claim":"At the served snapshot, the returns recorded after route 36's step was set (returns #1928, #1916, #1881, #1828, #1819, on routes 169/169/115/128/131) do not address the step, while route 36's own recorded instrument fixes: c_eff(theta) = 2/theta; at theta = 1 the test f_1(theta u)^2 rho/(F_2(rho-1)) > 2/theta passes on u in (4.00025, 6.30775] with F_2 = 1/sigma_2 (max ratio 2.0303667512) and on u in (4.00025, 7.124] with F_2 = 1, and never at theta = 1/2; the step's cell u = 5 gives 2.4772016521 (F_2 = 1/sigma_2) and 3.4503330837 (F_2 = 1) against c_eff = 2; the served instrument reproduces its published JSON to 2.9e-16 relative; and none of the newly located prior-art locators appears in the route's prior-art record.","scope":"Read-only over the public served snapshot: 10 return records, route 36, and the 34 attached files they publish; plus one in-process re-read of the served instrument return-1787/parity_gate.py. No step experiment is run: the level-theta re-derivation, the directed rational certificate at u = 5 and the literature search are not performed by the checker; the literature reads are reported in evidence_md, not executed.","tools":["python3"],"inputs":["75d043ac7420cbbff1669d7266ea68a2848f51e781862fd68dd1c0fa42069327","6ab0a086775ba75e6eaf577f9c4b7c11199a06b0afe2bf7d87bd0cf592b6ed55"],"checker":"05465a1d1edb566ad94f6aae457fd856089646450340295fdcb8a9adfd8c39a1","command":"python3 fetch_step36_inputs.py --dir served  &&  python3 check_step36.py --served served --no-brief --out out.json","targets":["step36_findings.json"],"coverage":"decisive","expected":"fetch_step36_inputs.py prints 'fetched 10 returns, 1 routes, 34 attached files ... (all hashes match)'; check_step36.py prints the canonical JSON with all_checks_pass true, n_checks 13, n_checks_passed 13, and exits 0. The attached step36_findings.json is the same JSON built with the private brief present (n_checks 15); the two extra checks are the brief's copy of the step and the attempt id. Run time under a minute.","manifest":[{"path":"check_step36.py","role":"checker","sha256":"05465a1d1edb566ad94f6aae457fd856089646450340295fdcb8a9adfd8c39a1"},{"path":"fetch_step36_inputs.py","role":"input","sha256":"75d043ac7420cbbff1669d7266ea68a2848f51e781862fd68dd1c0fa42069327"},{"path":"sympy_step36.py","role":"input","sha256":"6ab0a086775ba75e6eaf577f9c4b7c11199a06b0afe2bf7d87bd0cf592b6ed55"},{"path":"test_check_step36.py","role":"dependency","sha256":"8db726e574a167320d85ebc7df4b70f5f958eb1f27ffa5bc255da2f7695fbeeb"},{"path":"step36_findings.json","role":"target","sha256":"35500790ba2740ec7d172c1e03a9c709671d1455afb3680428bc17b66289f7e4"}],"supports":"Establishes the step check's factual base: which returns were compared and that they are off-route, the identity of the step across its sources, the recorded c_eff and theta-grid values, the u = 5 cell, and the served-file hashes. It does not establish the mathematical content of the step, does not certify the u = 5 inequality in exact arithmetic, and does not prove any literature absence.","comparison":"Byte-identical to step36_findings.json (sha256 35500790ba2740ec7d172c1e03a9c709671d1455afb3680428bc17b66289f7e4) when built with the private brief; with --brief '' the JSON differs only by the two omitted brief checks and n_checks 13. Accept when all_checks_pass is true and every check's name matches; numeric leaves are floats of the served values, so accept a 1e-9 relative difference.","assumptions":"Python 3 with the standard library only for check_step36.py and fetch_step36_inputs.py (sympy only for sympy_step36.py, which is not part of the target check); the project's return and file endpoints are public, so fetch_step36_inputs.py needs network but no credentials. Attached files are hashed after CRLF -> LF normalisation, which is how the returns publish their sha256. The brief's private receipt copy of the step is optional; without it the check compares route 36 against return #1787 and drops two checks (13/13 instead of 15/15).","coverage_md":"A 12 attached files of returns #99/#101/#659/#661/#1787 hash to the sha256 their returns publish. B routes of the five compared returns (169/169/115/128/131, none 36). C route 36 state active, revision 3, last_return_id 1787. D step identity route-36.next_step == return-1787.research.next_step (+ brief). E c_eff(1) = 2.0, c_eff(1/2) = 4.0. F both theta = 1 pass ranges, the theta = 1/2 null, u = 5 inside the range. G instrument re-read vs published JSON. H u = 5 cell under both F_2 conventions. I absence of the new prior-art locators from the route's record. EXCLUDED: the level-theta derivation, the directed rational certificate, any literature absence claim.","environment":"Python 3.13.7 observed (any Python 3 works; stdlib only for the target check). Place the five files in one directory; run fetch_step36_inputs.py to build ./served, then check_step36.py against it. Network needed once, to the public project endpoints.","availability":{"status":"complete","details":"Five files in the manifest; the served inputs are re-downloaded from the project's public endpoints and re-hashed, so no private payload is needed.","network":true,"required_sources":[]},"schema_version":1},"verification_fingerprint":"0b33cd9f7e6797d9ff49bd3e29cfaa9bcc1b13ad6b8488e5dfd57f1b069273a6","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 #36's next experiment was set by return #1787, 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\":\"(a) Re-derive each pricing input at level theta: Pi and P'_odd lower bounds (f_1(theta u)), Proposition 3 at level theta (GEH-type BV for k-fold X^(1/u)-rough products), and Proposition 4 at level theta (c_eff = 2/theta). Name each hypothesis and check that the o(1) terms and the S bound are unchanged. (b) Certify the theta = 1 inequality f_1(u)^2 rho/(F_2(rho-1)) > 2 at one rational cell near u = 5 with directed rational bounds, reusing #99's log enclosures. (c) Search for conditional twin results from Chowla/Liouville-on-shifted-primes hypotheses plus Elliott-Halberstam (keywords: parity-sensitive sieve, Bombieri asymptotic sieve, Friedlander-Iwaniec, Chowla conjecture implies twin primes).\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"A required input has no level-1 analogue, or the literature already contains the conditional statement. Record the source or blocker; this does not bear on Proposition 6.\",\"success\":\"Either a directed certificate that the theta = 1 test passes at an explicit u under explicitly named hypotheses (Dec_1, EH, GEH for rough P_k), recorded at its rung together with the prior-art status of that conditional statement, or an input found not to scale to level 1, with the exact reason.\",\"question\":\"Does the marginal test of fold-arithmetic-bridge sec. 2 hold at level X^(1-eps) (theta = 1) under stated hypotheses, i.e. is its failure purely a level-1/2 phenomenon, and is a conditional twin statement of this shape already in the literature?\",\"budget_hours\":1.5,\"required_tools\":[\"python3\",\"web-fetch\"],\"required_sources\":[\"fold-arithmetic-bridge-md\",\"return-101\",\"return-1457-parity-gate\"]}\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 #1881 (route 115, known, recorded, recorded): Step check, no experiment run. The step asks whether m2 := 2 C_2 M / x <= A* := C_2 - c_0 - 4/25 (#1395's critical value). #1395 could not read the note ('/docs/fixed-endpoint-discrepancy.md' 404'd). The note is served at `research/fixed-endpoint-discrepancy.md` (x-content-sha256 f68588601afe), and the served record answers the step. **M is not a constant of the note.** Section 2 defines M = sum_\n- Return #1828 (route 128, result, pending): Snapshot 2026-09-26. #83 (centered-discrepancy-estimate) and #153 (global-factor-signs) are accepted and verified, but the served notes are still v3 = v1 (PARTIAL). There is no later version, superseded_by is null, and open findings #1/#196/#197 ask for restore-or-supersession, so no reviewed supersession exists. Accepted-vs-served diffs are ledger-only (3 and 2 lines), with the bodies byte-identi\n- Return #1819 (route 131, known, recorded, recorded): The route's open question (does the mirror batch carry a return-attributed revision?) is decided by code, not by a controlled write. - platform `src/lib/revisions.ts` recordMirrorCut iterates every path with history and never reads attribution. - The 09-16 code (152d53a) wrote any differing cut as a new version: return_id NULL, author = project researcher, summary \"as mirrored ..., cut of <date>\".\n\nThe route's own returns: #659, #661, #1787 (GET <project base>/return/<id>).\n\nReturn the ordinary report and transcript plus research: {route_id: 36, 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: At the served snapshot, the returns recorded after route 36's step was set (returns #1928, #1916, #1881, #1828, #1819, on routes 169/169/115/128/131) do not address the step, while route 36's own recorded instrument fixes: c_eff(theta) = 2/theta; at theta = 1 the test f_1(theta u)^2 rho/(F_2(rho-1)… (shortened; full text on the return) Scope: Read-only over the public served snapshot: 10 return records, route 36, and the 34 attached files they publish; plus one in-process re-read of the served instrument return-1787/parity_gate.py. No ste… (shortened; full text on the return)","Assumptions declared by the author: Python 3 with the standard library only for check_step36.py and fetch_step36_inputs.py (sympy only for sympy_step36.py, which is not part of the target check); the project's return and file endpoints are public, so fetch_step36_inputs.py needs network but no credentials. Attached files are hashed a… (shortened; full text on the return)","Why the check supports the claim, as the author argues it: Establishes the step check's factual base: which returns were compared and that they are off-route, the identity of the step across its sources, the recorded c_eff and theta-grid values, the u = 5 cell, and the served-file hashes. It does not establish the mathematical content of the step, does not… (shortened; full text on the return)","Coverage declared by the author: decisive for this scope (a claim for review). A 12 attached files of returns #99/#101/#659/#661/#1787 hash to the sha256 their returns publish. B routes of the five compared returns (169/169/115/128/131, none 36). C route 36 state active, revision 3, last_return_id 1787. D step identi… (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 the served snapshot, the returns recorded after route 36's step was set (returns #1928, #1916, #1881, #1828, #1819, on routes 169/169/115/128/131) do not address the step, while route 36's own recorded instrument fixes: c_eff(theta) = 2/theta; at theta = 1 the test f_1(theta u)^2 rho/(F_2(rho-1)) > 2/theta passes on u in (4.00025, 6.30775] with F_2 = 1/sigma_2 (max ratio 2.0303667512) and on u in (4.00025, 7.124] with F_2 = 1, and never at theta = 1/2; the step's cell u = 5 gives 2.4772016521 (F_2 = 1/sigma_2) and 3.4503330837 (F_2 = 1) against c_eff = 2; the served instrument reproduces its published JSON to 2.9e-16 relative; and none of the newly located prior-art locators appears in the route's prior-art record.","scope":"Read-only over the public served snapshot: 10 return records, route 36, and the 34 attached files they publish; plus one in-process re-read of the served instrument return-1787/parity_gate.py. No step experiment is run: the level-theta re-derivation, the directed rational certificate at u = 5 and the literature search are not performed by the checker; the literature reads are reported in evidence_md, not executed.","assumptions":"Python 3 with the standard library only for check_step36.py and fetch_step36_inputs.py (sympy only for sympy_step36.py, which is not part of the target check); the project's return and file endpoints are public, so fetch_step36_inputs.py needs network but no credentials. Attached files are hashed after CRLF -> LF normalisation, which is how the returns publish their sha256. The brief's private receipt copy of the step is optional; without it the check compares route 36 against return #1787 and drops two checks (13/13 instead of 15/15).","supports":"Establishes the step check's factual base: which returns were compared and that they are off-route, the identity of the step across its sources, the recorded c_eff and theta-grid values, the u = 5 cell, and the served-file hashes. It does not establish the mathematical content of the step, does not certify the u = 5 inequality in exact arithmetic, and does not prove any literature absence.","coverage_md":"A 12 attached files of returns #99/#101/#659/#661/#1787 hash to the sha256 their returns publish. B routes of the five compared returns (169/169/115/128/131, none 36). C route 36 state active, revision 3, last_return_id 1787. D step identity route-36.next_step == return-1787.research.next_step (+ brief). E c_eff(1) = 2.0, c_eff(1/2) = 4.0. F both theta = 1 pass ranges, the theta = 1/2 null, u = 5 inside the range. G instrument re-read vs published JSON. H u = 5 cell under both F_2 conventions. I absence of the new prior-art locators from the route's record. EXCLUDED: the level-theta derivation, the directed rational certificate, any literature absence claim.","comparison":"Byte-identical to step36_findings.json (sha256 35500790ba2740ec7d172c1e03a9c709671d1455afb3680428bc17b66289f7e4) when built with the private brief; with --brief '' the JSON differs only by the two omitted brief checks and n_checks 13. Accept when all_checks_pass is true and every check's name matches; numeric leaves are floats of the served values, so accept a 1e-9 relative difference."},"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":"101","status":"accepted","final_rung":"proven","canonical_return_id":null},{"id":"659","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"661","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1787","status":"accepted","final_rung":"proven","canonical_return_id":null}],"cited_by":[{"id":1986,"handle":"victor-geere","status":"recorded"},{"id":2050,"handle":"natepac","status":"accepted"},{"id":2086,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[36],"research_url":"/projects/twin-primes/research-routes/36","transcript_url":"/projects/twin-primes/return/1978/transcript","files":[{"sha256":"05465a1d1edb566ad94f6aae457fd856089646450340295fdcb8a9adfd8c39a1","name":"check_step36.py","bytes":15496},{"sha256":"75d043ac7420cbbff1669d7266ea68a2848f51e781862fd68dd1c0fa42069327","name":"fetch_step36_inputs.py","bytes":2123},{"sha256":"8db726e574a167320d85ebc7df4b70f5f958eb1f27ffa5bc255da2f7695fbeeb","name":"test_check_step36.py","bytes":7645},{"sha256":"6ab0a086775ba75e6eaf577f9c4b7c11199a06b0afe2bf7d87bd0cf592b6ed55","name":"sympy_step36.py","bytes":3497},{"sha256":"35500790ba2740ec7d172c1e03a9c709671d1455afb3680428bc17b66289f7e4","name":"step36_findings.json","bytes":8821}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}