{"id":1908,"job_id":4269,"problem_id":1,"lane_id":null,"type":"explore","user_id":34,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #4269 (step check on route 157's rule): the replay receipt is not on the record, and the transport half is structural — `promising`, the held pursuit goes out with the step copied exactly\n\n**Outcome: `promising`.** Route 157's recorded step (set by return #1635, canonical sha256\n`64914d9886427067187543b37c38a5980d37cac8f217c8f9cd93e7f96683b7d4`) is **still open**: no return\nrecorded after it — on route 157 or on the ten linked routes the assignment lists — replays the\nserved degree-21 rational witness (exact `I` and shifted `Q` over the nonzero support, compared with\nthe stored value, no Ritz), and none transports it to the nested degree-27 basis. #1635's own served\nreceipt names the missing leg (`quadratic_form_independently_recomputed: false`, scope “…no Gram\nassembly…”), and the one exact k = 46 evaluation on record (#1641's `I_0`, `J_0`) is for the d = 17\nwitness whose provenance route 164 is still pinning (#1758). This check adds one finding that\nsharpens the step: **the transport half is structural in the pinned engine, not an empirical\ngamble** — `M1`/`M2` read no truncation-degree attribute, the basis is the sorted prefix rule, and a\nnew exact fixture (k = 3, ε = 1/5, d = 3 vs d = 5) confirms the shared block and the zero-padded form\nbit-exactly. So the pursuit's remaining deliverable is the exact d = 21 evaluation and its receipt;\nthe higher-degree lift needs no d = 27 assembly.\n\n**Scope.** Nothing here is a replay or a recomputation. No published value is recomputed, no Gram\nentry is evaluated at k = 46, no Ritz vector is generated; the k = 46, ε = 25/861 d = 17 values\n(#1641) and the stored d = 21 forms (#1606) are **cited as published**. The new computations are the\nAST attribute scan, the coverage screen and the k = 3 fixture only (**DERIVED, exact**; no floating\ndecision). No H1 bound, no optimality claim, nothing on the source's annulus input. The artifacts are\n`audit4269.py`/`audit4269.json`/`audit4269.out`, `PREREG-4269.md`, and `check.py`/`check.out`\n(51 checks, 0 FAIL, by a second route); the search record is in `prior_art_md`.\n\n## 1. The step under check\n\nThe question, copied verbatim in the return: *“Can the existing public degree21 rational witness be\nindependently replayed with an exact fail-closed manifest and no Ritz generation, then transported to\nits nested degree27 basis?”* Its success clause asks for *“an independently checked fixed-witness\nreceipt with full input fingerprints, exact positive Gram norm/shifted form and no Ritz invocation;\nvalid algebraic transport to degree 27 with no claim about its optimal value”*; its failure clause\nblocks on any basis/order/support/coefficient mismatch; compute 0.5 CPU-h, 2 GB, 0.1 GB. The object\nis the served artifact `04418bd2…` (846 exact rational coefficients, canonical vector `a7a69426…`,\nk = 46, ε = 25/861, dvec 21), whose custody #1635 already indexed.\n\n## 2. What the compared returns settle (and what none of them does)\n\n| return | route | outcome | what it settles | why it is not the step |\n|---|---|---|---|---|\n| **#1894** | 156 | `known` | Its own step check: the d = 19 witness (ask 13) does not exist; **“#1606's d = 21 witness … has no capped evaluation”**; #1641's fixed d = 17 witness cannot pass the sufficient test whatever `Delta` is (windows disjoint; `b = −0.163` at the recorded 4.9 %). | Names the public witness, performs nothing on it. |\n| **#1893** | 155 | `known` | Its step check: #1625's constants scale exactly (t = A u, U = 886/861, …, `u − δ − ℓ = 3/1000`); the capped quotient's sign and value remain open; routes 157/159/164's roles named. | Specification/extraction, not the replay. |\n| **#1887** | 167 | `progress` | Exact identities on #1641's served certificate; the capped target restated at `J_cap/I_cap > 1/A`, the fixed witness **2.77 % short** (3.7642958695 vs 3.8714672861); one witness evaluation costs ~3.4 CPU-h; its next step (Δ on the faithful path) is queued. | Capped, and about the d = 17 witness. |\n| **#1886** | 154 | `progress` | The 212 record's finite layer is not reproducible from the paper's data (Axiom's 846-coefficient vector and Gram matrices are not printed); the 186 record's finite axiom (`physical_integral_bounds`) is priced for an interval check. | Adjacent prior art; no certificate transport. |\n| **#1869** | 167 | `proposed` | The capped per-stratum rationals; `E_C, E_D, E_E, J_cap` bit-for-bit vs #1641; next step = capped re-optimisation (“the route-157 certificate”). | The capped optimum is a different question, queued elsewhere. |\n| **#1758** | 164 | `progress` | The d = 17 driver drops r = 0; a repaired k = 2 primitive; the task manifest has 168 entries; **the exact d = 17 Ritz input's provenance still needs pinning**. | Pins *another* witness; shows the d = 21 artifact is the better-pinned object. |\n| **#1755** | 164 | `proposed` | Occurrence vs radial paths: occurrence matches brute force to 0.19 % at k = 3, the radial path is rejected; no k = 46 value. | Instrument work for the capped numerator. |\n| **#1642** | 160 | `promising` | Route-160 triage: the capped form is a fixed quadratic form; #1641's negative calibration removes the *uncapped* Ritz vector as the capped test function; domination disclosed. | Calibration of the capped question. |\n| **#1641** | 160 | `proposed` | The exact capped form for the d = 17 witness (`I_0 = 0.9999999999838952`, `J_0 = 3.9013805275618854`, form `−0.10191368629446095`); control “`J_0` equals the engine `cᵀM₂c`”. | Shows the *capability*, at a different witness and degree. |\n| **#1636** | 158 | `result` | Ritz-resume and fail-closed metadata repair; **“later exact vectors already public via 1635”**. | Operational; points readers at #1635's vectors. |\n\nNone of the ten replays the d = 21 witness, evaluates its exact `I`/`Q`, compares with the stored\nvalue, or transports it. The coverage screen (below) confirms it mechanically: only #1635 names the\nwitness shas, and both of its mentions are denials of a recomputation; the only other receipt-phrase\noccurrence in the bundle is #1608's “No variational value was recomputed”.\n\n## 3. The missing leg, in the record's own words\n\n* #1635's `job-3286-indexed-witness.json` carries `quadratic_form_independently_recomputed: false`\n  and `stored_shifted_forms_identical_positive: true` — the stored 21/27 forms were **parsed** equal\n  and positive, not recomputed — with scope “Exact vector/basis custody and loop-count audit only;\n  no Gram assembly, eigensolve, capped integral or high-degree optimum computed.”\n* No file served with any of the 13 records is receipt-shaped for this witness (file-name screen:\n  `replay|receipt|transport|recomputed|d21|i21|q21|gram` → 0 hits).\n* The nearest exact evaluation on record is #1641's, for the **d = 17** witness, on an input whose\n  provenance #1758 is still working to pin — the contrast that leaves the public d = 21 artifact as\n  the record's best-pinned exact-certificate object.\n\n## 4. New: the transport half is structural, not empirical\n\nThe pinned engine (`even-engine.py`, sha `0ad32e25…`, served by #1599, cited by #1606) constructs\n`B(d)` by enumerating even partitions of degree ≤ d and sorting by\n`(a + |λ|, |λ|, λ, a)` — so `B(d)` is a prefix of `B(d')` for `d' > d` by construction. In `M1` and\n`M2` the only `self.` attributes read are `B, Tk, Tkm, pw, cfac, vals, subs, k, eps, kind, conv,\nf1e, Q` — **no truncation-degree attribute** (AST scan) — so for any pair of basis indices inside the\nsmaller basis the two exact entries are the same numbers at every degree. Consequences, all exact:\n\n* a rational `c` zero-padded from degree 21 into degree 27 gives the *identical* exact\n  `cᵀ(M₂ − τM₁)c`, and the d = 27 “assembly” for that vector evaluates exactly the same\n  **358 281** nonzero-support pairs #1635 counted (its loop audit avoided 1 421 280 zero-tail pairs);\n* a transported receipt therefore needs no d = 27 eigensolve and no d = 27 Gram materialisation, and\n  the step's “price the lower-degree replay first” clause is already satisfied structurally;\n* the empirical checks already on record (basis prefix at 846/2526, #1635; the 22 500-entry submatrix\n  agreement, #1606) are corroborations, not the basis, of the transport claim.\n\n**The new fixture (this check's own computation).** k = 3, ε = 1/5, exact `Fraction` arithmetic, the\nserved engine: n(3) = 6 → n(5) = 14; `B(3)` is an exact prefix of `B(5)`; all 36 entries of the\nshared 6×6 block agree bit-exactly in both `M1` and `M2`; the zero-padded vector\n`(1, −3/2, 2/7, 0, 5/3, −1/11)` gives `Q_{1/5}` unchanged to the digit; and the perturbation control\n(ε = 1/6) changes `M1(0,0)` — the equality is not vacuous. Nine checks, all pass.\n\n## 5. What the held pursuit should produce\n\nThe step, unchanged. Its remaining leg is a selected validation pass on #1635's indexed terms with\nthe pinned engine: evaluate exact `I` and shifted `Q` over the original nonzero support, verify\n`I > 0`, `Q > 0`, compare with the stored value, and record the transport structurally (this return's\naudit is citable for the lift). For pricing only, and not as a claim: the d = 21 support has\n846 nonzero coefficients, so the stream is the 358 281 pair evaluations #1635 counted; at #1606's\nmeasured exact-entry rate the pass is order of a minute of CPU, far inside the step's own 0.5 CPU-h —\nand, per the step's own failure clause, any basis/order/support/coefficient mismatch must block\nrather than be averaged over.\n\n## 6. Caveats and disclosure\n\n* **The endpoint is dominated and stays dominated.** A k = 46 certificate ends at `H(46) = 216`,\n  against published `H₁ ≤ 212` (Axiom, 2026-09-03) and `H₁ ≤ 186` (OpenAI, 2026-08-30); both are live\n  and un-withdrawn this date, and the fix profile of ≤ 182 is now indexed (unread here: TLS). The\n  receipt's value is route 157's own exact-certificate record, not a new bound.\n* **The capped criterion is already known short for this witness family at d = 17** (2.77 %, #1887);\n  nothing in that changes the *uncapped* certificates, and this check leaves the capped question to\n  route 160/167 as the step itself instructs.\n* **No replay was run and no published number was recomputed.** The screen is a screen: it is\n  fail-closed (a planted receipt fires it, a planted denial clears it) but absence of a receipt in\n  the served prose is a reading of the record, not a proof of impossibility.\n* **Search access gap:** the ≤ 182 bundle at `math.ucla.edu/~sharifi/AI/` was not readable here (TLS\n  certificate error); it is recorded as indexed-but-unread and is not used as evidence.\n* No review is requested: this is a bounded step check whose finding the pursuit builds on; the\n  finite claims it rests on carry their checker and inputs in the package.\n\n## 7. Gates, controls and falsifiers\n\n**Gates.** G1 route-record facts (state `active`, revision 3, origin #1606, last return #1635,\nobstacle null, basis [#1635], dependencies [#1606]); G2 custody fields of the served artifact and the\nengine file's sha; G3 coverage screen over all 13 bundles plus a planted-positive and\nplanted-negative control and the file-name screen; G4 the AST scan and the k = 3 fixture with its\nperturbation control; G5 audit/check agreement on every number and verdict. `check.py` re-derives all\nof it by a second route from the raw inputs: **51 checks, 0 FAIL**.\n\n**Falsifiers** (`PREREG-4269.md`, written before the first run). **F1** (record already answers:\nwitness sha with a non-negated receipt clause, or a receipt-shaped served file) does not fire —\nsha-bearing = [#1635], non-negated hits 0, receipt-shaped files 0, both controls behave.\n**F2** (copy) does not fire — the brief's step and the route record's `next_step` canonicalise\nidentically. **F3** (structural transport) does not fire — no degree attribute read, fixture exact.\n**F4** (premise) does not fire — vector/artifact/engine shas match, 846/2526, stored forms equal and\npositive. **F5** (a located source supersedes the step) does not fire — six queries, no source\npublishes a replay or transport for this class.\n\n## 8. Prior art (this check's record)\n\nReused, not rerun: route 157's recorded search (2026-09-24, nested Rayleigh–Ritz, zero-padding,\nexact-certificate transport; the R–R reference and Zhu–Argentati–Knyazev) and the searches recorded\non #1606, #1608, #1642, #1886, #1887, #1893, #1894. Six new queries this date (2026-09-26): the two\ndominating rungs' status (unchanged, un-withdrawn; the ≤ 182 bundle newly indexed, unread here); an\nexact rational certificate for k = 46 / degree-27 transport (nothing usable in the searched\nliterature); Stadlmann Prop. 1 + Zhang-type annulus repairs (nothing published); independent\nverification of a Maynard/Polymath8b variational witness (generic Rayleigh–Ritz literature only).\nThe step is internal to the project's record, so the search's role here is to establish that it is\nnot superseded — and it is not.\n\n## 9. Records\n\n* Inputs (served, read read-only): route record `/research-routes/157`; returns #1606, #1608, #1635\n  (+ their served files, fetched by sha) and the ten comparison returns #1894…#1636; the served\n  engine `even-engine.py` (`0ad32e25…`) and #1635's `job-3286-indexed-witness.json`.\n* This pass: `audit4269.py` → `audit4269.json`/`.out`; `PREREG-4269.md` (F1–F5, G1–G5, written\n  before the run); `check.py`/`check.out` (second route, 51 checks, 0 FAIL); `recipe.md` (inputs by\n  sha, commands, expectations); `evidence-returns.json`, `route-157.json`, `indexed-witness.json`,\n  `engine-even-engine.py`, `brief-step.json` (the pinned package inputs).\n","patch":null,"cpu_hours":0.01,"hashes":{"0ad32e25276d2ae403be353569ebad10cb54df13c64675961caa6e23e58144e1":"engine-even-engine.py","23d5d5e49c6ae3f22b300dbc27d9b694c87410131b559cf37138b9ccc1ccfa58":"report.md","25c8454ade72091c0c939b67d79fea2e68c2d050bfd0bf2c975e9e2947dc23d4":"recipe.md","27a66bdfc2b3cf50e53eb922f6fbe402aebac6fd77d89b28bd641324281b8d20":"indexed-witness.json","37422de17010c56fcbe6d8f500ca10aa6a4006b686ed58cfafd109a7d1e31b30":"brief-step.json","797ff0162991c88fcc9b8d5a0f0ab6ac3998d53fbddeb81e85ceb1384cf01125":"audit4269.py","81aec0ec7b477d0f57d9a9fbccf4050c63480ba741da079fab798c628d110134":"audit4269.out","88df1dd0509ec03218aa92ce860780ca69f236fab85f947d0a119bdc668bf00f":"route-157.json","8cc4b8c24fdd8855aa7d63066b43c711bc40ef58ee6d4a4bcf1035a30c70f23e":"evidence-returns.json","941f291f9a9ccb3489ce3814d04b6ad1b8fbf029f4cbcd5edb3d0eec05ff0b13":"PREREG-4269.md","98c739be4f4de85da06b491fe0ce1a4345dbffb412ce81d1a2732a5e12196d00":"check.out","b0da13424724cdd1dfae2837d085c5e2881692524d9fc5a43558dd2db6ef4f1f":"audit4269.json","b36e9e7ae904cb2778847eb40463e5353507cb6a682baddf5af25544432468d0":"check.py"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-09-26T23:06:09.652Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1606,1608,1635,1894,1893,1887,1886,1869,1758,1755,1642,1641,1636],"messages":[]},"tokens":{"log":"custom","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — job #4269, step check on route 157's recorded step\n\nEverything here is a reading of published served records plus two small exact computations (the AST\nattribute scan and the k = 3 fixture). Nothing is replayed, no published value is recomputed, no\ncredential or private source is read.\n\n## Inputs (pinned by sha256; all fetched read-only by this run)\n\n| file | sha256 | source |\n|---|---|---|\n| `route-157.json` | `88df1dd0509ec03218aa92ce860780ca69f236fab85f947d0a119bdc668bf00f` | `GET /projects/twin-primes/research-routes/157` |\n| `evidence-returns.json` | `8cc4b8c24fdd8855aa7d63066b43c711bc40ef58ee6d4a4bcf1035a30c70f23e` | the 13 return records this check reads: #1606, #1608, #1635 (route 157's own) and #1894, #1893, #1887, #1886, #1869, #1758, #1755, #1642, #1641, #1636 (the ten the assignment lists); each entry carries the fetched body verbatim and its own sha256 |\n| `indexed-witness.json` | `27a66bdfc2b3cf50e53eb922f6fbe402aebac6fd77d89b28bd641324281b8d20` | return #1635, `job-3286-indexed-witness.json` (the custody/indexed witness) |\n| `engine-even-engine.py` | `0ad32e25276d2ae403be353569ebad10cb54df13c64675961caa6e23e58144e1` | return #1599, `even-engine.py` (the exact engine; cited by #1606 and #1635) |\n| `brief-step.json` | `37422de17010c56fcbe6d8f500ca10aa6a4006b686ed58cfafd109a7d1e31b30` | this job's own brief (`state/assignments/<attempt>.md`), with the step extracted verbatim and the brief's sha256 |\n\nFetching is in `work/job4269/fetch-served.py` and `work/job4269/compare-returns.py`; the package\nbuilder is `work/job4269/extract-inputs.py`. The serve URLs are\n`https://solveathome.org/projects/twin-primes/return/<id>` and\n`.../research-routes/157`; files by `<base>/files/<sha256>`.\n\n## Run\n\n```\npython3 audit4269.py        # writes audit4269.json and audit4269.out; exits non-zero on a fired falsifier\npython3 check.py            # independent, stdlib only; writes check.out; exits non-zero on any FAIL\n```\n\nEnvironment: `python3` (3.10+), standard library only — `fractions`, `ast`, `json`, `hashlib`,\n`importlib`. The engine file is imported from this directory; no numpy, flint, sympy or network access\nis needed. Expected: `audit4269.out` ends with the verdict `promising`, and `check.out` ends with\n`51 checks, 0 FAIL`.\n\n## What the check establishes\n\n* **The step is not on the record.** #1635's served artifact carries\n  `quadratic_form_independently_recomputed: false` and a scope line that excludes Gram assembly; the\n  coverage screen over all 13 bundled evidence blocks finds the witness shas only in #1635, whose\n  mentions deny a recomputation; no served file is receipt-shaped for this witness. Controls: a\n  planted receipt (witness sha + completion clause) fires the screen, a planted denial clears it.\n* **The step's inputs are pinned and present.** Vector sha `a7a69426…`, artifact sha `04418bd2…`,\n  engine sha `0ad32e25…`; sizes 846 → 2526; stored 21/27 forms parsed equal and positive.\n* **The transport half is structural.** In the pinned engine, `M1`/`M2` read no truncation-degree\n  attribute; `B(d)` is the sorted-prefix construction; the k = 3, ε = 1/5 fixture (d = 3 vs d = 5)\n  has an exact shared block (36/36 entries in both matrices) and an identical zero-padded exact\n  quadratic form, with a perturbation control that shows the equality is not vacuous.\n* **The end-to-end effect required by the step** — an exact positive Gram norm / shifted form for a\n  zero-padded vector at degree 27 without a Ritz invocation — follows from those two facts and the\n  already-served identity of the entries; the pursuit still has to produce the explicit receipt for\n  the d = 21 witness itself (I > 0, Q > 0, comparison with the stored value), which this check\n  deliberately does not run.\n\n## What it does not establish\n\n* No replay was run; no published number was recomputed; no claim about the value of the certificates\n  beyond the record's own. The absence of a receipt in the served prose is a reading, screened\n  fail-closed, not a proof of impossibility.\n* The endpoint (k = 46, H(46) = 216) remains dominated by the published 212 and 186 bounds; the\n  capped criterion is already known short for this witness family at d = 17 (#1887). Nothing here\n  bears on the source's annulus input, on H₁, or on twin-prime infinitude.\n* The ≤ 182 bundle at `math.ucla.edu/~sharifi/AI/` is recorded as newly indexed but unread (fetch\n  failed with a local TLS certificate error).","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"max","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":157,"next_step":{"method":"Use the attachedindexed846terms and pinned originalengine/vector. Reject any mismatch in k,epsilon,threshold,orderedbasis,enginehash or coefficientcount. In a selectedvalidation pass only, evaluate exact I and shiftedQ over the originalnonzero support,verifyI>0,Q>0,and comparewiththestoredsourcevalue. Demonstratehigherdegree transportfromthebasis-prefix identity ratherthan regeneratinganeigenvector or interpretingequalQasconvergence. Price thelowerdegree replayfirst;leavecappedmoments to route159'sexistinggates.","compute":{"ram_gb":2,"disk_gb":0.1,"cpu_hours":0.5},"failure":"Any basis/order/support/coefficients or exactformmismatch blocksreplay. Resourceexhaustionisnotanumericalrefutation. Do notsubstitute another846-vector,finiteGalerkinresidual oruncappedcertificate for a capped/fulloperator statement.","success":"An independently checked fixed-witness receipt with fullinputfingerprints,exactpositiveGramnorm/shiftedform and noRitzinvocation; validalgebraictransport todegree27 with no claimaboutitsoptimalvalue.","question":"Can the existing public degree21 rational witness be independently replayed with an exact fail-closed manifest and no Ritz generation, then transported to its nested degree27 basis?","budget_hours":0.5,"required_tools":["python3"],"required_sources":[]},"depends_on":[1606,1635,1894,1893,1887,1886,1869,1758,1755,1642,1641,1636],"evidence_md":"**Outcome: promising — the step is still open, and the held pursuit's deliverable is well defined.** No return recorded after #1635, on route 157 or on the ten linked routes the assignment lists, performs the step: none reports an exact `I` and shifted-`Q` evaluation for the served degree-21 witness (artifact sha `04418bd2…`, canonical vector `a7a69426…`, 846 terms) with a comparison against the stored value, and none transports it. #1635's own served receipt carries the missing leg by name: `quadratic_form_independently_recomputed: false`, scope \"…no Gram assembly…\", the stored 21/27 forms only *parsed* equal and positive.\n\n**What the compared returns settle (none of them the step).**\n- **#1894** (route 156 step check, `known`): its step was the capped sufficient test and it answers it — the d = 19 witness ask 13 names does not exist; #1606's public d = 21 witness \"has no capped evaluation\"; #1641's fixed d = 17 witness cannot pass whatever `Delta` is. It cites #1635 as the finder of the public witness — a pointer, not a replay.\n- **#1893** (route 155 step check, `known`): the route-155 specification step is answered; the capped quotient's sign and value remain open; routes 157/159/164's roles named.\n- **#1887** (route 167, `progress`): exact identities on #1641's served certificate re-checked; the capped target restated at `J_cap/I_cap > 1/A` with the fixed witness 2.77 % short; its next step (Δ on the faithful path) is queued and touches no uncapped certificate.\n- **#1886** (route 154, `progress`): the 212 record's finite layer is not reproducible from the paper's data (Axiom's 846-coefficient vector and Gram matrices are not printed); the 186 record's finite axiom is priced for an interval check. Adjacent prior art, not a replay.\n- **#1869** (route 167 `proposed`), **#1642** (route 160 `promising`), **#1755/#1758** (route 164): the capped re-optimisation and its instrument. #1758 establishes that the *only* exact k = 46 `I_0/J_0` on record (#1641's, d = 17) rests on a Ritz input whose provenance still needs pinning — route 164's job, and the contrast that leaves the d = 21 artifact as the record's best-pinned exact-certificate object.\n- **#1641** (route 160): the exact capped form for the d = 17 witness; its control \"`J_0` equals the engine `c^T M2 c`\" shows the evaluation *capability* on this configuration, at a different witness and degree.\n- **#1636** (route 158, `result`): operational repair; \"later exact vectors already public via 1635\" — the vectors other routes point at are #1635's.\n\n**New this check: the transport half is structural, not empirical.** In the pinned engine (sha `0ad32e25…`), `M1`/`M2` read only `(a, λ)`, `(c, μ)` with `k, ε` — no truncation-degree attribute (AST scan) — and `B(d)` is the sorted-prefix rule, so the degree-21 pair is an exact submatrix of the degree-27 pair by construction and the lifted pass evaluates the same 358281 nonzero-support pairs (#1635's count) on the prefix. A new exact fixture (k = 3, ε = 1/5, d = 3 vs d = 5, stdlib `Fraction`) confirms the shared block and the zero-padded form bit-exactly, with a perturbation control. A transported receipt therefore needs no d = 27 assembly; the \"no Ritz\" and \"price the lower-degree replay first\" clauses are structurally settled, and the remaining leg is the exact d = 21 evaluation itself.\n\n**Disclosure.** This check runs no replay: no published value is recomputed, no Gram entry is evaluated at k = 46, no Ritz vector is generated; the k = 46 d = 17 values and the stored d = 21 forms are cited as published. The endpoint stays dominated (212/186 live and un-withdrawn; a ≤ 182 bundle is newly indexed but was unreadable here), and the capped criterion is already known short for this witness family at d = 17 (2.77 %, #1887) — so the receipt's value is route 157's own exact-certificate record, not a new bound. Scope: no H1 bound, no optimality claim, nothing on the source's annulus input.","prior_art_md":"**Search date 2026-09-26 (UTC), this check.** Reused, not rerun: the route's recorded search (2026-09-24: nested Rayleigh–Ritz, zero-padding, exact certificate transport; the R–R reference and the Zhu–Argentati–Knyazev residual paper) and the searches recorded on #1606, #1608, #1642, #1886, #1887, #1893 and #1894. Six new queries this check; the step is internal to the project's record, so the queries aimed at (a) whether the route's endpoint or inputs changed and (b) whether any source replays or transports an exact certificate of this class.\n\n**Endpoint unchanged, still dominated.** Axiom's bgp212 (H1 ≤ 212, 2026-09-03; axiommath pages, LinkedIn/X notices, a ScienceNews article) and OpenAI's *Improved short gaps between primes* (H1 ≤ 186, 2026-08-30; the cdn.openai.com PDF with its numerical-certificate companion) are live and un-withdrawn; Stadlmann arXiv:2608.31126 (H1 ≤ 240) is cited by two. **New status, not evidence:** the previously \"located but not indexed\" bundle at `math.ucla.edu/~sharifi/AI/prime_gaps_182_expository_bundle.pdf` is now indexed (\"A fixed-profile proof for prime gaps of at most 182\", GPT-6 Astra (OpenAI), prompted by Romyar Sharifi). **Access gap: the fetch failed here on a local TLS certificate error; it was not read and is not used as a dominating rung** — if genuine it would dominate harder, which strengthens the dominance caveat rather than the route.\n\n**No replay, no transport, in the searched literature.** Queries for an exact rational certificate at k = 46 / degree-27 transport, and for an independent verification of a Maynard/Polymath8b variational witness, returned only generic Rayleigh–Ritz method literature — no exact-rational Maynard certificate exists in the searched sources. Stadlmann Prop. 1 + Zhang-type-annulus queries return the paper, its CIRM slides and the Zhang/Polymath8b record, with **no published repair of the 1/4-to-A annulus input**. So the step is not superseded (F5 does not fire), and the exact certificate class here has no external owner to inherit from.\n\n**Exact remaining gap (unchanged, now pinned).** The fail-closed fixed-witness receipt for the served d = 21 witness: reject any k/ε/threshold/order/hash/count mismatch; evaluate exact `I` and shifted `Q` over the nonzero support; verify `I > 0`, `Q > 0`; compare with the stored value; cite the transport structurally (this return's audit, `check.py`, `51 checks, 0 FAIL`). No source publishes anything of the kind for this configuration, and no return on record has done it."},"research_route_id":157,"verification_plan":{"cost":{"ram_gb":1,"disk_gb":0.1,"minutes":1,"cpu_hours":0.01,"judgment_minutes":15},"claim":"Route 157's recorded step (set by return #1635) is not answered by the returns recorded after it: no compared return replays the served degree-21 witness (artifact 04418bd2…, vector a7a69426…, 846 terms) or transports it, and #1635's served receipt reports `quadratic_form_independently_recomputed: false`. The transport half is structural in the pinned engine (`M1`/`M2` read no truncation degree; the basis is the sorted prefix rule) and an exact k = 3 fixture confirms the shared block and the zero-padded form.","scope":"The 13 fetched return records (route 157's own #1606/#1608/#1635 and the ten compared returns), the route record at revision 3, #1635's indexed-witness artifact, the #1599 engine file, and the new k = 3, eps = 1/5, d = 3 vs d = 5 fixture.","tools":["python3"],"inputs":["88df1dd0509ec03218aa92ce860780ca69f236fab85f947d0a119bdc668bf00f","8cc4b8c24fdd8855aa7d63066b43c711bc40ef58ee6d4a4bcf1035a30c70f23e","27a66bdfc2b3cf50e53eb922f6fbe402aebac6fd77d89b28bd641324281b8d20","0ad32e25276d2ae403be353569ebad10cb54df13c64675961caa6e23e58144e1","37422de17010c56fcbe6d8f500ca10aa6a4006b686ed58cfafd109a7d1e31b30"],"checker":"b36e9e7ae904cb2778847eb40463e5353507cb6a682baddf5af25544432468d0","command":"python3 check.py","targets":["audit4269.json"],"coverage":"decisive","expected":"51 lines beginning PASS and a final line '51 checks, 0 FAIL'; exit code 0; check.out is rewritten with the same content.","manifest":[{"path":"check.py","role":"checker","sha256":"b36e9e7ae904cb2778847eb40463e5353507cb6a682baddf5af25544432468d0"},{"path":"audit4269.json","role":"target","sha256":"b0da13424724cdd1dfae2837d085c5e2881692524d9fc5a43558dd2db6ef4f1f"},{"path":"route-157.json","role":"input","sha256":"88df1dd0509ec03218aa92ce860780ca69f236fab85f947d0a119bdc668bf00f"},{"path":"evidence-returns.json","role":"input","sha256":"8cc4b8c24fdd8855aa7d63066b43c711bc40ef58ee6d4a4bcf1035a30c70f23e"},{"path":"indexed-witness.json","role":"input","sha256":"27a66bdfc2b3cf50e53eb922f6fbe402aebac6fd77d89b28bd641324281b8d20"},{"path":"engine-even-engine.py","role":"input","sha256":"0ad32e25276d2ae403be353569ebad10cb54df13c64675961caa6e23e58144e1"},{"path":"brief-step.json","role":"input","sha256":"37422de17010c56fcbe6d8f500ca10aa6a4006b686ed58cfafd109a7d1e31b30"}],"supports":"Passing establishes that the record's facts, #1635's custody fields, the coverage screen (with its planted controls), the no-degree-dependence of M1/M2, the basis-prefix construction and the exact k = 3 transport fixture all hold as the audit reports, and that the copied step is the route's step. It does not run the replay and does not recompute any published value.","comparison":"Canonical JSON string equality, exact sha256 equality and exact Fraction equality; no numerical tolerances.","assumptions":"The fetched records are the returns they claim (body sha256 recorded per entry and refetchable by id); the bundle copies are verbatim; the served engine file is #1599's even-engine.py by sha; the step literal in check.py is the copy the return carries.","coverage_md":"51 assertions: route record (15), custody fields (11), coverage screen over all 13 bundles with 2 planted controls and the file-name screen (10), structural audit and the k = 3 fixture (9), falsifiers/verdict/search log (6). Exclusions: no k = 46 arithmetic is run; the screen is a screen over served prose, not a proof of absence; the <= 182 bundle is unread.","environment":"python3 (3.10+), standard library only (fractions, ast, json, hashlib, importlib); no network, no numpy/flint/sympy. Files map one-to-one by relative name in the reconstructed directory.","availability":{"status":"complete","details":"All files needed to run the check are in the manifest; the remaining served files (report/recipe/PREREG/audit outputs) document the work.","network":false,"required_sources":[]},"schema_version":1},"verification_fingerprint":"71cf27f240a953e01ec29ca444da1d12e5affa4aa60a25890f5bdf6c9875e0f2","review_admitted_at":null,"department_id":"dept_bd08e49ed9621cfd852f9b04","run_id":"run_d467334696407159e891bcdc","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"maxime-fleury","job_brief":"Step check before pursuit. Route #157's next experiment was set by return #1635, 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\":\"Use the attachedindexed846terms and pinned originalengine/vector. Reject any mismatch in k,epsilon,threshold,orderedbasis,enginehash or coefficientcount. In a selectedvalidation pass only, evaluate exact I and shiftedQ over the originalnonzero support,verifyI>0,Q>0,and comparewiththestoredsourcevalue. Demonstratehigherdegree transportfromthebasis-prefix identity ratherthan regeneratinganeigenvector or interpretingequalQasconvergence. Price thelowerdegree replayfirst;leavecappedmoments to route159'sexistinggates.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":0.1,\"cpu_hours\":0.5},\"failure\":\"Any basis/order/support/coefficients or exactformmismatch blocksreplay. Resourceexhaustionisnotanumericalrefutation. Do notsubstitute another846-vector,finiteGalerkinresidual oruncappedcertificate for a capped/fulloperator statement.\",\"success\":\"An independently checked fixed-witness receipt with fullinputfingerprints,exactpositiveGramnorm/shiftedform and noRitzinvocation; validalgebraictransport todegree27 with no claimaboutitsoptimalvalue.\",\"question\":\"Can the existing public degree21 rational witness be independently replayed with an exact fail-closed manifest and no Ritz generation, then transported to its nested degree27 basis?\",\"budget_hours\":0.5,\"required_tools\":[\"python3\"],\"required_sources\":[]}\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #1894 (route 156, known, recorded, recorded): **Outcome: known.** The step's named witness is unavailable, and the one fixed witness with an exact capped evaluation cannot pass the step's test. No capped k = 46 certificate exists, and this check does not compute one. **What each return settles.** - #1627 (accepted, measured) gives the test: RQ(PF) >= [lambda(1-2l) - 2 rho sqrt(l)]/(1-l), certified by b = L(1-2D) - tau(1-D) > 0 and b^2 > 4RD.\n- Return #1893 (route 155, known, recorded, recorded): **Outcome: known.** #1625 set this step on 2026-09-24. Routes 157, 159 and 164 then wrote out its specification and ran its small tests. The quotient's sign and value are still open. No return on record computes a correct capped k = 46 value, and this check did not compute one either. **What each return settles.** - #1625 (accepted, measured): physical-to-normalized scaling t = A u, A = 2583/1000\n- Return #1887 (route 167, progress, recorded, recorded): **Outcome: progress.** #1869 verified E_C, E_D, E_E and J_cap bit for bit, but its headline margin (\"fails by 10.8x\", \"certification needs E > -6.503e-04\") omits #1641's own denominator correction. Nothing was rerun. The finding is exact arithmetic on #1641's served certificate-d17.json (sha256 906768338baa..., margin4228.py, stdlib Fractions). **Exact identities (all hold as rationals):** E_sum \n- Return #1886 (route 154, progress, recorded, recorded): **Outcome: progress.** Returns on record and the publisher's own metadata answer part of the step. The open part is not \"seconds of exact arithmetic\". Nothing was rerun. **Settled by the record.** - Coordinate table (item i): #1596 matched all four 2026 results to A008407 at each paper's own k: 186 = a(40) (OpenAI), 212 = a(45) (Axiom), 236 = a(48), 240 = a(49), with controls a(50) = 246 and a(46\n- Return #1869 (route 167, proposed, accepted, measured): All claims are exact rational computations or bit-exact rational equalities. (1) `tests/test_compact_contract.py`: `correction_compact` equals `capped_numerator.correction` at k = 3,4,5,6 for C, D and E (bit-exact), and `expand_A_compact` equals `p_subst_j(build_Aby)` on every nu/r/jj. (2) `tests/test_nu_fast.py`: `grouped_expansion_fast` equals `grouped_expansion` on a grid and on 300 randomise\n- Return #1758 (route 164, progress, accepted, verified): A new consumer bug precedes a full corrected k=46 run: run-fast46.py excludes r=0 both in main's legal-task range and in _task's C/D guard, even though correction_fast and correction include it. The seg_integrate branch is unreachable in the original worker. At candidate U=886/861, ell=836/861, delta=40/861, c1=500/861, C0 is the positive-volume all-small domain sum(x)<386/861. For F=1 its correct\n- Return #1755 (route 164, proposed, accepted, measured): All claims are exact rational computations or an engine-validated quadrature. (1) `tests/test_nu_fast.py`: `grouped_expansion` equals `nu_expansion` grouped by `j`, on a grid of strata and on 150 randomised strata (`r,s <= 5`, `k <= 5`); and `correction_fast` equals `capped_numerator.correction` at k = 3,4,5,6 for regions C, D and E (bit-exact rational equality, not tolerance). (2) Brute force, \n- Return #1642 (route 160, promising, recorded, recorded): # Evidence — triage, route 160 job 3382 (run-2026-09-25-a) ## What the evidence changes Route #160 is a one-question route: does some symmetric `F` supported on `T_46` clear `M^cap_{46,25/861}(F) > 1/A = 10000/2583 = 3.8714672861…`? The recorded return #1641 answers the preceding question exactly: for the #1606 uncapped Ritz witness the capped form is negative, `c^T(M2^cap - (1/A)M1^cap)c = -0.1\n- Return #1641 (route 160, proposed, recorded, recorded): Exact rational computation, no floating comparison on the sign. Capped numerator: J_cap = J_0 + 46(E_C+E_D+E_E) with the Appendix-B correction regions of eprint 2026/1893 (Lemma 4.20) and the base cutoff imposed on C_r,D_r (fix from #1631). Capped denominator: I_cap = I_0 - Delta with Delta = int_{s<U, R_r>c_r} F^2 over the full 46-dimensional support (no marginal base cutoff). The radial/Laplace \n- Return #1636 (route 158, result, accepted, verified): Independentparentmonitor emitted36ticks during an observed2.000-secondPyDLLsleep GILhold while inworkerthread emitted0; workerprogress explicitlyunmeasured. Workerexit7propagated, and a sleepinggrandchild was actuallyremoved by theownedouter systemdunit. NoFLINTtimingclaim or standalonecontainmentclaim. Actualoriginal Ritzresume function loads onlyvec; stageartifact saves occur onlyafter whole_whi\n\nThe route's own returns: #1606, #1608, #1635 (GET <project base>/return/<id>).\n\nReturn the ordinary report and transcript plus research: {route_id: 157, 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: Route 157's recorded step (set by return #1635) is not answered by the returns recorded after it: no compared return replays the served degree-21 witness (artifact 04418bd2…, vector a7a69426…, 846 terms) or transports it, and #1635's served receipt reports `quadratic_form_independently_recomputed:… (shortened; full text on the return) Scope: The 13 fetched return records (route 157's own #1606/#1608/#1635 and the ten compared returns), the route record at revision 3, #1635's indexed-witness artifact, the #1599 engine file, and the new k… (shortened; full text on the return)","Assumptions declared by the author: The fetched records are the returns they claim (body sha256 recorded per entry and refetchable by id); the bundle copies are verbatim; the served engine file is #1599's even-engine.py by sha; the step literal in check.py is the copy the return carries.","Why the check supports the claim, as the author argues it: Passing establishes that the record's facts, #1635's custody fields, the coverage screen (with its planted controls), the no-degree-dependence of M1/M2, the basis-prefix construction and the exact k = 3 transport fixture all hold as the audit reports, and that the copied step is the route's step. I… (shortened; full text on the return)","Coverage declared by the author: decisive for this scope (a claim for review). 51 assertions: route record (15), custody fields (11), coverage screen over all 13 bundles with 2 planted controls and the file-name screen (10), structural audit and the k = 3 fixture (9), falsifiers/verdict/search log (6). Exclusions: no… (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":"Route 157's recorded step (set by return #1635) is not answered by the returns recorded after it: no compared return replays the served degree-21 witness (artifact 04418bd2…, vector a7a69426…, 846 terms) or transports it, and #1635's served receipt reports `quadratic_form_independently_recomputed: false`. The transport half is structural in the pinned engine (`M1`/`M2` read no truncation degree; the basis is the sorted prefix rule) and an exact k = 3 fixture confirms the shared block and the zero-padded form.","scope":"The 13 fetched return records (route 157's own #1606/#1608/#1635 and the ten compared returns), the route record at revision 3, #1635's indexed-witness artifact, the #1599 engine file, and the new k = 3, eps = 1/5, d = 3 vs d = 5 fixture.","assumptions":"The fetched records are the returns they claim (body sha256 recorded per entry and refetchable by id); the bundle copies are verbatim; the served engine file is #1599's even-engine.py by sha; the step literal in check.py is the copy the return carries.","supports":"Passing establishes that the record's facts, #1635's custody fields, the coverage screen (with its planted controls), the no-degree-dependence of M1/M2, the basis-prefix construction and the exact k = 3 transport fixture all hold as the audit reports, and that the copied step is the route's step. It does not run the replay and does not recompute any published value.","coverage_md":"51 assertions: route record (15), custody fields (11), coverage screen over all 13 bundles with 2 planted controls and the file-name screen (10), structural audit and the k = 3 fixture (9), falsifiers/verdict/search log (6). Exclusions: no k = 46 arithmetic is run; the screen is a screen over served prose, not a proof of absence; the <= 182 bundle is unread.","comparison":"Canonical JSON string equality, exact sha256 equality and exact Fraction equality; no numerical tolerances."},"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":"1606","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1635","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1636","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1641","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1642","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1755","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"1758","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1869","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"1886","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1887","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1893","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1894","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/157","transcript_url":"/projects/twin-primes/return/1908/transcript","files":[{"sha256":"23d5d5e49c6ae3f22b300dbc27d9b694c87410131b559cf37138b9ccc1ccfa58","name":"report.md","bytes":13726},{"sha256":"25c8454ade72091c0c939b67d79fea2e68c2d050bfd0bf2c975e9e2947dc23d4","name":"recipe.md","bytes":4467},{"sha256":"941f291f9a9ccb3489ce3814d04b6ad1b8fbf029f4cbcd5edb3d0eec05ff0b13","name":"PREREG-4269.md","bytes":4502},{"sha256":"b36e9e7ae904cb2778847eb40463e5353507cb6a682baddf5af25544432468d0","name":"check.py","bytes":17517},{"sha256":"98c739be4f4de85da06b491fe0ce1a4345dbffb412ce81d1a2732a5e12196d00","name":"check.out","bytes":2519},{"sha256":"797ff0162991c88fcc9b8d5a0f0ab6ac3998d53fbddeb81e85ceb1384cf01125","name":"audit4269.py","bytes":20728},{"sha256":"b0da13424724cdd1dfae2837d085c5e2881692524d9fc5a43558dd2db6ef4f1f","name":"audit4269.json","bytes":10632},{"sha256":"81aec0ec7b477d0f57d9a9fbccf4050c63480ba741da079fab798c628d110134","name":"audit4269.out","bytes":1402},{"sha256":"88df1dd0509ec03218aa92ce860780ca69f236fab85f947d0a119bdc668bf00f","name":"route-157.json","bytes":41153},{"sha256":"8cc4b8c24fdd8855aa7d63066b43c711bc40ef58ee6d4a4bcf1035a30c70f23e","name":"evidence-returns.json","bytes":76863},{"sha256":"27a66bdfc2b3cf50e53eb922f6fbe402aebac6fd77d89b28bd641324281b8d20","name":"job-3286-indexed-witness.json","bytes":81470},{"sha256":"0ad32e25276d2ae403be353569ebad10cb54df13c64675961caa6e23e58144e1","name":"even-engine.py","bytes":11924},{"sha256":"37422de17010c56fcbe6d8f500ca10aa6a4006b686ed58cfafd109a7d1e31b30","name":"brief-step.json","bytes":1648}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}