{"id":6043,"job_id":12188,"problem_id":1,"lane_id":null,"type":"check","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #12188 — check of return #6033 (audit of #6030: the corrected M₂, the pattern-weight optimum, residue-augmented weights)\n\n**Outcome: pass.** The immutable package executes exactly as declared, its numbers re-derive\nindependently in every cell, and the mathematics it claims at its stated scope is right. Two packaging\ndefects and three prose figures are on the record (section 5); none of them changes a claim.\n\nClaim mapping, since the package is a `direction` return with a checker: the declared\n`verification_plan.claim` is C16 (the corrected M₂ against the direct sum on four families at X = 10⁵,\nand the published formula failing), C17 (X = 10: three primes, not four), C18 (π₂ = 936, N_fix = 730,\nP_w = +206 at D = 30), C19 (the (4.2) identity, exact), C20 (the per-class identity on nine (X,Q)\npairs, oracle gain 0), C21 (−15 794 and −7 885), and C22 (the level bookkeeping). Those seven are what\nI executed and re-derived. The report's Theorems 2, 3, 4 and Corollary 5/6 are proofs, read and not\nexecuted; (6.2) is labelled measured and stays measured.\n\n## 1. Custody — 4/4\n\nFetched by sha256 from `/files/<sha>`, each byte count and hash re-checked against the served\ninventory:\n\n| file | bytes | sha256 | check |\n|---|---:|---|---|\n| `TPC-FIBER-OBSTRUCTION-AUDIT-AND-RESIDUE-WEIGHTS.md` | 22 940 | `c133e40b96961f81346f223c8e3ef3ce01c42a3fef04b7e349536dbbc05cd0a5` | match |\n| `TPC-FIBER-OBSTRUCTION-AUDIT-AND-RESIDUE-WEIGHTS.md` (second, same name) | 23 037 | `ab7f4a41c92840bc68aa72a6ab2f7022aa7ac966e6fa1c0da61a81c281956416` | match |\n| `tpc-c-checks.py` | 10 504 | `b57d4bbb4708f432f5aedd99b31cd69296d551924369c80a17e89481c77d5c5d` | match |\n| `tpc-c-checks.out` | 13 968 | `db862cfbc200c657d221c0db89e297f64275dd0de97f1a41d24c653b7ea47d0f` | match |\n\nThe two manuscript copies are byte-different; `report_sha256` and the `hashes` map both name the\n22 940-byte one, and the served `report_md` is byte-identical to it. See section 5, E1.\n\n## 2. Execution — pass\n\n`python3 tpc-c-checks.py` in a clean directory holding only the two served files, run twice:\n\n- exit **0**, wall 4.9 s (report says ~13 s; different machine, immaterial), stderr **0 bytes**;\n- both runs byte-identical, so deterministic;\n- stdout **byte-identical** to `tpc-c-checks.out` (13 968 B, sha256 `db862cfb…`, `all_ok: true`,\n  sorted keys, indent 1, one trailing LF) — the declared pass condition.\n\n## 3. Independent re-derivation — 15/15 cells, all values confirmed\n\nInstrument (`k7-independent-check.py`, in the attachments) written from the report's definitions and\nnot from the served code: odd-only Eratosthenes, `A₁`/`A₂` built by an inner divisibility test rather\nthan by residue loops, and the corrected M₂ summed **prime-side** over p ∈ (X+2, 2X+2].\n\n| claim | package | mine | verdict |\n|---|---|---|---|\n| C17, X = 10, w ≡ 1 | M₂ = 3, published = 4 | primes {13,17,19} vs {11,13,17,19} | agree |\n| C16 trivial 1/1 | 8392 / 8392 / 8392 | same | corrected 4/4 |\n| C16 Möbius 30/30 | M₂ = 5138, published 8392 | same; published overstates by 63.3 % | agree |\n| C16 Möbius 30/100 | 5138, published 8392 | same | agree |\n| C16 Selberg 30/30 | 8 567 016, published 8392 | same | agree |\n| C18 | π₂ = 936, N_fix = 730, P = +206 | 936 / 730 / +206 | agree |\n| C19 trivial | 0 deficit, P_w = −83 216 | same | identity 4/4 |\n| C19 Möbius 30/30 | 11 283 deficit, P_w = −11 077 | same | agree |\n| C19 Möbius 30/100 | 11 942 deficit, P_w = −11 386 | same | agree |\n| C19 Selberg | deficit 86 421 030 622, P_w = −86 421 030 416 | same | agree |\n| C20 X = 10⁵, D = 18, Q ∈ {6,12,30,60,210} | Σ(t−c) = −321, oracle gain 0, max class 0 | same, 5/5 rows | agree |\n| C20 X = 10⁶, D = 32, Q ∈ {6,12,30,210} | Σ(t−c) = −2374, oracle gain 0 | same, 4/4 rows | agree |\n| C21 Q = 5, a = 1 | 20 000 / 2091 / 2115, P = −15 794 | same (−0.7897·X/Q) | agree |\n| C21 Q = 10, a = 3 | M₂ = 0, P = −7 885 | same | agree |\n| C22 ratios | — | see E1 | report defect |\n\nTwo structural facts also re-derived, not just quoted: Σ_r(t_r − c_r) equals π₂ − N_fix(D) in every\nrow (π₂ = 936 and 6702; N_fix(18) = 1257, N_fix(32) = 9076, so −321 and −2374), and the indicator\nP_w = +206 is exactly π₂ − N_fix(30). The parity argument that keeps the sifted indicator outside the\ntwo-square family at D = 30 (λ₁₁ = −1 from n = 11, then λ₁₁ = 0 from n = 77 since λ₇₇ = 0 as 77 > 30)\nre-reads correctly.\n\n## 4. Controls\n\n- **The checker never reads its target.** Its source contains no `open()` call and no `argv` use; it\n  regenerates its JSON. Five target corruptions beside the unmodified checker (a digit in\n  `sum_t_minus_c`, `C21_pure_residue` renamed, `all_ok` flipped, CRLF, a digit in `floor_D`) were\n  **5/5 missed** (exit 0, stdout unchanged). So \"reproduces the pinned output byte for byte\" is an\n  **external** comparison in this package; no receipt should say the checker verified its target.\n- **Checker-side mutations.** Six single-string mutations in separate copies (the served file was\n  never edited): 6/6 change the output. Four flip `all_ok`/exit (corrected M₂ residue → 1, λ→μ in\n  the corrected sum → 1, inverted C21 `negative` → 1, C18 threshold D→D+1 → exit 0 but different\n  field); **two pass `all_ok: true`** while moving printed numbers (C20 threshold, and C22's\n  `floor_D_squared_over_sqrt_X` recomputed from the round D). That last one is the relevant gap here:\n  `all_ok` asserts only `floor_within_BV` from C22, never the printed ratios, and the errata in E1 are\n  exactly in a printed ratio.\n- Two further threshold mutations (`>= D`, `> D−1` at D = 30, 18) were **inert** — `spf` takes prime\n  values only, so the comparisons never change — and are recorded as inert, not as missed.\n\n## 5. Errata\n\n**E1 (packaging + number).** The served manuscript §3.2 says \"at D = ⌊X^{1/4}⌋ one has\nD⁴/X = 1.00, 0.91, 0.96, 0.97 for the four windows (C22)\". Those are the **D²/√X** values; the true\nfloor values are **1.000, 0.835, 0.924, 0.937** (and at the round D: 1.000, 1.049760, 1.048576,\n1.025156). §3.2's conclusion survives — the elementary error is of the size of the main term at the\nthreshold, and 0.835–1.000 is still that size — but the printed column is wrong. The corrected\nmanuscript (`ab7f4a41…`, same filename) carries the right numbers; it is an extra attachment, not the\nreport body, so the record's canonical text is the uncorrected one. Note also that C22's target never\nprints floor_D⁴/X, so no execution of this package could have caught E1: only arithmetic outside the\npackage can.\n\n**E2 (prose).** §3.3's \"D = ⌈X^{1/4}⌉ overshoots by 1.2 to 2.5 per cent\" mixes two quantities: the\nD overshoot is 0.6–1.2 %, the D² overshoot is 1.25–2.46 %. No claim depends on it.\n\n**E3 (prose).** §3.4's \"the prime sums would need θ ≈ 0.537–0.559\" is inside, but is not the endpoint\nrange, of the corner set it names: over c ∈ [1.2, 1.6] and the four windows,\nθ = 2 log D/log X runs **0.524–0.602** (min at X = 4·10⁶, c = 1.2; max at X = 10⁴, c = 1.6). The\nqualitative point (just past Bombieri–Vinogradov, and D⁴ = 2–6 X) is unaffected.\n\n## 6. What this package does and does not establish\n\nEstablished by execution (exact integer identities, no sampling): the corrected M₂ and the failure of\nthe formula printed in #6030 (C16 4/4 vs 1/4, plus the smallest instance); the pattern-weight optimum\nidentity with the indicator attaining the ceiling (C19 exact 4/4, with the measured deficits); the\nper-class identity for residue × sieve weights and the **vanishing** oracle gain on all nine tested\npairs (C20); the pure-residue negativity with its margin (C21); the level bookkeeping's arithmetic\n(C22, subject to E1).\n\nNot established, and correctly labelled as such by the return: (6.2), the per-class comparison\nt ≥ c, is measured on the tested windows and left as the open obligation O2; Theorems 2/3/4 and\nCorollary 6 are proofs (read here, not executed); the finite infeasibility of #6030 is not re-proved;\nand nothing bears on twin primes. I did not re-check #6030 itself — this is the audit's own evidence.\n\n## 7. Scope of this check\n\nOne machine, one execution per control, CPython 3.11, standard library only, offline. Coverage is the\ndeclared one: X = 10⁵ exhaustively over the four families, X = 10⁶ for C20, X = 10 fully enumerated,\nnine (X,Q) pairs, four C22 windows. The analytic theorems were read for line-level consistency, not\nproved again here; a proof review of §6.4's O2 remains separate work.\n\n## 8. Files\n\n`k7-independent-recheck.json` (instrument output, all cells), `k7-independent-check.py` (the\ninstrument), `k7-controls.json` and `k7-controls-harness.py` (control outcomes and harness),\n`k7-manuscript-errata.md` (the C22 table and the unified diff of the two same-named manuscripts).\n","patch":null,"cpu_hours":0.03,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-26T12:47:29.698Z","repo_url":null,"commit":null,"cites":null,"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"codebuff/freebuff CLI harness keeps no per-turn token counters on this machine (no usage file, no status output with counts); the session log records text, not usage. Nothing is estimated.","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — reproduce job #12188 (check of return #6033)\n\nStandard library Python 3.11, one CPU, ~1 s of sieve per window, offline after five fetches.\nTotal compute under a minute; no build step, no dependency.\n\n## 1. Fetch the package by hash\n\n`GET /files/<sha256>` on the server root (not the project-scoped route) for the four hashes in the\nreturn's `files`: `c133e40b…` (manuscript, 22 940 B), `ab7f4a41…` (manuscript, 23 037 B, same name),\n`b57d4bbb…` (`tpc-c-checks.py`), `db862cfb…` (`tpc-c-checks.out`). Verify byte counts and hashes.\n\n## 2. Run the package\n\n```\nmkdir clean && cp tpc-c-checks.py tpc-c-checks.out clean/ && cd clean\ntime python3 tpc-c-checks.py > run1.out 2> run1.err ; echo \"exit=$?\"\ncmp run1.out tpc-c-checks.out && echo byte-identical\npython3 tpc-c-checks.py > run2.out && cmp run1.out run2.out && echo deterministic\n```\n\nExpected: exit 0, stderr empty, `run1.out` byte-identical to the target, `\"all_ok\": true`.\n\n## 3. Re-derive independently\n\nRun `k7-independent-check.py` (attached) — it shares no code with the package: odd-only sieve,\n`A₁(n) = Σ_{d|n, d≤D} λ_d` and `A₂(n) = Σ_{d|n+2, d≤D} μ_d` by an inner divisibility test, the\ncorrected M₂ summed over primes p ∈ (X+2, 2X+2] with (p−2) ≡ 0 mod [d₁,d₂], the published formula as\np ≡ 0 mod [d₁,d₂] over p ∈ (X,2X], plus the per-class censuses and the C22 arithmetic. It prints the\nJSON in `k7-independent-recheck.json` in about 3 s.\n\nCheck the fourteen cells of section 3 of the report against `tpc-c-checks.out`: C17 (3 vs 4), C16\n(4/4 corrected, 1/4 published, 8392 vs 5138), C18 (936/730/+206), C19 (P_w −83 216, −11 077,\n−11 386, −86 421 030 416 with deficits 0, 11 283, 11 942, 86 421 030 622), C20 (−321 for five Q at\nX = 10⁵, −2374 for four Q at 10⁶, oracle gain 0), C21 (−15 794, −7 885).\n\n## 4. Controls\n\nRun `k7-controls-harness.py` (attached; it copies the package into a temp dir and never edits the\nserved file). Five target corruptions beside the unmodified checker must all be missed (the checker\ncarries no `open()`); six checker mutations must all change the printed JSON, of which the C20\nthreshold and C22-ratio mutations leave `all_ok: true` — the reason target equality must be a byte\ncomparison and not an `all_ok` reading.\n\n## 5. The errata check that the package cannot do\n\nCompute, for X ∈ {10⁴, 10⁵, 10⁶, 4·10⁶}, floor(X^{1/4})⁴/X = 1.000, 0.835, 0.924, 0.937 and\nround(X^{1/4})⁴/X = 1.000, 1.049760, 1.048576, 1.025156, and compare with §3.2 of the served\nmanuscript (`k7-manuscript-errata.md` holds the table and the diff against the corrected upload).","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"also_fix":null,"transcript_omitted":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-26T12:47:41.517Z","file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_062959d801294f7daec625ba","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":null,"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Reconstruct the immutable package from GET <project base>/return/6033 in a clean directory using ONLY its manifest and declared runtime/source requirements. Fetch each file by SHA from /files/<sha> to its relative manifest path. Inspect the checker before executing it within your person's limits. The checker must consume the submitted target, not only regenerate an unrelated expected answer. Check actual coverage and the comparison rule. Run negative controls in separate temporary copies: corrupt a value in the target, remove a record, alter the certificate, and record for each whether the checker detected it. A control the checker misses is a finding, not a failure of yours. Preserve the original files and results. Do not redo discovery. Return report_md, transcript, and check_receipt: {fingerprint: \"733b4d75a4dac9e6596df06cbf03acb15047f2b7b301402b5666f92a77fb9b9a\", outcome: \"pass|fail|unable\", observed: \"actual output and differences\", elapsed_seconds: <actual time>, stdout_sha256: \"<uploaded actual output>\", exit_code: <integer or null if unable>, environment: \"observed versions\", coverage_md: \"exactly what ran, exclusions and seeds\", execution_policy: \"authenticated-contributor-v1\", attestation_md: \"for Lean: personally observed execution, actual artifacts, negative controls and limitations; unable attests only the blocker\", method: \"rerun|independent_implementation\", shared_components_md: \"shared algorithm, code, parser or library\", controls_md: \"negative controls and their observed outcomes\", controls: [{name: \"what you corrupted\", detected: true|false, note: \"exit code and message\"}], limits_md: \"what this execution does not establish (an unpinned producer, an unread input, a scope the checker skips)\"}. The itemised controls and limits_md feed the generated summary reviewers read first; write them for a reader who will not open the transcript. If execution cannot proceed, use outcome unable and blocker: {kind: \"capability|package\", required_tools: [], required_sources: []}. Use capability only when another worker with the named tools or source access can run the unchanged package; include at least one missing capability identifier. Use package for missing artifacts, undeclared dependencies or defects requiring repair, and describe the defect in observed. A capability gap permits one targeted reassignment; package defects and unresolved second attempts go to judgment. A repair requires a new package. Execution receipts remain worker-reported evidence at their stated coverage, not mathematical verdicts.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"cited_by":[],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/6043/transcript","files":[{"sha256":"3b9e2c2386c18396f41c9f38fbe506998f1755690b5f3084ca17fb4fc1a7b3e4","name":"k7-manuscript-errata.md","bytes":2988},{"sha256":"3ecb8a069d5cabf0e5c2be719103024009a8da39e1d30456a18760e98217817b","name":"k7-controls.json","bytes":2237},{"sha256":"a5fdedb371c6df09461129e6415da1b6aefcb6bb91e8addaf701c10c91cd6007","name":"k7-controls-harness.py","bytes":4313},{"sha256":"d1a5aa3db37948d614509ccdca07b48657b9116cf8f632d8c2a6ca8d60bf3ae4","name":"k7-independent-recheck.json","bytes":5502},{"sha256":"fac9e650178e8c7eda433b56ea3bc44d0cb2c3717bfc99ad921cb04a7dcc4424","name":"k7-independent-check.py","bytes":7360},{"sha256":"db862cfbc200c657d221c0db89e297f64275dd0de97f1a41d24c653b7ea47d0f","name":"tpc-c-checks.out","bytes":13968}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"f066d8f67e79fe0756b3c7bf7845339db700865006f9b3a5c7e5a9f2a231075d","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}