{"id":6044,"job_id":12194,"problem_id":1,"lane_id":null,"type":"check","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #12194 — check of return #6041 (sieve constants of O2, two corrections, the split of T(X))\n\n**Outcome: pass**, with one package defect and three prose/figure errata on the record. The immutable\npackage executes at its stated scope, exit 0 with `\"all_ok\": true`, deterministic, and **every\nprinted number of C23–C28 re-derives in an independently written instrument (160/160 cells, 0\ndisagreements)**. The declared expectation \"the JSON object in `tpc-d-checks.out` byte for byte\" is\n**not** met on this machine: one byte differs (a signed zero, §5 item 1). The checker does **not**\nread its target, so target agreement is an external byte comparison, which is how I made it.\n\n## 1. Package and custody\n\nFetched by hash from the server-root file route (`GET /files/<sha256>`) and re-hashed:\n\n| file | sha256 | bytes | role |\n|---|---|---|---|\n| `tpc-d-checks.py` | `54526993283e3dec…` | 12,390 | checker (declared) |\n| `tpc-d-checks.out` | `37482a8f08b5d24b…` | 6,887 | target (declared) |\n| `TPC-PARITY-SENSITIVE-CORRELATION-ATTACK.md` | `369a9585ac13c283…` | 22,516 | manuscript |\n\n3/3 hashes and 3/3 byte counts match the return's `hashes` map and `files` inventory exactly.\n\n## 2. Execution\n\n`python3 tpc-d-checks.py` in a directory holding only the two package files, unmodified, twice:\n\n- exit 0 both times; stderr 0 bytes; the two runs are byte-identical (deterministic);\n- elapsed 0.29 s (the manuscript's §8 figure of \"about 14 s\" does not reproduce here);\n- `\"all_ok\": true`, 15/15 gates true;\n- stdout is 6,888 B, sha256 `50d62786e00703b7…`; the served target is 6,887 B,\n  sha256 `37482a8f08b5d24b…`; `cmp` reports the first (and only) difference at byte 5588.\n\n## 3. Does the checker cover the claim?\n\nThe checker contains no `open()`, no `argv` and no file I/O: it regenerates a fixed JSON object and\nprints it. Seven corrupted targets placed beside the unmodified checker under the declared name —\na digit in C28's `N`, a digit in C25's `pi_2`, `\"all_ok\"` flipped, the whole C24 block deleted, CRLF\nendings, truncation to 3000 B, two lines swapped — are **7/7 invisible**: exit 0 and stdout identical\nto the reference run, and no target was rewritten. Target agreement in this package is therefore an\nexternal comparison (`cmp`), not a check. Eight single-string mutations in *copies* of the checker\n(the served file was never modified): 5 change the printed JSON, 1 is an invisible weakening\n(C25's 12 % tolerance loosened to 99 %, which prints nothing because the gate is already true), and\n2 are inert here (`all_ok` forced true, `C24_identity` forced true — the gates were already true).\nTwo of the 5 detectable mutations (`BETA2` changed to 4.3, and the C24/C28 sieve threshold moved from\n`z` to `z+1`) change printed fields while `all_ok` stays true: `all_ok` asserts the gates, and C26's\ngate is a comparison of the same constant it prints, so a wrong constant cannot flip it.\n\n## 4. Independent re-derivation of the declared claims\n\nMy own instrument (`b1-independent.py`, a linear sieve for μ and Λ, primes enumerated directly,\nresidue classes walked over primes rather than over n, the C27 pieces rebuilt from the definition)\nreproduces every printed cell: **160 agreements, 0 disagreements.**\n\n- **C23.** All six `(Q,a)` rows: `S_w`, `M_0`, `M_2`, `P_w`, the corrected and published\n  asymptotics, both errors and the overstatement. The algebra is exact: published − corrected =\n  `X(2−ind)/(φ(Q)log X)`, so for `ind = 1` the published form is off by exactly `X/(φ log X)` —\n  4,342.9 at `Q=6, a=1` and 2,171.5 at `Q=10, a=3`, which is what the package prints as\n  `published_overstates_B_by`. The parentheticals `−4482.2` and `−2227.9` are the printed form's\n  absolute errors against the measured `P_w`. The corrected error over the six pairs runs\n  **56.5 to 294.2** (the manuscript's \"−57 to −294\"), and the two admissible pairs agree exactly.\n- **C24.** For `Q ∈ {6,10,30,210}` at `X=10^5, z=17`: the identity `Σ_r(t_r−c_r) = π₂ − N_fix`\n  holds 4/4 (`−321`, `N_fix = 1257`, `π₂ = 936`), `max_r(t_r−c_r) = 0` so `sup = 0 = max(0, …)`, and\n  the classes with `t_r = c_r = 0` number **5, 7, 27, 195** — the non-uniqueness claim, confirmed.\n- **C25/C26.** Sifted counts 716, 4,357, 31,038 at `z = 10, 17, 31`; ratios 5.2263, 4.6549, 4.6312\n  against `16e^{−2γ} = 5.043788`; the exact local products reproduce to the printed digits\n  (`1/14 = 0.07142857…`, 0.04363284…, 0.03104576…); `s = log(2X)/log(X^{1/4}) = 4.30103, 4.24082,\n  4.20069` and `1/β₂ = 0.23439`.\n- **C27.** Three windows: the four pieces, `S_U`, `W_U` and the ratio reproduce to the printed\n  precision; the split identity closes to 2.0e−11, 3.5e−8 and 1.1e−9, i.e. `< 10^{-6}`.\n- **C28.** `4357 = 936 + 1257 + 2164`, `c/t = 1.3429`, `o/t = 2.312`, slack `321 = c − t`, and\n  `t ≤ c ⟺ N ≥ 2t + o`. C29 is present as `C28.upper_constant_over_c = 3.756 = 5.0438/1.3429`,\n  which is what §1.3 quotes.\n\nMapping the `verification_plan`'s declared claims (C23–C28) to these cells: C23 → §C23, C24 → §C24,\nC25/C26 → the sieve-constant rows, C27 → the split table, C28 → the three classes. C29 is a derived\nratio carried inside C28, correctly without its own gate.\n\n## 5. Findings (none changes a claim)\n\n1. **The declared byte-for-byte expectation fails by one byte.** `C27_split[1]` (`X=10^5, U=10`)\n   prints `\"residual_sum_check\": -0.0` where the served target has `0.0` (the split identity is\n   `round((T_bb+T_bs+T_sb+T_ss) − T, 6)`; the unrounded residual is −3.53e−08, and `round` of a tiny\n   negative gives signed zero). No other field of the 303 lines differs. The author's environment\n   (CPython 3.14, per the plan's `environment`) yielded `+0.0` there; CPython 3.11.2 here yields\n   `−0.0`, reproduced by my independent instrument as well. The mathematics is unaffected; the\n   *expectation* is not portable across platforms. Repair: print `0.0` if `abs(residual) < 1e-6`, or\n   drop the strict byte requirement for this field.\n2. **The manuscript's §2.1 table contradicts the package's own C23 output in two of six rows.**\n   *(a)* `Q=5, a=1`: the `M_0+M_2` cell reads 8385, but C23 prints `M_0 = 2091`, `M_2 = 2115`\n   (4,206), and a direct prime count confirms 2,091 primes ≡1 mod 5 and 2,115 ≡3 mod 5 in `(10^5,2·10^5]`.\n   The row's own arithmetic fails too: 8385 − 20000 = −11615, not the `P_w = −15794` it prints.\n   The `M_0+M_2` cell should be 4,206 (the `P_w` cell is right).\n   *(b)* `Q=10, a=7`: the row prints `M_0+M_2 = 3994` and `P_w = −6006`, internally consistent but\n   wrong: C23 prints `M_0 = 2092`, `M_2 = 2094` (4,186), so `P_w = 4186 − 10000 = −5814`, and a\n   direct prime count confirms 2,092 primes ≡7 mod 10 and 2,094 ≡9 mod 10. The first four rows, the\n   `(2.1)`, published and difference columns all agree exactly with C23.\n3. **§1.1's \"12 per cent deficit at z=31\" does not match any quantity in its own table.** The\n   measured ratio is 4.6312 against 5.0438, a deficit of 8.18 %; the asymptotic sieve prediction\n   `32C₂e^{−2γ}X/log²X = 34890.2` against `N = 31038` gives 11.0 %. Cosmetic, but the sentence is\n   the justification offered for the ratios \"approaching\" the limit, and the deficit grows from\n   7.7 % at `z=17` to 8.2 % at `z=31` while `1/log z` shrinks, so the stated `O(1/log z)` mechanism\n   is not what the three rows show.\n4. **§8's \"about 14 s\"** for the program does not reproduce: 0.29 s here (three runs, one CPU).\n5. **The checker's own docstring says `16 e^(-2 gamma) = 5.0449`**, while its code prints 5.0438 and\n   the manuscript uses 5.0438/5.04379 throughout. Comment-only: no output is affected.\n   Also dead: `threshold_X()` is defined and never called (it says so itself).\n\n## 6. Limits\n\nOne execution on one machine (CPython 3.11.2, Linux x86_64, standard library only, offline after\nthree fetches). The package's claims are finite numeric statements at named windows and are all\nre-derived; the analytic content of the manuscript (Theorem 3′, Corollary 5, Proposition 6,\nCorollary 7 and O3) is **read, not executed** — Proposition 6's proof and the Diamond–Halberstam–\nRichert constant `β₂` are quoted from the literature, as the plan itself states. Nothing here\ntouches O2, O3, or twin primes. My check does not evaluate the *decision* to refute #6033's clauses;\nit checks the evidence this return offers for that refutation, and that evidence is sound at its\nstated scope.\n","patch":null,"cpu_hours":0.01,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-26T13:02:29.260Z","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 session: it exposes no token counters and no usage file (its chat log has no usage fields), so no count can be read rather than estimated","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — reproduce job #12194 (check of return #6041)\n\nStandard-library Python 3.11, one CPU, well under 1 GB RAM, offline after three fetches. No build\nstep and no dependency. Total wall time under a minute.\n\n## 1. Fetch the package by hash and verify bytes\n\n`GET /files/<sha256>` on the **server root** (not the project-scoped route) for the three hashes in\nthe return's `files`:\n\n- `54526993283e3dec8018da5c97e2dd442d6ec44f58ceb7c0f5f82945faac6255` → `tpc-d-checks.py` (12,390 B)\n- `37482a8f08b5d24b1a2616bb10bde8258fee58721f951cccf20dd240e9db3ea7` → `tpc-d-checks.out` (6,887 B)\n- `369a9585ac13c2833531dbe661dedd4cba5b0e17118493b2742a6d203272bfeb` →\n  `TPC-PARITY-SENSITIVE-CORRELATION-ATTACK.md` (22,516 B)\n\nRe-hash each file; all three must match.\n\n## 2. Run the package unmodified, twice\n\nIn a directory holding only the two package files:\n\n```\npython3 tpc-d-checks.py > run1.out 2> run1.err    # exit 0, stderr empty\npython3 tpc-d-checks.py > run2.out                # exit 0\ncmp run1.out run2.out                             # identical (deterministic)\ncmp run1.out tpc-d-checks.out                     # ONE byte differs: byte 5588, line 246\n```\n\n`b1-stdout-run1.out` is the actual stdout of the first run (6,888 B). The single difference is\n`\"residual_sum_check\": -0.0` in `C27_split[1]` against `0.0` in the target; every other field agrees.\nTiming: 0.29 s per run.\n\n## 3. Negative controls\n\n```\npython3 b1-controls.py     # writes b1-controls.json\n```\n\n- **Target corruptions (7).** Write each corrupted copy of the target under the declared name\n  `tpc-d-checks.out` beside an unmodified `tpc-d-checks.py` and run: a digit in C28's `N`, a digit in\n  C25's `pi_2`, `\"all_ok\"` flipped to false, the C24 block deleted, CRLF endings, truncation to\n  3000 B, two lines swapped. All 7 are invisible to the checker (exit 0, stdout identical to the\n  reference run) and none is rewritten by it — the checker has no file I/O.\n- **Checker mutations (8), each in its own copy.** `BETA2 → 4.3`; the C23 `admissible_forms == 2`\n  branch → `== 3` (exit 1, `all_ok` false); C25's 0.12 tolerance → 0.99 (invisible); a printed-only\n  field changed (visible in stdout, `all_ok` unchanged); `all_ok` forced true (inert); C24's\n  threshold `z → z+1`; C28's threshold `z → z+1` (both change printed fields, `all_ok` unchanged);\n  `C24_identity` forced true (inert).\n\n## 4. Independent re-derivation\n\n```\npython3 b1-independent.py   # writes b1-independent.json; prints agreements/disagreements\n```\n\nA linear sieve for μ and Λ, primes enumerated directly, residue classes walked over primes, and a\nC27 routine rebuilt from the definition `A(n) = Σ_{d|n, d≤U} μ(d) log(n/d)`. Every printed cell of\nC23–C28 is compared against the target: **160 agreements, 0 disagreements** (integers compared\nexactly; floating-point cells within 1e−4 relative or the printed rounding).\n\n## 5. Manuscript figures\n\n`b1-manuscript-figures.md` holds the two §2.1 table rows checked three ways (package C23, this\ninstrument, and a direct count of primes by residue class in `(10^5, 2·10^5]`), plus the §1.1 and §8\nfigure discrepancies.","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":"2026-10-26T13:03:02.860Z","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_c25b61e78116a63a213c16ea","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/6041 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: \"eae2064a94faa04ac22d23d6f6b056eba407aa8880ed82ea67f23d587c973ed4\", 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/6044/transcript","files":[{"sha256":"122315060fe03fb444a6da76f6a4c8e48683992290b53db247a5a5be07bdafa4","name":"b1-independent.json","bytes":14968},{"sha256":"1e4ab3775d4a3e9ab4b7ae2d623c896d9c599f9390cb2fce62e833ff765fe3e3","name":"b1-independent.py","bytes":13223},{"sha256":"4e0c6425c949a158491410ea45e0074369715cc99a7752306a95f4e27c87f10a","name":"b1-controls.py","bytes":6850},{"sha256":"50d62786e00703b7e835842e0d5876f1612da3b679ae82fd319a998931485b64","name":"b1-stdout-run1.out","bytes":6888},{"sha256":"96bf2e71fc76190d187769537b3fe055fbab18f46827f92a6de1682baf9697b6","name":"b1-manuscript-figures.md","bytes":3579},{"sha256":"a0963d6064d80d8aea3fe21b7990637294d1f4c0ed9db0ea589e4f7f312fcc66","name":"b1-controls.json","bytes":4791}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"455310696fd06b420ca1413a814c48d850cb5ca854ad9643f0ce2ecada5bd932","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}