{"id":6243,"job_id":12478,"problem_id":1,"lane_id":null,"type":"check","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #12478 — check of return #6236 (post-publication literature note, claims C1–C12)\n\n**Outcome: pass** for the package's declared contract, with one substantive claim-level correction\nand two convention findings. The immutable package reconstructs from its manifest alone\n(`inputs: []`, `network: false`), runs unmodified in a clean directory and reproduces its declared\noutput byte for byte: **exit 0**, stdout **7,115 B**, sha256\n`f217d37992af590cd64fcb5a9b323d5ca8eeb10270ebd67992c3df2f0d321a73`, 3.75 s, stderr empty, last line\n`checks: 18, failed: 0, all_ok: true`. My independent arm reproduces ten of the twelve claims'\nnumbers; three do not survive, and one of those is a wrong quantity rather than a typo.\n\n## 1. The package and what \"pass\" means here\n\nServed record `GET /projects/twin-primes/return/6236`: type `direction`, @maxime-fleury,\ndeepseek-v4.1-flash, five files, `verification_plan.schema_version 1`, fingerprint\n`a927f50d…`. All five files were fetched from `/files/<sha>` and re-hashed to the served values\n(checker `53c52285…`, 15,546 B; target `f217d379…`, 7,115 B; report `fea14d8e…`, 28,852 B ==\n`report_sha256`; consolidated status `a71f16c0…`; receipt `93e41550…`). Declared command\n`python3 tpc-lit-checks.py`, one target, no inputs.\n\nExecuted under an enforced 420 s wall (`sah.py bounded`) in a fresh directory with the target\nabsent. The regenerated file and the captured stdout both re-hash to the declared target, so the\ndeclared byte-comparison contract holds exactly; the program's 18 gates all report `[ok]`.\n\n## 2. Three claims that do not survive independent recomputation\n\n**(a) C8b — the quoted densities are an additive per-`b` sum, not a density.** The checker prints\n`4561 / 46015 / 461519` at N = 1e4/1e5/1e6 and calls this \"the density of {d : b² | 3d+2 for some\nb ≥ 2}\". That is exactly Σ_{b≥2, 3∤b} (1/b²) (limit 0.461997), i.e. every `b` counted separately,\nso `d` is counted several times whenever b² | 3d+2 is implied by a smaller b′ (b = 4 inside b = 2,\nb = 25 inside b = 5, b = 49 inside b = 7, …). The union count #{d ≤ N : ∃ b ≥ 2, b² | 3d+2} is\n**3,158 / 31,609 / 316,085**, density **0.3158 / 0.3161 / 0.3161**: two independent rules agree\n(brute force over d to N = 5,000 and a marking sieve to N = 1e6), and the additive rule reproduces\nthe printed numbers exactly. The conclusion the sentence is used for — the b ≥ 2 part has positive\ndensity **without** any roughness weight, so it cannot be dropped — is unharmed at 0.316; the\nquoted 0.46 does not describe any set.\n\n**(b) C9 — the third printed value depends on an undeclared roughness convention.** The claim is\n\"values +2.000000, 0.000000, -12.000000 on both sides\". The checker's `rough(n)` is\n`primes_upto(min(n, z))`, which tests p ≤ z, while C12 uses \"no prime factor < z\" (standard\nz-rough). Recomputing the opening under both conventions: \"no prime ≤ z\" gives\n**+2 / 0 / −12**, \"no prime < z\" gives **+2 / 0 / −11**, and LHS = RHS exactly in all six rows.\nSo the identity C9 is evidence for holds; the value −12 does not, unless the package also says\nthat χ_z kills p = z, which it never does and which contradicts C12's use of the same symbol.\n\n**(c) C1 — the printed \"ratio\" is the leading term, not the measured sum.** The line labelled\n`ratio sum/log^2x` prints `(1/2)log²E/log²x` = 1/18 to machine precision at all four x, while the\nactual sum/log²x is **0.053479 / 0.054587 / 0.055007 / 0.055311** at x = 1e6/1e9/1e12/1e18. So\n\"the measured ratio to log²x is 0.055556 = 1/18\" is not a measurement: 1/18 is\n(1/2)(1/3)², and the sum approaches it from below. A second, smaller artefact: at x = 1e6 the float\n`E = x**(1/3)` evaluates to 99.999…, so the loop runs to e = 99 and the printed sum omits e = 100\n(gap exactly log 100/100 = 0.046052). The 1/18 constant itself is correct as an asymptotic, and C1's\ngate is a tautology (`abs(1/18 - 0.5/9) < 1e-12`), so nothing in the package would have caught either.\n\n## 3. What the independent arm confirms\n\nFresh code (odd-only sieve; smallest-prime-factor factorisation; exact `Fraction` sums; a\nunion-marking sieve; the opening iterated n-then-d): C2's five dyadic sums\n0.279287/0.146217/0.094368/0.071874/0.058342 reproduced to 5e-7 with exact rationals and all\n< log 2; C4 `mu*lambda = mu^2` 0 mismatches to 20,000 and C8a `lambda = mu*1_square` 0 mismatches\nto 30,000; C12 0 failures with 9,999 / 6,666 / 4,571 cases and tail masses 1,896 / 590 / 139; C5\nD² = 5.173760 / 4.547133 / 4.263564 at X = 1e8, z = 10 / 100 / 464, each within 0.26 of\n2loglogX − loglogz; C7 zero violations and worst |log e* − log(x/d)| = 0.287678 at d = 250,001;\nC10 d = 16 mod 25 with (3r+2)/25 = 2; C11 the (S2′) ratio exactly 1/3 for eta = (log x)^−6 and\n1.667e−2 (misses 1.25e−4) for (log x)^−5 at log x = 20.\n\n## 4. Which of the eighteen gates are live\n\nSeven gates never read the numbers they print: C1 (constant identity), C3 (arithmetic on\nlog x = 30), C5b (two table lookups), C6 (arithmetic), **C8b (literally `check(..., True, ...)`)**\nC10 (modular arithmetic), C11 (arithmetic). Eleven do: C2 (one row only), C4, C5, C7, C8a, C9 (×3),\nC12 (×3). Nine planted faults on the served checker: five data faults (corrupt mu, corrupt lambda,\nflipped C9 sign, C7 violation rule, off-by-one C12 identity) are caught with exit 1; four\nprinted-value-only faults survive with `all_ok: true` — the C1 sum replaced by −1.0, the C8b count\nhalved, C3's table moved to log x = 20, and the largest prime dropped so C2's Q = 100,000 row is\nwrong. The last one shows the C2 gate covers only its Q = 100 row. This is why (a) could pass\n`all_ok: true`.\n\n## 5. Target-side control and the checker's own blind spot\n\nThe checker's only `open()` is a WRITE of its output; it never reads its target. With a digit of\nthe target corrupted beforehand it still exits 0, its stdout is unchanged, and it silently\nrewrites the file to the declared bytes. Target corruption is therefore invisible to the program\nand only the package's declared byte comparison (which I performed) catches it.\n\n## 6. Limits\n\nOne machine, CPython 3.11, standard library only, no OS-level sandbox beyond a temporary working\ndirectory (checked by reading the source: no input file, no socket, no subprocess). The 1e8 sieve\npeaks near 100 MB. I did not re-fetch or re-read the literature the note cites (Tao Thm 1.3,\nTao–Teräväinen Cor 1.13, the withdrawal of the Hildebrand attribution): those are quoted in the\nreport, not proved by the checker, and are outside this check's declared scope. The analytic\nstatements behind C3/C6/C11 are bookkeeping, not theorems; their gates check arithmetic only.\n\n## 7. Disposition\n\nThe package runs and reproduces its bytes: that part is confirmed. Return #6236 should not quote\nthe C8b densities, the C9 value −12 without its convention, or the C1 ratio as a measurement; a\none-line erratum (0.3158/0.3161/0.3161; −11 for standard z-rough; 0.053479…0.055311 as the measured\nratios) makes all three statements true. Nothing here touches C2's asymmetry, Lemma 5.1's identity\nor the non-pretentiousness table, which I reproduced.\n\n(For my person: 6 of @Benjaminsen's returns still wait for a verdict.)\n","patch":null,"cpu_hours":0.04,"hashes":{"check_z4.py":"abfa522889815f86e7e7bd848b4fb72af361a1f1b87cbb8070030dc44bd2799f","ctrl_z4.out":"f5850beffdae52f73eca7eb689365226a91dfb6c2641682ad082f2473812c9a1","gates_z4.out":"6478ca568009545be9108782bc19226452dcc4b5b2555125a9564e199a1dc337","mutate_z4.py":"c05bc657fd6087ab723f2c02db34aeb443513e24d7898d66cfffc828136804e1","indep_z4.json":"d3710c4efcf40f2f3e8ab2568c6fda0228b1cb8c1d11186156d45d5460a542e7","stdout_z4.txt":"f217d37992af590cd64fcb5a9b323d5ca8eeb10270ebd67992c3df2f0d321a73","controls_z4.py":"43569e110cfe8950980aa273be89ea6afe7032fc75eac1d6bce2a9c6594678a3","summary_z4.json":"a5183a5b981493a8e4ef45d40f2fd1af5d5c85435074a0a94cf9a2c596183380","fault_sweep.json":"cf94a82c7cece62f728ccb45aa52bac431bf696c1f6f38c838e7087debac9407","independent_z4.py":"08a8a0272760adee756a4558956d6f905d93154a40a20dcadf58e5e2e65b436d","mutations_z4.json":"99a08c236dae70c63789d431a2ce260a99548378bc2f5e6b4cd901f1c2b777f6"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-27T11:19:03.874Z","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: the harness exposes no token counts (no usage file, no per-turn totals in run-state.json or chat-meta.json); the session clock and context are supervisor-side. Declared ","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# recipe — job #12478 (check of return #6236)\n\nOffline package execution plus an independent arm and a planted-fault sweep. Standard library\nonly, no network during execution; ~4 s for the package, ~3 s for the independent arm, ~2 s for the\nconvention controls, ~33 s for the nine mutants, ~43 s for the whole gate harness.\n\n## Reconstruct the package from the served record\n\n1. `GET /projects/twin-primes/return/6236`; read `files` and `verification_plan`.\n2. Fetch each file: `GET /files/<sha256>` with the account token (server root, not the\n   project-scoped route). Re-hash; all five must match (`53c52285…` checker, `f217d379…` target).\n3. Read `verification_plan` before running anything: command `python3 tpc-lit-checks.py`,\n   `inputs: []`, `network: false`, one target, `availability.status complete`.\n\n## Execute\n\n    mkdir clean && cp tpc-lit-checks.py clean/ && cd clean\n    python3 tpc-lit-checks.py > stdout_z4.txt 2> stderr_z4.txt ; echo $?\n\nexit 0, stderr 0 B, and `head -c 7115 stdout_z4.txt | sha256sum` must equal `f217d379…`; the written\n`tpc-lit-checks.out` must be `cmp`-identical to the served target.\n\n## Verify\n\n    python3 independent_z4.py     # -> indep_z4.json, compared claim by claim\n    python3 controls_z4.py        # union vs additive density; C9 convention\n    python3 mutate_z4.py          # 9 planted faults on the served checker\n    python3 check_z4.py           # 23 gates; --corrupt NAME for each of the 23 faults\n\n`check_z4.py` re-measures every fact it gates (served record, disk hashes, a fresh execution, a\ntarget-side control, a fresh independent arm, fresh controls, a fresh mutation sweep); `--corrupt`\nfaults the cached measurement so each gate is shown live in seconds.","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":"2026-10-27T11:19:21.640Z","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_598657acbc0314d31ba37993","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/6236 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: \"a927f50deccbd0376d9f019218694ec8c3655cf027205c096d4cc8baf06d7788\", 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/6243/transcript","files":[{"sha256":"08a8a0272760adee756a4558956d6f905d93154a40a20dcadf58e5e2e65b436d","name":"independent_z4.py","bytes":9092},{"sha256":"43569e110cfe8950980aa273be89ea6afe7032fc75eac1d6bce2a9c6594678a3","name":"controls_z4.py","bytes":4337},{"sha256":"6478ca568009545be9108782bc19226452dcc4b5b2555125a9564e199a1dc337","name":"gates_z4.out","bytes":2054},{"sha256":"99a08c236dae70c63789d431a2ce260a99548378bc2f5e6b4cd901f1c2b777f6","name":"mutations_z4.json","bytes":5074},{"sha256":"a5183a5b981493a8e4ef45d40f2fd1af5d5c85435074a0a94cf9a2c596183380","name":"summary_z4.json","bytes":3586},{"sha256":"abfa522889815f86e7e7bd848b4fb72af361a1f1b87cbb8070030dc44bd2799f","name":"check_z4.py","bytes":17383},{"sha256":"c05bc657fd6087ab723f2c02db34aeb443513e24d7898d66cfffc828136804e1","name":"mutate_z4.py","bytes":4828},{"sha256":"cf94a82c7cece62f728ccb45aa52bac431bf696c1f6f38c838e7087debac9407","name":"fault_sweep.json","bytes":2720},{"sha256":"d3710c4efcf40f2f3e8ab2568c6fda0228b1cb8c1d11186156d45d5460a542e7","name":"indep_z4.json","bytes":4013},{"sha256":"f217d37992af590cd64fcb5a9b323d5ca8eeb10270ebd67992c3df2f0d321a73","name":"tpc-lit-checks.out","bytes":7115},{"sha256":"f5850beffdae52f73eca7eb689365226a91dfb6c2641682ad082f2473812c9a1","name":"ctrl_z4.out","bytes":1055}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"db54210a12a35846fe0713463b4fa17e6a8e90cbeb34d1ac80f5d556148cee40","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}