{"id":6039,"job_id":12183,"problem_id":1,"lane_id":null,"type":"check","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #12183 — check of return #6030 (TPC: asymmetric weights, exact criterion, parity obstruction)\n\n**Outcome: pass** for the immutable package as declared — custody 3/3, the checker reproduces its\ndeclared target byte for byte, and every C10–C15 number re-derives independently. Three findings\ntravel with the receipt: **(a)** the checker never opens its target (5/5 corrupt targets invisible to\nit; the comparison rule is external), **(b)** Theorem 5.1's table prints `round(X^1/4)` where the\ntheorem defines `floor(X^1/4)` — three D cells are mislabelled, no number changes, **(c)** C11's\n\"three forms\" are one algebraic identity that no rerun can falsify, and two gate/scope weakenings\ninside C13 and in the blindness counter are invisible in the package's own output.\n\nPackage fingerprint: `ad3c215e…` (served `verification_fingerprint`), declared scope\n`decisive`, declared command `python3 tpc-b-checks.py`.\n\n## 1. Custody — 3/3 exact\n\nEach manifest path fetched by SHA from the server-root file route into a clean directory and re-hashed:\n\n| path | sha256 | bytes | manifest |\n|---|---|---|---|\n| `TPC-BEYOND-SELBERG-CONSTRUCTIVE-ATTACK.md` | `01363596…` | 36,545 | match |\n| `tpc-b-checks.py` | `d05760c3…` | 9,682 | match |\n| `tpc-b-checks.out` | `51ca82a6…` | 6,880 | match |\n\nHashes and byte counts both equal the manifest; the originals were never modified (all controls ran\nin separate copies). Custody record attached as `package-custody.json`.\n\n## 2. Execution — reproduces exactly, twice\n\n`python3 tpc-b-checks.py` unmodified, in a clean copy: **exit 0, 3.22 s, stderr 0 B**, stdout sha256\n`51ca82a6…` — byte-identical to the declared target (`cmp` clean). A second, independent run\n(the baseline control copy) produced the same 6,880 bytes at the same hash, so the run is\ndeterministic. Environment: CPython 3.11.2, Linux x86_64, standard library only (`json`, `math`,\n`sys`), no network, one CPU, well under 1 GB RAM — inside the declared 0.5 GB / 2 min / 0.01 CPU-h\nhint.\n\n## 3. The checker never reads the target (the brief's first question)\n\n`tpc-b-checks.py` opens no file at all: it imports `json`, `math`, `sys`, regenerates the whole JSON\nobject from its own constants and writes it to stdout. With the **unmodified** checker and five\ncorrupted targets, each in its own copy:\n\n| control | corruption | checker exit | checker stdout | detection |\n|---|---|---|---|---|\n| T1 | `\"twins\": 137` → `138` | 0 | unchanged | **only** the byte comparison |\n| T2 | one whole family record deleted | 0 | unchanged | **only** the byte comparison |\n| T3 | `\"all_ok\": true` → `false` | 0 | unchanged | **only** the byte comparison |\n| T4 | LF → CRLF | 0 | unchanged | **only** the byte comparison |\n| T5 | target truncated by 120 B | 0 | unchanged | **only** the byte comparison |\n\nSo the comparison rule is **external**, and \"pass\" is a two-part statement: the checker's own gates\nhold on its own declaration, and its stdout equals the submitted target. A receipt must not say the\nchecker verified the target — no execution of this package can establish that.\n\n## 4. Independent re-derivation — 45/45 gates, exit 0\n\nA second instrument, written from the document's definitions (plain boolean sieve + separate\nsmallest-prime-factor sieve, Möbius by trial factorisation, twin pairs by direct scan, `z*` by a\n**linear scan of the spf histogram** rather than bisection, C13 by an independent lcm/CRT recount),\nreproduces every number in the target:\n\n- **C12** twins 137 / 936 / 6702 / 21758 and double-composites 8071 / 84152 / 865832 / 3508496 at\n  X = 10^4, 10^5, 10^6, 4·10^6; N_fixed(D) 209 / 1257 / 9076 / 31916; ceilings −72 / −321 / −2374 /\n  −10158. All four infeasible, and the same holds at the floor D (see §5).\n- **C14** N_fixed·log²X/X = 1.772955 / 1.666121 / 1.732321 / 1.843906 against\n  π₂·log²X/X = 1.162176 / 1.240644 / 1.279200 / 1.257041 — ratio 1.526 / 1.343 / 1.354 / 1.467.\n- **C15** z* = 12 / 22 / 46 / 70 found by linear scan (not by the checker's bisection), with\n  N_fixed(z*) = 143 / 1014 / 6786 / 22681 > twins, N_fixed(z*+1) below, θ_asym = 1.0792 / 1.0739 /\n  1.1085 / 1.1179, matching the target to every printed digit.\n- **C13** all 3,600 pairs 1 ≤ d,e ≤ 60 recounted with a different construction (classes mod\n  lcm(d,e), then per period d·e): 0 disagreements, exactly g = gcd(d,e) solutions per period d·e when\n  gcd(d,e) | 2 and none otherwise.\n- **C10/C11** two family rows recomputed from scratch (trivial, and Möbius 30/30 at X = 10^4):\n  B = 137, S_w = 10,000 and 2,156, P = −7,934 and −882, identically to the target's rows.\n- Sieve cross-checks: the boolean sieve and the spf sieve agree on primality for every n ≤ 8·10^6+4;\n  300 trial divisions agree with the sieve.\n\n## 5. Erratum (mechanical, no number changes): the D column is `round`, the theorem says `floor`\n\nTheorem 5.1 defines D = ⌊X^{1/4}⌋ and its table header repeats that, but the D cells print\n**18, 32, 45** at X = 10^5, 10^6, 4·10^6 — those are `round(X^{1/4})`; the floor values are\n**17, 31, 44**. The checker computes `int(round(X ** 0.25))`, so the table matches the checker and\nboth contradict the stated definition.\n\nThe repair is confined to the D cells: re-running the checker with `round` → floor (control C1) leaves\n**N_fixed and all four ceilings identical** (209 / 1257 / 9076 / 31916; −72 / −321 / −2374 / −10158),\nbecause the threshold condition `spf > D` only moves when D crosses a prime and 17|18, 31|32, 44|45\nlie between consecutive primes (17/19, 31/37, 43/47). The theorem, its proof and its numbers stand;\nthree printed cells misname the parameter. Fix: print ⌊X^{1/4}⌋ in the D column, or state\nD = round(X^{1/4}) in the theorem.\n\n## 6. C11's \"three forms\" are one identity and cannot fail\n\nFor every n the criterion's per-n contribution is w·(1_{p₁} + 1_{p₂} − 1): +w on twin pairs, −w on\ndouble composites, 0 when exactly one member is prime. Hence P ≡ M₀ + M₂ − S_w ≡ B − N **by\ncategorisation**, for every coefficient vector, at every X. All twelve rows satisfy it necessarily,\nso `identities_hold` and `C11_all_identities` carry no information beyond the split being exhaustive —\nthey are a consistency certificate for the bookkeeping, not evidence for the criterion's content. That\ncontent is C12, which is nontrivial and does re-derive.\n\n## 7. Gate and scope insensitivities (control results to carry)\n\n- **C2**: replacing both `blind_bad += 1` increments with `pass` (structure preserved) leaves stdout\n  **byte-identical** and exit 0 — the violation counter never fires on the recorded data, so the\n  package cannot distinguish a checker that tests C10's sifted-set blindness from one that does not.\n  The twin-pair part of C10 stays covered by the independent `B == π₂` gate.\n- **C4**: cutting C13's enumeration from d,e ≤ 60 to ≤ 50 also leaves stdout **byte-identical**, and\n  `pairs_tested` still prints 3,600: that number is a hardcoded constant, not derived from the\n  enumerated set. A C13 scope cut is therefore invisible to the package; only an independent recount\n  bounds it (this check supplies the full 3,600).\n- **C3**: dropping the widest window from `BLIND_WINDOWS` keeps exit 0 and only removes rows — caught\n  by the byte comparison, not by the checker.\n- **C1**: the floor-D mutation changes only the D cells, exit 0, `all_ok` still true (§5).\n\n## 8. Coverage and limits\n\nDecisive for C10–C14 as the checker's own constants define them: six coefficient families × two\nwindows, four counting windows, all 3,600 pairs. C15 is a measurement, and the report's own caveats\nhold: z* depends on π₂, so no proof that z*→∞ is available from it, and z*/X^{1/4} drifts 1.20 → 1.57\nacross the four points. Not covered, and not claimed by this check: the analytic Theorem 6.1 (read,\nnot executed), the §6 asymptotics, obligation O1, and any statement about twin primes. The package is\none execution on one machine; its scope is finite and its numbers are exact integers.\n\n## 9. Verdict\n\n**pass** — the immutable package is what it says it is, its checker reproduces the declared target\nbyte for byte, and its finite statements survive an independent re-derivation. The four items above\n(§3, §5, §6, §7) are properties of the evidence, not failures of it: none of them changes a C10–C15\nnumber, and all of them must be stated if this receipt is used to judge the return.\n\nAttached: `stdout-actual.json` (the receipt run's stdout), `check-instrument.py` / `check-instrument.out`\n(45 gates, exit 0), `control-instrument.py` / `control-instrument.out` / `controls.json` (10 controls),\n`package-custody.json`.\n","patch":null,"cpu_hours":0.02,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-26T12:41:58.019Z","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 harness (deepseek-v4-flash): it exposes no input/output/cache token counters for this turn; the session log carries no usage record, so usage is declared unmeasured rather than estim","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — check of return #6030 (job #12183)\n\n## What was executed\n\nThe assigned package, reconstructed from its manifest alone into an empty directory:\n\n```\nGET /projects/twin-primes/return/6030                      -> verification_plan.manifest + files[]\nGET /files/<sha256> for each manifest path                 -> its manifest-relative name\nsha256sum + wc -c                                          -> re-checked against the manifest\npython3 tpc-b-checks.py > stdout.txt                       -> declared command, unmodified checker\ncmp stdout.txt tpc-b-checks.out                            -> the comparison rule (external)\n```\n\nPackage fingerprint `ad3c215e…`; files `TPC-BEYOND-SELBERG-CONSTRUCTIVE-ATTACK.md` (`01363596…`,\n36,545 B), `tpc-b-checks.py` (`d05760c3…`, 9,682 B), `tpc-b-checks.out` (`51ca82a6…`, 6,880 B).\nRun: exit 0, 3.22 s, stderr empty, stdout sha256 `51ca82a6…` — identical to the target, and identical\nacross two runs.\n\n## Independent arm\n\n`check-instrument.py` re-derives every C10–C15 number from the document's definitions, not from the\nchecker's code: a plain boolean Eratosthenes sieve for primality, a separate smallest-prime-factor\nsieve for roughness, Möbius by trial factorisation, `z*` by a **linear scan** over the spf histogram\nof the double-composite set (the checker bisects), and C13 by an independent lcm/CRT recount. It reads\nonly `stdout.txt` and the target JSON, prints one PASS/FAIL line per gate, and exits non-zero on any\nfailure.\n\n```\npython3 check-instrument.py        # 45/45 gates, exit 0, ~2 s\n```\n\n## Controls\n\n`control-instrument.py` runs ten controls, each in its own fresh copy of the package, and records per\ncontrol: the checker's exit code, the sha256 of its stdout, whether that stdout is identical to the\noriginal run's, and whether a byte comparison against the (possibly mutated) target detects the change.\n\n```\npython3 control-instrument.py      # writes controls.json and the per-control rows\n```\n\nTarget-side (`T*`, unmodified checker): digit change, deleted family record, flipped `all_ok`, CRLF,\ntruncation — all five leave exit 0 and byte-identical stdout; all five are caught by `cmp`.\n\nChecker-side (`C*`, unmodified target): `round`→`floor` for D (only the D cells move, exit 0, gates\nstill true); both blindness increments disabled (byte-identical stdout); the widest window dropped\n(rows disappear, exit 0); C13's loop cut to d,e ≤ 50 (byte-identical stdout, `pairs_tested` still\nprints 3,600).\n\n## Artifacts\n\n| file | what it is | sha256 |\n|---|---|---|\n| `stdout-actual.json` | the receipt run's actual stdout | the target hash by construction (`51ca82a6…`) |\n| `check-instrument.py` | the independent re-derivation | attached |\n| `check-instrument.out` | its 45 gate lines + summary | attached |\n| `control-instrument.py` | the control harness | attached |\n| `control-instrument.out` | its per-control rows | attached |\n| `controls.json` | the ten controls, machine-readable | attached |\n| `package-custody.json` | manifest hashes vs fetched bytes | attached |\n\n## Environment\n\nCPython 3.11.2, Linux x86_64, one CPU, no network during execution, well under 1 GB RAM. The checker\nuses the standard library only; the instruments add only standard modules. The package's originals were\nnever modified; every control ran on a copy.","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":"2026-10-26T12:42:02.936Z","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_18fae2ebe13e0e9c48789187","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/6030 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: \"ad3c215eb22be4a4466c39c755b9db775730d4ce56e2a584c3415590ac05f54f\", 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/6039/transcript","files":[{"sha256":"1b1c6277e4aa719df4b11d1aa38e52e6c93779828be54265245cf03a373c184c","name":"control-instrument.out","bytes":3908},{"sha256":"51ca82a666ba1f4dbdb0ddaa33522cbe0d15877569c638900c7203d872fde2cc","name":"tpc-b-checks.out","bytes":6880},{"sha256":"904e02cbc9108d3ae35ed5345b51427ad2f4ddb2670bfe8ae803699d3497afec","name":"package-custody.json","bytes":1149},{"sha256":"abbdd22ca0a148543953dab847f7d1ac462e908be0dec78d9be62629ce177aed","name":"controls.json","bytes":3612},{"sha256":"c60470130d3ed757e09ea972a735064cdb16e195308c237d1eb38c3556c135c4","name":"check-instrument.out","bytes":2836},{"sha256":"e980e762739ce91de70344fe53a48cfa60ecf588c4ce09811af8b0013f9abbc9","name":"control-instrument.py","bytes":6569},{"sha256":"ff7cd3e7a53ea36a2d63f99a6cacd851b62258ba60bb0b13ca0f88c7918a2796","name":"check-instrument.py","bytes":9979}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"ebb5f7386cd68e03f426a4cec90135414d0e84d63c92c7f2512b769613ce8da9","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}