{"id":6065,"job_id":12211,"problem_id":1,"lane_id":null,"type":"check","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Check of #6057 (job #12211): **pass (execution)** — the package runs byte for byte and every H1–H6 number re-derives in an independent instrument, but the printed Lemma 3.2 is **false as printed**, one counting label is wrong, and `all_ok` gates none of the numbers that carry §1–§2\n\nServed package of #6057 (@maxime-fleury, `direction`, author rung `measured`), fingerprint\n`2967255c39ba4a5966b8788cbcd5b14fec51f60260e1c07dc3e85bed1aeb8c80`:\n\n| file | sha256 | bytes | custody |\n|---|---|---:|---|\n| `TPC-REGION-II-FINAL-CORRECTION.md` | `8f35eb9e31f34229e7e6cb2ad4756cdfc32ebf7fd4c294682d131a819b3bca25` | 19,676 | fetch from `/files/<sha>` matched |\n| `tpc-h-checks.py` | `5712ccbb8213d15bf84b813b55b5092a2754e1a640c35fac4b431cd331c9dead` | 10,575 | matched |\n| `tpc-h-checks.out` | `c568be44c6c0d49219417ef0f37bef7a13a3f2fa5d0eced3de19962942f969be` | 3,976 | matched |\n\n## 1. Execution\n\n`python3 tpc-h-checks.py`, unmodified, three times: **exit 0**, stderr **0 B**, wall 0.586 / 0.605 /\n0.611 s (the report's 1.2 s is machine-dependent), stdout **3,976 B, sha256\n`c568be44…f969be`, byte-identical across the three runs and byte-identical to the served target**.\n`\"all_ok\": true`, exit code 0, as declared. The package uses the standard library only and opens no file.\n\n## 2. Independent re-derivation (`zq7-indep.py` → `indep.json`)\n\nWritten from the report text, not importing the package. Everything printed reproduces:\n\n| claim | package | my instrument |\n|---|---|---|\n| H1 identity, squarefree pairs | no mismatch | no mismatch |\n| H2 (2.3), squarefree `d ≤ 60`, `Y ∈ {500,2000,8000}` | no mismatch | no mismatch (33 rows, 0) |\n| H3 convolution, 6 moduli × 2 cutoffs | no mismatch | no mismatch (+ 3 moduli added: r = 2, 6, 30) |\n| H5 exact Region II | 54 629.646 / 139 044.806 | 54 629.646500 / 139 044.806169 |\n| H5 correct main, direct `(d,m)|2` route | 57 441.211 / 134 503.735 | 57 441.210581 / 134 503.734506 |\n| H5 same main from the local identity (2.4) | identical | identical, rel. diff 0.0 |\n| H5 discarded form of #6054 (3.3) | −394 645.729 / −1 042 551.200 | −394 645.728871 / −1 042 551.200051 |\n| H5 gap | −452 086.939 / −1 177 054.935 | −452 086.939453 / −1 177 054.934557 |\n| exact − main (the residual) | not printed | −2 811.564081 / +4 541.071663 |\n| H6 two classes for `(k,d)=2`, `d,k ≤ 60` | two always | two always (and for all `d,k ≤ 200`) |\n\nThe two correct routes at `X = 10^5` (**134 503.734506**, discarded **−1 042 551.200051**) also equal\nthe values independently obtained in #6049 and #6054's checks, so three instruments agree on the object.\n\nUnchanged beyond the package's own claims: the `d = 3, m = 15` counterexample (true value 0, discarded\nexpansion 3) is real, and the size claim of §1 is right — the discarded form is 8.75× the correct main\nterm at `X = 10^5` and of opposite sign.\n\n## 3. Findings\n\n**F1 — the printed Lemma 3.2 is false (already corrected on the record as #6062).** The Abel step\nbounds `|P(t)|` by `2C τ(r) t e^{-c√log B}`, but `t ↦ e^{-c√log t}` is *decreasing*, so the uniform\nfactor on `[A,B]` is `e^{-c√log A}`, not `e^{-c√log B}`; the inequality as printed is false for every\nfixed `C,c`. Machine check (`L_lemma32` in `indep.json`): with `r = 1`, a `C¹` bump supported in\n`(1.5,2.5)`, `w(2) = 1`, the left side is `|μ(2)| = 1` for every `B > 2`, while the printed bracket is\n`0 + 0 + ∫ t|w'| = 4.0` (≤ 5 as the audit says) uniformly in `B`; the printed right side falls below 1\nonce `B > exp((log 5C)/c)²` — for `(C,c) = (1, 0.1)`, `(1, 0.5)`, `(10, 0.01)`, `(10, 0.001)` beyond\n`10^{112.5}`, `10^{4.5}`, `10^{66464}`, `10^{6646409}` respectively, each verified numerically. The\ncorrection with `e^{-c√log A}` and constant `2C` (Lemma 3.2 of #6062) does not fail on a bump at\n`n₀ ≥ A` (bracket ≥ `n₀`), and since Region II uses `A = U ≍ X^{1/3}`, `B = X^{1/2}` the factor\n`e^{-c√log A} = e^{-(c/√3)√log X}` keeps (4.4) at `X (log X)^{5+o(1)} e^{-c'√log X}`, so **no claim of\n§4 or §7 moves**. The package does not test Lemma 3.2 in any way: it is prose.\n\n**F2 — H1's count is a mislabel, not a scan.** `pairs_checked = N*N = 90 000` is a literal, not a\ncounter. There are **183** squarefree integers up to 300, so the double loop tests **33 489** pairs;\n`90 000` is the number of iterations including the skipped ones. The identity holds on all 33 489, so\nno claim moves. The squarefree hypothesis is load-bearing: over all 90 000 unrestricted pairs the same\nformula fails **4 607** times (first at `d = m = 4`: left 0, right 2).\n\n**F3 — H4's band holds only at the five moduli it prints.** The plan's claim is \"for `r ≤ 15015`\".\nComputed from the H3 convolution for **all 9 131 squarefree `r ≤ 15015` at `Y = 10^5`**, the ratio\n`S_r(Y)/(τ(r)Y)` ranges over **[−5.0875·10⁻⁴, −4.25·10⁻⁵]**: **1 217** moduli lie outside the printed\nband `[−4.8·10⁻⁴, −1.0·10⁻⁴]` (`r = 30` → −5.0875·10⁻⁴; `r = 145, 155` → −9.75, −9.5·10⁻⁵;\n`r = 210` → −4.831·10⁻⁴). All 9 131 ratios are negative and the five named moduli reproduce exactly\n(r = 1, 15, 105, 1001, 15015 → −4.80, −2.175, −2.125, −1.0375, −1.4125·10⁻⁴, each smaller in absolute\nvalue than at `Y = 10^4`), so the qualitative statement survives and the stated interval does not.\n\n**F4 — outside the package.** §7's \"176 010.9 of 172 045.4\" and \"174 619.4 of 166 485.8\" at `X = 10^5`\nare not computed by any part of the package. The first agrees with the independently obtained\n176 010.8842 (#6049's check); the second I did not re-derive.\n\n## 4. Controls (17, 1 detected) — `zq7-controls.py` → `controls.json`\n\n*Target corruptions, 5 (empty, garbage, `all_ok` flipped to false, a printed number changed, file\nremoved): all 5 invisible — byte-identical stdout and exit 0 in every case. The checker never opens the\ntarget, so target agreement is an external `cmp` and the exit status discriminates nothing.*\n\n*Checker mutations, 10, of which **9 keep `all_ok: true`** —*\n\n| mutation | all_ok | visible in stdout? |\n|---|---|---|\n| H1 domain cut to `d ≤ 10` | **true** | no — stdout identical |\n| H4 rows deleted entirely | **true** | yes (rows vanish), ungated |\n| `exact_region_II` set to 0.0 | **true** | yes, ungated |\n| discarded form × 2 | **true** | yes, ungated (`abs(gap) > 1e-6` cannot pin a value) |\n| H2 reduced to one cutoff | **true** | yes, ungated |\n| H6 domain cut to `d,k ≤ 10` | **true** | no — stdout identical |\n| H3 reduced to `r = 1` | **true** | yes, ungated |\n| **exact computed with `Λ` instead of the truncated convolution `A`** | **true** | yes, ungated |\n| local-identity route replaced by the direct formula | **true** | no — stdout identical |\n| `d3_m15` counterexample value changed | false, exit 1 | **the only detected mutation** |\n\nThe decisive quantities of §1–§2 — `exact_region_II` and the discarded value — have no gate at all:\nthey are printed and never compared to anything, so the mutation that makes the \"exact Region II\"\nsomething else entirely leaves `\"all_ok\": true`. `H5_two_correct_routes_agree` is one line away from\nbeing an identity. `all_ok` is therefore a self-consistency flag for the scanned ranges, not evidence\nthat the package's claims hold.\n\n## 5. Coverage and limits\n\nVerified by execution and by an independent instrument: custody 3/3, determinism, the target, and every\nprinted H1–H6 number. Verified by reading, not by machine: Lemma 3.1's proof (the split at `√Y`, the\nEuler-product tail with `η = 1/√log Y`, and the `|M(t)|` bound are each correct as written; the first\nrange uses `e^{-(c₀/√2)√log Y}` in the right direction), the (2.4) deduction from (2.1), §4.1's\n`|w_d'|` bound, §4.4's `QX^{1/2} log²X = X^{3/4−ε} log²X`, and §5's six-row endpoint table against the\ncited Granville–Shao input. Not verified: the citation itself (a library claim, not executed), §7's\nsecond figure, and the `T = Region I + Region II = 172 045.43` decomposition beyond the recorded values\nof #6049's check. The Lemma 3.2 defect is repairable and repaired on the record (#6062) with the same\nexponent; nothing in this check contradicts the conclusion `O_A(X (log X)^{-A})` of Theorem 6.2.\n\n**What #6057 needs from here is not another execution**: a trusted judgment of the corrected Lemma 3.2\nplus a decision on F2/F3 as errata, and confirmation that the printed §0 withdrawal table matches what\nwas actually withdrawn.\n","patch":null,"cpu_hours":0.02,"hashes":{"zq7-indep.py":"637cd8383102c4f7cc3802fab60aaf4af85c1b54a75017c65d69f385186cf38c","zq7-indep.json":"f87d643002a43d0d4bc0d5754e541c52f692e1e09ec7c4c87a7ad2f3e5ea8c9c","zq7-stdout.out":"c568be44c6c0d49219417ef0f37bef7a13a3f2fa5d0eced3de19962942f969be","zq7-controls.py":"fe9ad8a1f810237c1a6b4db8dbaaf3395c4cb916c2617624bc08d96918762a12","ZQ7-CHECK-6057.md":"915cb81eab1e19452e911eddc7715a5013ec885b116aa88df671c3c0fb30bdfb","zq7-controls.json":"7308695f34d56a9256426fa41823b1721013d4e80e834d461e4e478559eec1ab"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-26T14:55:47.838Z","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 (DeepSeek V4.1 Flash, agent template base3-free-catalog): the harness keeps no per-assignment token record - no usage file, and the session run-state carries no counts fo","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe - reproduce this check of #6057\n\nAll paths relative to the department folder. Python 3.11; the package is standard library only, the\nindependent instrument uses the folder's machine-local scipy wheel tree.\n\n## 1. Custody\n\nFetch the three files by the sha256 in the return's `files` list from the server-root `/files/<sha>`\nroute and check bytes: `TPC-REGION-II-FINAL-CORRECTION.md` 8f35eb9e... (19,676 B), `tpc-h-checks.py`\n5712ccbb... (10,575 B), `tpc-h-checks.out` c568be44... (3,976 B).\n\n## 2. Execute\n\n    cd .solveathome/runs/run-2026-10-26-buffy-zq7/work/pkg\n    python3 tpc-h-checks.py > mine.1.out ; echo $?\n    sha256sum mine.1.out tpc-h-checks.out\n\nExpect exit 0, stderr empty, and both hashes equal to c568be44c6c0d49219417ef0f37bef7a13a3f2fa5d0eced-\n3de19962942f969be. The checker reads no file, so this comparison is external; it also never reads its\nown target, so a corrupted target changes nothing.\n\n## 3. Independent re-derivation\n\n    PYTHONPATH=/work/.solveathome/tools/pylibs_x86_64 python3 zq7-indep.py > indep.json\n\nReproduces H1 (33,489 pairs; 4,607 failures over all 90,000 unrestricted pairs), H2 including the\nweighted form (2.2) with w = 1/m, H3 at 9 moduli, H4 over all 9,131 squarefree r <= 15015, H5 at\nX = 4e4 and 1e5, H6 to d,k <= 200, and the Lemma 3.2 counterexample with its threshold B*.\n\n## 4. Controls\n\n    python3 zq7-controls.py > controls.json\n\n5 target corruptions (all invisible) and 10 one-line checker mutations (9 stay `\"all_ok\": true`).\n\n## 5. Read the analytic part\n\nLemma 3.1's proof is sound as written; Lemma 3.2 as printed is false (exponential evaluated at the\nwrong endpoint) and its correction is #6062's Lemma 3.2; no claim of Section 4 or 7 moves.","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":"2026-10-26T14:56:25.787Z","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_3cf5add99700de0f03a216c1","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/6057 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: \"2967255c39ba4a5966b8788cbcd5b14fec51f60260e1c07dc3e85bed1aeb8c80\", 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/6065/transcript","files":[{"sha256":"637cd8383102c4f7cc3802fab60aaf4af85c1b54a75017c65d69f385186cf38c","name":"zq7-indep.py","bytes":13519},{"sha256":"7308695f34d56a9256426fa41823b1721013d4e80e834d461e4e478559eec1ab","name":"zq7-controls.json","bytes":6913},{"sha256":"915cb81eab1e19452e911eddc7715a5013ec885b116aa88df671c3c0fb30bdfb","name":"ZQ7-CHECK-6057.md","bytes":8515},{"sha256":"c568be44c6c0d49219417ef0f37bef7a13a3f2fa5d0eced3de19962942f969be","name":"tpc-h-checks.out","bytes":3976},{"sha256":"f87d643002a43d0d4bc0d5754e541c52f692e1e09ec7c4c87a7ad2f3e5ea8c9c","name":"zq7-indep.json","bytes":4246},{"sha256":"fe9ad8a1f810237c1a6b4db8dbaaf3395c4cb916c2617624bc08d96918762a12","name":"zq7-controls.py","bytes":5270}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"915cb81eab1e19452e911eddc7715a5013ec885b116aa88df671c3c0fb30bdfb","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}