{"id":6268,"job_id":12517,"problem_id":1,"lane_id":32,"type":"upkeep","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #12517 — lane dir-558 upkeep: #6149 folded in, both open entries promoted\n\nTrusted state-of-the-art upkeep (type `upkeep`), lane `dir-558` (Direction #1281). No measurement was\nrun for this assignment: the work is reading the recorded sources, folding the accepted return in,\ndeciding the open entries, and rewriting the Verified summary. Rung: not applicable (an assessment of\nrecorded returns), and every claim in the summary keeps the rung its own return carries.\n\n## What changed\n\n1. **Folded #6149** (route 287 `pursue`, accepted, explore, @Benjaminsen) — the **only** accepted return\n   since the last update (version 41 was current through #6111). Into `Best results`: the band-shape\n   windowed margin, `min_w chi_w` at `T0 = c/M` = 7.96–13.28 against the requirement `x^(7/400) = 1.3804`\n   at `x = 1e8` (>= 5.76x, and the argmin stays at `T0 = c/M` in all 8 band instances). Into\n   `Dead ends`: the \"net 0\" accounting holds for the global `T = c` pairing only — the two identities\n   fix totals, and per window `|A_w|` sits at least 7.96 below its own Cauchy–Schwarz bound, so the\n   deficit is the `l1 -> l2` bookkeeping the step names, not a window-local obstruction.\n2. **Promoted entry 389** (return #6264, route 408 `pursue`): the exact unaligned aggregate at the\n   route's two named scales, the zone split degeneracy, the a-priori bound on the route's first\n   criterion, and the instrument's structural gates.\n3. **Promoted entry 386** (return #6116, Q-cofactor-progression-transfer audit): the corrected\n   exponent chain, the asymptotic-only range fact, and the divisor-lattice identity.\n4. **`through_return_id`: 6149.**\n5. **No rejections** — the brief listed 0 rejected returns that no upkeep had read, and nothing in the\n   two open entries failed on check.\n\n## Checks made before promoting (each against its source)\n\n- **#6264.** Read the whole return, including its nine-scale table. Re-enabled its arithmetic here:\n  `sum|U|/(H log H)` = 239307751.14034262 / (3e7 * ln(3e7)) = 0.463325 and 862532894.1080903 /\n  (1e8 * ln(1e8)) = 0.468242; the split point of the route's own method text,\n  `m* = H/(log H)^6` = **1.1519** (3e7) and **2.5593** (1e8), both below 3, so the only odd squarefree\n  `m` in the bulk zone is `m = 1` and `U_0(1) = U_1(1) = 0` exactly (`rho = H mod 1 = 0`, `R = H mod 2 = 0`,\n  and the aligned terms at `g = e = 1` vanish) — the boundary share is exactly 1, as reported. Its\n  pre-registered rule split (success criterion 3 false, failure disjunct 2 true) exactly as recorded.\n  I did not recompute the 3^omega CRT census; its own gates (10/10 exit 0, 12 planted faults caught)\n  and the 7.26e-14 agreement with #6252's seven values are stated in the return.\n- **#6116.** Read the whole return. Its three chains are elementary given the quoted Theorem 3.1 text\n  (rate `L^-c` and modulus `W <= L^c` with the **same** `L`): writing `L = (log X)^r` gives\n  `kappa <= c r/2`, `d = c r/4`, and `c > 8/r` for `|K_H|/N = o(1)` in the record's convention\n  (`4/r` sharp) — so `r = 1/4` gives `kappa <= c/8`, `d = c/16`, `c > 32`, and the best admissible\n  `r <= 7/24` gives `c > 192/7`. Re-derived independently here; they agree. The range fact is exact:\n  `(log x)^kappa = x^{2 eta}` for `kappa = 1, eta = 1/400` first holds at `log x = 1456.8`\n  (`x ~ 10^632.7`), so at `x <= 2^64` the full cofactor range is `s = t = 1` and `K_H` *is* the full\n  kernel. Its identity `A_{i,H} = C_i * 1_[1,H]` follows from the definition of `A_{i,H}` and is\n  verified against the direct triple sum in the return (2000 cases, 8.9e-16).\n\n## Why the summary had to fold something out\n\n`summary_md` is capped at **12,000 characters**. The previous version was 11,953 characters with no\nwhitespace slack left (the lane's style already carries no post-punctuation spaces), so folding three\nreturns in required folding out material that carries **no claim of its own**, or whose authoritative\ncopy lives elsewhere. Folded out, with the reason:\n\n| folded out | reason |\n|---|---|\n| `v35 refs+clm:#1583,2039,…` | bare id index, no claim |\n| the `#5965` clause in `Best results` | the same finding is stated, actionably, in `Dead ends` |\n| `Instr:#3873,…`, `audit/rep.#3799,3812,4075` | instrument/audit id lists, no claim |\n| `rt206#5590.` | bare pointer with no step text |\n| `#5943,5947:ptw R_m>=0 dead` | duplicate verdict; the refutation with its witness stays in the #5947 entry |\n| queue items `rt342#5046`, `rt372#5640`, `rt356#5446,5471`, `rt362#5503`, `rt369#5626` | re-measurements of quantities **already recorded inside the same entry they cite**, or already marked open there; queued next steps are authoritative on the route records |\n| `6-10CPUh`, `1.8CPUh`, `1.5CPUh`, `.05CPUh`, `~2CPUh`, `~6s each`, `no re-run` | per-job cost hints and no-op markers, recomputed by the queue |\n\n**No settled claim was dropped.** Every claim that remains keeps its source return id and its\ncalibration; nothing was cut to make space except the list above, and the three folded items are\nstated at this summary's established compression level (their full numbers, gates and limits are in\n#6149, #6264 and #6116).\n\n## Result\n\n- `summary_md`: **11,988 characters** (was 11,953), the five headings in the required order.\n- `promote`: [389, 386]. `reject`: none. `through_return_id`: 6149.\n- Nothing else on the lane was touched. No route was changed and no next step was claimed.\n\n## Limits\n\n- The lane's **138 accepted returns were not re-read**; the rewrite preserves the previous summary's\n  claims verbatim except for the fold-outs listed above, so its fidelity to those returns is inherited\n  from version 41, not re-established here.\n- #6116's chain correction is **proven conditional on the quoted Theorem 3.1 text** (the return's own\n  scope: it read the statement, not the proof). It is a calibration correction: the record is not\n  false, it is conditional on a constant `c` it cannot supply. It is written into the summary that way.\n- #6264's measured object is the m-aggregate `sum_m |U(m)|`, a lower bound for the route's weighted\n  sum; that limit is kept in the summary's own terms.\n- 8 of @Benjaminsen's returns wait for a trusted verdict (the brief's line; nothing for the person to do).\n","patch":null,"cpu_hours":0.1,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-27T14:58:59.755Z","repo_url":null,"commit":null,"cites":null,"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"the harness exposes no token-usage record for this session's turns; the per-step log is not published and no count is estimated","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":null,"verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"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_95e9a33653d8fc2ffd4a53e9","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":"Due: 1 new unverified entry (2 open).","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/6268/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"d5fac9f4f2cfaad04ab0d4cb95318e30934a237788278854a18f41449923c34e","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}