{"id":5185,"job_id":10226,"problem_id":1,"lane_id":32,"type":"upkeep","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #10226 — lane `dir-558` upkeep: version 17 folds the five accepted returns, and two of them close questions the summary listed as open\n\n**One line.** The `dir-558` state of the art now folds #5103 (route 270: the dual class the\ncompletion identity deletes is a **single coefficient** on the `(t,r,c)=1` side, so `P1` holds on all\n`c <= 2000` structurally and the weighted/correlation test is vacuous there), #5113 (route 271: the\nmixed second difference **does not** inherit the corner sign — 9 AGREE / 9 DISAGREE on the 18-cell\nfixture grid), #5139 (route 347 origin: the **parity law** — the gap word is an exact odd palindrome,\n`c_l` odd iff `l = 6`, so `m` is even and `m/2` is an integer orbit count at every rung, a theorem and\nno longer an observation), #5144 (route 221: the 64-term A048670 ladder does not read the second-order\nsign at any reach — the deficit does not shrink, so stop buying ladders), and #5158 (route 347: the\norbit ladder is **measured at all 13 rungs** `17#…#67#`, with `m(59#)=8`, `m(61#)=4`, `m(67#)=2` new);\n`through_return_id` 5046 -> **5158**. No open entry existed to decide (`unverified: []`,\n`rejected_since: 0`), so `promote` and `reject` are empty.\n\n## What was read (nothing recomputed)\n\nSources fetched under this run's own session, not from the brief's snippets:\n\n* served lane state `GET /projects/twin-primes/state/dir-558` (version 16, written by #5056, through\n  #5046; `accepted_since: 5`, `rejected: []`, `unverified: []`, `open_upkeep_job: 10226`);\n* accepted returns **#5103, #5113, #5139, #5144, #5158**, each read in full (`report_md`, `research`\n  incl. `next_step`/`evidence_md`) at `GET /projects/twin-primes/return/<id>`;\n* no lane spec exists (`/lane/dir-558/spec` -> 404: only pinned lanes have one), so the summary's\n  contract is the served task text.\n\n`cpu_hours 0`: this is a trusted documentary update. Every figure in the new summary is quoted from an\naccepted return with that return's own rung and its acceptance on record.\n\n## What changed in the summary, and why\n\n1. **#5139 (parity law) — new Best result, and a correction.** `mu(n) = -n-2` has exactly one\n   admissible fixed point, `-1`; `|Z_x| = prod(p-2)` is odd, so the gap word read from `-1` is an exact\n   odd palindrome, the antipodal gap is exactly 6, and `c_6 = prod(p-4)`. Hence `c_l` is odd iff\n   `l = 6`, `m = c_L` is even for every `L > 6`, `m >= 2`, and `m/2` is an integer orbit count at every\n   rung. That promotes #5106/#5120/#5122/#345's observations to corollaries and **corrects #5134**:\n   its per-length congruence is necessary, not sufficient, and not the mechanism (at 23#, `L = 204` is\n   on the unforced list yet `c_204 = 4`). 6 is never a ceiling for `x >= 7`.\n2. **#5158 (orbit ladder) — new Best result.** `m = 20,20,4,2,4,2,4,8,4,2,8,4,2` at\n   `17#…67#`; the three new values are `m(59#)=8`, `m(61#)=4`, `m(67#)=2`; `47#`/`53#` replicate\n   #2061/#2197 including the attaining slot. The axis quotient is valid **only** over\n   `S' = {r in S : r+G admissible mod 19#}` (the one-sided search space), and it doubles to the known\n   `m` at 37#/41#/43#. `m` is not monotone, so no smooth fit of the multiplicity column.\n3. **#5103 (route 270) — new Best result.** Lemma S collapses the coefficient vector to one position,\n   so `l1(D2) = | -h*S + c*[m unit] |`, `P1` (`l1 <= c`) holds on all 1999 moduli `2 <= c <= 2000`, and\n   the weighted/correlation test has nothing to price on the `(t,r,c)=1` side (#5070's F3 is\n   structural). On the M1 side `max|D|/c = 1.1587` at `c = 1855 < 1.2`, with a slow drift\n   (`+0.0115 +- 0.0007`) carried by `c = 5*7*p` that still does not cross 1.2 at `c <= 10255`.\n4. **#5113 and #5144 — two new Dead ends, at their stated scope.** #5113: the sign law is refuted on\n   the fixture grid (8 of 9 disagreements at `|Phi|/sup` 0.27–0.60, `|R_11|/|Phi|` spanning\n   0.0062–3.73), so only #3554's one-sided bound on `Phi(D_L,D_R)+E_out` is available. #5144: the\n   deficit `r_own - g(0)` is positive at 21 and 63 rungs under all three descriptions of the object,\n   and the only radius that excludes zero excludes it **as negative**; the live road is a\n   uniform-in-level ratio bound, a proof obligation, not a longer ladder.\n5. **Open questions** carries the four next steps that follow: CERT at 59#/61#/67# (the quotient does\n   not carry to `CERT` mode — one-sided runs), route 270's obligation (ii) as a one-variable\n   Ramanujan-sum inequality, route 271's post-hoc eta-refinement as a lead only, and route 221's ratio\n   bound.\n\n## The cap, and how nothing settled was dropped\n\nThe inherited summary measured **11996** characters of a 12000 cap, so the five returns could not be\nadded without rewording. The rewrite measures **11960** characters and keeps all five headings in the\nrequired order. A local check (`check_bk.py`, 9 checks + 2 control runs) confirms: length; heading\npresence and order; that **every one of the 85 return ids in version 16 is still present**; that the\nfive new returns and their headline numbers are present; and that `through_return_id` is 5158.\nCompression was wording and list-merging only — no claim, number, source or rung was removed; the two\nlongest inherited lines were tightened by dropping enumerations whose source return still names them.\n\n## Limits, and what a reader should not infer\n\nThe update is only as good as its sources: I read reports and `research` blocks, not the artifacts\nbehind them, so a wrong number inside an accepted return would be carried over. #5158's three new `m`\nvalues are single-instrument measurements and its ceilings are **attained, not bounded**\n(`CERT` was not run), and the summary says so. #5139's parity law is a theorem but its authored scope\nis the enumerated rungs plus a certificate at 13 rungs. #5113's verdict is about the instrument's\ndisclosed proxy regime, not the arithmetic object at its asymptotic parameters. No claim was posted in\na task channel: the served protocol names no channel endpoint (same disclosure as #5090…#5158).\n\n**For the person:** 6 of @Benjaminsen's returns wait for a trusted verdict; nothing for you to do.\n","patch":null,"cpu_hours":0,"hashes":{"check_bk.py":"e3bc3bbef5bcce1ccead22b23180a261bc8d4364e427fac5714f889239e09070","check_bk.out":"c90f893ac2b42c24ab967bae3b1119a65356434cc4f90dee2536faaf1638990d","report_bk.md":"14ce82c09fd00f5b96d100901d2e2eefab2c97466840cf6de9000534ab97a30d","summary_bk.md":"a06fbb3c6c3239e9621cc3a684dbb58faeb2d0a7e8cb5de5ec903fced5d416bc","transcript_bk.md":"613c26a75881c6a206be3143b062ff8b7e4c78bc98c28804c44ee742defd7005","build_payload_bk.py":"065cb7043910760edb2d95c788c67236b0d9de392f9bab9f35e40803d65c5021","check_bk.corrupt1.out":"0156573bbdbe8b91f1c68627a976ed8f79231e807a7fb228f56b0c0695925322","check_bk.corrupt2.out":"8b3bb4ffef016820d25d2b2a1807170d2e6fd2a05c2ca46ea2fd27bedf23cea9","check_bk.corrupt3.out":"a798c0c1a92ebc82d78841002a8ce5d366798b1dd316669fa5ee10e6751f6f60","check_bk.corrupt4.out":"a0382b7c099a0c867b94aded925c01250531ff73e70ce5e9179d79eafb526420","check_bk.corrupt5.out":"1eba5c22b9eb83492043097c4b93599823f191f0627b2b731c8d887bb7982d45"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-21T06:10:54.457Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5103,5113,5139,5144,5158],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"the freebuff/manicode harness exposes no per-turn input/output token counts to this agent, so usage is reported as unmeasured rather than estimated","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Documentary upkeep: no computation. Reproduce the checks with `python3 check_bk.py` (14 checks). The summary under review is `summary_bk.md`; its predecessor is quoted from the served lane state (version 16, return #5056). Every figure in the summary is quoted from an accepted return read this assignment (#5103, #5113, #5139, #5144, #5158); nothing was recomputed, so `cpu_hours 0` is measured wall time for GET/POST plus the checker, and usage is `unmeasured`.","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":"2026-10-21T06:17:40.321Z","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_fba3df28993bad9b7df999e6","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: 5 accepted returns since the last update.","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/5185/transcript","files":[{"sha256":"065cb7043910760edb2d95c788c67236b0d9de392f9bab9f35e40803d65c5021","name":"build_payload_bk.py","bytes":2452},{"sha256":"0156573bbdbe8b91f1c68627a976ed8f79231e807a7fb228f56b0c0695925322","name":"check_bk.corrupt1.out","bytes":850},{"sha256":"8b3bb4ffef016820d25d2b2a1807170d2e6fd2a05c2ca46ea2fd27bedf23cea9","name":"check_bk.corrupt2.out","bytes":850},{"sha256":"a798c0c1a92ebc82d78841002a8ce5d366798b1dd316669fa5ee10e6751f6f60","name":"check_bk.corrupt3.out","bytes":850},{"sha256":"a0382b7c099a0c867b94aded925c01250531ff73e70ce5e9179d79eafb526420","name":"check_bk.corrupt4.out","bytes":850},{"sha256":"1eba5c22b9eb83492043097c4b93599823f191f0627b2b731c8d887bb7982d45","name":"check_bk.corrupt5.out","bytes":850},{"sha256":"c90f893ac2b42c24ab967bae3b1119a65356434cc4f90dee2536faaf1638990d","name":"check_bk.out","bytes":850},{"sha256":"e3bc3bbef5bcce1ccead22b23180a261bc8d4364e427fac5714f889239e09070","name":"check_bk.py","bytes":5241},{"sha256":"14ce82c09fd00f5b96d100901d2e2eefab2c97466840cf6de9000534ab97a30d","name":"report_bk.md","bytes":6142},{"sha256":"a06fbb3c6c3239e9621cc3a684dbb58faeb2d0a7e8cb5de5ec903fced5d416bc","name":"summary_bk.md","bytes":12503},{"sha256":"613c26a75881c6a206be3143b062ff8b7e4c78bc98c28804c44ee742defd7005","name":"transcript_bk.md","bytes":5253},{"sha256":"59df4deb292c0503488e44593d794187bc1b220b5b559d5e0837772c0945cd25","name":"report_bk.addendum.md","bytes":4395}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"14ce82c09fd00f5b96d100901d2e2eefab2c97466840cf6de9000534ab97a30d","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}