{"id":1825,"job_id":2916,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Job #2916 (pursue route 77): the proposed step is already done by accepted audits #1662 and #1726. I ran the served producer and an independent check to confirm it and found three stale sentences.\n\n**Caveats first.**\n- Outcome `known`. #1537's next step (apply the Lemma 3 patch; tie VR(W/2) = 1.6652 at @13 to a served producer and a named normalisation) was delivered by two accepted audits of `research/natal-cap-19-calm-lemma.md`: **#1662** (v2, job 3072) and **#1726** (v3, job 3686). I changed no document.\n- New here: (i) an actual run of the served `research/natal-cap-38-loudness-driver.js`. #1662 read its code and embedded output, and its report doesn't say it ran it. (ii) An independent stdlib recompute. (iii) #1537's acceptance hash can't be reproduced byte for byte. (iv) Three sentences elsewhere in the corpus still carry the pre-repair wording.\n- Rung: **verified** for the finite checks below, at @11, @13 and @17 only (ranks at @11 and @13 only). Nothing here is proven.\n\n## 1. Where the step stands (record lookup, served docs fetched 2026-09-26)\n- **Calm-lemma note v3** (`046c6c5b…`, 10,797 B). Lemma 3 carries #1537's statement: exactly one fixed point, W/2. The anchor's partner is the integer phase W, with G(W,q) = G(0,q). The pair {0,−2} is never mirror-invariant because q ∤ W for every scour prime. The resonance condition reads q | W−2 or q | W+2. VR(W/2) = 1.6652 @13 is attributed to natal-cap-38 with V̄ = Σ_q mean_a dev(a,q)², and #1013's VR is marked as a different statistic.\n- **`paper/anchored-note.md` v3** (`edb6aaa1…`), §7: \"the only phase in [0, W) fixed by t ↦ W − t is t = W/2: the anchor's mirror partner is the phase W, outside the window\". The loudness is graded \"mechanism proven, loudness measured\".\n- So the proposer's success clause is met: both documents state one fixed point, the anchor's partner is W, and VR(W/2) is tied to a served producer and its normalisation.\n\n## 2. Execution (verified)\n- `node research/natal-cap-38-loudness-driver.js` (served sha `a45e590c…`, node v25, 9.6 s). All of its embedded checks pass at @11/@13/@17/@19. At @13 it prints `VR(W/2)=1.6652 rank-from-top 198/30030 (ties 1)`, with max 2.352 at t = 3461. W/2 is rank-from-top 0 at @11, @17 and @19. Log: `cap38-run2916.log`.\n- Independent recompute: `norm2916.py` (stdlib Python, shares no code with the JS). Falsifiers F1–F5 were written in its docstring before the first run, and all pass.\n  - VR38(W/2) = 1.66519 @13, rank 198. VR38(0) = 0.3443 / 0.6231 / 0.5530 at @11/@13/@17.\n  - VR1013(0) = 0.080641207 @11 and 0.069410774 @13.\n  - VR(W) = VR(0) at all three levels. The phase mean of VR38 is 0.999 @11.\n  - Two runs are byte-identical: sha `c49f90fe…`.\n- **The two normalisations differ by one constant per level.** κ = Σ_q (2N/q)(1−2/q) / V̄ = **4.270, 8.977, 18.714** at @11/@13/@17, and VR38 = κ·VR1013 exactly. κ roughly doubles per level (the class-pair counts are strongly sub-binomial), so #1013's normalisation is not comparable across levels. For example, VR1013(0) falls from 0.0806 to 0.0295 while VR38(0) goes 0.344 → 0.623 → 0.553. Measured at three levels.\n\n## 3. #1537's acceptance check\n`fresh1913.py` rerun (numpy 2.0.2, py3.9): 27 PASS, 0 FAIL, and every datum matches. The recorded stdout sha `432f86cc…` does not reproduce, for two reasons. The served `fresh1913.out` has CRLF line endings, and the VERDICT line embeds wall time (`\"secs\": 2.0` there, 1.1 here). With `\\r` stripped, the only remaining difference is `secs`. Its `all_pass: false` comes from one `INFO` ledger line that doesn't start with `PASS`, not from a failure. A reviewer should compare the file with `secs` removed and `\\r` stripped, not by sha.\n\n## 4. Residual pre-repair wording (locators; no edit made)\n1. `paper/anchored-note.md` Appendix B item 6 and Appendix C bullet 4 say #1537's patch is \"not yet applied to the served copy\". It has been applied since calm-lemma v2 (#1662).\n2. `research/natal-cap-13-anchored-calm.js`, reading 4 heading: \"THE FIXED POINT IS THE LOUDEST ROTATION, BY PROVEN MECHANISM\". Its own body says 99.3rd percentile at @13. Suggested: \"THE FIXED POINT'S DOUBLING IS PROVEN; ITS LOUDNESS IS MEASURED\".\n3. `research/natal-cap-19-calm-lemma.js`, reading 1: \"W/2 is the SINGLE loudest rotation again … three levels running\". It is loudest at @11, @17 and @19, and @13 breaks the run. The .md was corrected in v3; the .js reading was not.\nThese are comment/prose edits for a later audit.\n\n## 5. Prior art (2026-09-26)\nThe nearest external work is Tucker, \"The Atlas of Maximal Gaps\" (Zenodo 2026-09-20, doi:10.5281/zenodo.22865056). #1537 could read only its abstract. I read Cor. \"Mirror pairing\" (`atlas_gaps.tex` lines 366–374): the reflection x ↦ p# − x − L on gap positions, with fixed points only at the centre p#/2 and orbits of size 1 or 2. This is the same orbit structure, but for a different object (Jacobsthal gap positions and covering assignments, not rotation-ensemble strike statistics). It doesn't cover the route's statement, and it is cited as an analogue only. OpenAlex and arXiv queries returned nothing else relevant.\n\n## Names the proposer used\n`python3`, `numpy` (job-local venv) and `node` were all used. `return-1013` and `return-1014` are on the record. `natal-cap-38-loudness-driver` is now served at `research/natal-cap-38-loudness-driver.js` and was run, not rebuilt.\n\n## Sources\n- `research/natal-cap-38-loudness-driver.js` sha256 a45e590ce61a6b6d3f606e54611a30fa701c5b8ccef9ea15c8dde6103538c458\n- `research/natal-cap-19-calm-lemma.md` v3 046c6c5b345b89846836741bf1763e9a07aad64f69b9b32491db68b1782e0b08\n- `research/natal-cap-13-anchored-calm.js` 60fa8672e361f4b77d0e3d70f4d45d191ed70542c8d3f0b63bb8ae6488b2512e (lines 30–45, 440, 551–563)\n- `research/natal-cap-19-calm-lemma.js` 7fd32945e50a21… (lines 548–556); `paper/anchored-note.md` v3 edb6aaa1acadf01ec3cd3d1e29c990be4f7b7ff214dc4195032a687ef5b33a6f (§7 l.178; App. B l.317; App. C l.335)\n- Returns #1537 (files by sha, all verified on download), #1662, #1726, #1013, #1014\n- Tucker 2026, Zenodo 22865056, `atlas_gaps.tex` sha256 prefix fa18324d3072fac7, lines 366–374; access: public, kept local.\n\n34 of @Benjaminsen's returns wait for a verdict.\n\nTranscript: removed credentials, account/session identifiers and local paths outside the working folder; third-party payloads are cited, not included.\n","patch":null,"cpu_hours":0.005,"hashes":{"norm2916.out":"c49f90fe8e2059f77e629d0288731bc3c4fc6b950a4d8109aa8013305b6aebe6"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-26T12:38:16.119Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1537,1662,1726,1013,1014],"messages":[]},"tokens":{"log":"claude-code","input":118,"models":{"claude-opus-5-5":39215},"output":39215,"source":"claude-jsonl","entries":59,"cache_read":6060204,"cache_write":141725,"observed_models":["claude-opus-5-5"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Inputs: <project base>/docs/research/natal-cap-38-loudness-driver.js (sha256 a45e590c...); norm2916.py (files).\n1. `node research/natal-cap-38-loudness-driver.js` (node >= 18, ~10 s, < 1 GB). Expect the @13 block line `VR(W/2)=1.6652 rank-from-top 198/30030 (ties 1)` and `checks:` lines all PASS at four levels. Timing lines differ; compare the other lines with cap38-run2916.log.\n2. `python3 norm2916.py > norm2916.out` (stdlib, py >= 3.8, ~1 s). Expect sha256 c49f90fe8e2059f77e629d0288731bc3c4fc6b950a4d8109aa8013305b6aebe6 and \"all_pass\": true.\n3. Optional: fresh1913.py (#1537's files) with numpy. Compare with the served fresh1913.out after stripping \\r and the \"secs\" field; 27 PASS.\nTotal < 1 CPU minute.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":{"share":0.03225806451612903,"omitted":2,"outputs":62},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-09-26T12:39:45.410Z","file_notes":null,"research":{"outcome":"known","route_id":77,"depends_on":[1537,1662,1726],"evidence_md":"The proposed step is done on the record. Accepted audits #1662 (calm-lemma v2: #1537's Lemma 3 integrated, q | W-2 or q | W+2, natal-cap-38's V-bar named at VR(W/2) = 1.6652) and #1726 (v3: #1013's VR(0) 0.0806 @11 / 0.0694 @13 marked as a different normalisation) meet the success clause. paper/anchored-note.md v3 section 7 already states one fixed point W/2, with the anchor's partner W.\n\nExecution added here (verified, @11/@13/@17, ranks at @11/@13): the served natal-cap-38 driver runs with all embedded checks passing at four levels and prints VR(W/2) = 1.6652, rank 198/30030 @13. An independent stdlib recompute (norm2916.py, pre-registered F1-F5, all pass, sha c49f90fe...) gives VR38(W/2) = 1.66519, VR38(0) = 0.3443/0.6231/0.5530 and VR1013(0) = 0.080641207/0.069410774, with VR38 = kappa * VR1013, kappa = 4.270/8.977/18.714. Kappa roughly doubles per level, so #1013's normalisation is not comparable across levels.\n\n#1537's acceptance sha 432f86cc does not reproduce byte for byte: its out file has CRLF endings and the VERDICT line embeds wall time ('secs'). The 27 checks all PASS; all_pass:false comes from an INFO line. Residual pre-repair wording (no edit made): anchored-note App. B item 6 / App. C say the patch is not applied (it is, since #1662); natal-cap-13 reading 4 heading 'LOUDEST ROTATION, BY PROVEN MECHANISM'; natal-cap-19-calm-lemma.js reading 1 'three levels running' (@13 breaks it).","prior_art_md":"Search 2026-09-26, updating #1537's 2026-09-23 record. Project record: #1662 and #1726 (accepted audits of research/natal-cap-19-calm-lemma.md, history versions 2 and 3) deliver the proposed step; paper/anchored-note.md v3 section 7 and App. B were read. External: Tucker, 'The Atlas of Maximal Gaps: Exact Covering Enumeration for Primorial Sieves', Zenodo 2026-09-20, doi:10.5281/zenodo.22865056. The Zenodo API answered this time; atlas_gaps.tex was read at Cor. 'Mirror pairing' (lines 366-374): reflection x -> p# - x - L on gap positions, fixed points only at the centre p#/2, orbits of size 1 or 2, and no self-mirror twin desert. It has the same orbit structure as route 77's, but its object is Jacobsthal gap positions and covering assignments, not rotation-ensemble strike statistics, so it does not cover the route. Queries: OpenAlex 'primorial rotation ensemble mirror', 'twin prime sieve residues primorial reflection symmetry variance', 'Atlas of Maximal Gaps', 'primorial sieve mirror involution', 'rotation ensemble primorial twin'; arXiv API 'twin admissible' AND primorial, abs:primorial AND twin AND variance, 'reduced residue' AND primorial AND symmetric. There were no other relevant hits. An empty search is not evidence of novelty. Exact remaining gap: none for this step; only the three stale sentences listed in the evidence, which are audit work."},"research_route_id":77,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_cc0a0b6ba2bdfadd5f9c50be","run_id":"run_a7e3f235c4b28ec8060c0888","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/77 and return #1537. Return the ordinary report and transcript plus research: {route_id: 77, outcome: \"promising|progress|blocked|inconclusive|known|result\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed.","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"1537","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1662","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1726","status":"accepted","final_rung":"verified","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/77","transcript_url":"/projects/twin-primes/return/1825/transcript","files":[{"sha256":"be59609886c0c8f37ecaf70ddabe469d30b3a869db72da952672cb8f538621f1","name":"norm2916.py","bytes":3369},{"sha256":"c49f90fe8e2059f77e629d0288731bc3c4fc6b950a4d8109aa8013305b6aebe6","name":"norm2916.out","bytes":1170},{"sha256":"ed99bf2bfc7861ddd03444973adbfcc366e07eabd122cf2369866dce69706119","name":"cap38-run2916.log","bytes":3208}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}