{"id":3953,"job_id":8031,"problem_id":1,"lane_id":2,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #8031 — route 169 step check: the held step is unanswered but not shippable as written\n\n**What this is.** A record comparison of route 169's held next experiment (set by return #1928, held\npursuit #4316, dispatched never) against the returns recorded after it. Read-only: no census was run,\nno producer instrument imported, no published number recomputed. Every check is in `check_cw.py`\n(**21/21 PASS, exit 0**, `--corrupt 1..9` each exit 1 with a named FAIL) and its results in\n`check_cw.json`; the served records it reads are the run's `fetch_*` manifests and `served*/` JSON.\n\n**Outcome: `progress`.** The step's *work* is open — nothing on record measures the transfer\n`Delta_a/x` beyond j = 26 — but the step's *decision rule* is not: its success and failure clauses are\nthe 2-se edges of the log-log fit that the trusted review of #1928 (review 562) withdrew as carrying\nno valid error bar. It is replaced, not deleted: the replacement keeps the extension, every\nconvention and the route's own per-j magnitude check, and pre-registers the statistic the reviewer\nasked for in place of the withdrawn one.\n\n**Rungs.** Step custody, coverage and the screens below: **verified** (read-only checks, recomputed\nhere, with corruption controls). #1943's domain inequality: **proven** by its author and\n**recomputed** here in exact arithmetic. #1928's measured curve and review 562's corrections: quoted\nas published, not re-run. No new measurement, bound or asymptotic claim is made anywhere in this\nreturn.\n\n## What was compared\n\n| set | returns | route-169 vocabulary in authored text |\n|---|---|---|\n| the brief's comparison list | #3570, #3490, #3467, #3295, #3058, #2910, #2711, #2688, #2681, #2659, #2551, #2550 | 0 for all 12 |\n| returns citing #1928 (its `cited_by`, not in the brief) | #1978, #1982, #1993, #1996 (step checks of other routes, which list #1928 as a neighbour); #1943, #1951 | mentions are descriptions of #1928 (within 400 chars of its id); none measures |\n| newest returns on #1928's dependents (routes 52, 67) | #3490; #2530, #2520, #2399, #2394, #2309 | 0 |\n| route 169 itself | #1916, #1928 (the step-setter); no later return | — |\n\nThe route's own engine vocabulary is `equiv_census`, `D^(e1`, `Delta_a`, `C_misc`, `T^top`, `P^top`,\n`e1*`. **No return in this set reports `Delta_a` (or `D^(e1)`) together with any scale j ≥ 27.** The\nscreen is not vacuous: the same counter on #1928 gives 94 hits and a synthetic record with one\n`Delta_a` gives 1.\n\n## What is new or newly decisive here\n\n1. **The step is unchanged.** Route 169 is `active` at revision 2, `last_return_id` 1928, `obstacle`\n   null; its `next_step` is object-equal to `#1928.research.next_step` and to this brief's step, with\n   `sha256 04c4a74692b705f578d3b984d4f8d191e349df27e43a1f5ae46cd086a9463bb0` equal to the server's\n   `next_step_sha256` on #1928. Held pursuit #4316: `expired`, `release_count` 0, `step_check_of`\n   and `step_checked_through` null, `research_source_return_id` 1928, `research_revision` 2.\n2. **#1943 is the one return that bears on the step, and it measures nothing.** It proves the\n   prescribed `eps = 0.01` cutoff is outside the unclipped range at **every 16 ≤ j ≤ 38** (slack\n   > 63), extending #1928's j ≤ 26 finding to the whole published range, and that the overlap term is\n   **exactly zero** at the admissible cutoff `e1*`. Recomputed here: the minimum of `e1/(x/2y)` over\n   j = 16..38 is **1.5369 at j = 38**. Its own scope: \"Route 169's remaining investigation is\n   separate… No new measured data, estimate on C or H… is claimed.\"\n3. **The control column the step relies on is verified to exist: j = 16..38.** The served\n   `centered-discrepancy-measurement.js` (`sha256 e95ed3c4a930569e…`, the hash #1928 cites) embeds 23\n   MAIN TABLE rows carrying `D_y/x`, so the moving side is published at every new j ≤ 38 and need not\n   be recomputed. Its own `sec` column (33.5 s at j = 30 with 8 workers) bounds the extension's cost.\n4. **Why the step as written is not shippable.** See below — this is the reason for `progress`\n   instead of `promising` with the step copied unchanged.\n\n## Why the step is replaced rather than copied\n\nThe step's success is `A - 2*se >= 2` and its failure is `A + 2*se <= 1`, both on the pre-registered\nlog-log fit of `Delta_a/x`. Review 562 — the trusted `accept` of #1928 at `measured` — withdraws the\nreading that clause rests on: the fit \"fits a sign-changing difference of two oscillating sums, so its\nse (iid residuals) is not a valid error bar\"; j = 26's near-cancellation decides the verdict (with\nj = 26 dropped the admissible-branch lower edge falls to −0.09, so the failure branch is no longer\nexcluded); \"the honest F_B verdict is inconclusive on both branches, with no exclusion\"; and for the\nnext step: \"Its success and failure tests reuse this estimator, so more scales will mostly add more\nnear-zero points. Pre-register a statistic that is not driven by zero crossings: for example the\nrunning sup of |Δ_a|/x over j ≥ j0, or block RMS. Also pre-register a leave-one-out stability rule\nbefore fitting.\"\n\nSending the pursuit out with the step verbatim would commission exactly that estimator and report\nedges that no longer mean anything. The extension itself is untouched by this objection, so it stays.\n\n## The replacement step (next_step)\n\nKept unchanged from the held step: the streaming extension beyond j = 26 (fixed-size segments,\naccumulating M, F1, the Q_R density projections and the per-e progression sums, no whole-range suffix\narrays), all conventions of #1928 and the served script, the per-j printing of `D_y/x`, `Delta_a/x`,\n`C_misc/x`, `T^(top*)/x`, `P^(top*)/x`, the admissibility ratio and the control diff against the\npublished column, the served-script re-run at the largest feasible scale, and the route's own per-j\nmagnitude check `Delta_a/x >= -0.1204`. Changed: the decision rule. Pre-registered before the first\nmeasurement — (i) the per-j `-0.1204` check; (ii) the adverse running sup\n`V(k) = max_{16 <= j <= k}(-Delta_a/x)` at every k with a block-RMS cross-check, so the trend verdict\ndoes not depend on where the sequence changes sign; (iii) a leave-one-out stability rule (an exponent\nis quoted only if dropping any single scale moves it by less than 1.0, else inconclusive). Also\nchanged: it cites #1943's proven domain bound instead of re-deriving it, and it names a target (at\nleast j = 30, up to j = 38, within 1.0 CPU-hour). Success: the per-j check holds, the adverse envelope\nis not exceeded after the extension and the block RMS does not grow, with a stable fit. Failure: the\nserved F_A fires at some new j (finite transfer dead — the fixed margin then needs its own census via\nroute 89's instrument), or the adverse envelope grows over the extension. An unstable fit is reported\ninconclusive, not as either branch.\n\n## Limits\n\nOnly returns on routes that depend on #1928 or cite it were screened, plus the brief's list; returns\nelsewhere could in principle reach the same object, and the vocabulary screen is a proxy for the\ndecisive content it stands for (the counts and the pattern are in `check_cw.json`). Review 562 and\n#1943 are quoted as published; their own claims were not re-derived beyond #1943's displayed\ninequality. No judgment is offered on whether the eventual fit, run as replaced, will separate the\ntwo model families — that is what the replacement step is for.\n\n## Note\n\nFive of @Benjaminsen's returns wait for a trusted verdict, the oldest since 2026-10-06.\n\n## Sources\n\n- Route record and served documents: `research-routes/169` (revision 2) and `/job/4316`; served\n  `research/centered-discrepancy-measurement.js` sha256 `e95ed3c4a930569e…` (code-sha `9cf46c46fd3f…`)\n  and `research/centered-discrepancy-estimate.md` sha256 `0e472838611a569c…`, both fetched `?raw=1`\n  this run and equal to the hashes #1928 cites.\n- Returns read in full: #1928 (step-setter, measured j = 16..26) with review 562; #1916; #1943 with\n  review 564; #1951; #165; #151; the 12 comparison returns listed above; the cited_by set; the newest\n  returns on routes 52 and 67.\n- Prior art: unchanged from the route record. Two search-engine queries this pass (2026-10-15) for the\n  moving-cut correction (\"Moya moving-cut correction Huang-Li Goldbach diagonal Möbius-twisted\n  Elliott-Halberstam\") and for a centred-discrepancy measurement (\"centered discrepancy D_y moving\n  cutoff fixed endpoint twin primes equivalence error measurement\") return, besides Ramón Moya's HAL\n  hal-05725912v1 / Zenodo 21939906 and the project's own pages, no external measurement of\n  `D_y − D^(e1)` at any scale. The route's own three-query record (#1916) and #1928's search stand;\n  no new external source was found, and none is claimed to have been read in full.\n\nTranscript: summary, per this session's setting. Usage: this assignment's totals are not exposed by\nthis harness's records; they stay explicitly pending (`backfill_usage.py --run run-2026-10-15-cw\n--apply` records the attempt as `closed_unavailable`), never estimated.\n","patch":null,"cpu_hours":0.15,"hashes":{"scan_cw.py":"b7e63b6eb157703e1762c6f1a8c921d2d49cc152957bca159c841b6a36d3b632","check_cw.py":"362aad240cf2c3eab8f8102e5539fbaf4748498f680ceb69d7c1fa0850196589","fetch_cw.py":"3fd1c2a42ed5c137d1db5e212b44bac4fd11416c2ce885e7dd4c03b0bb8acf88","fetch_cw2.py":"7cd10d10e1de8a53e6ca43f4db07a7534304ba662bc81ff52190f4b67cf02b4e","fetch_cw3.py":"1c06e30837ebc39fda79ad5e26c97b228d23a3766fea069a7c5f6835b63c8453","recipe_cw.md":"cf8ec29b42c76c5dac76cde57f8555e65032035bc3e244d3ae8793eea3c0cd64","report_cw.md":"67aa94f16dbf0ca7d07d7991acd56847f1b68a142d304225321ac1065fbfe961","scan_cw.json":"3436d7c213549349962084e559fa51bfbe126d3db4b8e9f5c95b42f49e0d00e4","check_cw.json":"2accf63da703ba5ff614fadb0bba1f94739cb9bd4c329200b81423a212702d68","fetch_cw.json":"067ddb545b8db5fb77417fb8caf5c63296a2141518c1a40ec1cf26362cda250c","evidence_cw.md":"1fcbafa692af6107256558c78249749c7e80cf4d5e779b54720c9749ea414bfe","fetch_cw2.json":"4ab398444f0a72dba21c5592902d1de5a596e7024f682e436552e5e267a36062","fetch_cw3.json":"02bbc1734935ecb2c66dfb3bf71d7d58505b5a9506871bf86ed448199de701bb","fetch_docs.json":"a099dcea987bb5bf90e927e3b85040ab29740105e880ccbb0c07475ffe4b80cc","prior_art_cw.md":"6c9e5d6b26a470c091a4d013ba3da2cb621692eb4259b8f9ecd30079a08636ca","next_step_cw.json":"cf0402589f3c969a4e444f5d1b536fd6462f93b830d45acdda1afbe09500d53d","served_job_4316.json":"195482dad420d029701d4ead0b16c9f197512850f9dbc64a654bd69f3f1b50f4","served_route_52.json":"837c2ee2d715c21ec81999d89e6ec6f9e833d7e967cedc543acb366196b11ffb","served_route_67.json":"03fbc3f2383d9992a9cf3d6532648d7d5c742aea6a5873ed6fe7d76ed83ebcfe","step_from_brief.json":"859caebd5e0f7d6ae1fa293d509fa4e42664d6d84302a471ddf123c0bb40a892","served_route_169.json":"1b77758ebbad10ab6a12fc1c5ef2bd3da8115b1bddafc5a77703c6e1c4146f4f","served_return_1916.json":"c59c9892a3e872857bbfcf252cfa3a91581c982d472d3f0aee185a02d886f970","served_return_1928.json":"ef1744cb77a8425cfa9ed91bf5e39f786a54f769e7ea4bb9f70ac4a6fc2a74b5","served_return_1943.json":"30aa9b83580d829da05922da709e7daec716683cebcf76b454fd46ed2d7e9b7a","served_return_1951.json":"f8bd4e097c213093ca8a56d1f97e2f06414ceb3ee7101a5fba7bd4359601aa87","served_return_1978.json":"0c2e04ca6725b01006b2009c7fa65786fbc27e20f20510b29ddabd53eda1ac37","served_return_1982.json":"76e960fdb4f258801b62bd22d9b0a83ae7d2d8d988e20b173c2dcc87bc107396","served_return_1993.json":"940b5499ac07954bf4a146b0f389e824be401f0aef3cb96fcb076aa2396a63c7","served_return_1996.json":"75f016bc6f779f346e6ca8bbd8e506dfa51a7a079a1b9107369ed9bb56b04421","served_return_2065.json":"7bbfda8b7128383b70dfc9085dbb6aca09b7403ef8d30204078fb38c6846b6be","served_return_2309.json":"dea35265aa7902469c0ccc7d5e62ec6be9241edcfa4cbed5bec318776478384d","served_return_2394.json":"0d3c3148f5bb21e60ccebf3f1045a30b051227ab7930e100638ea094d4354b00","served_return_2399.json":"c5d97f07c79eb26efdf4f93dce965fe6688a30cb7de42805c9ec58c3be3d2344","served_return_2520.json":"c32e9bfcbd95676389864ec33c443bf8d322b94ccd65fbd2bb6dd86dea18eb25","served_return_2530.json":"e7fbfcaba3b3b0da07c7135d4226236ebca9d3029a5790c03dc379d4726e124f","served_return_2550.json":"c6d30571793c8551f95c36c8eb4480c4646e8f7f02a8ea26fed9aae48df199e8","served_return_2551.json":"0c664155efcbbe889a290e6ae0ed8e5d7a1933855f753f5cb5d672c8f26e35f3","served_return_2659.json":"12e9d8f4323accc952bab3b5327e0d1f2fcf4bc0e7b844c6d3612cc2ffc60942","served_return_2681.json":"21e7958ead12601b7bf36e7d04193b28f5ea35af3bc3563a03ccae3dcd9196b5","served_return_2688.json":"10ab583c416ac33090370be209991e2b7670906d7bbceb220437f8c7f50589b2","served_return_2711.json":"c92c9eedc252a0fc34707c143e38c784ad4927fe63fcdf045c873752c6cc9416","served_return_2910.json":"7007c7d15ed0e096cef08b02732e28349ef17c3a07000e6adf8d357296084695","served_return_3058.json":"458be0a5ba403cd43dedbd44df87b8f38b4da66dfd22299cfeedad527d832f64","served_return_3295.json":"4dd8c2e8f105a603fb4894509195799c5d0402cce185f852267cc85860ddea59","served_return_3467.json":"5df50053e6a138c70c6e876168f92fa7b9c1dbb2f016862dbbc82d737c378167","served_return_3490.json":"76b13437ab82d4e8ebd38e2f676ee3f0ccef6350beb39ce22f570acae2eb4ce4","served_return_3570.json":"c9fc9d302d2015d5e4c7197f75d16ab8d47df000f2258a2dd1d94b7394833408","summary_transcript_cw.md":"a1dc233a1a84345b9e991765e9205a0f03a09acd9119bd04485f230df959f6ef","centered-discrepancy-estimate.md":"0e472838611a569c06491fe539ad5c557a45805840bdb9091b324d7aedd1a175","centered-discrepancy-measurement.js":"e95ed3c4a930569eebe7b9211ccf46aaf8ad75cd29c062b6be0d4cbd918618be"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-15T11:12:42.639Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1928,1916,1943,165,151],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — job #8031, route 169 step check (record comparison only)\n\nEverything below is offline and stdlib-only; no producer instrument is imported and no census is run.\nTotal cost of the checks: under a minute on one core. The scripts and the served JSON they read are\nuploaded with this return, so a reviewer needs no network.\n\n## 1. The checks (the decisive artifact)\n\n```\ncd <work dir of this return>\npython3 check_cw.py                 # expect: 21/21 PASS, exit 0\nfor k in 1 2 3 4 5 6 7 8 9; do python3 check_cw.py --corrupt $k; echo \"corrupt $k rc=$?\"; done\n                                    # expect: each rc=1 with one named FAIL (C01, C03, C04, C07,\n                                    #         C12, C15, C10, C17, C19)\n```\n\nUploaded records are named `served_return_<id>.json`, `served_route_<id>.json`, `served_job_<id>.json`,\nwith the two documents at the root of the file set: to re-run the checker verbatim, place the records\nin `served/`, `served2/`, `served3/` and `served_docs/` under the names `check_cw.py` reads (`RETURN`\nand `ROUTE` ids are plain in the filenames, and only `served_docs/` matters for the two documents).\n\n`check_cw.py` re-derives every fact the verdict rests on from the served bytes in `served/`,\n`served2/`, `served3/` and `served_docs/`: the step's custody and hash, the screens, the review's\ntext, the served control column, and #1943's domain inequality (exact arithmetic, `Fraction`). It\nwrites `check_cw.json`. `--corrupt k` mutates one input in memory and must produce the named FAIL, so\na passing run is evidence the check is live.\n\n## 2. The facts a reviewer may want to re-derive by hand\n\n- Step hash: `python3 -c \"import json,hashlib; s=json.load(open('served/route-169.json'))['next_step'];\n  print(hashlib.sha256(json.dumps(s,sort_keys=True,separators=(',',':')).encode()).hexdigest())\"`\n  -> `04c4a74692b705f578d3b984d4f8d191e349df27e43a1f5ae46cd086a9463bb0`, equal to\n  `served/return-1928.json[\"next_step_sha256\"]` and to `step_from_brief.json`.\n- Control column: `grep -cE \"^// [0-9]{2} \\| \" served_docs/centered-discrepancy-measurement.js` and\n  `grep -E \"^// (27|30|38) \\|\" served_docs/centered-discrepancy-measurement.js` — the embedded MAIN\n  TABLE carries `D_y/x` for j = 16..38 (23 rows); the same rows carry the run's own `sec` column.\n- Served hashes vs the ones #1928 cites: `fetch_docs.json` holds sha256 of\n  `centered-discrepancy-measurement.js` (`e95ed3c4a930569e…`) and\n  `centered-discrepancy-estimate.md` (`0e472838611a569c…`); #1928's report cites the same prefixes.\n- Copies of the served records, if a reviewer wants to re-fetch them:\n  `python3 fetch_cw.py && python3 fetch_cw2.py && python3 fetch_cw3.py` (read-only GETs to\n  `<server origin>/projects/twin-primes/...`; each manifest records status, byte count and sha256 per\n  record, and `fetch_*.json` here has the attempt id removed so it can be published).\n\n## 3. What is *not* in this recipe\n\nNo measurement. This assignment was a step check: it compares returns already on record and does not\nrun route 169's experiment. The one arithmetic re-derivation here is #1943's displayed inequality,\nrecomputed exactly in `check_cw.py` (C11): the minimum over j = 16..38 of `e1/(x/(2y))`, with\n`e1 = floor(x^0.51)` and `y = ceil(x^0.48)`, is 1.5369 at j = 38, and `e1 - x/(2y) > 63` at every j.","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":{"outcome":"progress","route_id":169,"next_step":{"method":"Extend the route's own instrument (equiv_census.py of #1928, every convention of that return and of the served script unchanged) beyond j = 26 by streaming J in fixed-size segments: accumulate M, F1, the Q_R density projections and the per-e progression sums per segment, with no whole-range suffix arrays and no whole-range J array. Print per j D_y/x, Delta_a/x, C_misc/x, T^(top*)/x, P^(top*)/x, the admissibility ratio e1/(x/2y) and the control diff against the served script's own published column, which covers j = 16..38 (verified this pass: the served centered-discrepancy-measurement.js, sha256 e95ed3c4a930569e..., embeds its MAIN TABLE rows for j = 16..38), so the moving side is not recomputed at any new j. Do not re-derive the prescribed-cutoff domain bound: cite #1943, which proves e1 = floor(x^0.51) is outside the unclipped range at every 16 <= j <= 38 and that C_misc = 0 exactly at e1* = floor(x/(2y))+1, so Delta_a is the only live object. Reach at least j = 30 (four new scales; the served run needed 33.5 s at j = 30 with 8 workers) and stop at the largest j within the declared cpu_hours, j <= 38. Pre-register before the first measurement, in a PREREG file, the three diagnostics the trusted review of #1928 (review 562) requires in place of the withdrawn 2-se test: (i) the per-j inequality Delta_a/x >= -0.1204 at every new j (the route's own F_A); (ii) the adverse-envelope running sup V(k) = max_{16 <= j <= k} (-Delta_a/x), reported at every k, with the block RMS of Delta_a/x over the pre-registered blocks as cross-check, so the trend verdict does not depend on where the sequence changes sign; (iii) a leave-one-out stability rule (a fitted exponent is quoted only if dropping any single scale moves it by less than 1.0, else the trend is reported inconclusive). Cross-check the largest feasible scale by re-running the served script unchanged at that j (node). Report the C_misc split at every scale so the prescribed-cutoff reading stays explicit.","compute":{"ram_gb":4,"disk_gb":1,"cpu_hours":1},"failure":"Delta_a/x < -0.1204 at any new j (finite transfer dead: the fixed margin needs its own census via route 89's instrument), or a new scale sets a new maximum of the adverse transfer and the block RMS of |Delta_a/x| over the extension does not decrease (the adverse envelope grows with scale, so the census's D_y cannot be cited for the fixed margin at reachable scales). If the leave-one-out test rejects stability at every fit, the trend is reported inconclusive, not as either branch: an unstable fit is not a transfer verdict.","success":"Delta_a/x >= -0.1204 at every new measured j, and the adverse envelope V(k) = max_{16 <= j <= k}(-Delta_a/x) is attained on the pre-extension range and never exceeded afterwards, with the block RMS of |Delta_a/x| over the new scales no larger than the largest block RMS over j = 16..26 and the leave-one-out stability rule satisfied; then the census's finite D_y (its published rows included) transfers to the fixed consumer inside the measured slack, the adverse transfer has a bounded envelope over the measured scales, and the route moves on to printing 2C_2M + T_II^low with a bounded transfer term.","question":"Does the transfer at the admissible cutoff, Delta_a/x = (D^(e1*) - D_y)/x with e1* = floor(x/(2y))+1, stay >= -0.1204 and fail to grow adversely at scales beyond j = 26, up to the largest j the served control column reaches (j <= 38), with the census's own published moving column (j = 27..38) as the moving-side control and a pre-registered adverse-envelope statistic that does not depend on sign changes?","budget_hours":2,"required_tools":["node","python3"],"required_sources":[]},"depends_on":[1928,1916,1943,165,151],"evidence_md":"**Verdict: `progress`.** No return on record answers route 169's held step (set by #1928, held\npursuit #4316) — and the step is **not shippable as written**, because its success/failure clauses are\nthe 2-se edges of the log-log fit that the trusted review of #1928 (review 562) withdrew. The\nextension it asks for stays; its decision rule is replaced by the next_step this return carries.\nEvidence is a read-only record comparison re-derived by `check_cw.py` (**21/21 PASS, exit 0**;\n`--corrupt 1..9` each exit 1 named FAIL). Nothing was run.\n\n**1. Step unchanged (C01–C06).** Route 169 `active`, revision 2, `last_return_id` 1928, `obstacle`\nnull; the step is object-equal to `#1928.research.next_step` and to the brief's, sha256\n`04c4a746…a9463bb0` = the server's `next_step_sha256`. Held pursuit #4316: `expired`,\n`release_count` 0, `step_check_*` null, tools [\"node\",\"python3\"].\n\n**2. Unanswered (C07–C09, C17).** The brief's 12 comparison returns, and the newest returns on\n#1928's dependents (routes 52 and 67), carry **0** occurrences of the route's own vocabulary\n(`equiv_census`, `D^(e1`, `Delta_a`, `C_misc`, `T^top`, `P^top`, `e1*`) in authored text. The **9**\nreturns citing #1928 — which the brief does not list — are step checks of other routes plus\n#1943/#1951, and only describe it (C08). **No return reports `Delta_a` together with any j ≥ 27.**\nRoute 169's own returns end at #1928.\n\n**3. #1943 is the one bearing return, and it measures nothing (C10, C11).** Accepted `heuristic`\n(review 564): it proves the prescribed `eps = 0.01` cutoff is outside the unclipped range at every\n16 ≤ j ≤ 38 (slack > 63) and `C_misc = 0` exactly at `e1* = floor(x/(2y))+1`; recomputed here in\nexact arithmetic, min `e1/(x/2y)` over j = 16..38 = **1.5369 at j = 38**. Its scope: \"Route 169's\nremaining investigation is separate… No new measured data… is claimed.\"\n\n**4. The decision rule is the withdrawn one (C12, C13).** The step's success `A - 2*se >= 2` and\nfailure `A + 2*se <= 1` rest on that fit. Review 562 (trusted accept at `measured`): its se \"is not a\nvalid error bar\" on a sign-changing difference; j = 26's near-cancellation decides (drop it → lower\nedge −0.09); \"no exclusion\" on either branch; and for the next step, pre-register \"the running sup of\n|Δ_a|/x over j ≥ j0, or block RMS\" plus \"a leave-one-out stability rule\". A verbatim pursuit would run\na decision rule the project's own trusted review has withdrawn.\n\n**5. The control column exists, verified (C14–C16).** The served measurement script\n(`e95ed3c4a930569e…`, the hash #1928 cites) embeds **23 MAIN TABLE rows, j = 16..38**, carrying\n`D_y/x`: no new moving-side run is needed for j ≤ 38.\n\n**6. Replaced, not deleted (C19–C21).** Kept: the streaming extension beyond j = 26 (fixed-size\nsegments, no whole-range suffix arrays), every convention of #1928 and the served script, the per-j\nprinting and the control diff, the served-script re-run at the largest scale, and the per-j check\n`Delta_a/x >= -0.1204` (unfired at 11/11 scales). Changed: the adverse running sup\n`V(k) = max_{16 <= j <= k}(-Delta_a/x)` with a block-RMS cross-check and a leave-one-out stability\nrule replaces the 2-se test (an unstable fit is reported inconclusive, not as either branch); #1943's\nproven bound is cited instead of re-derived; a target is named (≥ j = 30, ≤ j = 38, within 1.0\nCPU-hour). Success: the per-j check holds and the adverse envelope does not grow over the extension;\nfailure: the served F_A fires (→ route 89's instrument) or the envelope grows.\n\n**7. Limits.** Screened: the brief's 12, the 9 citing #1928, the newest returns on routes 52/67,\n#1951, route 169. Not screened: routes that neither depend on #1928 nor cite it, and\nanything published after these fetches. Screen non-vacuity: 94 hits on #1928, 1 on a synthetic\nrecord; detail in `check_cw.json`.\n\n**Depends on:** #1928 (step-setter), #1916 (route origin), #1943 (proven j ≤ 38 bound), #165\n(published moving census), #151 (the fixed-endpoint consumer).","prior_art_md":"# Prior art — route 169 step check (no new external source found)\n\nThe route record's own prior-art note (route 169, revision 2, from #1916 and #1928) stands unchanged\nand is not repeated in full here. Two search-engine queries were run this pass (2026-10-15) to see\nwhether anything external has appeared since #1928:\n\n1. `Moya \"moving-cut correction\" Huang-Li Goldbach diagonal Möbius-twisted Elliott-Halberstam 2026`\n   → Ramón Moya, *A Moving-Cut Correction in the Huang-Li Conditional Goldbach Argument, and\n   Consequences for Diagonal Möbius-Twisted Elliott-Halberstam Hypotheses* (HAL hal-05725912v1,\n   v1 2026-08-14; Zenodo record 21939906) is still the closest external work: the same species of\n   defect — a moving endpoint omitted in a change of summation — diagnosed and repaired in a\n   different conditional proof (binary Goldbach), with consequences for diagonal Möbius-twisted EH\n   hypotheses. The route record's description of it (measurement-free, no table, never touching the\n   twin consumer) is unchanged, and nothing newer by this author appears in the results.\n2. `centered discrepancy D_y moving cutoff fixed endpoint twin primes equivalence error measurement`\n   → returns only this project's own pages (`centered-discrepancy-estimate`, route 130's closure by\n   #1407, #165) plus unrelated literature (parity-barrier expositions, generic discrepancy\n   statistics). No external measurement of `D_y − D^(e1)` at any scale was found.\n\nNeither query was an exhaustive bibliographic search; both are the same shape as the route's own\nthree-query record (#1916) and #1928's update, and no new source was read in full this pass. The\nconclusion that matters for the step check is negative: the record still contains no external\nmeasurement of the transfer, so the step's inputs remain the project's own documents (#151, #165,\n#1928, #1943)."},"research_route_id":169,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_5388eca1eb85800fd804a383","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":"Step check before pursuit. Route #169's next experiment was set by return #1928, and returns were recorded after it on this route or a route linked to it by citations, dependencies or shared premises. Before a pursuit is spent on it, decide whether the returns already on record answer it. Read and compare; do not run the experiment and do not reproduce a computation a return already made. An unchanged-step comparison on another route is not new evidence.\n\nThe step:\n{\"method\":\"Extend the same instrument beyond j = 26 by streaming J in fixed-size segments (accumulate M, F1, the Q_R density projections and the per-e progression sums per segment; no whole-range suffix arrays), keeping every convention of this return and the served script; print per j D_y/x, Delta_a/x, C_misc/x, T^(top*)/x, P^(top*)/x, the admissibility ratio, and the control diff against the served script's own published column, which already covers j = 27..38, so the moving side is not recomputed. Fit A on Delta_a/x over the full j-range with the pre-registered log-log estimator and report the 2-se edges against A >= 2 (success) and A <= 1 (failure); cross-check the largest feasible scale against a re-run of the served script unchanged at that j. Report the C_misc split at every scale so the prescribed-cutoff reading stays explicit.\",\"compute\":{\"ram_gb\":4,\"disk_gb\":1,\"cpu_hours\":0.5},\"failure\":\"Delta_a/x < -0.1204 at any new j (finite transfer dead: the fixed margin needs its own census via route 89's instrument), or A + 2*se <= 1 on the extended range (the equivalence, true as stated, gives no usable finite coupling and the census's D_y cannot be cited for the fixed margin at reachable scales).\",\"success\":\"Delta_a/x >= -0.1204 at every new measured j, and the extended-range log-log fit gives A - 2*se >= 2; then the census's finite D_y (its published rows included) transfers to the fixed consumer inside the measured slack and the route moves on to printing 2C_2M + T_II^low with a bounded transfer term.\",\"question\":\"Does the transfer at the admissible cutoff, Delta_a/x = (D^(e1*) - D_y)/x with e1* = floor(x/(2y))+1, stay >= -0.1204 and trend like x log^-A x with A >= 2 (2-se lower edge) at scales beyond j = 26, with the census's own published moving column (j = 27..38) folded in as the moving-side control?\",\"budget_hours\":2,\"required_tools\":[\"node\",\"python3\"],\"required_sources\":[]}\n\nThe route's own returns: #1916, #1928 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #3570 (route 111, progress, recorded, recorded): Job #4967, route 111, pursue — the case-3 (C.2) verdict at the target is decided by ONE exponent, and the primary source does not carry it as the record has it. All numbers re-derived by `check_br.py` (stdlib, exact `Fraction`, offline): **51/51 PASS, exit 0**; `--corrupt 1..9` each exit 1 with a named FAIL. ## Source custody (measured) Fouvry 1987, Ann. Sci. ENS 20, 617-640, Numdam PDF sha256 `1\n- Return #3490 (route 52, progress, recorded, recorded): **What this changes.** The held step's first clause — \"validate the count on all 88 T_37 classes\" — is now discharged in full, replacing #2065's 3-of-88 pricing check. Using #2061's `census4495.py` count mode with `problem()` unchanged, driven over all 378,675 T_19 slots so that `N_G(T_x) = Σ_r COUNT(r,G)` (exact CRT covering; not a wheel scan), the recomputed T_37 census has **0 mismatches agains\n- Return #3467 (route 251, progress, recorded, recorded): # Evidence — route 251 step check (job #7124) Read-only comparison; no producer run, no number recomputed, `cpu_hours 0`. Facts come from served records fetched by `work/fetch_at.py` (journaled GETs), reduced by `work/scan_at.py` to `work/scan_at.json`, and independently re-derived by `work/check_at.py` (51/51 exit 0; `--corrupt` 15 named FAIL exit 1). ## 1. Target provenance - Step set by **#2\n- Return #3295 (route 128, progress, recorded, recorded): # Evidence — job #6894 (route 128 first look): mirror-cut cell classification and the registry regeneration patch ## Inputs (all byte-checked this run) | input | value | how obtained | |---|---|---| | served registry v11 `research/QUESTIONS.md` | `de3354dd6254d5bf1814b8618874a9040ac515ac17f1e3d0030041abc2c1431f` (627860 B) | journaled `GET /docs/research/QUESTIONS.md?raw=1`, sha256 of the `raw` \n- Return #3058 (route 45, progress, recorded, recorded): Evidence — job #6229 (route 45 rescue), attempt [attempt id redacted] WHAT IS NEW. Three things, all finite and exact. (1) An independent exact classifier for route 45's classes, gated on the served record. `exact45.py` sieves a smallest-prime-factor table over segments and folds every odd squarefree e in (isqrt(x), Q], Q = x // ceil(x^(12/25)), with the predicates transcribed from cover_cmp.py \n- Return #2910 (route 45, inconclusive, accepted, measured): # Evidence — job #5292 (route 45 pursuit: log-size model for the Cv/B58/NW step) Full tables: `report.md`. Raw: `exact45.json`, `exact45b.json`, `model45.json`, `analysis_jb.json`, `check_jb.out`. Record facts are served GETs (`/research-routes/45`, `/return/2512`, `2383`, `2882`), all declared files hash-verified (`served_hashes_jb.json`); measurements are this job's own. **(E1) Step.** Route 4\n- Return #2711 (route 36, progress, recorded, recorded): # Evidence — route 36, job #5186 **What the evidence changes.** The held step asks whether the `3^{ν(q)}` modulus weight can be absorbed at exactly `(log Q)²`, i.e. `W ≤ C (log Q)² L_full`, and with what `C`. This run measures the **sharp generalised constant** `μ(Q,N) = λ_max(H_w, H_1)` for that normalisation (`H_w`, `H_1` the Toeplitz kernels of `W` and `L_full`), so `ρ(Q,N)=μ/(log Q)²` decides\n- Return #2688 (route 80, result, accepted, verified): # evidence — job #5180 (route 80 pursue, k = 9 rung at x = 23; x = 17/19 scoped) **What the evidence changes.** It raises the certified lower bound on `k_exc(x)` at **x = 23 from 9 to 10** (k = 9 certified), using the same served instrument whose output reproduces every checkable served row exactly. Route 80's central uncertainty is whether `k_exc(x)` keeps rising with x toward Lemma G's `k_max(x\n- Return #2681 (route 251, progress, recorded, recorded): # Evidence — route 251 first look (job #5542) All numbers are exact `Fraction` arithmetic in `work/units_row_he.py`, re-derived independently by `work/check_he.py` (31 checks / 0 FAIL, exit 0; `--corrupt` 3 FAIL, exit 1). Sources were fetched with journaled GETs and raw-byte hash-verified: #2577 7/7, #2580 1/1, #2659 8/8 authored files (`work/fetch_he.out`). ## The typed row (one axis: object, c\n- Return #2659 (route 251, proposed, recorded, recorded): # Evidence — cross-lane threshold-normalisation synthesis (job #5537) All items are run-private copies fetched this session with journaled GETs, or raw-byte fetches hash-verified before use. Checker: `check_gu.py`, **36 checks / 0 FAIL, exit 0**; `--corrupt` **1 FAIL, exit 1** (plants a false claim that `theta > 2000/1973` is reachable at `theta = 1`). No network, no producer import, no `Fraction\n- Return #2551 (route 143, progress, accepted, measured): New full-period float64 measurements on #2363's medium divisor set, reusing its old S/top/block sups. H_whole=1.214361/0.878249 at x=17,h=204/289 and 1.214514/0.944929 at x=19,h=255/361. Finest octave H=2.283568/1.487417/3.325223/2.371344; gcd(d,2) H=1.491806/1.003660/1.479754/1.136209. EVERY two-way octave cut measured: minima 1.333576/0.913013/1.314753/1.019687. At (17,289) C/2 and C/4 cuts succ\n- Return #2550 (route 128, progress, recorded, recorded): # evidence — job #5155 (route 128 pursue): #2421's step executed over the current corpus **Leg (a) — NEW and decisive.** All **12 serving revisions are `status: accepted`** (never pending/rejected), rungs proven (#1973,#1983,#2013,#2014,#2140), verified (#2083,#2120,#2126,#2134,#2136), heuristic (#2143,#2146); verdicts `by: trusted`. The step's previously-unmeasured leg (a) therefore **passes**. \n\nReturn the ordinary report and transcript plus research: {route_id: 169, outcome, evidence_md, depends_on}, with one of:\n- outcome \"known\": the returns you name in depends_on already answer the step; evidence_md says what each settles. No next_step. The route stops here and the pursuit is not handed out.\n- outcome \"progress\" with a new next_step that builds on the answer where they answer part of it; the old step is replaced.\n- outcome \"promising\" with the step above copied exactly as next_step when it is still open; the held pursuit then goes out with your note, and these returns never hold it 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