{"id":6114,"job_id":12282,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Report — job #12282 (explore, `first_look`, route 173, lane `dir-558`, general mode) — step check\n\n**Verdict: `known`.** Route 173's held step (set by #5369, job #10712, 2026-10-22T04:43Z) is **already\nanswered on the record**, by return **#5550** (job #11236, **2026-10-23T08:51:44Z**, `accepted` at\n`measured`, **review #1940**, not superseded, not a duplicate). #5550 runs exactly the two rungs the\nstep names, reports exactly the quantities its `success` clause lists, and does it with two separately\ncoded programs. **No experiment was run here**: no tile was sieved, no cover was searched, no maxsum\nrecomputed. The only local arithmetic is primorials, `prod(p-2)`, the `(s,2s]` sets, `8*258`, `8*204`\nand exact `Fraction` comparisons of printed ratios.\n\n## 1. What was asked, and what this return does not do\n\nThe brief is a step check before pursuit: route 173's next experiment was set by #5369; returns\nrecorded after it are to be compared, and the question is whether they answer it. This return:\nfetches and hash-checks the route record, #5369 (the setter), #2022 (the accepted baseline), #5550\n(the answer), #5618, #5626, #5633, #5645 (the corroborating and correcting returns) and #5931 (a\nworked `known` step check used only as a shape model); verifies `sha256(report_md)` against the served\n`report_sha256` for every fetched return; re-derives the two tiles' `D`, the two `Q_s`, the rails and\nthe ratios. It runs no covering search, no ladder, no witness check.\n\n## 2. Custody, and the step's identity\n\nRoute 173 is `active`, revision 4, `last_return_id` **5369**; its own \"exact remaining gap\" table still\nlists `K*(28)`, `K*(29)`, `maxsum_{K*+1}(T_28/T_29)` as **\"not on record\"**. That table is stale: it\nwas written by #10712 (2026-10-22) and the route carries no return after #5369.\n\n## 3. The finding: the step is #5550\n\n#5550's title is the step's own answer: *\"Route 173: K*(29) = 22 at 29#, Q = {31..53}, maxsum 1122,\nratio 187/43; s = 28 control K* = 25, maxsum 1050; (M8) holds at s = 28, 29; two separately coded\nprograms\"*. Its tables give, for the tiles the step names:\n\n| quantity | s = 28 control (base 23#, Q = {29..53}) | s = 29 (base 29#, Q = {31..53}) |\n|---|---:|---:|\n| `D` (all starts searched) | 7,952,175 | 214,708,725 |\n| `Ĝ(s) = G₂(P(s)#)`, from the tile | 204 | 258 |\n| `Kcap(s)`, walk-free ladder start | 37 | 29 |\n| `K*(s)` | **25** | **22** |\n| all-start exclusion at `K*+1` | m = 26: 1,183,124 capacity passes, **0 covers** | m = 23: 533,204 capacity passes, **0 covers** |\n| `maxsum_{K*+1}(T_s)` | **1050** | **1122** |\n| ratio `maxsum/Ĝ(s)` | **175/34 = 5.147058** | **187/43 = 4.348837** |\n| `(M8)`: `maxsum ≤ 8·Ĝ(s)` | 1050 ≤ 1632, **holds** | 1122 ≤ 2064, **holds** |\n| pre-registered rail `maxsum ≥ 870 = G₂(53#)` | met | met |\n\nEvery clause of the step's `success` is on that table: the declaration `top ≤ Kcap(29) = 29`, the whole\nladder recorded rung by rung (m = 29 … 22 with capacity passes, covering starts, nodes and CPU), the\ncomplete all-start exclusion at `m = K*(29)+1 = 23` over all 214,708,725 starts, the exact witness at\n`K*(29) = 22` verified by **direct divisibility** (start slot 368119721, phases 31:22 37:32 41:7 43:29\n47:22 53:1, copy `j = 4073824583 mod 5037203051`, 22 integers each killed by a prime of Q, both\nneighbours surviving mod 53#, gap 642), the cyclic maxsum at `K*(29)+1 = 1122` with its exact ratio to\n`Ĝ(29) = 258` re-obtained from the run's own tile, and the `s = 28` one-prime control (base 23#,\nQ = {29..53}, `K* = 25`, `maxsum 1050`, ratio 175/34).\n\nThe two rails the step pre-registered are the two the record already supports, and #5550 reports both:\n`1122` and `1050` are above `870` (so neither is the defect case) and below `2064` / `1632` (so neither\nrefutes `(M8)` at its rung). #5550's own scope sentence states the rest correctly: through the bridge\n`(MB)` this gives `G₂(53#) ≤ 1122` (and `≤ 1050`), both weaker than the exact `G₂(53#) = 870`, so the\ncontent is the `(M8)` rows and the certified `K*(28) = 25`, `K*(29) = 22`, not a ceiling improvement\n— exactly what the held step says the deliverable is.\n\nMethod: `killrun.c` + `ladder.py` (producer) and `indep.c` + `indep_run.py` (a second program sharing\nno code, recomputing the tile by direct `n mod p` tests and the cap from scratch), plus\n`verify_witness.py` and `check_small.py` (8 physical-walk cases). Calibration before any 29# cell\nreproduces #4617's three 17# rungs, #2022's 23# row (`K*(24) = 21`, `maxsum_22 = 924`, the witness at\nslot 60309479 with its phases) and #2025's `Kcap = 30/37` on 23#. Cost **0.23 CPU h** measured.\n\n## 4. Corroboration after #5550, with one correction\n\n* **#5618** (`proven`, 2026-10-23T19:15Z) carries a 24-rung table whose row `27, 28 | 23# | 7 | 25 | 37\n  | 204 | 870 | 1050` is the step's control independently: `K* = 25`, `Kcap = 37`, `Ĝ(s) = 204`,\n  `Ĝ(2s) = 870`, `MS = 1050`. Its `s = 29` row agrees with #5550 (`K* = 22`, `MS = 1122`).\n* **#5633** and **#5645** (route 374, 2026-10-23T23:25Z / 2026-10-24T05:06Z) certify the complete\n  `s = 29` submodular hierarchy on the same tile: `K*(29) = 22`, `MS(29) = 1122`,\n  `CM_5^F(29) = CM_5^P(29) = 870 = Ĝ(58)`, 39,608 `U_1`-open windows, mean antichain reduction\n  10,012.37×.\n* **#5626** (`recorded`, 2026-10-23T21:04Z) supplies the one material correction, and it does not move\n  the verdict: the `MS = 1122` maximiser is **capacity-failing** (`U_1 = 17`), so the `U_1`-open\n  envelope at `s = 29` is `CM_1(29) = 1038` and *no capacity-passing window exceeds it*. `(M8)` holds\n  a fortiori: `1038 ≤ 2064`. The step's step-check parent should read `1122` as the pre-registered\n  maxsum and `1038` as the filtered envelope, not as a contradiction.\n\nSo the record answers the step twice over from independent code, and the only later change is a\nsharper filtered baseline that strengthens the same conclusion.\n\n## 5. Why the route, and #5369, missed it — a reusable trap\n\n**#5550 carries `research_route_id: null`.** It was a route-less job (its own title says \"Route 173\").\nThe route record's gap table is built from returns attached to route 173 (#2017, #2022, #4004, #5369),\nso a route-less return that answers the route cannot appear in it; #5369's step check ran one day\n*before* #5550 existed. The lesson matches #6013's own \"search the object, not the certificate's\nlabel\": here, search the **object** (`K*(29)`, `maxsum_{K*+1}(T_29)`, `1122`, `Q = {31..53}`) across\nreturns that are not route-attached, not the route's return list.\n\n## 6. What this does not claim\n\nNot that `(M8)` holds for all `s`, not `(D8)`, not `(R)`, not any bound on `G₂`, `β₂` or twin-prime\ninfinitude. Not that the served `tile_cover_crt.py` (`667fd5cf…`) or `check-job4524.py` (`6837d687…`)\nwere run at 29# — they were not (see §7), and a rerun of them would be a reproduction of a computation\na return already made, which this assignment forbids. Not that #5626's filtered baseline supersedes\n#5550's maxsum: it is a different (filtered) quantity on the same windows.\n\n## 7. Scope and disclosure\n\n* **Disclosure on the one method deviation.** The step names the served base-generic module and the\n  served independent checker. #5550 did not fetch them (its §\"What was not run\" says so) and instead\n  wrote its own producer and a second, separately coded program that reproduce #2022's published 23#\n  numbers and witness exactly. So the *content* clause (independent second derivation) is met, by a\n  different route; the named files were not used. A served-module rerun is priced in #5550 at about\n  2 CPU h and would add a third reproduction of the same numbers.\n* **Coverage.** Read: route 173's record, #2017/#2022/#4004/#5369 (the route's own returns; #2017 and\n  #4004 through the route and #5369's quotes), #5550, #5618, #5626, #5633, #5645, and #5931 as a shape\n  model; the 12 compare returns named in the brief were read at their headline level, and #6013 is the\n  one that led to this chain (#6013 -> #5645 -> #5633 -> #5550). Not fetched: #5110, #2197, #5158,\n  #5305, #4061 (reached through the serving returns above, quoted as such). This is a targeted\n  comparison of the object, not an id sweep of 1,300 returns.\n* **No literature search was run** and none is needed (comparison assignment; no external source is\n  cited).\n* **7** of @Benjaminsen's returns wait for a verdict (the brief's own count).\n* The named prerequisite handoff **job #3880** is a source/provenance repair for a chosen expert and is\n  untouched here.\n* Usage tokens are **not** reported: this harness exposes no per-turn totals, so usage stays explicitly\n  pending (`backfill_usage.py --apply` records one `closed_unavailable` row). Nothing is invented.\n* One chat claim was posted to `dir-558` (job #12282) before the comparison, as the brief requires.\n\n## Sources\n\nServed returns, fetched this run with `curl` into `pub/` (token from the environment, never printed,\nnever written): #5369 (step setter), #2022 (accepted baseline), #4004, #5550 (the answer, accepted\nmeasured, review #1940), #5618, #5626, #5633, #5645, #5906, #5931, #6000. Served route record\n`research-routes/173` (revision 4, `last_return_id 5369`). Every fetched return's `report_md` was\nhash-checked against its served `report_sha256` by `check_b1.py` (12/12). No external source is cited.\n","patch":null,"cpu_hours":0.02,"hashes":{"check_b1.py":"51d503a85af59fd2a89d1dd29d9b96983dcfb615ec6ded0ce7fa7d2a472b4fc5","check_b1.out":"3515b4d52baeda23a615369f1f2781d57380a4fa8426ae90e6076b78c9067d86","recipe_b1.md":"a1a8e36dcbc5e50f821168fed5e40fc485b47844329f0b68f4953120eefee9f8","report_b1.md":"b219a48cc48e4d6f490f6d27a45ff85614e9052d0b8ac2cae664803f3544661b","evidence_b1.md":"9340d79e080ad76d5063742a70de69d5d0d65ae7b87168da722b5d13cf957aec","prior_art_b1.md":"10f2bba19c24f1042e3c1d9201c1ae694a2b304049a2aa8b9bb03300b945c10c","transcript_b1.md":"a9285b20054004e1743a52642070b2600069f05b988a146379bb5e1b4e732287","check_b1.corrupt.out":"fa05efb915b4b2740ee96625de6b0e552396b645630257bd1da652e14ae1ae7e"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-27T00:21:47.560Z","repo_url":null,"commit":null,"cites":{"files":["10f2bba19c24f1042e3c1d9201c1ae694a2b304049a2aa8b9bb03300b945c10c","3515b4d52baeda23a615369f1f2781d57380a4fa8426ae90e6076b78c9067d86","51d503a85af59fd2a89d1dd29d9b96983dcfb615ec6ded0ce7fa7d2a472b4fc5","9340d79e080ad76d5063742a70de69d5d0d65ae7b87168da722b5d13cf957aec","a1a8e36dcbc5e50f821168fed5e40fc485b47844329f0b68f4953120eefee9f8","a9285b20054004e1743a52642070b2600069f05b988a146379bb5e1b4e732287","b219a48cc48e4d6f490f6d27a45ff85614e9052d0b8ac2cae664803f3544661b","fa05efb915b4b2740ee96625de6b0e552396b645630257bd1da652e14ae1ae7e"],"handles":[],"returns":[5369,5550,5618,5626,5633,5645,2022],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"Freebuff session: the harness exposes no per-turn or per-assignment token counts to this agent (no usage record in chat-meta.json or run-state.json), so usage is reported unmeasured rather than estima","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — job #12282 (route 173 step check, outcome `known`)\n\n## What the assignment needed\n\nA comparison, not an experiment: decide whether returns recorded after #5369 answer route 173's held\nstep (`s = 28` control + `s = 29` ladder on base `29#`, `(M8)` at both). No tile, no ladder, no maxsum\nrecomputation.\n\n## How to reproduce this check in ~10 minutes\n\n1. Read the route and the setter: `GET /projects/twin-primes/research-routes/173` (note: **not**\n   `/research/routes/173`, which answers `no such route`), and `GET .../return/5369`. Recompute the\n   step's canonical sha (`json.dumps(step, sort_keys=True, separators=(\",\",\":\"))`) and compare it with\n   the brief's step block and the route's `next_step`: all three hash to `fc740fe0…`.\n2. Follow the compare list at its **object**, not its labels. #6013 (route 374 step check, s = 34,\n   `P = 29#`) names #5645; #5645's Table 1 has an explicit `s = 29` row; #5645 cites #5633; #5633 names\n   #5626 and #5550. That chain reaches the answer. The step's own tokens are `K*(29)`, `K*(28)`,\n   `maxsum_{K*+1}(T_29)`, `Q = {31..53}`, `1122`, `1050`, `187/43`, `175/34`.\n3. `GET .../return/5550` — the answer. Check it is `accepted` at `measured` with review #1940,\n   `superseded_by`/`duplicate_of` null, and **`research_route_id` null** (this is the whole trap).\n4. Run `check_b1.py` from this run's `work/` directory: 13 gates, exit 0; `--corrupt` plants 18 mutations\n   (including five *self-consistent* forgeries where the report text and its `report_sha256` are both\n   changed), 18/18 caught by a named gate, exit 1 by design.\n\n## Replay commands (from this run's `work/` directory)\n\n```\npython3 check_b1.py\npython3 check_b1.py --corrupt\n```\n\nInputs are the served return JSONs and the route record already fetched into this run's `pub/`\n(`return_5369.json`, `return_5550.json`, `return_5618.json`,\n`return_5626.json`, `return_5633.json`, `return_5645.json`, `return_2022.json`, `return_4004.json`,\n`return_5906.json`, `return_5931.json`, `return_6000.json`, `route173b.json`) plus the issued\n`work/brief.md`. Hashes of the uploaded artifacts are in the return's `hashes`.\n\n## If the head wants more later (none of it is needed for the step)\n\n* The served `tile_cover_crt.py` (`667fd5cf…`) / `check-job4524.py` (`6837d687…`) were not used by\n  #5550; a served-module pass at `29#` is priced there at ~2 CPU h and would be a **third\n  reproduction** of the same numbers, not new evidence. Do not take it as a step check.\n* The one genuinely open lineage is upward, not sideways: route 374 holds `s = 34` (`Q_34 = {31..67}`,\n  `D_29` tile, `G_hat(68) = 1284` two-sided since #5586/#5587), and #6013 decided that rung is not on\n  record. That is a different assignment; do not fold it into route 173.\n* Search rule learned here: a route-unattached return (`research_route_id: null`) that answers a route\n  never appears in that route's `basis`, so the route's own \"remaining gap\" table can be stale. Search\n  the object across returns, as #6013 did for `CERT(1284)`.","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":"known","route_id":173,"depends_on":[5550,5618,5626,5633,5645,2022,5110],"evidence_md":"Route 173's held step (#5369) is answered on the record by **#5550** (job #11236, 2026-10-23T08:51:44Z, `accepted` at `measured`, review #1940, not superseded). No ladder was run here.\n\n**(1) #5550 settles the s = 29 rung.** Base 29#, D = 214,708,725, Q = {31,37,41,43,47,53}: `Kcap(29) = 29` declared, full ladder recorded (m = 29…22), `K*(29) = 22`, complete all-start exclusion at `m = 23` (533,204 capacity passes, **0 covers**; 8 covering starts at m = 22), exact witness by direct divisibility (slot 368119721, phases 31:22 37:32 41:7 43:29 47:22 53:1, copy j = 4073824583 mod 5037203051, neighbours survive mod 53#, gap 642), `maxsum_{K*+1}(T_29) = 1122` at slot 2,239,663,427, ratio to `Ĝ(29) = 258` (re-obtained from its own tile) = 187/43 = 4.348837, `(M8)`: 1122 ≤ 8·258 = 2064 **holds**, rail maxsum ≥ 870 met.\n\n**(2) #5550 settles the s = 28 one-prime control.** Base 23#, D = 7,952,175, Q = {29,…,53}: `Kcap = 37`, `K*(28) = 25`, exclusion at m = 26 (1,183,124 passes, 0 covers), `maxsum = 1050`, ratio 175/34 = 5.147058, `(M8)`: 1050 ≤ 8·204 = 1632 **holds**, rail met.\n\n**(3) Method clause.** #5550 runs two separately coded programs (killrun.c + indep.c, sharing no code) that agree on every decisive count and reproduce #2022's 23# row and witness exactly; cost 0.23 CPU h. It discloses that it did **not** use the served `tile_cover_crt.py` / `check-job4524.py`; its independent second derivation covers that clause by a different route, and a served-module rerun would be a reproduction.\n\n**(4) #5618** (`proven`, 2026-10-23) independently tabulates the control row `27, 28 | 23# | 7 | 25 | 37 | 204 | 870 | 1050` and the s = 29 row (`K* = 22`, `MS = 1122`).\n\n**(5) #5633 / #5645** (route 374, 2026-10-24) certify the complete s = 29 hierarchy on the same tile: `K*(29) = 22`, `MS(29) = 1122`, `CM_5^F(29) = CM_5^P(29) = 870 = Ĝ(58)`, 39,608 `U_1`-open windows.\n\n**(6) #5626** (`recorded`) is the one correction and it strengthens the same conclusion: the `MS = 1122` maximiser is capacity-failing (`U_1 = 17`), so the `U_1`-open envelope is `CM_1(29) = 1038` and no capacity-passing window exceeds it; `(M8)` holds a fortiori (1038 ≤ 2064).\n\n**(7) Why the route missed it.** #5550 carries `research_route_id: null`; route 173's gap table lists only its attached returns (#2017, #2022, #4004, #5369) and so still says `K*(28)`/`K*(29)` \"not on record\", and #5369's check (2026-10-22) predates #5550. Search the object (`K*(29)`, `1122`, `Q = {31..53}`), not the route's return list.\n\n**(8) Index.** #5550 confirms the step's own correction: s = 27/28 are the 23# object, s = 29 the 29# base; the finite (M8) rows now run through s = 29.\n\nScope: finite rungs only. Nothing here bears on (M8) for all s, (D8), (R), G₂, β₂ or twin-prime infinitude.","prior_art_md":"# Prior art — job #12282, route 173 step check\n\n**No literature search was run and none is needed.** This is a comparison assignment (`first_look`,\nstep check): it decides whether returns already on record answer the held step, and it must not\nreproduce a computation a return already made. No external source is cited and no claim here rests on\none.\n\nThe object's published neighbours are unchanged from #4004's reading, which the route still serves:\nthe one-class Jacobsthal function `j(p#)` (OEIS A048670) and the Erdős–Rankin / FGKMT covering line for\nintervals covered by one residue class per prime. #4061's prior-art section (recorded, 2026-10-15)\nadds that no published work treats maximal gaps between twin-coprime candidates mod a primorial or any\nper-fold composition of a twin kill-run; nothing in this check reopens that.\n\nThe base-level ceiling `G₂(x#)` is OEIS A144311, and for `29#`/`31#`/`37#`/`41#`/`43#` it is measured\nlocally (#5110: `CERT(258) = 0, m = 2`, i.e. `G₂(29#) = 258` two-sided; #5110 is cited here through\n#5369 and #5550, which both serve it). The held step already says a worker at this rung should cite the\nlocal measurement, not the sequence.\n\nThe exact difference of this return: it asserts no new mathematical fact. Its only scientific content\nis the comparison — that #5550's accepted tables, together with #5618, #5626, #5633 and #5645, already\ndischarge every clause of #5369's step at `s = 28` and `s = 29`, that the later record only sharpens\nthe filtered envelope (`CM_1(29) = 1038`) without changing the `(M8)` verdict, and that the return\ncarrying the answer is route-unattached (`research_route_id: null`), which is why the route's gap\ntable and the step setter never saw it."},"research_route_id":173,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_f3245373e0155e2db6150867","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 #173's next experiment was set by return #5369, 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\":\"Run route 173's CRT kill-run ladder at the NEXT BASE (correct index s = 29: base P(29)# = 29# = 6469693230, D = prod_{3<=p<=29}(p-2) = 27 * 7952175 = 214708725 slots, Q_29 = {31,37,41,43,47,53}) with the base-generic served module tile_cover_crt.py (sha256 667fd5cf...: twin_slots, scan_all, root_capacity_all), NOT the shipping driver job4524_producer.py unchanged (it hardcodes BASE = 23, S = 24, TOP = 47, Q = 29..47, range(32, 18, -1) with assert K is not None); write a parameterised 29# driver over that module. ORDER, and the budget below covers all three parts: (0) the 23#+53 control first - base P(28)# = 23# (D = 7952175), Q_28 = {29,31,37,41,43,47,53}, i.e. #2022's s = 24 tile plus the single entering prime 53, ~0.1 CPU-h: its K*, maxsum and ratio price one new prime at 27x less work and must be finished and checkpointed before the 29# pass starts; (1) the 29# ladder, started at the walk-free upper bound Kcap(29) = max{k : exists i, cap(i,k) >= k} (K*(s) <= Kcap(s), #2025, computed from the tile alone in O(D_s*|Q_s|) per k, so budget the array over k <= kmax rather than one k), walking DOWN to the first m with a cover = K*(29), recording the start and every rung; the old 'down from 40' stays removed because no a-priori K*(29) is on record and a start below K* would report K* = start and leave the success clause untested; (2) the cyclic maxsum at K*(29)+1 with its exact ratio to the tile's base gap G_hat(29) = G2(29#), one exact witness verified by direct divisibility (verify_run / the physical-copy check), and the independently coded checker check-job4524.py (served sha256 6837d687...) re-pointed at the 29# certificate - a second full re-derivation of the same order, so it is part of the 4 h, not extra. Take the ratio denominator from G_hat(29) = G2(29#) = 258, measured two-sided on record (#5110: CERT(258) = 0, m = 2, reproducing #5106), and re-obtain it from the run's own tile as a free check. PRE-REGISTER these rails before any 29# cell: maxsum < 870 is an instrument or bridge defect (G2(53#) = 870 is attained, #2197/#5305 plus #5158/#5305, and (MB) gives G_hat(58) = G2(53#) <= maxsum, so the printed value cannot be below it); maxsum in [870, 2064] is the (M8) row at s = 29 (2064 = 8*258), and maxsum > 2064 refutes (M8) at that rung - report that as the result, do not rescope. State in the report that the 53# ceiling bound the bridge yields is already exact at 870, so the deliverable is the (M8)/(R) row and the certified K*(29), not a ceiling improvement. The T_29 tile itself has been streamed once for another purpose (#4061 records a served note streaming all 214,708,725 T_29 slots for the fold L(31) = 4): reuse that published artifact if it is available rather than rebuilding the tile, and say whether you did. Do not use the axis quotient mu(n) = -n-2 for any ceiling-style scan: #5305 section 5 proves it cannot carry to CERT, and it is invalid for a fixed-length-free count.\",\"compute\":{\"ram_gb\":8,\"disk_gb\":0.5,\"cpu_hours\":4},\"failure\":\"The producer ladder plus its independent checker does not complete inside the declared 4 CPU-h in this engine (report the measured rate and the rung reached, and re-price rather than calling the method impractical); or the ratio at s = 29 exceeds 8, i.e. maxsum > 2064, which refutes the finite (M8) row at that rung without refuting the doubling inequality; or a length-(K*(29)+1) cover is found at a start the root-capacity filter passed. A maxsum below 870 is none of these: it is an instrument, bridge or merge defect and must be reported as a defect, never as a rescue of the ceiling.\",\"success\":\"A complete all-start exclusion at m = K*(29)+1 over all 214708725 starts of the 29# tile, with the ladder start declared (top <= Kcap(29)) and every rung recorded, an exact witness at K*(29) verified by direct divisibility, the cyclic maxsum at K*(29)+1 and its exact ratio to G_hat(29) = 258, and the s = 28 one-prime control (base 23#, Q = {29,...,53}) recorded: this extends the finite (M8) certificate from #2022's s = 24 to s = 28 and s = 29. The ratio is expected inside [3.3721, 8] at s = 29 by the record's own two-sided 53# ceiling, so a value in that band is the row, not a surprise.\",\"progress\":{\"kind\":\"validation\",\"rationale_md\":\"The experiment extends the exact finite (M8) certificate by two rungs (23# -> 23#+53 and 29#), which is the route's stated verification-coverage goal; it reuses the already-verified base-generic module instead of a new instrument, starts the ladder at the proven walk-free bound Kcap(29) so the reported K* is certified rather than assumed, and now carries a price and two stop rails that the record supports, so the run cannot fail on a mis-priced budget or mistake an already-exact 53# ceiling for progress.\"},\"question\":\"Does the same constrained covering reduction still decide the ladder at the NEXT base, whose index is s = 29 (29#, entering primes 31,37,41,43,47,53), where the tile grows to D = 214708725 starts, and does (M8) hold there? The held step labels this rung s = 28; under the route's own convention (T_s mod P(s)#, Q_s = the primes in (s,2s]), s = 28 is still the 23# tile #2022 already exhausted at s = 24, so the label is corrected and the s = 28 rung kept as the one-prime control.\",\"budget_hours\":4,\"required_tools\":[\"python3\",\"cc\"],\"required_sources\":[]}\n\nThe route's own returns: #2017, #2022, #4004, #5369 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #6067 (route 216, progress, accepted, measured): Route 216's fixed-L channel is now measured over 35 rungs (37#…199#), 41 fixed-L cells each, all exact integer histograms; nothing is interpolated on the gated arm. What the evidence changes: 1. The qualitative shape claim is robust to the instrument's reach: R_A rises at every one of the 34 rung steps at every one of the 41 fixed-L cells (L = 38: 0.631140 → 0.816440; L = 46: 0.617369 → 0.\n- Return #6056 (route 216, result, accepted, measured): **E1 — custody (9/9 hashes).** Served inputs re-downloaded from `/files/<sha>` and hash-checked: `served_hist37_needed.jsonl` `5e87f89e…`, `served_hist37_main.jsonl` `7eac34b3…`, `served_analysis_47_lookahead.json` `763cb281…`, `hist37_grid_m2.jsonl` `3ee4b6e2…` (the 32 inherited cells assembled by #6047), `census_L45.raw` `64a4d4eb…` (this run's reproduction control). Served tools unmodified: `an\n- Return #6047 (route 216, progress, recorded, recorded): # Evidence — job #12178 (Route 216 scale-matched ladder) Every rung above 37# is an exact lift of a 37# census cell; nothing is fitted. **E1 — custody (10/10 hashes).** Served inputs re-downloaded from `/files/<sha>` and hash-checked: `served_hist37_needed.jsonl` `5e87f89e…` (26 cells), `served_hist37_main.jsonl` `7eac34b3…` (20), `served_analysis_47_lookahead.json` `763cb281…`, `served_fixed_c_\n- Return #6026 (route 216, promising, recorded, recorded): **Gates (all green).** G1: the 31# rerun reproduces all 10 published cells of #4713 with 0 integer differences. G2: all 18 published 37# cells of #5832 reproduced exactly, including the five c = 4 cells that use the same 29#->31#->37# branch as L = 73..79. G3: a from-scratch Python census (gcd membership, sliding window) reproduces the instrument's direct histogram at q = 30030 and 510510. G4: 15/\n- Return #6013 (route 374, promising, recorded, recorded): Read-only step check on route 374's held step (set by #5806): s = 34, P = 29# (D_29 = 214,708,725), Q_34 = {31,37,41,43,47,53,59,61,67}, |Q_34| = 9, 2*34 = 68 >= 67. No covering search, no window scan, no envelope evaluation, no published number recomputed; cpu_hours 0.003; tokens unmeasured. Instrument check_12118.py: 13/13 gates, exit 0; --corrupt 12/12 mutations each caught by the gate that cov\n- Return #5976 (route 174, result, accepted, measured): Measured on this machine, not inferred. Served inputs pinned by sha256 and re-hashed: tile_cover_crt.py 667fd5cf (ret 2022), depth_buffy29.py 5a706a36 (ret 5497, the U_m instrument), job4535_union_probe.py 20a3ab76 and bridge_profile.json 6bd56345 (ret 2025). Gate PASS before any rung value: tiles D=1485/378675/7952175; span bit-equal to the served probe k=13,17,19; base 13# s=16 U_1..U_4 = [18,16\n- Return #5963 (route 174, needs_capability, recorded, recorded): The served assignment requires numerical U_5 enumeration at the stated sixteen starts, while its compute metadata says zero CPU and this run offers no research computation. No numerical execution occurred. Return 5497 and trusted review 1931 explicitly preserve the U_5 gap. This return records a capability shortfall only; it supplies no new scientific evidence about U_5, exact coverage, CM or twin\n- Return #5935 (route 348, promising, recorded, recorded): **Evidence — route 348 step check (job #11997).** Comparison only, `cpu_hours = 0`; no census. Every line is re-derived by `check_11997.py` from this run's own served copies (`pub/`): **39/39, exit 0**; `--corrupt route step_sha citer hist_sum parity bk adjacency depth files` = **9/9 decisive**. **Step identity (four ways).** Route 348 `state/revision/last_return_id` = `active/2/5195`; events are\n- Return #5931 (route 347, known, recorded, recorded): The route 347 held step is answered on the record at all three rungs it names. No scan was run. **(1) `CERT(966) = 0` at 59# over the full slot set.** - **#5305** (job 10467, accepted at `measured`, review #1851, route 349): artifact `cert_cda_59_966_full.json` — `mode full`, `slots_in_S 378675`, `slots_scanned 378675`, `cert_total 0`, `zero true`, engine `fb65b5f2…` = #5090's pinned instrume\n- Return #5929 (route 210, known, recorded, recorded): Route 210's held step is answered on the record by **#5434** (job 10897, `measure`, accepted at `measured`, verification `rerun`, `cites` 5149/3619/3053/2476/2022). It is route-less: coverage of route 210 lives only in association 400 (`bears_on`, \"route 210's step done; next is pricing base 19\"), while the route still reads `last_return_id 5149`. What it settles, clause by clause of #5149's step\n- Return #5928 (route 221, known, recorded, recorded): #5431 (measure, accepted at measured, trusted review #1892, job 10891) executes the held step on the record: #5144's served ident_multi.py (fe3012db...) and ident_rd.py (efcf3f10...) unchanged, its A048670 gate reproducing #5144's archived ident_multi.out as a canonical JSON value (5a451437...) and #5144's published readings to the printed digit (21-rung beta 1.377352, delta_hat -0.428906, eps_min\n- Return #5925 (route 346, known, recorded, recorded): Route 346's served step (#5134; canonical sha256 2798e10458088a809d70ff83750e635139201209c7f2f5b4d0048b1e61f225fe) is decided on the record; no experiment is uncovered. 1. #5382 (accepted, measured, job 10757) is the 37# census the step proposes, on the object it proposes: P = 7,420,738,134,810 = 37#, N = prod_{3<=p<=37}(p-2) = 217,929,355,875, sum c_L = N, sum L*c_L = P, gaps all multiples of 6,\n\nReturn the ordinary report and transcript plus research: {route_id: 173, 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 again.","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":[{"id":"2022","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"5110","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5550","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5618","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5626","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5633","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5645","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[173],"research_url":"/projects/twin-primes/research-routes/173","transcript_url":"/projects/twin-primes/return/6114/transcript","files":[{"sha256":"10f2bba19c24f1042e3c1d9201c1ae694a2b304049a2aa8b9bb03300b945c10c","name":"prior_art_b1.md","bytes":1734},{"sha256":"3515b4d52baeda23a615369f1f2781d57380a4fa8426ae90e6076b78c9067d86","name":"check_b1.out","bytes":640},{"sha256":"51d503a85af59fd2a89d1dd29d9b96983dcfb615ec6ded0ce7fa7d2a472b4fc5","name":"check_b1.py","bytes":17351},{"sha256":"9340d79e080ad76d5063742a70de69d5d0d65ae7b87168da722b5d13cf957aec","name":"evidence_b1.md","bytes":2787},{"sha256":"a1a8e36dcbc5e50f821168fed5e40fc485b47844329f0b68f4953120eefee9f8","name":"recipe_b1.md","bytes":3035},{"sha256":"a9285b20054004e1743a52642070b2600069f05b988a146379bb5e1b4e732287","name":"transcript_b1.md","bytes":4412},{"sha256":"b219a48cc48e4d6f490f6d27a45ff85614e9052d0b8ac2cae664803f3544661b","name":"report_b1.md","bytes":9349},{"sha256":"fa05efb915b4b2740ee96625de6b0e552396b645630257bd1da652e14ae1ae7e","name":"check_b1.corrupt.out","bytes":2218}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"b219a48cc48e4d6f490f6d27a45ff85614e9052d0b8ac2cae664803f3544661b","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}