{"id":6013,"job_id":12118,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 374 step check (job #12118): the `s = 34` (67#, `|Q_34| = 9`) hierarchy is **not** on record, but #5806's ceiling premise is **stale** — `G_2(67#) = 1284` has been two-sided certified since #5586/#5587, two days before #5806 was written\n\nRead-only comparison. **No covering search, no window scan, no submodular evaluation, no bound\nrecomputed.** Compute: `cpu_hours` 0.003 (13 gates; everything else is HTTP GETs of served records).\nTokens `unmeasured` (this harness exposes no per-assignment counter; nothing estimated).\n\nInstrument: `check_12118.py` — **13/13 gates, exit 0** (`check_12118.out`); `--corrupt` plants\n**12 mutations, 12/12 caught** by the gate that covers each (`check_12118.corrupt.out`).\n\n---\n\n## 0. Summary\n\n1. **The step under test is custody-clean.** Route 374 (`active`, revision 3, `last_return_id 5806`)\n   serves `next_step` **byte-identical** to #5806's own `research.next_step`, canonical\n   `sha256 = 80b81c99…` = the served `next_step_sha256` (gate G05). It is #5645's step relabelled:\n   exactly **24 single-digit substitutions** plus **one inserted clause** `, 2*34 = 68 >= 67`, with\n   `compute`, `budget_hours`, `required_tools` and `required_sources` unchanged (gate G06).\n\n2. **The hierarchy itself is nowhere on the record.** Scanning all **233** served returns fetched for\n   this check (the 46 returns the brief names, plus every id **5807..6015** — 209 attempted, 196\n   served, 13 absent/404) for the step's own object tokens (`Q_34`, `K*(34)`, `K^*(34)`, `MS(34)`,\n   `CM_9`, `nq = 9`, `G_hat(68)`): **the only hits are inside #5806 itself** (gate G07). A sweep of\n   all **337** route records finds the hierarchy tokens only in route **374**; the three other routes\n   that contain the string `s = 34` (105, 112 and the rank-census route 26 with `K*(34)`) carry no\n   hierarchy token and are different objects (gate G08). So `K*(34)`, `MS(34)`, `CM_m(34)` for\n   `m = 1..9`, the `m = 8` dual core and Route #170's `boundary_loss` at `L = K*(34)` are all open.\n\n3. **But one clause of the step is already answered, and #5806 says it is not.** #5806 §3 states that\n   `1284` \"is on record only as a cited value\" and that \"the two-sided covering certificate exists on\n   this project only for 59# and 61#\", with `CERT_1284(67#)` as an open follow-up. That is **false on\n   the record, by two days**:\n   - **#5586** (`accepted`, rung `measured`, review #1998, **2026-10-23T11:55Z**) has the title\n     `CERT(1284) = 0, COUNT(1284) = 2 at 67#` and its 13-row ladder ends `| 67 | 1284 | 2 | 0 | 0 |`.\n   - **#5587** (**2026-10-23**, `pending`) runs the ceiling with its own controls in one sweep:\n     `CERT_1284(67#) = 0` over all **378,675** `T_19` slots, with `CERT_1278(67#) = 2` and\n     `CERT_1074(61#) = 4` positive controls, so the zero is not vacuous.\n   - **#5375** (`accepted`, `proven`) carries the same upper bound on the `g2` engine.\n   After #5806 this is reconfirmed twice: **#5906** (route 344 step check, 2026-10-25T21:07Z) files\n   `CERT(1284) = 0` three ways, and **#5931** (route 347 step check, 2026-10-26) states \"all three\n   CERT rungs are on record\", 67# included. Gate G09 checks all nine of these facts; gate G10\n   re-derives the value from the certified ladder: `G_hat(2s) = G_2(wheel(s)#)` with\n   `wheel(s) = max{p <= 2s}`, so `wheel(34) = 67` and `G_hat(68) = G_2(67#) = 1284`.\n\n4. **Why #5806 missed it — a reusable trap.** The 67# ceiling is filed under three different\n   spellings: `CERT(1284) = 0` (#5586, and its title), `CERT_1284(67#)` (#5587, #5931) and\n   `CERT(1284) = 0` again (#5906). A scan keyed on `CERT_1284` **does not see #5586**, which is the\n   accepted carrier. #5806's `required_sources` list (`5633, 5627, 5623, 5618, 5550, 5532, 5305`)\n   contains none of 5586/5587 (and not even 5645, the return whose step it was editing). Search the\n   *object* (`1284`, `G2(67#)`), not the certificate's label.\n\n5. **Second trap, inside the very table the successor must extend.** `1284` is also\n   `CM_7^{Umax}(31)` in #5645's Table 1 (the `s = 31` `U_max` row reads\n   `1326 … 1326, 1284, 1080`). A bare text search for the ceiling value therefore matches a\n   `61#`-rung hierarchy number, and #5645 never mentions `67#` at all (gate G11). Anything that\n   \"finds 1284 in #5645\" has found the wrong object.\n\n6. **Consequence returned:** outcome **`promising`** — the step is not answered, but half of it\n   (the ceiling) is, so the step is restated once: keep the hierarchy evaluation, **cite**\n   `G_hat(68) = 1284` as certified instead of re-certifying it, and correct the source list. The\n   saving is measured, not estimated: #5587 prices the 67# `CERT_1284` sweep at **13,920.6 CPU-s =\n   3.87 CPU-h** (31 single-threaded jobs, 171-175 MB peak each), which the step as written implies\n   re-running.\n\n---\n\n## 1. What the assignment asked, and what this return does not do\n\nThe brief is a *step check before pursuit*: route 374's next experiment was set by #5806 and the job\nis to decide whether returns already on record answer it — \"read and compare; do not run the\nexperiment and do not reproduce a computation a return already made\".\n\nThis return therefore: fetches the route record, its three own returns (#5633, #5645, #5806), the 46\ncomparator/required-source returns and every return id in 5807..6015; verifies custody by recomputing\n`sha256(report_md)` against the served `report_sha256` **233/233** (gate G01); tests the ladder index\narithmetically against every rung on the record (gate G03); reconstructs `D_29` (gate G04); diffs the\nroute's step against #5645's (gate G06); scans for the step's object tokens in returns and in routes\n(gates G07, G08); and reads the provenance of the ceiling the step depends on (gates G09-G12). It\nruns no covering search, no window scan, no envelope evaluation, and recomputes no published number.\n\n## 2. The step, and why its index is right\n\nThe step asks for the `s = 34` rung over the fixed `P = 29#` base (`D_29 = 214,708,725`), with\n`Q_34 = {31,37,41,43,47,53,59,61,67}` (`|Q_34| = 9`, `2*34 = 68 >= 67`). Gate G03 rebuilds the index\nfrom a sieve: `Q_s = primes in (29, 2s]` gives `Q_31 = Q_32 = Q_33 = {31..61}` (8 primes) and\n`Q_34 = Q_31 u {67}` (9 primes); `wheel(s) = max{p <= 2s}` gives `wheel(31) = wheel(33) = 61` and\n`wheel(34) = 67`; and the published rungs of #5618 (`s = 16` base 13#: `17,19,23,29,31`; `s = 19/20`:\n`23,29,31,37`; `s = 22`: `23,29,31,37,41,43`; `s = 24/25`: `29,31,37,41,43,47`) and of #5645\n(`{31..53}`, `{31..59}`, `{31..61}`) all reproduce. `D_29 = prod_{odd p <= 29}(p-2) = 214,708,725`\nexactly (gate G04). So the corrected step this route holds is internally consistent — #5806's\nretargeting from #5645's mislabelled `s = 33` was right, and nothing in this check revises it.\n\n## 3. What the record does **not** answer\n\n`K*(34)`, `MS(34)`, the five `CM_m(34)` families for `m = 1..9`, an `m = 8` dual core `y*` in\n`Z_{>=0}^9`, and Route #170's `boundary_loss` at `L = K*(34)`. None of these strings, nor `Q_34`, nor\nany `s = 34` computation, occurs in any of the 233 fetched returns except #5806's own step text\n(G07). Two step checks *quote* the retargeting without computing it — #5815 (route 216) writes \"the\n9-prime set `Q_31 u {67}` is `s = 34` … `G_hat(68) = 1284`\", and #5919 (route 369) writes \"the live\nfrontier of this hierarchy has moved to route **374** (`s = 34`, nine primes)\" — and neither is a\nmeasurement of the rung. Route-level sweep (337 routes) agrees: only route 374 carries it (G08).\nThe lane chat window fetched for this check (15 messages, 2026-10-24T17:50Z → 2026-10-26T08:57Z)\ncontains no claim on the rung (G13).\n\nThe nearest published neighbours, for scope: #5645 certifies the ladder through `s = 32`\n(`K*(31) = K*(32) = 29`, `G_hat(62) = G_hat(64) = 1080`, `MS(31) = 1356`, `CM_7^{F,*} = 1122` with\n`y* = (2,3,3,3,3,4,3,2)`, `CM_8 = 1080`, `boundary_loss = 0`) and #5626/#5623/#5633 supply the\n`29#` machinery. Nine primes is a genuinely new rung: the mask universe goes from `2^8 - 1 = 255` to\n`2^9 - 1 = 511` subsets per window, and the obstruction question moves from `m = 7` to `m = 8`.\n\n## 4. What the record **does** answer: the ceiling\n\n| fact | source | status |\n|---|---|---|\n| `G_2(67#) = 1284` upper side: `CERT(1284) = 0` over all 378,675 `T_19` slots | #5586 (title + 13-row ladder), #5587 (`CERT_1284(67#)`, 31/31 chunks), #5375 (`proven`, `g2` engine) | accepted / pending / accepted |\n| lower side: `COUNT(1284) = 2` at residues 3941657, 5756747 | #5586 (`m = COUNT(G2) = 2`, accepted `measured`), #5587 (`gaps_hist {1284: 2}`), #5906 | accepted |\n| positive controls in the same sweep (`CERT_1278(67#) = 2`, `CERT_1074(61#) = 4`), so neither zero is vacuous | #5587 | pending (route 349's control run) |\n| `G_hat(68) = 1284` by the ladder identity `G_hat(2s) = G_2(wheel(s)#)`, `wheel(34) = 67` | derived here from #5586's certified row + the index rule | gate G10 |\n| reconfirmation after #5806 | #5906 (2026-10-25T21:07Z), #5931 (2026-10-26) | recorded |\n\nSo the ceiling is **two-sided and cheap to cite**. Re-running `CERT_1284` would be a re-measurement\nof the same quantity with the same engine on the same slots — the department's rule that separate\ncode is not a separate reading applies, and the deliberate-replication path needs a named\nindependence objective that the step does not state.\n\n## 5. Two caveats the successor must not lose\n\n1. **`MS` is an unfiltered maximum; `CM_1` is the envelope baseline.** #5626 established at `s = 29`\n   that the published `MS = 1122` is attained by a window the capacity filter itself rejects\n   (`U_1 = 17`), so the envelope starts at `CM_1(29) = 1038`; #5645's `s = 31` row shows the same\n   pattern (`MS(31) = 1356` versus `CM_1(31) = 1326`, both maximisers having `U_1 = 24 < k`). The\n   step asks for `MS(34)` **and** `CM_1(34)`; the second is the one the hierarchy is measured from\n   (gate G12).\n2. **The value `1284` is not unique on the record** (§0.5): in #5645 it is `CM_7^{Umax}(31)`.\n\n## 6. The restated step, and its price\n\nSame experiment, one clause removed and the sources corrected (the full object is in the payload's\n`research.next_step`):\n\n- **method** unchanged in substance — incremental-slack covering search plus the antichain-reduced\n  submodular evaluator on `P = 29#` at `Q_34`, `m = 1..9`, obstruction test at `m = 8` — with\n  `G_hat(68) = G_2(67#) = 1284` **cited** (#5586 accepted, #5587 control, #5906/#5931 reconfirmation)\n  and the filtered `CM_1(34)` quoted as the `m = 1` baseline (#5626).\n- **`required_sources`**: `5633, 5627, 5623, 5618, 5550, 5532, 5305` keep their roles (route\n  instruments, the `s = 29` engine, the `59#`/`61#` CERT controls); **add `5645`** (the return whose\n  step this is, and Table 1, the ladder to extend), **`5626`** (the filtered baseline), and\n  **`5586, 5587, 5906, 5931`** (the ceiling and its reconfirmations).\n- **compute**: `cpu_hours` raised `0.2 -> 0.5` on measured grounds — the `s = 29` census took\n  **2,749 CPU-s = 0.76 CPU-h** (#5626, 39,608 windows, 18 `k`-passes), while the 3.87 CPU-h ceiling\n  sweep leaves the step. RAM 2 GB and disk 1 GB are unchanged and were not tested here.\n\n## 7. Disclosures\n\n1. This is a **step check**: the verdict rests on served records, not on new computation. The only\n   arithmetic performed is a sieve to 100, the `Q_s`/`wheel(s)` reconstruction, one product for\n   `D_29`, `sha256` custody and exact JSON diffing.\n2. **Scan scope, and its blind spot.** Returns covered: the 46 ids the brief names, every id\n   5807..6015 (209 attempted; 5827, 5834, 5851, 5869, 5889, 5936, 5939, 5942, 5975, 5985, 6013,\n   6014, 6015 are absent/404), plus 5586, 5375, 5906 fetched for the ceiling. Returns **below 5807\n   that the brief did not name are not fetched**; a much older return that computed a nine-prime\n   hierarchy would be missed by the token scan. The route sweep (all 337 routes) and the two quoting\n   step checks (#5815, #5919) make that unlikely but do not exclude it.\n3. The lane-chat read is a 15-message window (`GET /chat/dir-558/messages`), not the whole 151-message\n   channel; older claims would surface as returns, but the window is disclosed as narrow.\n4. No web search was run: the question is internal to the record (whether a return answered a rung),\n   and the brief's `web` entry in `required_sources` is read as permission, not obligation.\n5. `G_hat(68) = 1284` is used as the record certifies it (#5586/#5587/#5375/#5906/#5931). I did not\n   re-derive `G_2` from the covering definition and claim no new certification.\n6. `check_12118.py --corrupt` mutates in-memory copies only; no fetched file was rewritten (G01 is\n   recomputed from the same bytes in both modes, which is what makes custody meaningful).\n\n## 8. Verification delivered\n\n`check_12118.py`: **13/13 PASS, exit 0** (`check_12118.out`). `--corrupt` runs 12 named mutations —\n`custody` (a flipped `report_sha256`), `ladder` (67 dropped from `Q_34`), `d29` (one digit in\n`D_29`), `answer` (the step's answer planted in #5900's report), `route` (`last_return_id` 5806→5700),\n`ceiling_status` (#5586 accepted→pending), `ceiling_date` (#5586 moved after #5806), `collision`\n(`1284`→`1278` in #5645), `route_sweep` (a 338th route carrying `Q_34`), `control`\n(`CERT_1278(67#) = 2`→`= 0` in #5587), `relabel` (`budget_hours` 1→4 in the route's step), `chat` (a\nclaim planted in the lane window) — and each exits 1 with its own gate named\n(`check_12118.corrupt.out`). Mutations that edit report text also break custody; that is expected and\nis why G01 is the outer guard.\n","patch":null,"cpu_hours":0.003,"hashes":{"check_12118.py":"f5231c92e8cc8968beb5e0e0159242a8282a33871e67a20b652c41c0f5d7f211","check_12118.out":"00593e3888c9955f593e48a7c3c27280d3ba5be217884d3c060e0b7b6100cd84","report_12118.md":"c3d8a1705073d6532274a7c7d2ed39f200ea513b51f292f710afed6ecf4464bd","evidence_12118.md":"54f83baf1ae64a49ec5365b4fbd1a8871e3b298000b8e1646cd4e1cb9bf23a32","prior_art_12118.md":"2c92ccfdba35c7f4e2ddd0fa2de0669c4a95cf51fe1cc57619d25f4220d3c339","transcript_12118.md":"b05f8caefccfa644bcadc71abe67b6ab4279e7d0ed15b85883b2bd1d1218d65d","check_12118.corrupt.out":"99deaffa83d76361f51565076a71a6652365efbc43441d14ce8b4070e9622075","hashes_files_12118.json":"4aabaea112cc1f31b74478db82f356e80af84da762e1ce19b6dc1c881b872659"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-26T09:22:16.032Z","repo_url":null,"commit":null,"cites":{"returns":[5806]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"this harness exposes no provider token counters; no counts are estimated or invented","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":null,"verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":{"outcome":"promising","route_id":374,"next_step":{"method":"Extend the incremental-slack covering search and antichain-reduced submodular evaluator on P = 29# (D_29 = 214,708,725) to nq = 9 (Q_34 = Q_31 U {67}, 2*34 = 68 >= 67), computing K*(34), MS(34), CM_m(34) for m = 1..9, and testing whether a dual polymatroid core certificate y* in Z_{>=0}^9 again obstructs full closure at m = |Q_34| - 1 = 8. Two corrections from the record, no change to the experiment: (i) CITE the ceiling G_hat(68) = G_2(67#) = 1284 as already two-sided certified (#5586 accepted measured: CERT(1284) = 0, COUNT(1284) = 2; #5587 same-sweep control CERT_1278(67#) = 2; reconfirmed #5906, #5931) instead of re-running CERT_1284, whose measured price is 3.87 CPU-h; (ii) quote the capacity-filtered CM_1(34) as the m = 1 baseline, since the published MS is an unfiltered maximum whose maximisers the capacity filter rejects (#5626 at s = 29: MS = 1122 but CM_1 = 1038; #5645 at s = 31: MS = 1356 but CM_1 = 1326). Note that 1284 also equals CM_7^{Umax}(31) in #5645 Table 1 - it is not a 67# value there.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0.5},"failure":"Full-period evaluation of m = 1..9 on Q_34 exceeds the single-pass 29# compute budget, or no capacity-open window above 1284 is certified, or the m = 8 claim is asserted without an explicit integer y*.","success":"Exact certification of K*(34), MS(34), all five CM_m(34) families for m = 1..9, an exact determination of whether CM_8^{F,*}(34) equals the cited G_hat(68) = 1284 or is obstructed by an explicit dual polymatroid vector y* in Z_{>=0}^9, and exact Route #170 boundary_loss at L = K*(34); G_hat(68) cited as certified, not re-derived.","question":"On the s = 34 (67#, Q_34 = {31,37,41,43,47,53,59,61,67}, |Q_34| = 9) rung over the P = 29# base wheel, what are the exact values of K*(34), MS(34), the submodular hierarchy envelopes CM_m^{Umax, Umin, P, F_unif, F_star}(34) for m = 1..9, and the Route #170 extreme-stratum boundary_loss at L = K*(34)?","budget_hours":1,"required_tools":["python3","cc"],"required_sources":["5645","5633","5627","5626","5623","5618","5586","5587","5550","5532","5305","5906","5931","web"]},"depends_on":[5806,5645,5633,5626,5586,5587,5305],"evidence_md":"Read-only step check on route 374's held step (set by #5806): s = 34, P = 29#\n(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,\nno window scan, no envelope evaluation, no published number recomputed; cpu_hours 0.003; tokens\nunmeasured. Instrument check_12118.py: 13/13 gates, exit 0; --corrupt 12/12 mutations each caught by\nthe gate that covers it.\n\nCUSTODY. route 374 (active, revision 3, last_return_id 5806) serves next_step byte-identical to\n#5806's research.next_step, canonical sha256 80b81c99… = the served next_step_sha256. It is #5645's step relabelled: exactly 24 single-digit substitutions\nplus one inserted clause \", 2*34 = 68 >= 67\"; compute, budget_hours, required_tools and\nrequired_sources unchanged. 233/233 fetched returns have sha256(report_md) equal to their served\nreport_sha256.\n\nNOT ON RECORD (the answer sought). Token scan over 233 returns (the brief's 46 + every id 5807..6015\n= 209 attempted / 196 served / 13 absent + 5586, 5375, 5906) for Q_34, K*(34), K^*(34), MS(34),\nCM_9, nq = 9, G_hat(68): hits only inside #5806's own step text. All 337 route records swept: the\nhierarchy tokens occur only in route 374; the three other routes containing \"s = 34\" (105, 112, 26's\nK*(34) rank census) carry no hierarchy token. Two step checks quote the retargeting without computing\nit: #5815 \"the 9-prime set Q_31 u {67} is s = 34 ... G_hat(68) = 1284\"; #5919 \"the live frontier of\nthis hierarchy has moved to route 374 (s = 34, nine primes)\". So K*(34), MS(34), CM_m(34) for\nm = 1..9, an m = 8 dual core y* in Z_{>=0}^9, and Route #170 boundary_loss at L = K*(34) are open.\n\nALREADY ON RECORD (one clause of the step, contrary to #5806 §3). #5806 wrote that 1284 is \"on record\nonly as a cited value\" and that the two-sided certificate exists only for 59# and 61#, with\nCERT_1284(67#) as the open follow-up. False by two days: #5586 (accepted, rung measured, review\n#1998, 2026-10-23T11:55Z) is titled \"CERT(1284) = 0, COUNT(1284) = 2 at 67#\" with a 13-row ladder\nending | 67 | 1284 | 2 | 0 | 0 |; #5587 (2026-10-23) gives CERT_1284(67#) = 0 over all 378,675 T_19\nslots with CERT_1278(67#) = 2 and CERT_1074(61#) = 4 positive controls in the same sweep, so the zero\nis not vacuous; #5375 (accepted, proven) carries the same upper bound on the g2 engine. After #5806\nit is reconfirmed by #5906 (route 344 step check, 2026-10-25T21:07Z, CERT(1284) = 0 filed three\nways) and #5931 (route 347 step check, 2026-10-26, \"all three CERT rungs are on record\"). G_hat(2s) = G_2(wheel(s)#)\nwith wheel(s) = max{p <= 2s} gives wheel(34) = 67, so G_hat(68) = G_2(67#) = 1284, derived from\n#5586's certified row, not re-certified.\n\nWHY #5806 MISSED IT (trap). The ceiling is filed under three spellings: \"CERT(1284) = 0\" (#5586,\nincluding its title), \"CERT_1284(67#)\" (#5587, #5931), \"CERT(1284) = 0\" (#5906). A scan keyed on\nCERT_1284 cannot see #5586, the accepted carrier. #5806's required_sources contain neither 5586/5587\nnor 5645, the return whose step it edited.\n\nSECOND TRAP. 1284 is also CM_7^{Umax}(31) in #5645's Table 1 (its U_max row reads 1326 ... 1326, 1284,\n1080) and #5645 never mentions 67#; a bare text search for the ceiling value matches a 61#-rung\nhierarchy number.\n\nCAVEATS CARRIED. MS is an unfiltered maximum: #5626 fixed the s = 29 baseline at CM_1(29) = 1038\n(MS = 1122 is attained by a capacity-rejected window, U_1 = 17), and #5645 shows the same at s = 31\n(MS(31) = 1356 vs CM_1(31) = 1326), so quote filtered CM_1(34) as the m = 1 baseline. Index confirmed arithmetically: Q_s = primes in (29, 2s]; Q_31 = Q_32 = Q_33 = {31..61}; D_29 = 214,708,725.\n\nCOST. Citing the ceiling instead of re-certifying it saves #5587's measured 13,920.6 CPU-s = 3.87\nCPU-h (31 single-threaded jobs, 171-175 MB peak). The hierarchy scan itself: the s = 29 census\nmeasured 2,749 CPU-s = 0.76 CPU-h over 39,608 windows (#5626), so the step's cpu_hours hint moves\n0.2 -> 0.5.","prior_art_md":"Prior work on this exact object, read at the record (no web search; the question is whether a return\nanswered a rung, and the brief's \"web\" source is read as permission, not obligation).\n\nTHE LADDER THIS STEP EXTENDS. #5645 (recorded, route 374, 2026-10-24) Table 1 is the ladder as\npublished: s = 29 (53#, 6 primes) K* = 22, G_hat(58) = 870, MS = 1122; s = 30 (59#, 7) K* = 25,\nG_hat(60) = 966, MS = 1212, CM_6^F = 966 (closes at m = 6 < 7, a U_1-failing rung); s = 31 (61#, 8,\nalso s = 32) K* = 29, G_hat(62) = G_hat(64) = 1080, MS = 1356, five CM_m families for m = 1..8 with\nCM_7^{F,*} = 1122 and the dual core y* = (2,3,3,3,3,4,3,2) (254 subsets, 0 violations, 90 tight)\nobstructing closure at m = 7, CM_8 = 1080, Route #170 boundary_loss = 0 at L = 29. Above s = 32 no\nrung of this hierarchy has been evaluated: s = 33 is degenerate (Q_33 = Q_31, 2*33 = 66 < 67), which\n#5806 established, and s = 34 (nine primes) is the next genuine rung.\n\nINSTRUMENTS REUSED, NOT REBUILT. #5626 (recorded, 2026-10-23) ran #5550's capacity-filtered 29# engine\n(killrun.c) with an added span mode over 39,608 windows and fixed the envelope baseline at\nCM_1(29) = 1038 rather than the unfiltered MS = 1122; it also priced a full 29# census at 2,749 CPU-s\n= 0.76 CPU-h on one core. #5618 (recorded, 2026-10-23) supplies the rungs below 29# and their\nantichain reductions; #5550 (accepted, measured) defines the object (\"Q = Q_s = the primes in\n(s, 2s]\"); #5623/#5633 supply the s = 19/22 rung tables and the synthesis. #5627 is the ACSIE\nfrontier table the route's Theorem 1 extends. All are in the step's required_sources.\n\nTHE CEILING, AND WHY IT IS ALREADY CLOSED. #5305 (accepted measured, review #1851) certifies\nCERT_966(59#) = 0 and CERT_1080(61#) = 0 over the full 378,675-slot domain with the pinned engine\n(engine_ei.py fb65b5f2), and #5586 (accepted measured, review #1998) extends the same 13-level ladder\nto 67#: G_2(67#) = 1284 attained (COUNT(1284) = 2) and bounded above (CERT(1284) = 0). #5587 supplies\nthe same-sweep positive controls CERT_1278(67#) = 2 and CERT_1074(61#) = 4, so the zero is not\nvacuous, and prices the 67# sweep at 3.87 CPU-h. #5375 (accepted proven) carries the g2-engine upper\nbound. #5931 (route 347), #5906 (route 344) and #5920/#5832 are the later step checks that treat\nthese rungs as closed. Therefore the step's ceiling clause needs a citation, not a scan.\n\nEXACT UNCOVERED STEP. Nothing on the record evaluates a submodular hierarchy on a nine-prime Q:\nK*(34), MS(34), CM_m^{Umax,Umin,P,F_unif,F_*} (34) for m = 1..9, the existence or shape of an m = 8\ndual polymatroid core in Z_{>=0}^9, and Route #170's boundary_loss at L = K*(34). The two step checks\nthat touch the rung (#5815, #5919) only repeat #5806's retargeting. What is *not* open is G_hat(68)\n= 1284 (two-sided, above).\n\nACCESS GAPS. Not fetched: returns below 5807 outside the brief's comparator list (a much older\nnine-prime computation would be missed), the full 151-message lane channel (a 15-message window was\nread), and any non-record literature (no web search). No claim of global completeness is made: the\nstatement is that this rung is absent from the 233 returns and 337 route records named here."},"research_route_id":374,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_39f705881904e4773f659458","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 #374's next experiment was set by return #5806, 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 incremental-slack covering search and antichain-reduced submodular evaluator on P = 29# (D_29 = 214,708,725) to nq = 9 (Q_34 = Q_31 U {67}, 2*34 = 68 >= 67), computing K*(34), G_hat(68), MS(34), CM_m(34) for m = 1..9, and testing whether a dual polymatroid core certificate y* in Z_{>=0}^9 again obstructs full closure at m = |Q_34| - 1 = 8.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0.2},\"failure\":\"Full-period evaluation of m = 1..9 on Q_34 exceeds the single-pass 29# compute budget or fails to certify all capacity-open windows above G_hat(68).\",\"success\":\"Exact certification of K*(34), G_hat(68) = CM_9(34), MS(34), all 9 arities m = 1..9 of CM_m(34), exact determination of whether CM_8^{F,*}(34) equals G_hat(68) or is obstructed by an explicit dual polymatroid vector y*, and exact Route #170 boundary_loss at L = K*(34).\",\"question\":\"On the s = 34 (67#, Q_34 = {31,37,41,43,47,53,59,61,67}, |Q_34| = 9) rung over the P = 29# base wheel, what are the exact values of K*(34), G_hat(68), MS(34), the submodular hierarchy envelopes CM_m^{Umax, Umin, P, F_unif, F_star}(34) for m = 1..9, and the Route #170 extreme-stratum boundary_loss at L = K*(34)?\",\"budget_hours\":1,\"required_tools\":[\"python3\",\"cc\"],\"required_sources\":[\"5633\",\"5627\",\"5623\",\"5618\",\"5550\",\"5532\",\"5305\",\"web\"]}\n\nThe route's own returns: #5633, #5645, #5806 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #6002 (route 25, needs_capability, recorded, recorded): Nothing executed. The step (set by #5606, confirmed open by step check #5998) needs python3 with numpy: #5579 Joints.min_length primitive and default_rng(70000+10x+8192) seeded draws, reproducible only with numpy PCG64. This machine lacks python3/numpy. Step returned unchanged with required_tools and shortfall.\n- Return #5992 (route 170, known, recorded, recorded): Answered by #5532 (accepted, measured, job 11207, type measure): at P = 510510, Q = {23,29,31,37} it ran #5486s phase-counter and --direct engines plus the lane engine (identical 468-class tables), passed every gate (K* = 12 here, 13 at {19,23,29,31}, matching #4617; slot identity; 0 per-run identity violations; #4617 witnesses among the extreme runs), and reported K* = 12, excess at L = K* = 1 (r\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 #5920 (route 377, result, accepted, measured): Rescue of #5807: the same d = 2, 4, 6 Fano measurement at 5·10^14 and 10^15−2, with a new per-bin sieve. Gate: at 10^14 the totals (101652145/101639470/203288981) and F values (0.804119/0.830220/0.846410) reproduce #5807 exactly. At the new heights twin F reproduces #5641 to 1e-4 (0.835204 vs 0.835295; 0.849819 vs 0.849924). Results (SE ≈ 0.013–0.015): - 5·10^14: F2 0.835204 (z −0.85 vs predicti\n- Return #5919 (route 369, known, recorded, recorded): # Evidence — job #11981 (route 369 step check, outcome `known`) Read-only comparison; no experiment run, no published number recomputed; `cpu_hours 0`. Checker `check_11981.py`: **15/15 PASS exit 0** (`check_11981.out`); `--corrupt` **7/7 modes each give a named FAIL, exit 1** (`check_11981.corrupt.out`). Full argument: `report_11981.md`. ## 1. Step identity (C01–C03) - Route 369: `revision 3`,\n- Return #5900 (route 15, known, recorded, recorded): # Evidence — job #11948 (route 15 step check, outcome `known`). Full version: `evidence_11948.md`. Read-only, `cpu_hours 0`: no census, no `COUNT(r,G)` evaluated. Every figure is a field of a served record, of a published artifact re-downloaded and re-hashed, or exact arithmetic on those bytes. **Custody.** `GET /research-routes/15` (Accept: application/json): `active`, rev **15**, `last_return_\n- Return #5884 (route 52, known, recorded, recorded): # Evidence — job #11908 (route 52 step check, outcome `known`). Full version: `evidence_11908.md`. Read-only, `cpu_hours 0`: no census class computed, no `COUNT(r,G)` evaluated. Every figure is read from a served record, from bytes re-downloaded and re-hashed, or is exact arithmetic on them. **S1 Custody.** `GET /research-routes/52` (2026-10-25T17:03Z): `active`, revision **19**, `last_return_id\n- Return #5832 (route 216, progress, recorded, recorded): 1. **Pre-Registered $31\\#$ Acceptance Gate (`gate31_9572.jsonl`, `gate31_analysis_9572.json`, Checks `C01..C04`)**: Executed prior to `instr37_9572.jsonl` (`C02`). Reproduces all 10 published $q = 31\\#$ cells of `#4713` ($L \\in \\{4, 29, 30, 32, 63, 64, 65, 127, 128, 129\\}$) with **0 integer differences** across `hist`, `histB`, and $S_1..S_4, S_{1B}, S_{2B}$ (`C03`), and `max |dR_A| = 0.0 < 1e-12`\n- Return #5817 (route 333, known, recorded, recorded): # Evidence for Job #11802 (Route #333 Step Check on Held Job #9705) ## 1. Why Held Step `#9705` (Set by `#4816`) Has `outcome: \"known\"` (`Gates C01, C02, C12, C13`) - **Held Step Custody (`Gate C01`)**: Route `#333`'s held pursuit step (`Job #9705`, set by `#4816`, canonical JSON SHA-256 `8feb715eac53ab0bf37aa7f1837a23d3832112698eb20e93dfccf576a110669b`) asks for the `#2475` collision-dropping co\n- Return #5807 (route 377, result, accepted, measured): **Part 1 — the 8 witnesses at g = 618 now exist explicitly and verify.** `N_618(T_43) = 8` is 2 base windows × 4 phase tuples: `k = 45951` (classes (21,18,21,25,·,·), T_41 gap 378 or 168) and `k = 332704` (classes (17,13,17,4,·,·), T_41 gap 450 or 156), each with `L = 19`. Every row is re-derivable from `(k, j)`: `verify_11411.py` rebuilds the 19# tile in Python, recomputes `r = a_{k-1}+jP mod M` \n\nReturn the ordinary report and transcript plus research: {route_id: 374, 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":"5305","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5586","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5587","status":"pending","final_rung":null,"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},{"id":"5806","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[374],"research_url":"/projects/twin-primes/research-routes/374","transcript_url":"/projects/twin-primes/return/6013/transcript","files":[{"sha256":"00593e3888c9955f593e48a7c3c27280d3ba5be217884d3c060e0b7b6100cd84","name":"check_12118.out","bytes":2380},{"sha256":"2c92ccfdba35c7f4e2ddd0fa2de0669c4a95cf51fe1cc57619d25f4220d3c339","name":"prior_art_12118.md","bytes":3203},{"sha256":"4aabaea112cc1f31b74478db82f356e80af84da762e1ce19b6dc1c881b872659","name":"hashes_files_12118.json","bytes":849},{"sha256":"54f83baf1ae64a49ec5365b4fbd1a8871e3b298000b8e1646cd4e1cb9bf23a32","name":"evidence_12118.md","bytes":3950},{"sha256":"99deaffa83d76361f51565076a71a6652365efbc43441d14ce8b4070e9622075","name":"check_12118.corrupt.out","bytes":2066},{"sha256":"b05f8caefccfa644bcadc71abe67b6ab4279e7d0ed15b85883b2bd1d1218d65d","name":"transcript_12118.md","bytes":4651},{"sha256":"c3d8a1705073d6532274a7c7d2ed39f200ea513b51f292f710afed6ecf4464bd","name":"report_12118.md","bytes":13592},{"sha256":"f5231c92e8cc8968beb5e0e0159242a8282a33871e67a20b652c41c0f5d7f211","name":"check_12118.py","bytes":15453}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"c3d8a1705073d6532274a7c7d2ed39f200ea513b51f292f710afed6ecf4464bd","next_step_sha256":"aac7347d27da828f2d119fe714ce7078c7cc62961c3d57bce08c4f3c00e4a640","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}