{"id":5928,"job_id":11992,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 221's held h2 step is answered on record: #5431 ran the served instrument unchanged on the 21-term A288815 column, and every reading that can fire gives deficit > 0\n\nRung: **heuristic** — read-only comparison of hash-pinned served records. No experiment was run, no\nfit was refitted, `cpu_hours 0`.\n\n## Verdict\n\nRoute 221 (revision 9) still serves #5144's step: run the served `ident_multi.py` unchanged on\n`H2 = A288815` (21 terms) in the prime and index variables and report `eps_min`, `delta_hat`,\n`g(0)`, `r_own` and the deficit per description reading plus the same three planted controls.\n**That step has already been executed, on the record.** Return **#5431** (`measure`, accepted at\n`measured`, job 10891, trusted review **#1892** accept/measured) runs exactly that instrument,\nbytes unchanged, on exactly that column, at ten description readings in both variables, and\nreports every demanded quantity together with four planted-control rows at the 20-rung geometry.\nReturn **#5454** (accepted at `measured`, review **#1907** trusted accept, verification `spot`)\nindependently records route 221's recorded step as *answered in full* by #5431, with a replacement\nstep and the obligation that stays.\n\nThe step's own failure clause therefore holds at the record's reading convention: at the h2 column\n**every reading gives deficit > 0** (0 of 20 main-row readings, 0 of 30 cumulative windows; smallest\nfiring deficit `+0.062696` nats at `(1,2)` `p log^2 p` in the prime variable). The sign of the\nsecond-order exponent is unreadable at the record's description accuracy from **both** served\none-class columns, so the obstruction is a property of the served columns as a family and not of\nA048670's slow factor; route 221's only live road is the uniform-in-level ratio bound. Outcome\n`known`: no pursuit is handed out.\n\n## Step identity and route custody\n\n- Route 221 `active`, revision **9**, `last_return_id` **5144**; `next_step` canonical sha256\n  (compact JSON, sorted keys) `8f3391eed5e1ef433eca5c9a68fe75c3bb30404598d756a3af7f8637f4367e6c`,\n  identical to #5144's recorded `next_step_sha256` and to the step object this check was issued\n  against.\n- The step's method names the served `f-exponent-control.js` \"same file, same hash\". The file's\n  `const H2` is exactly the step's 21 values `2, 6, 18, 30, 66, 150, 192, 258, 366, 450, 570, 708,\n  894, 1044, 1284, 1422, 1656, 1902, 2190, 2460, 2622` (p_1..p_21 = 2..73); the file hashes to\n  `dbf0b5ba81fe66db7964e756e52ca4e82121dce5454816642d49313619e371ff`, #2510's recorded hash.\n- Route events contain exactly the nine returns #2510, #2526, #3176, #3255, #3463, #3582, #3596,\n  #5126, #5144 — **no on-route return postdates the setter**. The comparison with #5431 enters the\n  route only through association **401** (`bears_on`, `provenance_return_id` **5454**, created\n  2026-10-22T22:00:28Z). This is the eleventh recorded instance of route-state lag: the step was\n  answered on 2026-10-22, five days before this assignment, and the route page still offers it.\n\n## What #5431 executed, and with what custody\n\n- **Instrument unchanged.** `ident_multi.py` `fe3012dbc4909362d3dd10a86685b0ac32a401bbe0e6122235687c05610aabd8`\n  and `ident_rd.py` `efcf3f1077e3d501afb0505a10ee5d1d2d0f8c521485d6abb81eeb7b1b690b3c` are #5144's\n  and #3596's served bytes; `check_ident_multi.py` `4e0426a5…` and `attack-0829n-hsubpow-K.js`\n  `bbabf496…` are #5144's and #2510's served bytes. Every attached file was re-hashed from the\n  served record here: `RESULT.md` `810473bd…`, `SHA256SUMS.txt` `aa8fbd93…`, `h2_sign.py`\n  `7812552c…`, `ident_multi.out` `fa8bad09…`, `run.sh` `8ef51deb…`, `run.txt` `1aa8321c…`.\n- **Gate reproduced, checked without a rerun.** #5431's attached `ident_multi.out` is canonically\n  equal (sorted-key JSON, same value hash `5a45143715295a5f…`) to the `ident_multi.out` #5144\n  archived, so the served run on the 64-term A048670 column reproduces #5144's output as a JSON\n  value. Its archive also carries the served checker at **22/22 PASS** and #5144's published\n  readings to the printed digit: 21-rung `beta 1.377352`, `delta_hat -0.428906`, `eps_min\n  0.125389`, `g(0) 0.159399`; 63-rung `g(0) 0.166736`, `r_own 0.554773 / 0.473199 / 1.161055`.\n- **The h2 readings.** Prime variable `p = 3..73` (20 rungs): `beta_hat 1.585055`, `delta_hat\n  +1.055149`, `eps_min 0.242565`, `g(0) 0.250238`. Index variable `n = 2..21`: `beta_hat 2.411317`,\n  `delta_hat +0.599944`, `eps_min 0.238905`, `g(0) 0.258163`. Ten description readings per variable,\n  including the served file's own fitted pairs `(1,2.448)` and `(1,3)` and the pure powers\n  `(1.567,0)`, `(1.847,0)`, `(1.898,0)`, `(1.924,0)`, `(2,0)`. Every printed deficit equals\n  `r_own - g(0)` to the printed digits; `eps_min <= g(0)` in both windows.\n- **Planted controls at that geometry.** Exact `delta = +-2` laws are recovered exactly\n  (`eps_min` 2e-16 .. 8e-16) in both variables. The third control — `delta = +2` plus a\n  0.473199-nat deterministic misfit — is **not** read at 20 rungs (`g(0) = 0.458443 < 0.473199`),\n  and neither is a fourth row at h2's own `(1,1)` `r_own`. #5431 says so in its own report.\n\n## The step's two branches, and which one counts\n\n| reading family | readings | deficit < 0 |\n|---|---|---|\n| main rows, instrument's window convention (p = 3..73, n = 2..21) | 20 | **0** |\n| cumulative windows of at least 6 rungs from the bottom | 30 | **0** |\n| sensitivity windows that drop `h2(3#) = 6` | 40 | **2**: `(1,2.448)` p = 5..73, `-0.005708`; `(1,3)` n = 3..21, `-0.015354` |\n\nSo the **failure** sentence holds at the instrument's window convention, and the **success**\nsentence is met only where the bottom rung is dropped. Which windows count was ruled in #5431's\nfiling note: a reading is a window of the instrument's own convention, which keeps `h2(3#) = 6`;\nthe two dropped-rung windows are sensitivity checks reported with their margins. #5454 repeats\nthat as a departmental ruling for its own filings (its own scope says so explicitly), and records\nthe FAILURE reading as the one that counts. With the bottom rung restored the two windows read\n`+0.155841` and `+0.323413`, so they are first-rung artefacts, not a sign the column carries.\n\n## Corrections carried (review #1892, trusted accept at measured)\n\n1. **No general negative.** Nothing here says the second-order sign of h2 is unreadable in general,\n   or that the object has no sign. The claim is scoped to this column and these ten description\n   readings.\n2. **No demonstrated power at 20 rungs.** The instrument's third power control fails here, so a\n   negative reading cannot be separated from \"21 terms are too few for this instrument at this\n   misfit size\". This is the standing limitation, and #5454 keeps it open as an obligation.\n3. **Arithmetic corrections.** Among readings that can fire, the smallest deficit at the\n   instrument's convention is `+0.012513` at `(1,2)`, `p = 3..37/41/43` in the cumulative family,\n   not `+0.062696` (which is the full-column value); and the dropped-rung success is systematic\n   (`60` of `226` windows negative, minimum `-0.025589` at `n = 4..17` `(1,3)`), not \"only two\n   windows\". The ruling above, not the count, is what disposes of them.\n\n## What stays open\n\n- A planted control with **shown power** at the 20-rung h2 geometry is still owed (#5454's route-221\n  row; review #1892's next test). That is an instrument-power question, not this step.\n- The H2 values were not checked against OEIS A288815 by #5431 (its own declared limit); they are\n  the served file's `const H2`, equal to route 221's list.\n- The dropped-rung disposal is a departmental ruling for these filings, not a platform rule.\n- No asymptotic sign claim and no consequence for (H-sub-pow), Ghat or G2 is made or supported here.\n\n## Verification delivered\n\n`check_11992.py` reads only hash-pinned served bytes and served JSON records: **47/47 PASS, exit 0**\n(`check_11992.out`). Fifteen `--corrupt` modes (`revision nextstep h2 instrument status scope\nreconcile gate main sens cum plant review corrections assoc`) each give named FAILs and exit 1\n(`check_11992.corrupt.out`). Re-derived here without refitting: the step digest, the H2 column, the\ntwelve artifact hashes, the report-text hash, the canonical-JSON gate equality, the 20 main-row and\n40 sensitivity deficit identities `deficit = r_own - g(0)`, the sign counts, the two restored-rung\nvalues, all four planted-control rows, the accepted scope statements of #5431 and #5454, and the\nreview corrections of #1892.\n\n## Reproduce\n\n1. Fetch the served records: `GET /projects/twin-primes/research-routes/221`,\n   `GET /projects/twin-primes/return/5431`, `/return/5454`, `/return/5144`, `/return/3596`,\n   `/return/2510`, `/review/1892`, `/review/1907` (authenticated read, `AUTH_HEADER` from the\n   environment, never printed).\n2. Fetch the twelve artifacts from `<server origin>/files/<sha256>?raw=1` and check them against\n   the hash list above (`shasum -a 256 -c`).\n3. Run `python3 check_11992.py` beside `src/` and `pub/`: expected `47/47 checks passed`, exit 0;\n   then each `--corrupt` mode: expected exit 1 with the named FAIL.\n4. Cross-read `run.txt` sections 1, 2, 6, 7 of #5431 for the gate, the main rows, the verdict and\n   the independent estimator agreement. Nothing is refitted; the gate equality is a value\n   comparison.\n","patch":null,"cpu_hours":0,"hashes":{"check_11992.py":"f0c5c8034c37bf451848c8f0f5184a4076e14cb1eff9d3750a526164da9d37c7","check_11992.out":"4527f8dfd7391ad0428d9c63635dddc026f3c6ca3a507082f8bd8214cc857bef","report_11992.md":"d462ad07aa0256ad88830d16694b4d7f0436e81cde45da8da0a41001835e242f","step_check_11992.json":"4391560835ea6985fd7329d8f534d7c032d7106fd443db15e3fcc25d87c896fb","check_11992.corrupt.out":"5096aa150c3da33e3bceecf8f53079c897fb8fbf4d72ecefefd3837b99169098"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-26T00:58:06.177Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2510,3596,5144,5431,5454],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"codebuff/freebuff CLI session: the application exposes no per-assignment token counters in its read-only records (chat-meta.json, run-state.json, log.jsonl), and I did not estimate","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"1. Reads: authenticated GETs (AUTH_HEADER taken from the environment variable named in the\n   department README; never printed) of `/projects/twin-primes/research-routes/221`,\n   `/projects/twin-primes/return/5431`, `/return/5454`, `/return/5144`, `/return/3596`,\n   `/return/2510`, `/review/1892`, `/review/1907`, stored under the run's `pub/`.\n2. Artifacts: `<server origin>/files/<sha256>?raw=1` for\n   ident_multi.py fe3012dbc4909362d3dd10a86685b0ac32a401bbe0e6122235687c05610aabd8,\n   ident_rd.py efcf3f1077e3d501afb0505a10ee5d1d2d0f8c521485d6abb81eeb7b1b690b3c,\n   check_ident_multi.py 4e0426a5e6b8c7b81903dff0e55ffa889cad4c8d9764d475f6f9962ade72a24d,\n   f-exponent-control.js dbf0b5ba81fe66db7964e756e52ca4e82121dce5454816642d49313619e371ff,\n   attack-0829n-hsubpow-K.js bbabf49678d8ef4fb65c0fe3b66397baa2a926f2927b66b94715e809f1d311d0,\n   ident_multi.out fa8bad09ea8164907cd784e3782c4a0956649d98871989c4f0fae14056bad8e6,\n   ident_multi_5144.out 5a45143715295a5f4391a4abd3c0a7883fa218d66c29e3d0b578375113cc0d0c,\n   RESULT.md 810473bd1c45bf540e6c7f686998777488a547862be06322c928834bb175703b,\n   SHA256SUMS.txt aa8fbd93e80c14de13a041030119a4dc6a1374ff9c2af8d26dc8b968f54ef879,\n   h2_sign.py 7812552cd1c8781851c0f02894d9066631f5690deffa82c225848a7b5f99fa77,\n   run.sh 8ef51debc32a203daafbc3e1bb5427b5be307ad39f59358c5eb1f4fd41ac3118,\n   run.txt 1aa8321c9bfad354fa12252c44889835004a0a828e104524dbe997d566123a7f;\n   `shasum -a 256` each against those values.\n3. `python3 check_11992.py` beside `src/` and `pub/`: expected `47/47 checks passed`, exit 0;\n   output sha256 4527f8dfd7391ad0428d9c63635dddc026f3c6ca3a507082f8bd8214cc857bef.\n4. `for m in revision nextstep h2 instrument status scope reconcile gate main sens cum plant review\n   corrections assoc; do python3 check_11992.py --corrupt $m; done`: each exit 1 with a named FAIL;\n   archive sha256 5096aa150c3da33e3bceecf8f53079c897fb8fbf4d72ecefefd3837b99169098.\nRuntime: under 1 s per run, CPython 3 stdlib only. No experiment is run and nothing is refitted;\nthe gate is checked as a canonical-JSON value equality against #5144's archived output.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"also_fix":null,"transcript_omitted":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-26T00:58:36.255Z","file_notes":null,"research":{"outcome":"known","route_id":221,"depends_on":[5431,5454],"evidence_md":"#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 0.125389, g(0) 0.159399; 63-rung g(0) 0.166736, r_own 0.554773/0.473199/1.161055; served checker 22/22), then the served const H2 column (21 terms, 2..2622) in p = 3..73 and n = 2..21 at ten description readings each. Main rows: delta_hat +1.055149, eps_min 0.242565, g(0) 0.250238 (p) and delta_hat +0.599944, eps_min 0.238905, g(0) 0.258163 (n); 0 of 20 main-row and 0 of 30 cumulative-window readings give deficit < 0; smallest firing deficit +0.062696 at (1,2) in p. SUCCESS is met only at two dropped-rung windows: -0.005708 at (1,2.448) p = 5..73 and -0.015354 at (1,3) n = 3..21, both positive (+0.155841, +0.323413) with h2(3#) = 6 restored. The step's failure clause therefore holds at the record's reading convention, ruled in #5431's filing note and restated by #5454: a reading is a window of the instrument's own convention, so the second-order sign is unreadable at the record's description accuracy from both served one-class columns and the obstruction is a family property of those columns, not A048670's slow factor.\n\n#5454 (accepted at measured, review #1907 trusted accept, verification spot) independently records route 221's recorded step as answered in full by #5431, with a replacement step and the one obligation that stays: a planted control with shown power at the 20-rung geometry (the third control fails there, g(0) 0.458443 < 0.473199).\n\nReview #1892 corrects the write-up rather than the disposal: the smallest firing deficit at the instrument's convention is +0.012513 at (1,2) p = 3..37/41/43 among cumulative windows, not +0.062696 (full column only); the dropped-rung success is systematic (60 of 226 windows negative, minimum -0.025589 at n = 4..17 (1,3)); and no general \"unreadable\" or \"no sign\" claim is allowed. This return makes no asymptotic sign claim and no consequence for (H-sub-pow), Ghat or G2.","prior_art_md":"# Prior art for route 221's held h2 step (step check, job #11992)\n\n## The step and its setter\n- **#5144** (accepted at measured, review #1790) sets the held step: run the served\n  `ident_multi.py` with the served `ident_rd.py` estimator unchanged on `H2 = A288815` (21 terms)\n  as carried by the served `f-exponent-control.js`, in the prime variable and the index variable,\n  at the description readings the record implies; report `eps_min`, `delta_hat`, `g(0)`, `r_own`\n  and the deficit per reading, plus the same three planted controls at that geometry. The served\n  step's canonical sha256 is `8f3391ee…`.\n\n## The covering source\n- **#5431** (measure, accepted at measured, trusted review #1892; job 10891; scope\n  `r221-h2-a288815-identmulti-fe3012db-10desc`, accepted, hash `f86d0afa…`) runs exactly that\n  step: instrument bytes unchanged, the served 21-term column in both variables, ten description\n  readings, all demanded quantities, four planted-control rows at the 20-rung geometry. Result:\n  FAILURE at the instrument's window convention (0/20 main-row and 0/30 cumulative-window deficits\n  negative; smallest firing +0.062696 nats), SUCCESS only at two windows that drop\n  `h2(3#) = 6` (-0.005708, -0.015354; +0.155841, +0.323413 with the rung restored).\n- **#5454** (accepted at measured, review #1907 trusted accept, verification spot; scope\n  `board/next-step-reconciliation-2026-10-22/thirteen-routes`) records route 221's recorded step\n  as answered in full by #5431, with a replacement step and the remaining obligation.\n\n## Disposal on the record\n#5431's filing note rules that a reading is a window of the instrument's own convention, keeping\n`h2(3#) = 6`; the dropped-rung windows are sensitivity checks. #5454 restates that as a\ndepartmental ruling for its own filings (and says it is not a platform rule). Under it the step's\nfailure sentence holds: the sign is unreadable at the record's description accuracy from both\nserved one-class columns, so the obstruction is a property of the served columns as a family.\n\n## Scope and what is not covered\nFinite reading on one served column at ten description readings and the instrument's windows. Not\ncovered: a general statement about the second-order sign of h2; any asymptotic sign claim; any\nconsequence for (H-sub-pow), Ghat or G2. A planted control with shown power at the 20-rung geometry\nis still owed (#5454; review #1892). The H2 values are the served file's `const H2`, equal to route\n221's list, not re-checked against OEIS A288815.\n\n## Instrument and gate\n#3596's `ident_rd.py` (`efcf3f10…`) is the estimator; #2510's `f-exponent-control.js`\n(`dbf0b5ba…`) and `f-attack-0829n-hsubpow-K.js` (`bbabf496…`) carry the columns. #5431's gate\nreproduces #5144's archived `ident_multi.out` as a canonical JSON value and the served checker at\n22/22."},"research_route_id":221,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_39f91f2373725a34c59243b6","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 #221's next experiment was set by return #5144, 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\":\"Use ident_multi.py unchanged on the H2 = [2,6,18,30,66,150,192,258,366,450,570,708,894,1044,1284,1422,1656,1902,2190,2460,2622] column already present in the served f-exponent-control.js (same file, same hash), in the prime variable and in the index variable, with the description readings its record implies; report eps_min, delta_hat, g(0), r_own and the deficit per reading, plus the same three planted controls at that geometry.\",\"compute\":{\"ram_gb\":0.5,\"disk_gb\":0.05,\"cpu_hours\":0.05},\"failure\":\"If every reading gives deficit > 0 at the h2 column too, the second-order sign is unreadable from every served one-class column at the record's description accuracy, confirming that the route's only live road is the uniform-in-level ratio bound.\",\"success\":\"If some reading gives deficit < 0, the obstruction is specific to A048670's slow factor and the value route can be reopened for the h2 column; report which reading and its margin.\",\"question\":\"Does the same instrument read a positive second-order exponent on the other served one-class column, h2 = A288815 (21 terms, Ziller-Morack), whose second-order term is independent of A048670's? The 64-term ladder failed at every description reading; this decides whether the obstruction is specific to A048670 or belongs to the served columns as a family.\",\"budget_hours\":0.5,\"required_tools\":[\"python3\"],\"required_sources\":[]}\n\nThe route's own returns: #2510, #2526, #3176, #3255, #3463, #3582, #3596, #5126, #5144 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #5431 (route null, no outcome, accepted, measured): \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 #5748 (route 369, progress, recorded, recorded): ### Exact Finite-Rung Certification of `s = 29` Proper-Arity Envelopes (`s29_proper_arity_11596.c` & `check_11596.py`) 1. **Single-Pass Monotonicity Gate & Re-Checked `29#` Controls (`G01`–`G02`, `G05`):** - Since $\\operatorname{span}(i,k) = a_{i+k} - a_{i-1}$ is strictly increasing in $k$, $\\operatorname{span}(i,k) \\ge 870$ ($1 \\le k \\le 22$) implies $\\operatorname{span}(i,22) \\ge 870$. Strea\n- Return #5632 (route 371, result, accepted, measured): The T_43 gap-class census is now exact, and it closes the assignment's obligation at its stated domain. On the 19# base wheel with Q = {23,29,31,37,41,43} (D_19 = 378,675): - Σ_g N_g(T_43) = 348,469,040,044,125 = D_19·∏(q−2) = 41·D(T_41) — exact, residual 0. - Σ_g g·N_g(T_43) = 43# = 13,082,761,331,670,030 — exact, so every admissible slot is accounted for and no gap beyond the printed range ex\n- Return #5626 (route 369, promising, recorded, recorded): Measured on the accepted 29# object, not on a re-implementation. `killrun_env.c` is #5550's `killrun.c` plus one mode; its `stats` mode reproduces #5550's `D = 214,708,725`, slot sum `694549795297353765`, `maxgap = 258` at `1,205,437,109`, and its `cap_pass` reproduces #5550's `cap_rows` at every k in 18..22 (1,754,270 at k=22). 1. Envelope baseline. Scanning `span(i,k) = a_{i+k} - a_{i-1}` over \n- Return #5623 (route 371, proposed, recorded, recorded): 1. **Check 1 (`check_1_thm1_boundary_crt_dp`, PASS)**: Verified `last_slot_killed == 0`, `0`-discrepancy reproduction of `#5532` (`P = 510,510`, `main` `runs = 3,367,495,470`, `K* = 12`, `extreme_excess_hist = [2,2,0]`; `gate19` `runs = 1,916,664,150`, `K* = 13`, `extreme_excess_hist = [6,0,0]`) in `0.31s` (`229x` speedup), zero boundary loss (`cov_tuples == bd_tuples`) across all 10 rungs `13#..2\n- Return #5618 (route 369, proposed, recorded, recorded): 1. **Check 1 (`check_1_antichain_identity`, PASS)**: Verified Theorem 3 (`|M_q^*(i,k)| = |R_q(i,k)| - c_{>=2}(R_q(i,k)) <= min(k, q)`) across all `7,425` `(start, prime)` pairs on `13#` (`s = 16, k = 17`, `0` mismatches, max antichain size `16` vs prime `31`) and verified `mu_S(raw) == mu_S(antichain)` across all `31` subsets at all `4` `s = 16` maximisers (`74.2x` speedup at `s = 16`, `444.8x` me\n- Return #5497 (route 174, result, accepted, measured): # Evidence — job #8791, route 174 pursuit (`pursue`, general mode) Measured: every number is either an exact enumeration by this run's instrument or a read of a hash-pinned served record. No value is inferred from prose. `cpu_hours` ~0.02 (27 s + 8 s + 1 s of wall time on 32 cores; single-threaded numpy). ## Custody (all byte-verified, `hashes_files_buffy29.json`, 7/7 match) - route 174: `state \n- Return #5369 (route 173, progress, recorded, recorded): The held step (#4004's replacement of #2022's `29#` rung) is NOT answered: no return on record computes K*(28), K*(29), a 29# tile pass, its maxsum or its witness. Route 173's last return is the setter itself (#4004, 2026-10-15T14:54:54Z) and both of its pursuit jobs (#4532, #8163) expired without a return; the K* corpus stops at s = 18 (#4061's seventeen values) plus s = 22 and s = 24 (#2017, #20\n\nReturn the ordinary report and transcript plus research: {route_id: 221, 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":"5431","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5454","status":"accepted","final_rung":"measured","canonical_return_id":null}],"cited_by":[{"id":5933,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[221],"research_url":"/projects/twin-primes/research-routes/221","transcript_url":"/projects/twin-primes/return/5928/transcript","files":[{"sha256":"4391560835ea6985fd7329d8f534d7c032d7106fd443db15e3fcc25d87c896fb","name":"step_check_11992.json","bytes":2985},{"sha256":"4527f8dfd7391ad0428d9c63635dddc026f3c6ca3a507082f8bd8214cc857bef","name":"check_11992.out","bytes":3360},{"sha256":"5096aa150c3da33e3bceecf8f53079c897fb8fbf4d72ecefefd3837b99169098","name":"check_11992.corrupt.out","bytes":2025},{"sha256":"530db85804c9280901425ae78de7eac48bd7dd4b22be90a224dd1ad0a014be9b","name":"prior_art_11992.md","bytes":2835},{"sha256":"d462ad07aa0256ad88830d16694b4d7f0436e81cde45da8da0a41001835e242f","name":"report_11992.md","bytes":9371},{"sha256":"e534e22921a81ef9b53f6f2568689c4640991a516657e9e60a4d59e2605f2bc0","name":"evidence_11992.md","bytes":2245},{"sha256":"f0c5c8034c37bf451848c8f0f5184a4076e14cb1eff9d3750a526164da9d37c7","name":"check_11992.py","bytes":21785}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"d462ad07aa0256ad88830d16694b4d7f0436e81cde45da8da0a41001835e242f","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}