{"id":5931,"job_id":11994,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 347 step check: all three CERT rungs are on record — CERT_966(59#) = 0 (#5305, and #3507 eight days before the step), CERT_1080(61#) = 0 (#5305), CERT_1284(67#) = 0 (#5586, #5587)\n\n**Job #11994** (`explore`, stage `first_look`, lane `dir-558`, **general mode**, research route **347**,\nassignment 1 of 1). **Outcome: `known`.** Read-only comparison: no covering scan was run, no census was\nrecomputed, `cpu_hours 0`.\n\n## 1. The step under test, and its custody\n\n`GET /research-routes/347` (`Accept: application/json`): `state active`, **revision 2**,\n`last_return_id 5158`, `origin_return_id 5139`, `next_step` object = #5158's recorded\n`research.next_step` **exactly** (canonical sha256 `987382f2aaf7d0fb663fe83081429f2eead50b5dd39d2c1bc55ce05b1d83b380`\n= `#5158.next_step_sha256`). #5158 is `accepted` at `measured` (review #1792, accept/measured).\n\nThe step asks four things: (a) `CERT(966) = 0` at 59# over the **full** slot set `S` (not `S'`),\nwith #5090's engine; (b) price it before running it; (c) certify or honestly price 61# (1080) and\n67# (1284) using the CERT/COUNT ratio measured at 59#; (d) keep `COUNT(966) = 8` as the matched\nlower bound. Every one of them is on the record.\n\n## 2. Clause by clause\n\n**(a) `CERT_966(59#) = 0` over the full domain — measured twice, by two drivers.**\n**#5305** (job 10467, `measure` stage, route 349, **accepted at `measured`**, review #1851) attached\n`cert_cda_59_966_full.json`: `mode full`, `slots_in_S 378675`, `slots_scanned 378675`,\n`cert_total 0`, `zero true`, engine file sha256 `fb65b5f2…` = the pinned #5090 instrument,\n`wall_s 169.1` on 16 workers. **#3507** (job 7219, route 15, `recorded`, **2026-10-13T14:09:35Z**,\ni.e. eight days *before* the step was written on 2026-10-21) reached the same conclusion with its own\nresumable driver `census_bd.py` over served `census4495.py`: `CERT(966) = 0 at every one of the\n378,675 T_19 slots`, `nonzero_CERT_Gstar 0`, `G2(59#) = 966`, `nmax = 8`, same two `T_19` slots\n`{3259691, 6439031}`, whole level `elapsed_s 1676.0` (three scans).\n\n**(d) The matched lower bound `COUNT(966) = 8`.** #5158 measured `m(59#) = 8`; **#5305's own\npositive control** `CERT_960(59#) = 8` at slots `3259691` (4 systems) and `6439031` (4 systems) —\n`CERT_{G-6}` recovers the ceiling multiplicity exactly — and #3507's `nmax = 8`. The two instruments\nagree, so 59# is two-sided: `G2(59#) = 966` attained and bounded above.\n\n**(c) 61#: `CERT_1080(61#) = 0` over 378,675 slots**, `cert_total 0`, `zero true`, `wall_s 2094.3`\non 16 workers (#5305, `cert_cda_61_1080_full.json`), with #5158's `m(61#) = 4` as the counting half\nand #5587's `CERT_1074(61#) = 4` as a same-rung positive control. `G2(61#) = 1080` is measured.\n\n**(c) 67#: `CERT_1284(67#) = 0`** over the complete domain, 31/31 chunks (#5587,\n`cert67_1284.json`), with its positive control **`CERT_1278(67#) = 2`** at residues `3941657` and\n`5756747` in the *same* sweep — the very two residues where **#5586** (`accepted, measured`) counts\n`COUNT(1284) = 2`, with the identical CRT positions and `gaps_hist {1284: 2}`. So 67# is also\ntwo-sided. Measured 67# cost: `13,920.6` CPU-s = **3.87 CPU-h** for `CERT_1284`, `13,516.8` for\n`CERT_1278`.\n\n**The CERT/COUNT ratio at 59# is measured.** #3507's three scans of the level took 737 s\n(`CERT_960`), 758 s (`CERT_966`) and 181 s (`COUNT_966`): **CERT/COUNT = 758/181 = 4.19**, and the\nreturn states the reason (`COUNT` mode returns 0 immediately when `r+G` is not a slot and prunes\nharder). #5305's independent pair (169.1 s `CERT_966` on 16 workers) and #5587's price check (a\nnode-model projection of ~160 CPU-h against 3.87 CPU-h measured, a 40× overestimate) are the same\ncolumn of information.\n\n## 3. What the step would add, and why it is not worth a pursuit\n\nNothing that changes a number. Its three measurements, its positive controls, its cost curve and its\nratio are all published, twice at 59# and twice at 67#. Repeating them would be a **re-measurement of\nthe same quantities 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, which the step does not state. The step's own failure clause (\"would\ncontradict the cited A144311 length\") therefore cannot fire: the lengths are certified, not cited.\n\nThe evidence that the *route's* contribution turned into is worth keeping: the axis quotient is\nvalid for fixed-length `COUNT` and invalid for `CERT` (#5305 §5, structural: the partner slot's\nwindow ends at `mu(n)`, which is admissible, so it can never carry a covered run). That is why the\nstep correctly forbids `S'` here, and it is already decided on route 349.\n\n## 4. Corrections and traps worth carrying forward\n\n- **Route-state lag, 13th instance.** Route 347 still serves #5158's step with\n  `last_return_id 5158` although 59#, 61# and 67# were all certified on 2026-10-21/23. The only\n  links are associations **466** (provenance #5900: \"supplies m(61#) = 4, the counting half that\n  turns #5305's ceiling into G2(61#) = 1080\") and **472** (provenance #5906: \"#5158 states CERT was\n  not run at 59#/61#/67# — the clause that #5586 and #5587 later fill\"). Check\n  `associations[].provenance_return_id` before reading a route's step as open.\n- **#5305 prose slip (data unaffected).** Its §3b parenthetical reads\n  `1531841 + 8167139 = 9699484 = 19# − 206`; the sum is `9,698,980 = 19# − 710`, which is exactly\n  `psi_708(r) = −r−708−2`. The 206 belongs to the 204-length formula. The attached artifact is\n  correct; only the sentence is not.\n- **Two of the three rungs are `accepted`; the 67# certificate has one accepted and one pending\n  carrier.** #5586 (route 344) is `accepted measured` and states `CERT(1284) = 0, COUNT(1284) = 2 at\n  67#`; #5587 is `pending` (no reviews yet) but supplies the positive control in the same sweep.\n  The accepted half alone already carries the upper bound.\n- `known` closes the route: no `next_step`, no `obstacle`, and the earlier route text's\n  \"59#…67# remain uncertified\" is superseded.\n\n## 5. Verification delivered\n\n`check_11994.py`: **38/38 PASS, exit 0** (`check_11994.out`). It re-reads the served records and the\nreturns' own uploaded artifacts (13 files fetched by content address and re-hashed to the served\nsha256) and re-derives, without any scan: `|Z_19| = 378,675` by an independent flag array over 19#;\n`psi_966(3259691) = 6439031`, `psi_1284(3941657) = 5756747`, `1531841 + 8167139 = 19# − 710`; the\nsum of the control's systems = 8 = `m(59#)`; the CERT/COUNT ratio 758/181 = 4.19; the whole-level\ncost 737+758+181 = 1,676 s = the artifact's `elapsed_s`. Nine `--corrupt` modes (`sha cust c59 c61\nc67 ctrl date ratio slots`) each produce a named FAIL and exit 1 (`check_11994.corrupt.out`).\n\n5 of @Benjaminsen's returns wait for a verdict; nothing for the person to do.\n","patch":null,"cpu_hours":0,"hashes":{"check_11994.py":"77698c01e0f5233da7a9501cfef0d8407e6b1cb130402226526bb01bd885d70f","check_11994.out":"fec20f0b7dde924585a2b89016f6079e5494b2982d24c33555bb53a7040d3925","recipe_11994.md":"d5cef095ad403bbd2e7d828bd6fc5d118145cc9955e7b9069331c5f202ec2f4b","report_11994.md":"aee391f2044d1025411b39437e5a6e8175be4a5787d9d2887685ef3c54bf82cf","evidence_11994.md":"f922ecdd45f6be870f343d9ffbbf53328eca16126ad15178edde0cb95a59dcdb","prior_art_11994.md":"6a1effd54308d2bc9b813a6eec5871650cc4d2572319e912a4d72fbb808a0403","transcript_11994.md":"3d1881e7ce9f8bbe7e184ce16692e88f2f0a21e6351bfa45c01fc47c294947b1","step_check_11994.json":"c054a519f346a718b51108914cf36682f1f9f40cbc32c5223d1c18a1324fa6fa","check_11994.corrupt.out":"71f4707f889eae71a239e95743650aec24beb30e4d49617a9f50a38264c65c8b"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-26T01:29:05.187Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5305,5587,5586,3507,5158,5900,5906],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"the Freebuff/Codebuff harness exposes no per-assignment token counters; the chat log records message entries, not billable usage, so no count is invented","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"## What this comparison reads\n\nAuthenticated GETs only; the credential is taken from the environment variable the department README\nnames and is never printed. Nothing is computed on the primes, no covering scan is run, `cpu_hours 0`.\n\n1. `GET /projects/twin-primes/research-routes/347` with `Accept: application/json` (default is prose)\n   — `state`, `revision`, `last_return_id`, `next_step`, `associations`.\n2. `GET /projects/twin-primes/return/{5158,5305,5586,5587,3507,5906}` — reports, statuses, reviews,\n   `created_at`, and each return's `files[]` inventory of name + sha256.\n3. `GET /files/<sha256>` for the thirteen artifacts named in `work/wantfiles.json`; each download is\n   re-hashed and must equal the served sha256 (`work/filehashes.json`).\n4. `python3 check_11994.py` in the run's `work/` directory — 38 checks over the stored bytes:\n   - custody: route state/revision/`last_return_id`/origin; canonical sha256 of the served\n     `next_step` (`json.dumps(sort_keys=True, separators=(\",\",\":\"))`) equals\n     `#5158.next_step_sha256` `987382f2…`; object identity with `#5158.research.next_step`;\n   - the 59# certificate `cert_cda_59_966_full.json` (`cert_total 0`, `slots_scanned ==\n     slots_in_S == 378675`, `mode full`, engine sha `fb65b5f2…`, `wall_s 169.1`), the 61#\n     certificate, and the 59# positive control `CERT_960 = 8` at `{3259691: 4, 6439031: 4}`;\n   - the 67# certificate (#5587, 31/31 chunks, `total 0`), its positive control `CERT_1278 = 2`,\n     and the equality of that control's residues and CRT positions with #5586's accepted\n     `COUNT(1284) = 2`;\n   - #3507's `census59_bd.json` (`nonzero_CERT_Gstar 0`, `G2 966`, `nmax 8`, `residues19\n     [3259691, 6439031]`, `elapsed_s 1676.0`) and its `created_at` < #5158's;\n   - independent arithmetic: `|Z_19| = 378,675` by an own flag array over 19# (primes 2..19, kill\n     `n` and `n+2`), `psi_966(3259691) = 6439031`, `psi_1284(3941657) = 5756747`,\n     `1531841+8167139 = 19#−710`, `758/181 = 4.19`, `737+758+181 = 1676`;\n   - every fetched file's sha256 against the served value.\n5. `for m in sha cust c59 c61 c67 ctrl date ratio slots; do python3 check_11994.py --corrupt $m; done`\n   — each mode plants one false claim in memory (a hash, the step text, a certificate total, a slot\n   count, the 67# total, the control's system split, #3507's date, the ratio sentence, the slot\n   count) and must exit 1 with a named FAIL. `check_11994.corrupt.out` holds all nine.\n\n## What the checker deliberately does not do\n\nIt does not re-run `CERT_966(59#)`, `CERT_1080(61#)` or `CERT_1284(67#)`, and it does not rebuild a\ncensus: those are the computations the record already holds, and re-running them is the experiment\nthe assignment forbids. The `CERT/COUNT` ratio is read from #3507's measured scan times and\nre-divided; the certificates are read from the returns' own artifacts and their internal\nconsistency (full-domain slot counts, zero totals, positive controls at `G−6`) is checked.\n\n## Restoring the inputs\n\n`pub/return*.json` and `pub/route347.json` are the served records; `pub/art/` holds the artifacts\nnamed `<return>__<filename>`. The mapping name → sha256 is `work/wantfiles.json`, the verification\nresult is `work/filehashes.json`.","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":"2026-10-26T01:29:13.814Z","file_notes":null,"research":{"outcome":"known","route_id":347,"depends_on":[5305,5587,5586,3507,5158],"evidence_md":"The route 347 held step is answered on the record at all three rungs it names. No scan was run.\n\n**(1) `CERT(966) = 0` at 59# over the full slot set.**\n- **#5305** (job 10467, accepted at `measured`, review #1851, route 349): artifact\n  `cert_cda_59_966_full.json` — `mode full`, `slots_in_S 378675`, `slots_scanned 378675`,\n  `cert_total 0`, `zero true`, engine `fb65b5f2…` = #5090's pinned instrument, `wall_s 169.1`,\n  16 workers. The step's `S'` is correctly not used.\n- **#3507** (job 7219, route 15, `recorded`, created 2026-10-13T14:09:35Z — eight days *before* the\n  step was written) reached it with an independent driver (`census_bd.py` over served\n  `census4495.py`): `CERT(966) = 0 at every one of the 378,675 T_19 slots`,\n  `census59_bd.json: nonzero_CERT_Gstar 0`, `G2 = 966`, `nmax = 8`, same slots\n  `{3259691, 6439031}`, whole level `elapsed_s 1676.0`.\n\n**(2) The matched lower bound `COUNT(966) = 8`.** #5158's `m(59#) = 8`; #5305's positive control\n`CERT_960(59#) = 8` at slots 3259691 (4 systems) + 6439031 (4 systems), i.e. `CERT_{G-6}` recovers\nthe multiplicity with a second instrument; #3507 `nmax = 8`. Hence `G2(59#) = 966` attained *and*\nbounded above.\n\n**(3) 61#.** #5305 `cert_cda_61_1080_full.json`: `G 1080`, `mode full`, 378,675/378,675 slots,\n`cert_total 0`, `zero true`, `wall_s 2094.3` (16 workers); #5158's `m(61#) = 4` is the counting\nhalf and #5587's same-rung control `CERT_1074(61#) = 4` is non-vacuous. `G2(61#) = 1080` measured.\n\n**(4) 67#.** #5587 `cert67_1284.json`: `L 1284`, `mode cert`, `31/31` chunks, `total 0`, complete.\nIts positive control in the same sweep, `CERT_1278(67#) = 2`, sits on residues 3941657 and 5756747 —\nexactly the two residues of **#5586** (`accepted, measured`), `COUNT(1284) = 2` with identical CRT\npositions and `gaps_hist {1284: 2}`. So `G2(67#) = 1284` is two-sided with an accepted carrier.\n\n**(5) The CERT/COUNT ratio and the prices.** #3507's 59# level took 737 s (`CERT_960`), 758 s\n(`CERT_966`) and 181 s (`COUNT_966`): **ratio 4.19**, \"COUNT ~4x cheaper per slot than CERT\", and\n737+758+181 = 1676 s = the artifact's `elapsed_s`. #5305's independent CERT_966(59#) = 169.1 s on 16\nworkers agrees in kind. 67# measured cost is 13,920.6 CPU-s = 3.87 CPU-h (CERT_1284) and 13,516.8\nCPU-s (CERT_1278), which also corrects route 349's node-model projection (~160 CPU-h) by ~40×.\n#3507's price curve names 59# 1,344 CPU-s (0.373 CPU-h), 61# 2.47 CPU-h, 67# 9.59 CPU-h on one core.\n\n**Corrections carried, not repeated:** #5305 §3b's parenthetical `1531841 + 8167139 = 9699484 =\n19# − 206` is wrong arithmetic (sum = 9,698,980 = 19# − 710 = the `psi_708` pairing); artifacts are\nunaffected. Route 347 still serves #5158's step with `last_return_id 5158` although the rungs were\ncertified on 2026-10-21/23 — route-state lag 13th instance; coverage lives only in associations 466\n(#5900) and 472 (#5906).\n\n**Scope.** Read-only. Nothing here recomputes a census, re-runs a CERT or moves a ceiling; the\nmultiplicity and ceiling columns are unchanged, and the step's failure clause cannot fire because\nthe lengths are certified rather than cited. `cpu_hours 0`.\n\n**Verification.** `check_11994.py` 38/38 PASS exit 0; nine `--corrupt` modes each a named FAIL,\nexit 1. 13 served artifacts fetched by content address and re-hashed to their served sha256; own\nsieve `|Z_19| = 378,675`; own exact arithmetic on `psi_966`, `psi_1284`, the 47# pair and the\nsystem sums.","prior_art_md":"# Prior art for route 347's CERT step: what answers it\n\n## The step and its setter\n\n- **#5158** (`result`, job 10157, **accepted** at `measured`, review #1792) set the step: run\n  `CERT(966) = 0` at 59# over the **full** slot set `S` with #5090's engine, price it first, then\n  attempt 61# (1080) and 67# (1284) under the CERT/COUNT ratio measured at 59#, keeping\n  `COUNT(966) = 8` as the matched lower bound. Canonical sha256\n  `987382f2aaf7d0fb663fe83081429f2eead50b5dd39d2c1bc55ce05b1d83b380` was still the route's\n  `next_step` when this comparison was made (route rev 2, `last_return_id 5158`).\n- #5158 measured the counting half at all 13 rungs (`m(59#) = 8`, `m(61#) = 4`, `m(67#) = 2`) and\n  said in terms that **CERT was not run** at 59#/61#/67# — the clause the returns below fill.\n\n## The covering returns, rung by rung\n\n- **59#, upper side — #5305** (job 10467, `measure`, route 349, **accepted** at `measured`, review\n  #1851, 2026-10-21): `cert_cda_59_966_full.json` — `mode full`, `slots_in_S 378675`,\n  `slots_scanned 378675`, `cert_total 0`, `zero true`, engine `fb65b5f2…` (= #5090's `engine_ei.py`\n  bytes), `wall_s 169.1` on 16 workers. Same return: `CERT_960(59#) = 8` at slots `3259691` (4) and\n  `6439031` (4), a **positive control that recovers `m` with an independent instrument**, and\n  `CERT_1080(61#) = 0` over the same 378,675 slots (`wall_s 2094.3`).\n- **59#, independently and earlier — #3507** (job 7219, route 15, `recorded`, 2026-10-13, i.e.\n  eight days *before* the step): served `census4495.py` + its own driver `census_bd.py`:\n  `CERT(966) = 0` at every one of the 378,675 `T_19` slots, `G2 = 966`, `nmax = 8`, residues\n  `{3259691, 6439031}`, `nonzero_CERT_Gstar 0`, level `elapsed_s 1676.0`. The rung was certified\n  before it was asked for.\n- **61# — #5305** again: `CERT_1080(61#) = 0` over 378,675/378,675 slots, 2,094.3 s; the same-rung\n  positive control `CERT_1074(61#) = 4` is #5587's.\n- **67# — #5586** (job 11317, route 344, **accepted measured**): `CERT(1284) = 0`,\n  `COUNT(1284) = 2` at 67#, the count on residues `3941657`, `5756747` with positions\n  `347362490524712435263487` and `7510959060555554620614317`, `direct_gcd_all_positions` and\n  `sigma_closed` true.\n- **67# positive control — #5587** (job 11319, route 349, `pending`): `CERT_1284(67#) = 0` over\n  31/31 chunks, and in the **same sweep** `CERT_1278(67#) = 2` on exactly the two residues above,\n  `gaps_hist {1284: 2}`; 13,920.6 CPU-s for `CERT_1284`, 13,516.8 for `CERT_1278` — against route\n  349's own node-model projection of ~160 CPU-h (40× overestimate).\n\n## Cost and ratio, already measured\n\n- #3507 §2: 59# 1,344 CPU-s (0.373 CPU-h) per census, 61# 2.47, 67# 9.59 CPU-h on one core; whole\n  59# level 0.88 CPU-h. Its three scans (737, 758, 181 s) give **CERT/COUNT = 758/181 = 4.19** at\n  59# (`COUNT` returns 0 at once when `r+G` is not a slot and prunes harder). #5305 §6: full-domain\n  CERT at 47#/53#/59#/61# = 263/161/169/2,094 s on 16 workers.\n\n## The method negative these rungs rest on\n\n- **#5305 §5** (accepted): the axis quotient `mu(n) = -n-2` is valid for fixed-length `COUNT` and\n  **invalid for `CERT`**, because the partner slot's window ends at `mu(n)`, which is admissible, so\n  a covered run longer than `G` can never be seen from the partner (47#/53# control at `G-6`: 4 → 0,\n  2 → 0). That is why #5158's instruction to use the full `S` is right.\n\n## What is still not covered\n\n- The **67# certificate's review**: #5587 is `pending`; the accepted carrier is #5586 (enough for\n  the upper bound), leaving #5587's control sweep unreviewed.\n- Above 67#: 71# and 79# are model-priced only (#3507: >126 and >606 CPU-h from cut slices).\n\nWith these returns the step is answered in full: the ceilings at 59#, 61# and 67# are **attained and\nbounded above**, so `G2(59#) = 966`, `G2(61#) = 1080`, `G2(67#) = 1284` are computed values, not\ncitations, and the CERT/COUNT ratio and per-rung wall times are measured. No experiment remains\nuncovered on this route."},"research_route_id":347,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_a8d77f66ca2dea8d8dd0c5c8","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 #347's next experiment was set by return #5158, 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 CERT(966) = 0 at 59# with the same engine, over the FULL slot set S (S' does not apply: CERT counts one-sided runs, and the mirror of a run starting after an admissible slot is a run ENDING before one, whose left neighbour need not be admissible -- so the axis quotient must not be used and no count may be doubled). Price it first with `engine_bf.py slice 59 966 cert <n>`, then `engine_bf.py chunks 59 966 cert <dir>`, and attempt 61# (1080) and 67# (1284) only with the CERT/COUNT ratio that 59# measures. Report the ratio, the per-rung verdict and the wall time; keep COUNT(966) = 8 from this return as the matched lower bound.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":1},\"failure\":\"CERT(966) > 0 at 59# would contradict the cited A144311 length for 59#: a finding about the ceiling ladder the project cites, which is its own return and not a defect in this count. If the CERT scan costs more than the budget at 59#, the ceilings stay cited and only the measured cost curve is reported -- the multiplicity column does not change either way.\",\"success\":\"CERT(966) = 0 at 59# together with COUNT(966) = 8 > 0 makes G2(59#) = 966 computed instead of cited (A144311), the CERT/COUNT ratio is measured at one rung, and with that ratio 61# and 67# are either certified inside the hour or priced honestly as out of reach.\",\"question\":\"Do the ceiling lengths at 59#, 61# and 67# hold as UPPER bounds -- is G2(59#) = 966, G2(61#) = 1080, G2(67#) = 1284 -- given that this return only shows they are attained, and what does a CERT scan cost relative to COUNT at these rungs?\",\"budget_hours\":1,\"required_tools\":[\"python3\"],\"required_sources\":[]}\n\nThe route's own returns: #5139, #5158 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\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- Return #5921 (route 345, known, recorded, recorded): # Evidence — job #11983 (route 345 step check, outcome `known`) Read-only comparison; no experiment run, no published census recomputed; `cpu_hours 0`. Checker `check_11983.py`: **20/20 PASS exit 0** (`check_11983.out`, `check_11983.json`); six `--corrupt` modes (`sha status quote gap6 job rungs`) each give a named FAIL, exit 1 (`check_11983.corrupt.out`). Fetched bytes kept in `pub/`. ## 1. Ste\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 #5906 (route 344, known, recorded, recorded): # Evidence — job #11961 (route 344 step check, outcome `known`) Full argument: `report_11961.md`. Verification suite: `check_11961.py` (34/34 exit 0; `--corrupt` 13 named FAILs exit 1), outputs `check_11961.out`, `check_11961.corrupt.out`, `check_11961.out.json`. Read-only: no census was run, no `COUNT`/`CERT` was re-evaluated, `cpu_hours 0`. ## S1 Custody of the step `GET /research-routes/344` \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 #5899 (route 392, progress, recorded, recorded): Two passes on #5847's unmodified lift.c (sha a0ca4dae…) complete the 23# classification. Sector C (3∤tau, gcd(tau,19#)>2): 787,175 tau × 23 = 18,105,025 values, max G_d = 300 at 128 offsets (least 397,868, mod6 {0:0,2:69,4:59}), zero at 366, none above 300, mean 175.759786. Sector A re-run with hist_pt: 829,440 tau × 23 = 19,077,120 values, reproduces #5828 exactly (366 at 128 pure-twin offsets, l\n- Return #5847 (route 392, progress, recorded, recorded): # Evidence — the 3|d sector of the 23# paired-offset profile (job #11815) Exact, finite, integer. Object: `A_{x,d} = {n mod x# : gcd(n,x#)=gcd(n+d,x#)=1}`, `G_d(x#)` = largest circular gap, `h2(x#) = max over even d`, space = even `d <= 23#/2` (55,773,217 values). ## Coverage (complete sector, no sampling) `3|d` iff `3|tau` (19# is divisible by 3), so the sector is all `tau <= 19#/2` with `3|tau\n- Return #5828 (route 392, progress, recorded, recorded): Exact, finite, integer evidence at 23# (M = 223,092,870), produced by an independently re-derived 19#->23# two-class lift (`lift.c`, criterion of #1424) and checked by a second, unrelated per-offset bitset instrument (`direct_h2`). Established (rung: measured; the two rungs below it are verified reproductions): 1. h2(23#) = 366 is ATTAINED. 128 half-period offsets of the family sig(tau) = {2} (82\n- Return #5822 (route 392, promising, recorded, recorded): ### Exhaustive $19\\#$ Paired-Offset Profile Resolves Route #392's First-Look Obligation (Branch `(b)` Confirmed) 1. **Word-Parallel Engine (`dprof_word_11795.c`) & Gates (`C01–C06`, 0 Mismatches)**: - Using odd-residue bitset compression ($K = M/2 = 4{,}849{,}845$ bits $= 75{,}779$ words at $19\\#$), $64$ pre-shifted tables `B_shift[ob][w]`, and an $O(1)$ skip via the **Middle-Interval Zero Lem\n- Return #5810 (route 392, proposed, recorded, recorded): Exact enumeration by `dprof.c` (one core, x86_64, integer only), gated against published values. GATES (all pass). `G_2 = 66 / 108 / 150 / 204` at 13#/17#/19#/23# = the `G2-STATE.md` §2 ladder; full-sweep maxima `150` (13#) and `192` (17#) = `h2` = OEIS A288815; density law `#A_{x,d} = prod_{p<=x}(p - m_p(d))` (m_p = 1 iff p|d) 15/15 exact at 13#; reflection `G_{M-d} = G_d` 15/15 exact. PROFILE.\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- Return #5765 (route 387, promising, accepted, measured): Independent replay of pending #5753 under the pinned Lean v4.35.0-rc3 (commit 470d5ce1): GapWordPalindrome.lean exit 0, stdout byte-identical to the served .out (sha 740a5ae0...); all 26 axiom reports standard (propext/Classical.choice/Quot.sound), the four decide certificates axiom-free; corrupt control reproduces both decide refutations (36:54, 42:34, exit 1), differing from the served .out only\n\nReturn the ordinary report and transcript plus research: {route_id: 347, 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":"3507","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5158","status":"accepted","final_rung":"measured","canonical_return_id":null},{"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}],"cited_by":[{"id":5933,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[347],"research_url":"/projects/twin-primes/research-routes/347","transcript_url":"/projects/twin-primes/return/5931/transcript","files":[{"sha256":"3d1881e7ce9f8bbe7e184ce16692e88f2f0a21e6351bfa45c01fc47c294947b1","name":"transcript_11994.md","bytes":6658},{"sha256":"6a1effd54308d2bc9b813a6eec5871650cc4d2572319e912a4d72fbb808a0403","name":"prior_art_11994.md","bytes":4023},{"sha256":"71f4707f889eae71a239e95743650aec24beb30e4d49617a9f50a38264c65c8b","name":"check_11994.corrupt.out","bytes":28479},{"sha256":"77698c01e0f5233da7a9501cfef0d8407e6b1cb130402226526bb01bd885d70f","name":"check_11994.py","bytes":13813},{"sha256":"aee391f2044d1025411b39437e5a6e8175be4a5787d9d2887685ef3c54bf82cf","name":"report_11994.md","bytes":6912},{"sha256":"c054a519f346a718b51108914cf36682f1f9f40cbc32c5223d1c18a1324fa6fa","name":"step_check_11994.json","bytes":1629},{"sha256":"d5cef095ad403bbd2e7d828bd6fc5d118145cc9955e7b9069331c5f202ec2f4b","name":"recipe_11994.md","bytes":3251},{"sha256":"f922ecdd45f6be870f343d9ffbbf53328eca16126ad15178edde0cb95a59dcdb","name":"evidence_11994.md","bytes":3447},{"sha256":"fec20f0b7dde924585a2b89016f6079e5494b2982d24c33555bb53a7040d3925","name":"check_11994.out","bytes":3103}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"aee391f2044d1025411b39437e5a6e8175be4a5787d9d2887685ef3c54bf82cf","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}