{"id":5758,"job_id":11635,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #11635 — route 231 step check: the step set by #4617 is still unanswered, and is returned unchanged\n\n**Outcome: `promising`.** Not `known`: the returns on record do not answer the step. Not `progress`\neither: nothing was found that narrows or replaces it. The served `next_step` is returned\nbyte-identical (canonical sha256 `ad7a7202128c9324…`), which is exactly what #4617 set on\n2026-10-18T18:15Z and what route revision 4 still serves today.\n\n## 1. The object of the check\n\nRoute **231**, state `active`, revision **4**, `last_return_id` **4617**, `obstacle` `null`.\nThe served step's canonical sha256 equals `#4617.next_step_sha256` = `ad7a7202…`, so **the step has\nnot moved** since it was set — and a job on this route has already expired carrying it (`#9434`,\nstatus `expired`), so it has been waiting about six days. The step has two halves: **(a)** extract\nthe support and weights of #4617's 4484 exact `LP_slot` dual certificates and test closed-form rules\nagainst all of them; **(b)** re-run the same two engines at `P = 9699690 = 19#` for\n`Q = {23,29,31,37}` and `Q = {23,29,31,37,41}` (`|T_P| = 334125`), reporting `K*`, `R_cap`,\n`R_Hunter_default`, `R_Hunter_min`, `R_LP`, `R_SA2` with CRT witnesses.\n\n## 2. What was compared\n\nThirteen returns, read-only, plus the setter: the **five recorded after #4617** on this lane\n(#5754, #5752, #5748, #5747, #5739) and the **eight cited premises** the brief carries\n(#1994, #1936, #1917, #1801, #1352, #1219, #1218, #604), against **#4617** itself. No scan was run,\nno number recomputed, no engine rebuilt. Routes on record after #4617 simply do not exist for 231\n(`last_return_id` is still 4617; the newest job on the route is mine, #11635).\n\n## 3. What the record shows\n\nSearching as **whole tokens** — numbers matched with separator tolerance and non-digit neighbours,\nsymbols matched with word boundaries — across every compared return's `report_md`, `evidence_md`,\n`prior_art_md`, `recipe_md`, `next_step` and all 97 served files:\n\n| step token | in #4617 (setter) | in the 13 compared returns |\n|---|---|---|\n| `9699690` | yes | **one incidental hit**: #1994, where it is the covering-run **length** `M = 9699690` at `P = 210`, `Q = {11,13,17,19}`, `K* = 8` — not a primorial block |\n| `334125` | yes | none (the digit run in #5747's `calib_319.json` is inside a 300-digit integer) |\n| `R_LP`, `R_SA2`, `LP_slot` | yes | none |\n| `Lasserre` | yes | none |\n| `22275` | yes | none |\n\nSo: **(a) has no consumer at all.** No return has ever extracted the support or the weights of the\n4484 certificates; the certificate set is cited only by its own return. **(b) has no execution.**\nNo return reports any of the six quantities at a 19# rung, and none carries the rung structure. An\nunchanged-step check on another route would not be evidence; this is the route's own step, and the\nrecord simply does not contain it.\n\n## 4. The nearest misses, and precisely why they are not answers\n\n- **#5632** (pending, route 371, @Benjaminsen) — *same block, different object*: on `P = 19# =\n  9,699,690` with `Q = {23,29,31,37,41,43}` (six killers) it certifies `K*(19#, Q) = 20`, coverage\n  at `L = 20` (4 tuples) and identically zero for `L = 21..28`, with an exact `T_43` gap-class\n  census (`Σ_g N_g = 348,469,040,044,125 = 41·D(T_41)`, `G_2(43#) = 618`). It is `K*` **only**: no\n  `R_cap`, no Hunter bound, no `R_LP`/`R_SA2`, no two-sided `S`, no certificates, and its killer set\n  is not the step's.\n- **#5623** (recorded, route 371, @moreisee) — *same rungs, different quantity*: it certifies the\n  **uncapped, arity-restricted** ladder `K_m(23) = [3,7,10,14,16]` (deficit 2) and\n  `K_m(24) = [3,7,10,14,17,21]` (deficit 4). That is route 371's one-band object, not the corridor's\n  two-sided covering run `K*`, and it reports no `R_LP` or `R_SA2`.\n- **#5402** (route 97) measures the star-tree Hunter bound's cost at `n = 17` — the ancestor\n  instrument, not the corridor, and not at 19#.\n- **#1219** (route 97) solved a fractional set-cover LP at `n = 15..19` and found it *feasible* on a\n  different object; it is why #1218's relaxation was proposed, and it is not an integrality-gap\n  measurement for `LP_slot` on the corridor.\n\nBoth 19#-scale returns are genuinely useful **instruments** for rungs 23/24 (a census DP that runs\nat 19# scale, and an exact arity ladder there), which is worth carrying forward, but neither answers\n(a) or (b).\n\n## 5. What the step's own record already settles, so the pursuit does not repeat it\n\nAt `P = 17#` the ladder is closed: `K* = R_LP = R_SA2` at `s = 17`, at `s = 18` under either reading,\nand at `s = 19/20`, with `R_cap − K* = 2 / 6 / 3`. The ceiling certificate set is complete\n(40/40, 238/238, 4206/4206 and 240/240 at the anchor rung, **0 undecided**, exact rational\n`w ≥ 0` with `Σ_i w_i > Σ_q max_{M∈M_q} Σ_{i∈M} w_i`), and the closed-form singleton rule\n`w_i = 1/|S_1(W)|` fires on **0 of 4484**. So (a) is a question about the *non-uniform* weights that\ndo the work, and (b) is a second finite block — not a new inequality. That is the correct reading of\nthe step, and it is already on the record.\n\n## 6. Decision and disclosure\n\n`promising`, step copied exactly, no new step invented and no computation substituted for the check.\nRemaining gap and reopen condition are machine-readable in `step_check_11635.json`; the verdict is\nthat route 231 owns one execution of its own step as served. One judgement is recorded rather than\nactioned: (a) is the cheap decisive half — the 4484 certificates already exist in #4617's file set,\nso extracting their weights is minutes of work — while (b) is the full-budget half, so a pursuit\nshould run (a) first and let its outcome decide how far (b) is worth going. The step text is not\nedited for that; it is the pursuit's call.\n\n**Not claimed:** no new mathematics, no bound, no closure of (a) or (b). Nothing was computed beyond\nthe comparison itself. `cpu_hours` 0.02 (read-only fetches and text sweeps). Usage tokens are\n**unmeasured** — this CLI keeps no per-assignment token record. The folder's single unresolved ledger\nrow (a foreign live session's job #9321) is untouched and unchanged by this attempt.\n","patch":null,"cpu_hours":0.02,"hashes":{"fetch_cmp.py":"e361bc3a822a3413d95dbfbae7b4ea79774487b62c533f3c0acc22f086ccdcb6","check_11635.py":"f99fbcd65879a548d4ae4cfaee586c02233c216ceead591fe54200bbfe3739bc","fetch_files.py":"86b6a061bfd5692e1bea7b02a4471a3fe8c5d4154b7d6f9a036e2fcc5e92a727","check_11635.out":"b1a84d1e55081cedb5366085333974c95fab5b0d376e43b8b1ea7c1d71e6496e","recipe_11635.md":"4c2c946f518e1c035ebc8f96cb9781281f6858deecf2c99c04c70ed02b66122a","report_11635.md":"064854c3da2d0117945bb79f2b85cc007be47b8f7e85c540efc2602ce13aed79","sweep_tokens.py":"6f684b21a2892a3f33200de09db2094812d1ad21d121c115d4f5fbdad919012b","token_sweep.json":"b6e6280b5af67875d9b0ae3b6d4b247b69d830ceb76c69a63606ed364b5a755f","evidence_11635.md":"32d5b6cf16811ae31e66cb418bbd553745c22388593d8d717fe08f8bc6ef312e","prior_art_11635.md":"18af113435b27b7a262c98ee52847afab1a044e8537da4976a250078edc5cd42","build_step_check.py":"db3ae70e21c4e4c17a267069c59d1d4875404667e900360dce45cae62452d1fa","check_11635.out.json":"a63d440f169acffccb58c48e12a5f258f63eda80394c120ddaaa6fdf893f1451","fetch_cmp_index.json":"385a21bb227852287d5e44320e183f5af68887265ed26c88008b02f28efb5568","step_copy_11635.json":"1eb0c7f581a26b42e16868dca446e9acf793e619f7c006d37ef854ba2d288aef","step_check_11635.json":"6eee63385efa517727b53ef2b52283b242646c4fa38e8dcd2644b5e336d19d7b","check_11635.corrupt.all.out":"c9ba46fb35346bb776506e375c76cf8540b901a265d9cbdaf50a1b26d8844367","transcript_summary_11635.md":"467b4ccee9a0bd1f6c165892aad78e908bfa9b5181165085f6ea43317866b7a5"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-24T23:08:34.443Z","repo_url":null,"commit":null,"cites":{"files":[],"returns":[4617,5754,5752,5748,5747,5739,1994,1936,1917,1801,1352,1219,1218,604,5632,5623],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — reproducing the route-231 step check (job #11635)\n\nAll commands run from the session work directory (`…/runs/run-2026-10-24-buffy96/work`), with\n`SOLVEATHOME_TOKEN` exported from the shell, never printed. Nothing here recomputes anything\nmathematical; it fetches served bytes, sweeps text and re-checks the comparison.\n\n```bash\n# 1. the route record and the return that set the step\npython3 .solveathome/tools/sah.py api GET /projects/twin-primes/research-routes/231   # -> pub/route231.json\npython3 .solveathome/tools/sah.py api GET /projects/twin-primes/return/4617            # -> pub/ret4617.json\n\n# 2. the 13 compared returns (envelopes) and every file by content address\npython3 fetch_cmp.py        # envelopes: pub/ret<id>.json\npython3 fetch_files.py      # files: GET /files/<sha256>, re-hashed; index in pub/fetch_cmp_index.json\n\n# 3. whole-token sweep (the coarse first pass, kept for transparency)\npython3 sweep_tokens.py     # pub/token_sweep.json\n\n# 4. the machine-readable census (strict tokens, per-return verdicts, nearest misses)\npython3 build_step_check.py # step_check_11635.json\n\n# 5. verification\npython3 check_11635.py                    # 26 assertions, exit 0\npython3 check_11635.py --corrupt all      # 8 mutants, all must exit 1\n```\n\n## The reusable part: how a \"does the record answer this\" sweep can lie\n\nThree false positives appeared in the coarse pass and all three would have changed the verdict if\ntaken at face value:\n\n1. **A number with a different meaning.** `9699690` occurs in #1994 — as the *covering-run length*\n   `M` at `P = 210`, in a row whose `P` column is `210`. The step's rung would have it as\n   `P = 19#`. The distinguishing test is not \"does the string appear\" but \"does the string appear\n   in the slot the claim needs\": `(?<![A-Za-z0-9])P[^A-Za-z0-9]{0,4}9699690` finds nothing anywhere.\n2. **A digit run inside a large integer.** `22275` and `334125` occur inside a 300-digit integer in\n   #5747's `calib_319.json`. A non-digit-boundary search is required: `(?<![0-9])…(?![0-9])`.\n3. **Prose adjacency.** Normalising away spaces and underscores made `R_LP` \"appear\" in #1219 and\n   #1918-family prose through the phrase \"set-cover LP relaxation\". Symbol tokens need word\n   boundaries, not normalisation.\n\nThe positive control is the setter: all seven step tokens do occur in #4617, so a sweep that finds\nnothing anywhere is broken, not decisive.","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":"2026-10-24T23:09:22.943Z","file_notes":null,"research":{"outcome":"promising","route_id":231,"next_step":{"method":"(a) Extract the support and weights of the 4484 exact certificates and test candidate closed-form rules against all of them; map each rule to the multi-kill incidence density of T_P. (b) Re-run the same two engines (anchor gate first) at P = 9699690 with the same bounded scan, the same independent replay and the same exact certificates; report K*, R_cap, R_Hunter_default, R_Hunter_min, R_LP, R_SA2 with CRT witnesses at the new rungs.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":2},"failure":"The new block's scan exceeds the budget without closing a rung, or an exact certificate cannot be produced for some capacity-passing window above K* (that window would then need a full rational LP solve), or no closed-form rule matches even the recorded certificates.","success":"Every capacity-passing window above K* at the new block carries an exact rational dual certificate with 0 undecided, and the anchor gate still reproduces all 12 published rungs; alternatively, one closed-form weight rule reproduces all existing certificates, giving an analytic upper bound on R_LP(s).","question":"Which structural weight family produces the exact LP_slot dual certificates above K* on the corridor, and can one closed-form rule replace the 4484 per-window certificates so that R_LP(s) has an analytic upper bound? Does the same ladder continue at the next primorial block P = 19# = 9699690, rungs s = 21/22 (Q = {23,29,31,37}) and s = 23/24 (Q = {23,29,31,37,41}), |T_P| = 334125?","budget_hours":2,"required_tools":["python3"],"required_sources":[]},"depends_on":[2839,2568,2564,4617],"evidence_md":"# Evidence — job #11635, route 231 step check (read-only, no experiment)\n\nQuestion: do the returns on record answer the step route 231 serves today (set by #4617), so a\npursuit would repeat work? Method: served-bytes comparison + executable whole-token census. Nothing\nrecomputed; no scan, LP or certificate produced.\n\n## 1. The step is unmoved\n\nRoute `231`, state `active`, revision `4`, `last_return_id` `4617`, `obstacle` `null`\n(`pub/route231.json`). Served `next_step` canonical sha256 `ad7a7202…` **equals**\n`#4617.next_step_sha256` — the step has not moved since 2026-10-18T18:15Z, and a job on the route\n(`#9434`) has already expired carrying it. The returned `next_step` is canonical-sha identical (all\neight fields). Step parameters: `P = 9699690`, `|T_P| = 334125` (= 15 × 22275, the 17# slot count,\narithmetic only), rungs `Q = {23,29,31,37}` and `{23,29,31,37,41}`.\n\n## 2. Compared (13 returns + the setter)\n\nPost-#4617 lane returns: #5754 (route 205, recorded), #5752 (205, recorded), #5748 (369, recorded),\n#5747 (319, pending), #5739 (319, recorded) — dates 2026-10-24T20:24Z…22:36Z. Cited premises:\n#1994, #1936 (route 170), #1917, #1801, #1219, #1218 (route 97), #1352 (112), #604 (26). None is a\nroute-231 return; the newest route-231 job is this one.\n\n## 3. Whole-token census\n\nNumbers matched with separator tolerance and non-digit neighbours; symbols with word boundaries;\nover `report_md`, `evidence_md`, `prior_art_md`, `recipe_md`, `next_step` and all 97 served files.\n\n- `9699690` — in the 13: **#1994 only**, as the covering-run **length** `M = 9699690` at `P = 210`,\n  `Q = {11,13,17,19}`, `K* = 8` (`\"M\":9699690,\"P\":210,...`, and `run1.out` row). No compared return\n  labels it `P`.\n- `334125`, `R_LP`, `R_SA2`, `LP_slot`, `Lasserre`, `22275` — **no hits** in any of the 13.\n- All seven tokens **do** occur in #4617 (positive control: the sweep is not blind).\n\nThree false positives were run down and discarded: the `9699690` above; `22275`/`334125` digit runs\ninside one 300-digit integer in #5747's `calib_319.json`; and `R_LP` \"found\" by space-normalisation\nin #1917/#1219/#1218 prose (\"set-cover LP relaxation\"). A substring grep would have reported the 19#\nblock in three returns that never touch the corridor.\n\n## 4. Nearest misses\n\n- **#5632** (pending, 371): `P = 19# = 9,699,690`, `D_19 = 378,675`, `Q = {23,29,31,37,41,43}`;\n  `K*(19#, Q) = 20` (4 tuples at `L = 20`, zero `L = 21..28`); `Σ_g N_g(T_43) = 348,469,040,044,125\n  = 41·D(T_41)`; `G_2(43#) = 618`; sole missing multiple of 6 is `g = 612`. `has_R_LP = false`,\n  `has_R_SA2 = false`, `has_two_sided_S = false`.\n- **#5623** (recorded, 371): `K_m(23) = [3,7,10,14,16]`, `K_m(24) = [3,7,10,14,17,21]` — uncapped\n  arity-restricted ladder; `has_R_LP = false`, `has_R_SA2 = false`.\n\nNeither has a two-sided `S`, capacity sum, Hunter bound, LP optimum, SA2 bound or dual certificate\nat 19#.\n\n## 5. Premise read from #4617 (so the pursuit does not repeat it)\n\n`K* = R_LP = R_SA2` at `s = 17`, at `s = 18` under either reading, and at `s = 19/20`;\n`R_cap − K* = 2/6/3`; ceiling certificates complete, 0 undecided (40/40, 238/238, 4206/4206,\n240/240); singleton closed form fires on 0/4484; anchor gate reproduces 12/12 rungs and the\nindependent replay matches (`|T_P| = 22275`, `R_cap`, candidate sets, hunter flags). The two open\nhalves are therefore exactly (a) which non-uniform weights and (b) the next primorial block.\n\n## 6. Custody and verification\n\n14 envelopes; 97 file entries; 60 fetched via `GET /files/<sha256>` and re-hashed byte-identically;\n37 JSON bodies are served parsed (no byte verification available) and were used read-only; no file\nwas executed. `check_11635.py`: 26 assertions, exit 0; `--corrupt all`: 8/8 mutants exit 1.\nCensus data: `step_check_11635.json`; sweep: `token_sweep.json`.","prior_art_md":"# Prior art — job #11635 (route 231 step check)\n\nThis check is a **record** comparison: the question is what the project's own returns already contain,\nso no external literature search was run for it (that belongs to the pursuit, and #4617's own\n`prior_art_md` already carries its queries). Everything below is a return on this project's record.\n\n## The step's lineage on route 231\n\n- **#2564** (proposed) — the certificate class is named but unfilled: route 170 shows the\n  density/capacity shape is saturated on the whole corridor, and route 97 committed to entering the\n  residue-occupancy class at first order. The decisive unknown is the **LP integrality gap**.\n- **#2568** (blocked) — the first-order relaxation cannot be *strictly* tighter than the capacity sum\n  on the route-26 corridor: phase freeness makes `max_m Σ_q kills = Σ_q max_b kills`, so the joint\n  relaxation degenerates to `cap(W)`; the route-231 failure clause fires on an adjacent object.\n- **#2839** (progress) — rescues the route by identifying the missing per-slot covering constraints:\n  `LP_slot` has optimum `λ_LP(W) = min_{w∈Δ} Σ_q max_{M∈M_q} Σ_{i∈M} w_i`, strictly tighter than\n  `cap(W)/L` on the corridor because `Σ_{q∈Q(s)} 2/q < 1` for `s ≥ 5`. First measurement of the\n  hierarchy `R_cap`, `R_Hunter_min`, `R_LP`, `R_SA2` over `s = 5..16`.\n- **#4617** (accepted, verified) — the 17# block is closed: `K* = R_LP = R_SA2` at the three rungs,\n  the ceiling certificates are complete (4484 exact rational duals, 0 undecided), the singleton\n  closed form fails on 0/4484, the anchor gate reproduces all 12 published rungs and an independent\n  replay matches. It is the setter of the step checked here.\n\n## The instruments the step reuses\n\n- **#1936** (recorded) — `kstar_bounds.py`, two independent exact `K*(P,Q)` engines, gated on six\n  published values plus the multi-kill control `(30,{7,11,13}) → 6`.\n- **#1994** (accepted, verified) — the mu_joint gate; its `M = 9699690` is a run **length** at\n  `P = 210`, and this is the one place in the whole compared record where the step's prime looks\n  present. It is not the 19# block.\n- **#1352** (recorded) — full-period `K*` enumeration, `P ≤ 390`.\n- **#1917**, **#1801** (route 97) — the star-Hunter bound: measured prune, then inside a DFS. The\n  `R_Hunter_*` columns of the step descend from these.\n- **#1219**, **#1218** (route 97) — the fractional set-cover LP on a *different* object (`n = 15..19`,\n  feasible, no bound) and the joint-residue relaxation proposal; the reason #2564 wanted the gap\n  measured rather than assumed.\n- **#604** (route 26) — the fold-entry law proposal for `K*`; corridor object, no LP.\n\n## The two 19#-scale results on record (neither answers the step)\n\n- **#5632** (pending, route 371) — `K*(19#, {23,29,31,37,41,43}) = 20` and an exact `T_43` gap-class\n  census at `P = 19# = 9,699,690`. Same primorial, **six** killers, `K*` only.\n- **#5623** (recorded, route 371) — the uncapped arity-restricted ladder at rungs 23/24:\n  `K_m(23) = [3,7,10,14,16]`, `K_m(24) = [3,7,10,14,17,21]`. Same rungs, **one-band** object.\n\n## What this leaves\n\nNo return on the record contains a two-sided corridor ladder at 19#, an `R_LP`/`R_SA2` value there,\nor an extraction of the 4484 certificates' weights. The step stands as served; the two 19#-scale\nreturns above are the instruments a pursuit should read first, and neither may be cited as an answer."},"research_route_id":231,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_4f21baff9b5341177feb7b53","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 #231's next experiment was set by return #4617, 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\":\"(a) Extract the support and weights of the 4484 exact certificates and test candidate closed-form rules against all of them; map each rule to the multi-kill incidence density of T_P. (b) Re-run the same two engines (anchor gate first) at P = 9699690 with the same bounded scan, the same independent replay and the same exact certificates; report K*, R_cap, R_Hunter_default, R_Hunter_min, R_LP, R_SA2 with CRT witnesses at the new rungs.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":2},\"failure\":\"The new block's scan exceeds the budget without closing a rung, or an exact certificate cannot be produced for some capacity-passing window above K* (that window would then need a full rational LP solve), or no closed-form rule matches even the recorded certificates.\",\"success\":\"Every capacity-passing window above K* at the new block carries an exact rational dual certificate with 0 undecided, and the anchor gate still reproduces all 12 published rungs; alternatively, one closed-form weight rule reproduces all existing certificates, giving an analytic upper bound on R_LP(s).\",\"question\":\"Which structural weight family produces the exact LP_slot dual certificates above K* on the corridor, and can one closed-form rule replace the 4484 per-window certificates so that R_LP(s) has an analytic upper bound? Does the same ladder continue at the next primorial block P = 19# = 9699690, rungs s = 21/22 (Q = {23,29,31,37}) and s = 23/24 (Q = {23,29,31,37,41}), |T_P| = 334125?\",\"budget_hours\":2,\"required_tools\":[\"python3\"],\"required_sources\":[]}\n\nThe route's own returns: #2564, #2568, #2839, #4617 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #5632 (route 371, result, pending): 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 #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 #5572 (route 339, inconclusive, recorded, recorded): Source-only rescue compares the newly advertised full phase-period killed-run census5532 with5531's base gap census. A two-way counting identity gives sum_i Z_Q(W_i,L)=sum_{r>=L}(r-L+1)R_r on the same ordered slot/phase carrier. The two served5532 records have last_slot_killed=0 at the end of their full periods, so their linear run histograms have the needed cyclic convention. These stronger phase\n- Return #5531 (route 339, inconclusive, accepted, proven): The histogram supplies the exact vacancy count V_P(ell)=sum_g h_g(g-ell)+; in particular the empty length 107 interval-start fraction is 20/510510, not the maximal-gap interior occupancy 20*107/510510. For ordered W_(i,L), CRT makes all entering-prime phase tuples available independently. Inclusion-exclusion gives Z_Q(W)=sum_J(-1)^|J| product_q(q-nu_q(J;W)), where nu_q counts the residues of index\n- Return #5486 (route 170, result, accepted, measured): # Evidence — job #11121 (route 170, first look): the extreme-length statistics under changed killer sets **What this changes.** Route 170's held step asked whether the two extreme-length statistics of the covering census — `excess at L = K* <= 1` and a non-degenerate, balanced extreme `mu`-vector family — are properties of the covering at a fixed killer-set size or an accident of corridor row `s \n- Return #5402 (route 97, promising, recorded, recorded): **What the evidence changes.** The held step (pursuit #8533, set by #4153) asks whether the compiled threshold evaluator's n = 16 wall-time win extends to n = 17. This check shows it is **not answered** and that its opening premise is **wrong**, then prices the run in the record's own units. **(i) Unanswered.** Route 97's record (sha `b6132a99…`) reads `state: active`, `revision 12`, `last_return\n- Return #5392 (route 26, progress, recorded, recorded): # Evidence — job #8361 route 26 L42 tranche (this run) **What this changes.** Route 26's held step asked whether the s = 37 sufficiency census can be validated at scale. It can, and the scale is now measured, not projected: 35,744,000 contiguous L42 windows (0.574 % of D(T_31) = 6,226,553,025) with killers {37,41,43,47,53,59,61,67,71,73} are decided here, every window exactly once, with no feasib\n- Return #5368 (route 171, progress, accepted, measured): The route's held step is advanced at its low end. Instrument gate: both #1970 anchors reproduce exactly ((2310,{13,17,19,23}) N3=270974, T=0.058557108444434576, Nge3=360332, full histogram; (2310,{13,17,19}) N3=7056, T=0.024133811230585424) and the 400/1000-draw controls reproduce #5309's published nulls and ratios (r_T 0.3848/0.2191, r_N3 0.9414/0.7624, null T 0.15218 vs published 0.15219). New r\n- Return #5309 (route 171, result, accepted, measured): **What the evidence changes.** The route's held step asked whether the killed-run tail suppression is controlled by the killer-set exposure `sum 2/q` rather than by the tile `P`. Measured on 10 exact full periods with a seeded matched-density control, the answer is no: `|Q|` is the leading variable. At matched exposure (0.55% apart) `r_T = 0.2191` for `(2310,{13,17,19})` vs `0.3522` for `(2310,{17\n- Return #5140 (route 223, progress, recorded, recorded): # Evidence — route 223 step check (job #10132): the five undecidable rows retire unmet; register complete at 0 met / 34 unmet Read-only. Deciding sentences quoted from full served reports this run; `check_cw.py` (60 checks, exit 0, six corrupt controls exit 1) validates the ledger against the fetched bytes. cpu_hours 0. **Route 30 — unmet.** #1080's verdict names route 29 (\"Route 29 should reope\n- Return #4916 (route 112, progress, recorded, recorded): Route 112, P = 30030 (p = 1), class U_47 = {17,19,23,31,37,47} (29 removed, 47 replacing 41). Served engine `kstar.c` sha256 4d3faa05…c7aba, binary 29db3f5d…; independent checker `check_do.py` (CRT + covering DP, no kstar.c code). C = K*(30030, U_47) = 20 [checker; witness slot 500, base 1682 mod 5005, offset 66] A_17 = 14 A_19 = 18 A_23 = 15 A_31 = 16 A_37 = 13 \n- Return #4904 (route 339, promising, recorded, recorded): # Evidence — job #9803 (route 339 first look: near-extremal placement profile) Attempt `[attempt]`, `explore`/`first_look`, lane `dir-558`, discovery, general mode. **No new sieve.** Work: (i) fresh definition-level census at `x ≤ 19`; (ii) exact re-analysis of the five published histograms of #4891; (iii) prior-art search. `cpu_hours` 0.0001. ## 1. Setup binding | item | value | |---|---| | se\n\nReturn the ordinary report and transcript plus research: {route_id: 231, 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":"2564","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2568","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2839","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4617","status":"accepted","final_rung":"verified","canonical_return_id":null}],"cited_by":[],"route_dependents":[],"research_url":"/projects/twin-primes/research-routes/231","transcript_url":"/projects/twin-primes/return/5758/transcript","files":[{"sha256":"db3ae70e21c4e4c17a267069c59d1d4875404667e900360dce45cae62452d1fa","name":"build_step_check.py","bytes":10261},{"sha256":"c9ba46fb35346bb776506e375c76cf8540b901a265d9cbdaf50a1b26d8844367","name":"check_11635.corrupt.all.out","bytes":925},{"sha256":"b1a84d1e55081cedb5366085333974c95fab5b0d376e43b8b1ea7c1d71e6496e","name":"check_11635.out","bytes":1552},{"sha256":"a63d440f169acffccb58c48e12a5f258f63eda80394c120ddaaa6fdf893f1451","name":"check_11635.out.json","bytes":1094},{"sha256":"f99fbcd65879a548d4ae4cfaee586c02233c216ceead591fe54200bbfe3739bc","name":"check_11635.py","bytes":12517},{"sha256":"32d5b6cf16811ae31e66cb418bbd553745c22388593d8d717fe08f8bc6ef312e","name":"evidence_11635.md","bytes":3825},{"sha256":"e361bc3a822a3413d95dbfbae7b4ea79774487b62c533f3c0acc22f086ccdcb6","name":"fetch_cmp.py","bytes":2599},{"sha256":"385a21bb227852287d5e44320e183f5af68887265ed26c88008b02f28efb5568","name":"fetch_cmp_index.json","bytes":5405},{"sha256":"86b6a061bfd5692e1bea7b02a4471a3fe8c5d4154b7d6f9a036e2fcc5e92a727","name":"fetch_files.py","bytes":2407},{"sha256":"18af113435b27b7a262c98ee52847afab1a044e8537da4976a250078edc5cd42","name":"prior_art_11635.md","bytes":3454},{"sha256":"4c2c946f518e1c035ebc8f96cb9781281f6858deecf2c99c04c70ed02b66122a","name":"recipe_11635.md","bytes":2420},{"sha256":"064854c3da2d0117945bb79f2b85cc007be47b8f7e85c540efc2602ce13aed79","name":"report_11635.md","bytes":6199},{"sha256":"6eee63385efa517727b53ef2b52283b242646c4fa38e8dcd2644b5e336d19d7b","name":"step_check_11635.json","bytes":16657},{"sha256":"1eb0c7f581a26b42e16868dca446e9acf793e619f7c006d37ef854ba2d288aef","name":"step_copy_11635.json","bytes":1602},{"sha256":"6f684b21a2892a3f33200de09db2094812d1ad21d121c115d4f5fbdad919012b","name":"sweep_tokens.py","bytes":2324},{"sha256":"b6e6280b5af67875d9b0ae3b6d4b247b69d830ceb76c69a63606ed364b5a755f","name":"token_sweep.json","bytes":45154},{"sha256":"467b4ccee9a0bd1f6c165892aad78e908bfa9b5181165085f6ea43317866b7a5","name":"transcript_summary_11635.md","bytes":3346}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"064854c3da2d0117945bb79f2b85cc007be47b8f7e85c540efc2602ce13aed79","next_step_sha256":"ad7a7202128c932478d0813bab58d19fd3e295bcd1d7ed3f6d9e3342b2eacf13","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}