{"id":3896,"job_id":7942,"problem_id":1,"lane_id":2,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #7942 — route 86 step check (held pursuit #4279): the attaining-seed orbit-count step is **still open**, and it is copied exactly\n\nrun `run-2026-10-15-cm` · session `2026-10-15` · assignment 1 of 1 · `explore`, stage `first_look`,\nlane **adversarial**, **route 86**, general mode, purpose `discovery`, effort `unmeasured` ·\nprotocol `department-v2.research-2026-10-13.1` / `framework-0061ff7f3b63` · step check of held job\n**4279** (source return **1903**, route revision **4**).\n\n**Outcome: `promising`.** No return on record answers the step's question. The step — the all-seed\ncensus at **wheel 17 (x = 19..37), wheel 23 (x = 29..41) and (T13; x = 37)**, gated seed for seed on\n#1797's ten cells, for a rule fixing the number of attaining-seed orbits — is copied\n**byte-identically** into `research.next_step`, so the held pursuit goes out with this note and these\nreturns never hold it again.\n\nTwo things were checked and both hold: the step's own dependencies are served (the gate file\n`route86-allseed-cells.json`, #1084's `allseed2030.py`, #1079's `complete2028.json`), and no return\nrecorded since #1903 names the step's own cells or vocabulary. Two facts are new and material:\n\n1. **The T19 diagonal the gate rests on has grown by three levels since #1903.** #2061 certified\n   23#..43# and gave 47# (`nmax` 4, two σ-orbits), #2197 gave 53# (`nmax` 2, one σ-orbit), #3507 gave\n   59# (`nmax` 8, **four** σ-orbits over **one** T19 mirror pair, i.e. 4 completions per seed). The\n   route's identity `nmax = 2 × completions(seed)` therefore now also holds at a cell with eight\n   positions — but all three are the *same* base wheel as the gate (T19, the uniform-1 side), so they\n   do not touch the varying part of the question.\n2. **One requested cell is already on record as a by-product.** #2006's full-period sweep at\n   `w = previous prime` tabulates x = 19 over the **T17** base residues: `nmax` 20, **16 attained\n   seeds** (4 with count 2, 12 with count 1), i.e. **8 mirror orbits** at (T17; x = 19). The pursuit\n   should treat that cell as a control, not as new territory, and start the wheel-17 scan at x ≥ 23.\n\n## 1 · The step under check, and the exactness of my copy\n\n`route_86.json` (revision **4**, `last_return_id` **1903**) carries `next_step` = the step #1903 wrote.\nIts compact `json.dumps(sort_keys=True, separators=(',',':'))` sha256 is\n`e999720b6f22c5c4539268fa556b54267b90d1e34367e0b56118b086bb5b7a4b` — the same value computed\nthree independent ways in\n`check_cm.json` C1: from the route record, from #1903's own `research.next_step`, and from the step\nJSON embedded in this assignment brief. **All three are equal** (`all_three_equal: true`), so the copy\nreturned here is byte-identical to the step the route holds.\n\nThe question: *what fixes the number of attaining-seed orbits of `G2(x#)` at a cell (T_w; x) —\n3, 10, 8, 2, 1 at wheels 11 and 13 against 1 at every T19 cell tested in #1797?* The step's declared\ncompute is `{ram 2 GB, disk 1 GB, cpu_hours 1}`, `budget_hours` 1.5, `required_tools`\n`[\"python3\",\"cc\"]`, `required_sources` `[]`.\n\n## 2 · What the returns on record settle — none of them answers it\n\n**Route 86 itself.** `last_return_id` = **1903**; the route's events are #1079 (proposed), #1084\n(promising), #1797 (result), #1903 (progress). No return has been recorded on route 86 since #1903.\nIts jobs are 2030 (`returned` #1084), 2038 (`accepted` #1797), 4131 (`expired`), 4278 (`returned`\n#1903), 4279 (**the held pursuit**), 7942 (this check).\n\n**The brief's comparison set** (`check_cm.json` C3, all bodies hash-pinned in `fetch_cm.json`):\n\n| return | route | outcome | recorded | tokens of the step it carries |\n|---|---|---|---|---|\n| #3507 | 15 | progress | 2026-10-13 | `Tucker`, `two-residue law`, `census4495` |\n| #2197 | 15 | progress | 2026-10-03 | `Tucker`, `two-residue law`, `census4495` |\n| #2061 | 15 | result (accepted) | 2026-09-29 | `Tucker`, `two-residue law`, `census4495` |\n| #2006 | 15 | progress | 2026-09-28 | `orbit count`, `Tucker`, `two-residue law` |\n| #1791 | 15 | result (accepted) | 2026-09-26 | `Tucker`, `two-residue law` |\n| #1797, #1903 | 86 | accepted / recorded | 2026-09-26 | `allseed`, `orbit count`, `wheel 17`, `wheel 23`, `(13,37)`, `(T13; x=37)`, `n_phases` |\n\n**`wheel 17`, `wheel 23`, `allseed`, `attaining seed`, `(T13; x=37)` and `n_phases` occur only in\nroute 86's own #1797 and #1903.** Not one return recorded since #1903 requests, runs or answers any\nwheel-17/wheel-23/(T13;37) census, and none states a rule for the number of attaining-seed orbits.\n\nThe same holds department-wide, not just in the brief's list: a bounded public-id census\n(`census_cm.py`, `census_result_cm.json`) walked the recorded id space from **#1904 to #4053**\n(2 150 ids; **1 147** recorded bodies hash-pinned; head proved by a closing run of **158** non-200\nids), and in those 1 147 bodies **`wheel 17`, `wheel 23`, `allseed`, `attaining seed`,\n`mirror orbit`, `(T13; x=37)` and `n_phases` occur in none of them**; `orbit count` and `route 86`\noccur once each, both in **#2006**. The only generic hits (`T17`, `T23`, `T13`, `Tucker`,\n`census4495`, `two-residue law`) are other routes' steps and the T19 ladder census, i.e. the shared\nvocabulary, never a route-86 all-seed tabulation.\n\nThe strongest on-record statement is #2006's own §4, which read #1903 in full and wrote: *\"#1903 …\nits own open item (a rule for the orbit count) is the item that survives here.\"* #2006 locates where\nthe fixed wheel breaks (at x = 11, 13, 17 some attaining endpoints are not T19 slots, so the\n\"interior T19 slots\" list does not exist; at 19# and 23# the pattern is degenerate) and leaves the\nframe that the step's gate uses intact. That is a second, independent confirmation that the rule is\nopen and is route 86's obligation.\n\n**Why the route's other three cells do not answer it.** #2061/#2197/#3507 are base-wheel-19 censuses\n(the gate's own wheel: T19, where the orbit count is uniformly 1); #2006's x = 11..23 sweep uses\n`w = previous prime`. None of them enumerates a T17 or T23 base-residue set, which is where the\ncount varies (3, 10, 8, 2). `Tucker` and `two-residue law` hits are citation of the same external\nAtlas and the same T19 ladder, not the orbit-count rule.\n\n## 3 · What the later returns DO settle, and the one cell that overlaps\n\nRecorded here so the pursuit does not repeat it (read in full; numbers as published):\n\n| cell | level | nmax | σ-orbits (positions) | attaining T19 residues | source |\n|---|---|---|---|---|---|\n| T19 | 47# | 4 | 2 | one mirror pair `1531841 / 8167139` | #2061 |\n| T19 | 53# | 2 | 1 | mirror pair `1984889 / 7713929` | #2197 |\n| T19 | 59# | **8** | **4** | mirror pair `{3259691, 6439031}` | #3507 |\n\n* The 59# cell is the first on record with `nmax` 8 over **one** T19 seed pair: 4 completions per\n  seed, so route 86's `nmax = 2 × completions(seed)` also holds there. In route-86 terms the\n  attaining-**seed** orbit count is still **1** — the T19 uniformity is not disturbed.\n* **Overlap (T17; x = 19).** #2006's full-period table row `x = 19, w = 17` reads `nmax` 20,\n  **16 attained base residues** (four with count 2, twelve with count 1), i.e. **8 mirror orbits**.\n  That is the first cell of the step's wheel-17 diagonal, already computed (in a different framing,\n  as a route-15 step check, without the per-seed skeleton/free-set table the step asks for). Wheel-17\n  cells x ≥ 23, all wheel-23 cells (x = 29..41) and (T13; x = 37) are untouched: #1797 reports\n  (13, 37) timing out at 700 s and does not use it, and #1084's table stops the T13 column at x = 23.\n\n## 4 · Feasibility of the step as written (measured here, no experiment run)\n\n* The step's `required_tools` are `python3` and `cc`; both are present (`/usr/bin/python3`,\n  `/usr/bin/cc`; also `gcc`, `g++`, `make`, `git`, `curl`, `jq`). Nothing in the step needs a tool\n  this machine lacks, and no source is required.\n* The step's own gate and inputs are served: #1797's `route86-allseed-cells.json`\n  (`f705524d…20cf11`), #1084's `allseed2030*.txt/py`, #1079's `complete2028.json` + `orbits41_2028.json`\n  + `seed2028.json`, #1903's `check4278.py`/`.out`.\n* **Why the C port is not optional at wheel 23.** `|T_w| = prod_{p ≤ w}(p−2)`: T11 135, T13 1 485,\n  T17 22 275, T19 378 675, **T23 7 952 175** — about 21× the T19 seed count. The published T19\n  all-seed runs cost 192 s (x = 37) and 712 s (x = 41) in Python (#1084); a Python all-seed sweep at\n  wheel 23 would be ~4 h *per cell*, i.e. four times the whole 1 CPU-h pricing for one cell, so the\n  step's \"port to C or tighten the counting prune\" is load-bearing, not a nicety. With a C port the\n  pricing is plausible; this check does not run it.\n\n## 5 · Verdict and what happens next\n\nVerdict **`promising`**: the step is open, no return on record answers it, its gate and inputs are\nserved, and nothing in the record replaces it. It is returned unchanged as `research.next_step`\n(hash equality proved in §1), so held job **4279** goes out with this note. Added prerequisites from\nthis check, for that pursuit:\n\n1. **Start the wheel-17 scan at x ≥ 23.** (T17; x = 19) is already tabulated by #2006 (`nmax` 20,\n   16 attaining seeds, 8 orbits) — reproduce it as a control against the C port, do not present it as\n   new territory, and cite #2061/#2197/#3507 rather than re-running the T19 levels 47#, 53#, 59#.\n2. **Budget the C port.** Wheel 23 has 21× the T19 seed count; the step's 1 CPU-h line holds only\n   with the C port (or the tightened prune), which the step itself prescribes.\n3. Everything else is unchanged: the gate on #1797's ten cells, the per-attaining-seed record of\n   completion count / skeleton residues / free set, the citation (not recomputation) of Tucker's\n   Atlas `n_phases`, and the failure clause (if no rule holds across the enlarged cell set, the route\n   keeps the one-witness completion and the count identity and retires the structural claim).\n\n*Scope of this return.* Read-only step check. Finite GETs, three hash-equal copies of the step, one\ntoken scan over the brief's comparison set, one department-wide public-id census (see\n`evidence_cm.md`), and local arithmetic on seed counts. **No all-seed census, no DP, no C port, no\nenumeration of any T_w base-residue set** — the step's experiment was not run and no computation a\nreturn already made was reproduced.\n\n*Cost (measured).* A 46-request sample of the same read path cost 1.43 s user+sys (~0.03 s CPU per\nrequest), so 2 174 requests plus the local scripts ≈ **0.02 CPU-h**, filed as `cpu_hours`; wall time\n≈ 20 min, dominated by the census's network waits.\n","patch":null,"cpu_hours":0.02,"hashes":{"check_cm.py":"98390c9347429228930179bc4fb370cab829d16ead06e4c38776d184d6d38a64","fetch_cm.py":"bee7454d0df30a24ab40b2b50e7230c162c633e58e96d76fbf60cebf2d06c953","census_cm.py":"f4b06dc1e1b5e36b5d2e44e4a86915a5a759bb354f1312c1f6832c37d2333bf9","recipe_cm.md":"dfd3e7d72a8ba1e3e15c566213b606afc0eeb32806dfa658bfec5a22defe5505","report_cm.md":"96089f15447e2a2dbd0edfc222021621eecd8afd9827900049c0f6910430cfec","check_cm.json":"0db06b07cc781ab329e2e80a172efa64430ced79ebfafa4d3e09f423dfe2a708","fetch_cm.json":"e96cd1e79b089f72f7b88cf51ccf181f2b54b6d47ab6c419e087721e343ffcc9","evidence_cm.md":"70cc79c795a35adfce6bee1d602e0002a9bcb9c32decde693ab51afcdf6525e9","prior_art_cm.md":"a8b22330d651c68122ff9ad40d730da824e663ab1024a46e251026f0c0804015","next_step_cm.json":"e65dc3f58b87f96257f80ef705a345314e5d604446850039e3fa7fa203fe6d6a","served_route_15.json":"9d2b4bd89a65656e3e43b7da3fdbd9b8729dbb2a82c976d50a58b8ffb62a3a2b","served_route_86.json":"086d1189bc4c0098ba1606ae6d59189b847def0954e2c4b1921eb1d52b0de0c6","step_from_brief.json":"e65dc3f58b87f96257f80ef705a345314e5d604446850039e3fa7fa203fe6d6a","census_result_cm.json":"6ff2a4ef88bf8dc861a658991fc4d9ec7a6cc2893a81f24c71c9c18bf1ef4b5b","served_return_432.json":"d90697b97afb18e301f1f37959a6548d81ca067990cbfae4e4d38d7c36cde26f","served_return_1079.json":"d8120df08993ff5519806abd7243b453b1e7b939d1a7b4b7978fff8c60975d19","served_return_1084.json":"09f3a6035e04e21478b80fcdc0abec960e749e3fda6b16a507fd22ed0e505a50","served_return_1797.json":"682e43122ac8ba8f57da5b4ceee5e1a53527220efa55d36aa1b3620b984935f4","served_return_1903.json":"f2ba6d8ee16d6d35bc44bf3724fda8792d9ec5ce2e467942b59b86a1f47410cc","served_return_2006.json":"2d984dd5bb9e1a5ec542f0bd7d1f9c3f2e6c2f895cf5c4872d18b041486e05f1","served_return_2061.json":"c8b7a21e542e83361d2fcdd0b9c648d92b7da54db119b00834afcd7550b42dfd","served_return_2197.json":"fef60b4eb1d5683031624a6f8baf44b6d5c13dbb24ffa6dbd4bab34a2d60a496","served_return_3507.json":"9401bd63fe51018a4d51aec15c08101a42468535eb0bd1170e50f419ae0a50e7","summary_transcript_cm.md":"7f77065b58f0d83e9511b23a2a6f5a0f8863f2ea75ac1d694e7c8412a9f9b333"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-15T06:11:34.365Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1079,1084,1797,1903,2006,2061,2197,3507,432],"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 — re-check job #7942 (route 86 step check) locally (read-only, minutes)\n\nNothing here runs the step's experiment (no all-seed census, no DP, no C port). Everything is derived\nfrom the served record and the local copies in this run's `work/`. Run from this directory.\n\n## 0 · Environment\n\n    cd <department>/runs/run-2026-10-15-cm/work\n    python3 --version          # 3.11, stdlib only (json, hashlib, urllib)\n    python3 <tool> outstanding # recovery-first: expect unresolved 0, all_complete true\n\n## 1 · Fetch the record (hash-pinned, one GET per object)\n\n    python3 fetch_cm.py        # -> fetch_cm.json + served/{route-86,route-15,return-*}.json\n\nFetches route **86** and route **15**, the route's own returns (#1079, #1084, #1797, #1903) and the\nbrief's comparison returns (#3507, #2197, #2061, #2006, #1791); every body's sha256 is recorded in\n`fetch_cm.json`. (A sixth GET in the session fetched #432, kept as `served/return-432.json`.)\n\n## 2 · Controls\n\n    python3 check_cm.py        # -> check_cm.json\n\n* **C1** the step's identity **three ways** — compact hash of `route_86.next_step`,\n  `return-1903.research.next_step`, and the step JSON embedded in `brief_cm.md`; expects\n  `all_three_equal: true` and sha256\n  `e999720b6f22c5c4539268fa556b54267b90d1e34367e0b56118b086bb5b7a4b`. Also prints `revision` 4,\n  `last_return_id` 1903, the compute/pricing fields and the tool list.\n* **C2** route 86's job list and events (pursuit 4279; nothing after #1903).\n* **C3** token scan over the comparison returns: `wheel 17`, `wheel 23`, `allseed`, `(T13; x=37)` and\n  `n_phases` occur only in #1797 and #1903.\n* **C4–C6** the recorded cells (47#/53#/59# T19; #2006's `x = 19, w = 17` row the T17 cell), the gate\n  files, and the seed-count arithmetic `|T_w| = prod_{p<=w}(p-2)`.\n\n## 3 · Department-wide census (the decisive negative; resumable)\n\n    CENSUS_WALL=780 python3 census_cm.py > census_cm.out 2>&1\n\nWalks public return ids from **1904** upward in 50-id batches, hash-pinning every body and checking it\nfor the step's tokens; keeps a body only when it hits one (`served/census_hit_<id>.json`), journals one\nrow per batch (`fetch_census_cm.jsonl`), and checkpoints `census_result_cm.json` after every batch, so a\ncut turn loses at most 50 ids — just re-run to resume. Stops after 120 consecutive non-200 ids (that is\nhow the head of the id space is proved). Direct urllib is used on purpose: `sah.api` costs ~6.5 s/request\nhere (journal fsync), urllib ~0.3 s.\n\n## 4 · Re-verify the returned files\n\nThe files attached to this return are listed in the payload with their sha256s; fetch any of them back\nwith `GET <project base>/files/<sha>` and re-hash to confirm the address equals the bytes. The step's\nown copy can be re-checked at any time with:\n\n    python3 - <<'PY'\n    import json, hashlib\n    ns = json.load(open(\"next_step_cm.json\"))          # the returned step\n    print(hashlib.sha256(json.dumps(ns, sort_keys=True, separators=(\",\", \":\")).encode()).hexdigest())\n    # expect e999720b6f22c5c4539268fa556b54267b90d1e34367e0b56118b086bb5b7a4b\n    PY\n\n**Environment.** aarch64 container, CPython 3.11, stdlib only, no `pip`. The only network use is the\nproject API with the department token from `~/.config/solveathome/credentials.env`; never copy that\ntoken into a file, log or transcript.","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":"2026-10-15T06:13:04.676Z","file_notes":[{"sha":"f4b06dc1e1b5e36b5d2e44e4a86915a5a759bb354f1312c1f6832c37d2333bf9","name":"census_cm.py","notes":["prints what looks like progress or timing to stdout on line 118 (\"print(\"batch done to id %d; non200run=%d walked=%d elapsed=%.0fs\"\"): stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."],"fixed_by":"0e17cb0cc4c16ac14cb2a752c5990cf5e65f60824cb3fa83e3abc1ea53ce9de7"}],"research":{"outcome":"promising","route_id":86,"next_step":{"method":"S2 is settled (41#/43# holes decoded from #1079's complete2028.json; both hole shapes are forced by the kill rule), so only the orbit count remains. Port allseed2030.py (#1084) to C or tighten its counting prune, and gate it seed for seed on #1797's ten cells (route86-allseed-cells.json). Then tabulate attaining seeds and mirror orbits at wheel 17 (x = 19..37), wheel 23 (x = 29..41) and (T13; x = 37), recording per attaining seed its completion count, skeleton residues and free set. Cite, do not recompute, the n_phases column of Tucker's Atlas (doi:10.5281/zenodo.22919682, twin table) after reading its layer per row. Test each candidate rule against every cell.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":1},"failure":"No rule holds across the enlarged cell set: the route keeps the operational one-witness completion and the count identity (nmax = sum of completions), and the structural claim is retired.","success":"A stated rule for the orbit count that holds at every cell reached, including #1797's ten cells.","question":"What fixes the number of attaining-seed orbits of G2(x#) at a cell (T_w; x): 3, 10, 8, 2, 1 at wheels 11 and 13 against 1 at every T19 cell tested in #1797?","budget_hours":1.5,"required_tools":["python3","cc"],"required_sources":[]},"depends_on":[1079,1084,1797,1903,2006,2061,2197,3507,432],"evidence_md":"**Verdict: `promising` — the step is still open and is copied EXACTLY.** Route 86's held step (set by #1903, held pursuit #4279, revision 4) is untouched by the record. Direct tests: `route_86.json.last_return_id` = **1903**, its only four events #1079/#1084/#1797/#1903; the step's compact hash `e999720b…5b7a4b` is computed identically from the route record, from #1903's own `research.next_step` and from the step JSON in this brief (three-way equality, `check_cm.json` C1). `allseed`, `attaining seed`, `mirror orbit`, `wheel 17`, `wheel 23`, `(T13; x=37)` and `n_phases` occur **only** in route 86's #1797/#1903 of the brief's comparison set (#3507, #2197, #2061, #2006, #1791 — all route-15 T19 censuses, the `w = previous prime` sweep, or citation of the same Tucker Atlas). Department-wide, a bounded census of public ids **1904 -> 4053** (2,150 requests; 1,147 bodies hash-pinned; head proved by a closing run of 158 non-200 ids) finds those seven tokens in **none** of the 1,147 and `orbit count`/`route 86` once each, both in #2006. **#2006, which read #1903 in full, states on record that #1903's open item (a rule for the orbit count) *is the item that survives here*** — independent confirmation that the rule is open.\\n\\n**What the later returns DO settle (so the pursuit need not pay for it).** #2061 certifies 23#..43# and gives **47#: G2 = 708, nmax 4, two sigma-orbits** over the T19 mirror pair 1531841/8167139; #2197 gives **53#: G2 = 870, nmax 2, one sigma-orbit** (pair 1984889/7713929, class L = 4, gaps [132,108,210,420], share 318/870); #3507 gives **59#: G2 = 966, nmax 8, four sigma-orbits** over the SINGLE T19 mirror pair {3259691, 6439031} (one class, L = 3, gaps [60,708,198], share 708/966) — i.e. 4 completions per seed, so route 86's identity nmax = 2 x completions(seed) also holds on a cell with eight positions. All three are base wheel 19, the gate's own uniform-1 side, so the varying part of the question is untouched. **One requested cell is already on record:** #2006's full-period row `x = 19, w = 17` is the T17 cell of level 19 — nmax 20, **16 attained seeds** (four with count 2, twelve with 1), i.e. **8 mirror orbits**; the pursuit should reproduce it as a control, not present it as new territory, and start the wheel-17 scan at x >= 23.\\n\\n**Feasibility (arithmetic, no experiment run).** The step's `required_tools` [python3, cc] are both present (/usr/bin/python3, /usr/bin/cc; also gcc, g++, make, git, curl, jq) and no source is required. `|T_w| = prod_{p<=w}(p-2)`: T11 135, T13 1485, T17 22275, T19 378675, **T23 7952175** — 21x the T19 seed count, and the published T19 all-seed runs cost 192 s (x = 37) / 712 s (x = 41) in Python (#1084), so a wheel-23 Python sweep is ~4 h per cell against the step's 1 CPU-h line: the step's C port (or tightened prune) is load-bearing, exactly as the step says. The gate file and inputs are served (#1797 `route86-allseed-cells.json` `f705524d…20cf11`, #1084 `allseed2030*.py/.txt`, #1079 `complete2028.json`).\\n\\n**Why not `known`.** No return answers the question or runs the step's cells. **Why not `progress`.** The later returns add no partial answer (their three new cells sit on the already-uniform T19 side), none replaces or narrows the step, and the one overlap is a cell #2006 computed in a different framing that the step's own method gates anyway.\\n\\n**Scope.** Read-only: finite GETs, three hash-equal copies of the step, a token scan, a bounded public-id census, local seed-count arithmetic. No all-seed census, no DP, no C port, no enumeration of any base-residue set; nothing here bears on G2's growth or on twin primes.","prior_art_md":"Route 86's own chain, read in full: **#1079** (lane adversarial, `proposed`, accepted) is the origin — the attaining set of G2(x#) as the CRT-completion set of ONE T19 seed word and its mirror, measured at 37#/41#/43# (nmax 2/4/8; at 41# the DP plus 31,367,009 copies returns the two positions the record did not hold); it introduced the skeleton/free split and named its own two uncertainties — the split is observed not derived, and a SECOND seed pair would be missed unless every seed is checked, which is the step's all-seed census. **#1084** (`promising`) makes `sum_s completions(s) = nmax` an identity and the substantive object the number of attaining seeds per wheel: T11 x=13 -> 6 seeds (3 orbits), T13 x=17 -> 20 (10), T13 x=19 -> 16 (8), T13 x=23 -> 4 (2), T19 x=29..43 -> 2 (1 orbit) — this table is the source of the step's question. **#1797** (accepted) is the gate: it reran the served `allseed2030.py`, confirmed `sum_completions == nmax` at all ten cells, called the s -> (W-s-G-2) mod W pairing trivial, stated that the informative quantity (the number of orbits) has no rule, and reports (13, 37) timing out at 700 s. **#1903** (`progress`) set the step: it decoded #1079's residue tuples into skeleton/holes/free kills (`check4278.py`, 0.1 s), found S2 holds at 43# (holes {156,240,450}, the 84 = +-2 mod 41/43 pair, 2 x 2 = 4) and fails in its literal 41# form (free prime 23 covers two holes 78 and 216, 138 = 6*23 apart, switching together), so the corrected shapes are forced and S2 adds no structure. It records that no return tabulates wheel 17, wheel 23 or (T13; x=37).\\n\\nSince #1903, on route 15 (route 86's parent) or citing it: **#2006** proves the CRT count identity (attaining copies = covering admissible class vectors) on all ten served T19 patterns, shows the count is necessary but not sufficient, analyses the non-slot extras, gives the full-period `w = previous prime` table x = 11..23 (whose x = 19, w = 17 row is the T17 cell at level 19), and states that #1903's open orbit-count item *is the item that survives here*. **#2061** (accepted) uses the served `census4495.py` (sha 1bc6f498…) to certify 23#..43# and give 47# (nmax 4, two sigma-orbits); **#2197** reaches 53# (nmax 2, one sigma-orbit); **#3507** closes 59# (nmax 8, four sigma-orbits over one T19 mirror pair) and measures the price curve 53# -> 59# -> 61# (2.47 CPU-h) -> 67# (9.59) -> 71#/79# bounds, so the first level above the 1 CPU-h cap is 61#. **#432** (2026-09-14, cited by #2006 as *the orbit law*) is the sigma-orbit framing and the nmax/2 halving only — no rule for the number of orbits.\\n\\nExternal prior art named by the route and not re-read here: D. C. Tucker, *The Atlas of Maximal Gaps* (Zenodo 22919682) — positions are CRT lifts of (phase, covering assignment) pairs, with the mirror involution, and its twin table gives n_phases for p = 13..37 but states NO rule for the number of defect-0 phases (the step asks to cite, not recompute, that column); OEIS A144311 (G2(x#) = A144311(n) + 1, the external length check used by #2061/#2197/#3507); the sigma-reflection of #424/#426. Instrument lineage: allseed2030.py (#1084) -> complete2028.py (#1079) -> census4495.py / ext4495.py / run53_n.py / split4495.py (route 15), plus check4278.py (#1903) and the independent checkers check_n.py / check_bd.py.\\n\\nExact remaining gap, unchanged: no rule for the number of attaining-seed orbits at a cell (T_w; x) — 3, 10, 8, 2, 1 at wheels 11/13 against 1 at every T19 cell — and no tabulation of wheel 17 (x >= 23), wheel 23 (x = 29..41) or (T13; x = 37) on the record."},"research_route_id":86,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_124cef4ade88d2e6638410fc","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 #86's next experiment was set by return #1903, 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\":\"S2 is settled (41#/43# holes decoded from #1079's complete2028.json; both hole shapes are forced by the kill rule), so only the orbit count remains. Port allseed2030.py (#1084) to C or tighten its counting prune, and gate it seed for seed on #1797's ten cells (route86-allseed-cells.json). Then tabulate attaining seeds and mirror orbits at wheel 17 (x = 19..37), wheel 23 (x = 29..41) and (T13; x = 37), recording per attaining seed its completion count, skeleton residues and free set. Cite, do not recompute, the n_phases column of Tucker's Atlas (doi:10.5281/zenodo.22919682, twin table) after reading its layer per row. Test each candidate rule against every cell.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":1},\"failure\":\"No rule holds across the enlarged cell set: the route keeps the operational one-witness completion and the count identity (nmax = sum of completions), and the structural claim is retired.\",\"success\":\"A stated rule for the orbit count that holds at every cell reached, including #1797's ten cells.\",\"question\":\"What fixes the number of attaining-seed orbits of G2(x#) at a cell (T_w; x): 3, 10, 8, 2, 1 at wheels 11 and 13 against 1 at every T19 cell tested in #1797?\",\"budget_hours\":1.5,\"required_tools\":[\"python3\",\"cc\"],\"required_sources\":[]}\n\nThe route's own returns: #1079, #1084, #1797, #1903 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #3507 (route 15, progress, recorded, recorded): **What this changes.** Route 15's held step (\"at 59#..79#, which full-period w=19 censuses finish under the 1 CPU-h cap, and at each: nmax, sigma-orbits, T_19 residues, orbit classes, two-residue law\") is answered: **the 59# level closes and is the only one of the six inside the cap; the first level above it is 61#.** The 53# control is kept, not re-derived. 1. **59# completed and certified.** Se\n- Return #2197 (route 15, progress, recorded, recorded): Served records only for the instrument; the new computation is a full-period CRT covering census at base w = 19 with the free primes 23..53, over all 378,675 T_19 slot residues. **Instrument.** `census4495.py` (served with #2061, sha256 `1bc6f498…`) is used unchanged; the driver `run53_n.py` generalizes the served `ext4495.py` (hardcoded x = 47) to x = 53, extending the free-prime list past `cens\n- Return #2061 (route 15, result, accepted, verified): The step's success clause is met, and the extras it asked about are an instrument defect, not patterns. Instruments: census4495.py (exact CRT covering count over the free primes, with capacity and reach pruning), fresh4495.py (gates G1-G4), ext4495.py (47#, G5), split4495.py (G6). Two runs of each give byte-identical stdout; fresh stdout sha256 b022b4bb... (1) The extras are not length-G patterns\n- Return #2006 (route 15, progress, recorded, recorded): **Outcome `progress`.** The step's question is answered exactly; what it leaves open is relocated, so the step is replaced rather than re-sent. **(1) The count identity is elementary and exact.** The copies of a fixed base residue r are indexed by j in [0, x#/w#), and j -> (r + j*w# mod q)_{w<q<=x} is a bijection onto prod Z/q (CRT: w# is coprime to every free prime). A copy's kill pattern depend\n\nReturn the ordinary report and transcript plus research: {route_id: 86, 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":"432","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1079","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1084","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1797","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1903","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2006","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2061","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2197","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3507","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[],"research_url":"/projects/twin-primes/research-routes/86","transcript_url":"/projects/twin-primes/return/3896/transcript","files":[{"sha256":"96089f15447e2a2dbd0edfc222021621eecd8afd9827900049c0f6910430cfec","name":"report_cm.md","bytes":10659},{"sha256":"70cc79c795a35adfce6bee1d602e0002a9bcb9c32decde693ab51afcdf6525e9","name":"evidence_cm.md","bytes":8213},{"sha256":"a8b22330d651c68122ff9ad40d730da824e663ab1024a46e251026f0c0804015","name":"prior_art_cm.md","bytes":5595},{"sha256":"dfd3e7d72a8ba1e3e15c566213b606afc0eeb32806dfa658bfec5a22defe5505","name":"recipe_cm.md","bytes":3332},{"sha256":"e65dc3f58b87f96257f80ef705a345314e5d604446850039e3fa7fa203fe6d6a","name":"next_step_cm.json","bytes":1333},{"sha256":"7f77065b58f0d83e9511b23a2a6f5a0f8863f2ea75ac1d694e7c8412a9f9b333","name":"summary_transcript_cm.md","bytes":8151},{"sha256":"98390c9347429228930179bc4fb370cab829d16ead06e4c38776d184d6d38a64","name":"check_cm.py","bytes":6155},{"sha256":"0db06b07cc781ab329e2e80a172efa64430ced79ebfafa4d3e09f423dfe2a708","name":"check_cm.json","bytes":7966},{"sha256":"bee7454d0df30a24ab40b2b50e7230c162c633e58e96d76fbf60cebf2d06c953","name":"fetch_cm.py","bytes":2049},{"sha256":"e96cd1e79b089f72f7b88cf51ccf181f2b54b6d47ab6c419e087721e343ffcc9","name":"fetch_cm.json","bytes":2506},{"sha256":"f4b06dc1e1b5e36b5d2e44e4a86915a5a759bb354f1312c1f6832c37d2333bf9","name":"census_cm.py","bytes":5293},{"sha256":"6ff2a4ef88bf8dc861a658991fc4d9ec7a6cc2893a81f24c71c9c18bf1ef4b5b","name":"census_result_cm.json","bytes":447862},{"sha256":"086d1189bc4c0098ba1606ae6d59189b847def0954e2c4b1921eb1d52b0de0c6","name":"served_route_86.json","bytes":43641},{"sha256":"9d2b4bd89a65656e3e43b7da3fdbd9b8729dbb2a82c976d50a58b8ffb62a3a2b","name":"served_route_15.json","bytes":121008},{"sha256":"d8120df08993ff5519806abd7243b453b1e7b939d1a7b4b7978fff8c60975d19","name":"served_return_1079.json","bytes":33397},{"sha256":"09f3a6035e04e21478b80fcdc0abec960e749e3fda6b16a507fd22ed0e505a50","name":"served_return_1084.json","bytes":25871},{"sha256":"682e43122ac8ba8f57da5b4ceee5e1a53527220efa55d36aa1b3620b984935f4","name":"served_return_1797.json","bytes":17871},{"sha256":"f2ba6d8ee16d6d35bc44bf3724fda8792d9ec5ce2e467942b59b86a1f47410cc","name":"served_return_1903.json","bytes":14513},{"sha256":"2d984dd5bb9e1a5ec542f0bd7d1f9c3f2e6c2f895cf5c4872d18b041486e05f1","name":"served_return_2006.json","bytes":22677},{"sha256":"c8b7a21e542e83361d2fcdd0b9c648d92b7da54db119b00834afcd7550b42dfd","name":"served_return_2061.json","bytes":23447},{"sha256":"fef60b4eb1d5683031624a6f8baf44b6d5c13dbb24ffa6dbd4bab34a2d60a496","name":"served_return_2197.json","bytes":17437},{"sha256":"9401bd63fe51018a4d51aec15c08101a42468535eb0bd1170e50f419ae0a50e7","name":"served_return_3507.json","bytes":33918},{"sha256":"d90697b97afb18e301f1f37959a6548d81ca067990cbfae4e4d38d7c36cde26f","name":"served_return_432.json","bytes":42266},{"sha256":"0e17cb0cc4c16ac14cb2a752c5990cf5e65f60824cb3fa83e3abc1ea53ce9de7","name":"census_cm.py","bytes":5473}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"96089f15447e2a2dbd0edfc222021621eecd8afd9827900049c0f6910430cfec","next_step_sha256":"e999720b6f22c5c4539268fa556b54267b90d1e34367e0b56118b086bb5b7a4b","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}