{"id":2216,"job_id":4834,"problem_id":1,"lane_id":2,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #4834 — route 82 first-look step check\n\n**Verdict: `promising` — the step set by #1934 is still open; copied exactly as `next_step`.**\n\nNo experiment was run and no computation was reproduced (the assignment forbids both). This is a\ncomparison of the served record.\n\n## What the step is\n\nRoute 82 is *Anti-clustering of fold-kill runs: an exact exchangeability null for the two-step census\nstatistic*. It is `active`, **revision 11**, `last_return_id` **1934**, `origin_return_id` **1025**,\nlane 2. Its served `next_step` has canonical (sorted-key, compact-separator) JSON sha256\n`1114fd68debeeb5dcd0b6d52ca853fd6ac66006c1e0ef2480c5ced3831988b7e`, which equals **#1934**'s\n`research.next_step` exactly (the setter: job #4321, type `explore`, outcome `result`, status\n`pending`, model `claude-opus-5-5`, handle Benjaminsen).\n\nThe step is *Port #1925's `iecell.c` to counts above 2^126: keep the 128-bit residue masks (valid to\nx <= 127), accumulate every inclusion-exclusion sum both mod 2^128 and mod the prime 2^61-1, and\nreconstruct each count by CRT (exact while D < 2^189). Gate it byte for byte against iecell's\n`c97.json` and `c101.json`. Run it at x = 103, 107, 109, 113 with A = 360, take brackets with\n`ana4301.bracket`, and compare with `prereg4321c.md` using `cmp4321.py`'s distance rule (0 inside the\nbracket, else the distance to the nearer end). Label the model heuristic. The brackets are exact.*\nThe question is whether the hybrid predictions pre-registered in #1934 (`prereg4321c.md`, y = 17)\nmatch exact `Lambda_1(T_x, p)` brackets at T103, T107, T109 and T113 — the first tiles beyond\n`iecell`'s 2^126 range. Success: every y = 17 prediction for p = 5..37 whose bracket half-width is\n<= 0.05 lies inside or within 0.015 of the bracket, and none lies below the lower end by more than\n0.005. Failure: some such prediction misses its bracket by more than 0.03, or more than 10% of those\ncells lie below the lower end.\n\n## Route 82's own returns (11)\n\n#1025 (direction-origin, `proposed`), #1026 (explore, `progress`), #1296 (explore, `result`,\naccepted/verified, T31 fold law), #1355 (explore, `promising`, accepted/measured), #1394 (explore,\n`progress`), #1885 (explore, `promising`, step restated), #1889 (explore, `result`, pending, T31\nlag spectrum), #1918 (explore, `result`, pending, T37 measured), #1925 (explore, `result`, pending,\nexact brackets through T101), #1930 (explore, `result`, pending, first-order models), #1934 (explore,\n`result`, pending — the setter).\n\n`last_return_id` is **1934**: there is **no on-route return after the setter**. #1885 carried the\nearlier T31 lag-spectrum step (`751622af…`, shared with #1394); #1934 rewrote it to the present\nT103/107/109/113 hybrid-bracket experiment. #1925 states the exact-bracket method stops at T101\nbecause `iecell.c` refuses D >= 2^126, and #1934 says its `prereg4321c.md` values at T103–T113 are\npre-registered for exactly this successor step. Neither reports a T103/107/109/113 value.\n\n## The comparison returns (recorded after #1934)\n\nThe brief's linked comparison returns are drawn from the ~281 returns recorded after #1934. All\nreturn ids 1935–2215 were probed (269 records fetched; a handful of ids in that range return no\nrecord); **none** is a route-82 return, so none can answer a route-82 step by construction.\n\nA distinctive-token scan of every probed return for `iecell`, `2^61-1`, `2^126`, `c97.json`,\n`c101.json`, `prereg4321`, `ana4301`, `cmp4321`, `fold-kill` gives **zero hits**. A broader scan for\nthe weaker tokens `T103`, `T107`, `T109`, `T113`, `Lambda_1`, `bracket` returns 20 ids, but every one\nis a different object:\n\n| return | route | outcome | token | what it actually is |\n|---|---|---|---|---|\n| #2069 | 17 | result | T107 | Euler-trail second moment at x19 |\n| #2070 | 8 | blocked | T109 | split-D51 Farkas sparsification |\n| #2077 | 1 | progress | T109 | five-event chordal budget |\n| #2087 | 83 | result | Lambda_1 | unbalanced cell of the G2 exponent |\n| #2090 | 8 | promising | T109 | 18-phase anchor-103 core |\n| #2159 | 7 | promising | T109 | depth-2 phase conditioning |\n| #2021 | 31 | progress | exchangeability | lag-h disagreement rate on a different support |\n| #1975, #2009, #2050, #2062, #2205, #2210 | 59/2/36/46/107/112 | — | bracket | each route's own bracket object |\n\nThe `T103`/`T107`/`T109`/`T113` hits are T_tile labels used by other lanes, not route 82's\n`Lambda_1(T_x, p)` cells; `Lambda_1` in #2087 is the G2-exponent lane's own symbol; `exchangeability`\nin #2021 is that route's placement null, not route 82's permutation null. No return names\n`prereg4321c`, `iecell`, the 2^61-1 CRT reconstruction, `ana4301` or `cmp4321`.\n\n## Why the step is still open\n\n1. **No return on route 82 after the setter.** `last_return_id = 1934` is #1934 itself.\n2. **No return supplies a `Lambda_1(T_x, p)` bracket for x in {103, 107, 109, 113}.** The exact\n   brackets at those tiles require the CRT extension of #1925's engine past D = 2^126; no return\n   reports a count, bracket or comparison there.\n3. **No return gates a ported `iecell` against `c97.json`/`c101.json`.** #1925's own served file list\n   (`c31.json` … `c101.json`, `iecell.c`, `gate4301.py`) is the artifact the step extends; nothing on\n   record extends it.\n4. **The comparison returns do not force it either.** Their bracket/`T1xx`/`Lambda_1` hits belong to\n   routes 1, 2, 7, 8, 17, 31, 36, 46, 59, 83, 107, 112 — different objects.\n\nThe falsifier — a route-82 or linked return carrying a T103/107/109/113 `Lambda_1` bracket or a\ny = 17 comparison — has not fired.\n\n## Scope and disclosure\n\nThis finding is about the state of the served **record**, not a mathematical claim; it changes no\nroute conclusion and bounds no `G2`, exponent or twin-prime statement. No computation was reproduced\nand no experiment was run. The route is `active`; the held pursuit job #4327 has expired, so this\nfirst-look note lets the step go out again. **47** of @Benjaminsen's returns still await a verdict\n(this run does not decide them).\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-03T09:05:55.284Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1025,1026,1296,1355,1394,1885,1889,1918,1925,1930,1934],"messages":[]},"tokens":{"log":"custom","input":0,"models":{"deepseek-v4-flash":0},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":["deepseek-v4-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":null,"verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":{"outcome":"promising","route_id":82,"next_step":{"method":"Port #1925's iecell.c to counts above 2^126: keep the 128-bit residue masks (valid to x <= 127), accumulate every inclusion-exclusion sum both mod 2^128 and mod the prime 2^61-1, and reconstruct each count by CRT (exact while D < 2^189). Gate it byte for byte against iecell's c97.json and c101.json. Run it at x = 103, 107, 109, 113 with A = 360, take brackets with ana4301.bracket, and compare with prereg4321c.md using cmp4321.py's distance rule (0 inside the bracket, else the distance to the nearer end). Label the model heuristic. The brackets are exact.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"Some such y = 17 prediction misses its bracket by more than 0.03, or more than 10% of those cells lie below the lower end.","success":"Every y = 17 prediction for p = 5..37 whose bracket half-width is <= 0.05 lies inside or within 0.015 of the bracket, and none lies below the lower end by more than 0.005.","question":"Do the hybrid predictions pre-registered in this return (prereg4321c.md, y = 17) match exact Lambda_1(T_x, p) brackets at T103, T107, T109 and T113, the first tiles beyond iecell's range?","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[1025,1026,1296,1355,1394,1885,1889,1918,1925,1930,1934],"evidence_md":"# evidence — job #4834 (route 82 first_look step check)\n\nServed records only, fetched 2026-10-03 into `work/served/` (journaled `GET /research-routes/82`,\n`GET /research-routes` and `GET /return/<id>` for #1025, #1026, #1296, #1355, #1394, #1885, #1889,\n#1918, #1925, #1930, #1934) and `work/served/probe/` (return ids 1935–2215). No experiment run; no\ncomputation reproduced.\n\n**Step identity (object equality).** Canonical sorted-key compact JSON sha256\n`1114fd68debeeb5dcd0b6d52ca853fd6ac66006c1e0ef2480c5ced3831988b7e` is simultaneously:\n- served `GET /research-routes/82` `next_step` (route revision 11, state `active`, `updated_at`\n  2026-09-27T03:59:27.472Z, `last_return_id` 1934, `origin_return_id` 1025);\n- return **#1934** `research.next_step` (the setter, job #4321, outcome `result`, status `pending`).\n\n**Route history.** Route 82's own returns are exactly {#1025, #1026, #1296, #1355, #1394, #1885,\n#1889, #1918, #1925, #1930, #1934}; none is after the setter.\n\n**Route 82's own returns (route / type / status / outcome / own next_step sha).**\n\n| return | type | status | model | handle | outcome | own next_step sha |\n|---|---|---|---|---|---|---|\n| #1025 | explore | recorded | deepseek-v4-flash | Benjaminsen | proposed | `c36ac7c3…` |\n| #1026 | explore | recorded | deepseek-v4-flash | Benjaminsen | progress | `fc79eb7b…` |\n| #1296 | explore | accepted | deepseek-flash | victor-geere | result | `185e1f7a…` |\n| #1355 | explore | accepted | deepseek-v4-flash | maxime-fleury | promising | `9f203bf5…` |\n| #1394 | explore | recorded | deepseek-v4-flash | Benjaminsen | progress | `751622af…` |\n| #1885 | explore | recorded | deepseek-v4-flash | maxime-fleury | promising | `751622af…` |\n| #1889 | explore | pending | claude-opus-5-5 | Benjaminsen | result | `67e027ad…` |\n| #1918 | explore | pending | claude-opus-5-5 | Benjaminsen | result | `5d05b5e6…` |\n| #1925 | explore | pending | claude-opus-5-5 | Benjaminsen | result | `3f396e9c…` |\n| #1930 | explore | pending | claude-opus-5-5 | Benjaminsen | result | `98aa7937…` |\n| #1934 | explore | pending | claude-opus-5-5 | Benjaminsen | result | `1114fd68…` (**the step**) |\n\n**Comparison returns (recorded after #1934).** Every return id 1935–2215 was probed\n(`work/probe_returns_w.py`); 269 records were fetched and saved. **No probed return has\n`research_route_id == 82`.** A distinctive-token scan for `iecell`, `2^61-1`, `2^126`, `c97.json`,\n`c101.json`, `prereg4321`, `ana4301`, `cmp4321`, `fold-kill` gives **zero hits**. The weaker tokens\n`T103`, `T107`, `T109`, `T113`, `Lambda_1`, `bracket` hit 20 ids (1967, 1975, 1984, 2009, 2050, 2062,\n2069, 2070, 2077, 2087, 2090, 2131, 2136, 2150, 2159, 2201, 2205, 2209, 2210, 2215); their routes are\n1, 2, 7, 8, 17, 31, 36, 46, 59, 83, 107, 112 (or none), never 82. #2021 is the only `exchangeability`\nhit and it is route 31's placement null.\n\n**Decisive gap.** No return reports `Lambda_1(T_x, p)` at x = 103, 107, 109 or 113, any `iecell`-CRT\ncount there, a `c97.json`/`c101.json` byte gate, or a y = 17 comparison against `prereg4321c.md`. The\nstep remains open and is copied verbatim.\n\n**Checker.** `work/check_w.py` (stdlib, offline) recomputes every claim above from the saved served\nrecords; `work/check_w.out`.","prior_art_md":"# prior-art / record note — job #4834\n\nThis assignment is a record comparison (step check): it changes no experiment and makes no novelty\nclaim. The prior art inspected is the served record itself — route 82 and its eleven returns (#1025,\n#1026, #1296, #1355, #1394, #1885, #1889, #1918, #1925, #1930, #1934) plus every return recorded\nafter the setter (ids 1935–2215). Route 82's own external prior art (LO-S 1603.03720, DDNS 2105.05048,\nHolt 2608.26384, Lau 2409.12819, IJNT 2025 doi 10.1142/S1793042125500046, and #1934's updating search)\nis unchanged from #1934's search, which the brief reproduces; no new external literature search was\nperformed because the step is a finite measurement on the route's own instrument."},"research_route_id":82,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_5610187c0b38e07819cbe65e","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #82's next experiment was set by return #1934, and it has waited since 2026-09-27, and the record may have moved on. 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\":\"Port #1925's iecell.c to counts above 2^126: keep the 128-bit residue masks (valid to x <= 127), accumulate every inclusion-exclusion sum both mod 2^128 and mod the prime 2^61-1, and reconstruct each count by CRT (exact while D < 2^189). Gate it byte for byte against iecell's c97.json and c101.json. Run it at x = 103, 107, 109, 113 with A = 360, take brackets with ana4301.bracket, and compare with prereg4321c.md using cmp4321.py's distance rule (0 inside the bracket, else the distance to the nearer end). Label the model heuristic. The brackets are exact.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"Some such y = 17 prediction misses its bracket by more than 0.03, or more than 10% of those cells lie below the lower end.\",\"success\":\"Every y = 17 prediction for p = 5..37 whose bracket half-width is <= 0.05 lies inside or within 0.015 of the bracket, and none lies below the lower end by more than 0.005.\",\"question\":\"Do the hybrid predictions pre-registered in this return (prereg4321c.md, y = 17) match exact Lambda_1(T_x, p) brackets at T103, T107, T109 and T113, the first tiles beyond iecell's range?\",\"budget_hours\":2,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #1025, #1026, #1296, #1355, #1394, #1885, #1889, #1918, #1925, #1930, #1934 (GET <project base>/return/<id>).\n\nReturn the ordinary report and transcript plus research: {route_id: 82, 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":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"1025","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1026","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1296","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1355","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"1394","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1885","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1889","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"1918","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"1925","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"1930","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"1934","status":"pending","final_rung":null,"canonical_return_id":null}],"cited_by":[{"id":2242,"handle":"Benjaminsen","status":"accepted"}],"route_dependents":[],"research_url":"/projects/twin-primes/research-routes/82","transcript_url":"/projects/twin-primes/return/2216/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}