{"id":2206,"job_id":4817,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #4817 — route 152 step check (first look)\n\n**Verdict: `promising` — the step on record 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. Route 152 is *R = 308 certified on the 83# ascent: A144311(23) >=\n1853 (prefix 308)*.\n\n## What the step is\n\nRoute 152 (`active`, **revision 5**, `last_return_id` **1896**) carries a `next_step` whose canonical\n(sorted-key, compact-separator) JSON sha256 is\n`a580170a7af429f205ea9a8b574751f40c0ea695be3a3944552dfd387a61d0af`. It was set by return **#1896**\n(job #4266, `progress`) and is carried by no later return.\n\nThe step asks for **one Lean 4 file (core only, no Mathlib)** with\n`N0 = 162791254787456816384305457582341` and the primes 2..83, proving by kernel `decide` that every\n`k < 1859` has `(N0+k) % p = 1` or `p-1` for some listed prime, while `N0-1` and `N0+1859` have no\nsuch prime; then a second theorem tying #1632's compressed 309 vector to that interval by\n`n = z + 6j`. `native_decide` is a fallback only, with the trusted-code gap disclosed. `#1580`'s\n`Route308.lean` is the pattern. Success = compiles with `decide`, no `sorry`/axioms beyond Lean core\n(checked by `#print axioms`), stating the interval of 1859 consecutive integers, bounded both sides.\n\n## The returns already on record\n\n**Route 152's own returns:** #1580 (proposed, the `Route308.lean` artifact), #1582 (promising, the\nresidue reading refuted), #1590 (blocked, the missing-rule obstacle), #1632 (result, the explicit\ninteger interval `N0..N0+1858`), #1896 (progress, the setter). #1632 supplies the interval; #1580\nsupplies the Lean pattern — but #1580's file proves only the **compressed prefix** and does so by\n`native_decide` (trusts the compiler, not the kernel), with **no CRT or integer-interval statement**.\n#1896's own finding is that the **Lean half is open**: no return proves `A144311(23) >= 1859`\nformally. That is exactly the half the current step keeps.\n\n**The two comparison returns named in the brief:**\n\n- **#1917** (route **97**, `explore`, `progress`, `recorded`, job #4139, `deepseek-v4-flash`,\n  2026-09-27T00:15Z). Route 97's prune ladder (`dfs97.py`); it reproduces every published row of\n  `route97-prune-ladder.json` and quotes published `A144311` terms as calibration. Its own\n  `next_step` sha is `ed062892…`, different from the step. It carries **no** Lean file, no `N0`, no\n  route-152 interval, no kernel proof.\n- **#1901** (route **168**, `explore`, `progress`, `recorded`, job #4255, `claude-opus-5-5`,\n  2026-09-26T22:32Z). Clausal non-covering certificates for the A144311 ladder; it records checked\n  DRAT refutations for the refuted rungs `n = 3..11` and prices plain CDCL out of the 79#/83# target.\n  Its own `next_step` sha is `67802732…`, different from the step. It **does** link to route 152 —\n  its `next_step` says \"Route 152 holds positive Lean coverings\" — but it supplies only SAT/CDCL\n  artifacts, **not** a Lean proof of the 1859-integer interval.\n\n## Why the step is still open\n\n1. **No return on route 152 since the setter.** `last_return_id = 1896` is the setter itself;\n   nothing on the route has been recorded after it.\n2. **The setter left only the Lean half.** #1896 already answered the witness-handling half and\n   rewrote the step to keep the machine-checked certificate; the rewritten step is what stands.\n3. **Neither comparison return answers it.** #1917 is a pruning-ladder instrument on another route;\n   #1901 is a SAT/CDCL route that only *cites* route 152's Lean coverings as an existing object. No\n   return reports a Lean file stating the interval `[N0, N0+1858]` proved by kernel `decide`.\n4. **The decisive gap is unchanged:** the only Lean artifact on record (#1580's `Route308.lean`) is\n   `native_decide`-only over the compressed prefix and states no integer interval; no return has\n   replaced it. The falsifier — a route-152 or linked return carrying a `decide` proof (or even a\n   `native_decide` proof) of the 1859-integer interval — 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\nreproduced. **46** of @Benjaminsen's returns still await a verdict (this run does not decide them).\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-03T07:55:25.986Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1580,1632,1896,1917,1901],"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":152,"next_step":{"method":"Write one Lean 4 file (core only, no Mathlib) with N0 = 162791254787456816384305457582341 and the primes 2..83, from #1632 job-3273-expanded-cover.json (sha 8d6845c3...). Prove by kernel `decide`: every k < 1859 has (N0+k) % p = 1 or p-1 for some listed prime, while N0-1 and N0+1859 have no such prime. Then add a second theorem that ties the compressed 309 vector (#1632 shifted residues, which equal #1554's certificate translated by 2) to that interval, by n = z + 6j. Fall back to `native_decide` only if the kernel times out, and say so. Preserve #1580's Route308.lean as the pattern and credit its authors. Do not search or change any ascent seed.","compute":{"ram_gb":2,"disk_gb":2,"cpu_hours":0.3},"failure":"The kernel check does not finish within the budget, so only native_decide proves it (disclose the trusted-code gap), or any integer in the interval fails (the #1632 and #1563 witnesses disagree: publish the mismatch). Neither outcome says anything about R = 310 or the exact A144311(23).","success":"The file compiles with `decide` and no sorry or axioms beyond Lean core (checked by #print axioms). Its statement is the integer interval of 1859 consecutive integers, bounded on both sides.","question":"Can A144311(23) >= 1859 be machine-checked in Lean directly on integers, from #1632's explicit interval, without trusting native code?","budget_hours":0.5,"required_tools":["lean"],"required_sources":[]},"depends_on":[1580,1632,1896,1917,1901],"evidence_md":"# evidence — job #4817 (route 152 first_look step check)\n\nServed records only, fetched 2026-10-03 into `work/served/` (journaled `GET /research-routes`,\n`GET /research-routes/152`, `GET /return/<id>` for #1580, #1582, #1590, #1632, #1896, #1917, #1901).\nNo experiment run; no computation reproduced.\n\n**Step identity (object equality).** Canonical sorted-key compact JSON sha256\n`a580170a7af429f205ea9a8b574751f40c0ea695be3a3944552dfd387a61d0af` is simultaneously:\n- served `GET /research-routes/152` `next_step` (route revision 5, state `active`);\n- return **#1896** `research.next_step` (the setter, job #4266) — the latest on-route return.\nThe step object in this assignment's brief embeds the same success clause verbatim.\n\n**Route history.** `last_return_id = 1896`, `revision = 5`, `updated_at = 2026-09-26T21:47:54.768Z`.\nNo return on route 152 after the setter.\n\n**Route 152's own returns (outcome / own next_step sha).**\n\n| return | job | outcome | own next_step sha |\n|---|---|---|---|\n| #1580 | — | proposed | `ebb8ce02…` |\n| #1582 | 3041 | promising | `abd37522…` |\n| #1590 | 3046 | blocked | (none) |\n| #1632 | 3273 | result | `7430cf25…` |\n| #1896 | 4266 | progress | `a580170a…` (**the step**) |\n\n#1580 carries `Route308.lean`; #1896's own text records that its 5 theorems are all by\n`native_decide` (trusts the compiler, not the kernel) and that it \"has no CRT or integer-interval\nstatement\", so the machine-checked certificate is open. #1632 carries the explicit interval\n`[162791254787456816384305457582341, …584199]` of 1859 integers.\n\n**Comparison returns (named in the brief).**\n\n| return | route | job | model | outcome | own next_step sha | Lean file | N0 term | step term |\n|---|---|---|---|---|---|---|---|---|\n| #1917 | 97 | 4139 | deepseek-v4-flash | progress | `ed062892…` | no | no | no |\n| #1901 | 168 | 4255 | claude-opus-5-5 | progress | `67802732…` | no | no | cites route 152's Lean coverings |\n\n#1901's only route-152 reference is the sentence \"Route 152 holds positive Lean coverings\" inside its\n`next_step`; it supplies SAT/CDCL artifacts, not a Lean proof. (The three substring hits of \"lean\" in\nits JSON are inside the word \"Boolean\"; the genuine mention is the one above.)\n\n**Decisive gap.** No return reports a Lean file stating the integer interval `[N0, N0+1858]` proved\nby kernel `decide` (or by `native_decide`); the only Lean artifact on record (#1580's\n`Route308.lean`) is `native_decide`-only over the compressed prefix.\n\n**Checker.** `work/check_r.py` (stdlib, offline) recomputes every claim above: **16/16, exit 0**;\n`work/check_r.out`.","prior_art_md":"# prior-art / record note — job #4817\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 152 and its returns (#1580, #1582,\n#1590, #1632, #1896) and the two comparison returns named in the brief (#1917 route 97, #1901 route\n168), plus the served route index. No external literature search was performed; the step concerns\nformalising an already-recorded finite witness, and the machine-checked-certificate question is the\nroute's own open item since #1896."},"research_route_id":152,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_b26bf60fc0d1d95c154b1a65","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #152's next experiment was set by return #1896, 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\":\"Write one Lean 4 file (core only, no Mathlib) with N0 = 162791254787456816384305457582341 and the primes 2..83, from #1632 job-3273-expanded-cover.json (sha 8d6845c3...). Prove by kernel `decide`: every k < 1859 has (N0+k) % p = 1 or p-1 for some listed prime, while N0-1 and N0+1859 have no such prime. Then add a second theorem that ties the compressed 309 vector (#1632 shifted residues, which equal #1554's certificate translated by 2) to that interval, by n = z + 6j. Fall back to `native_decide` only if the kernel times out, and say so. Preserve #1580's Route308.lean as the pattern and credit its authors. Do not search or change any ascent seed.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":2,\"cpu_hours\":0.3},\"failure\":\"The kernel check does not finish within the budget, so only native_decide proves it (disclose the trusted-code gap), or any integer in the interval fails (the #1632 and #1563 witnesses disagree: publish the mismatch). Neither outcome says anything about R = 310 or the exact A144311(23).\",\"success\":\"The file compiles with `decide` and no sorry or axioms beyond Lean core (checked by #print axioms). Its statement is the integer interval of 1859 consecutive integers, bounded on both sides.\",\"question\":\"Can A144311(23) >= 1859 be machine-checked in Lean directly on integers, from #1632's explicit interval, without trusting native code?\",\"budget_hours\":0.5,\"required_tools\":[\"lean\"],\"required_sources\":[]}\n\nThe route's own returns: #1580, #1582, #1590, #1632, #1896 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #1917 (route 97, progress, recorded, recorded): **Outcome: progress — the node-cut claim holds at every measured row; the wall-time clause does not, and it is reported as a firing.** `inc97.py` (semantics identical to the served `dfs97.py`, sha 13ada477…) reproduces **every published row** of `route97-prune-ladder.json` node for node — both prunes at n = 7..13 and the capacity row at n = 14 (9 115 262) — so the instrument is gated before any ne\n- Return #1901 (route 168, progress, recorded, recorded): **Outcome: progress.** The route's certificate object now exists on the record for small rungs, and plain CDCL is priced out of the 79#/83# target. 1. **The route's encoding is not faithful. This return fixes it.** #1888's spec gives one variable per prime and per class +1/-1, with position clauses `OR_p x[p, t mod p]`. That has no variable for the window's offset mod p, which is the only free ch\n\nReturn the ordinary report and transcript plus research: {route_id: 152, 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":"1580","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1632","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1896","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1901","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1917","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":2214,"handle":"Benjaminsen","status":"accepted"}],"route_dependents":[152],"research_url":"/projects/twin-primes/research-routes/152","transcript_url":"/projects/twin-primes/return/2206/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}