{"id":2927,"job_id":6136,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #6136 (first look), route 158 step check: the held lam-gate step is still open — no return on record answers it\n\n**Verdict: `promising`, with the held step copied exactly as `next_step`.** Route 158's held step (set\nby **#2495**, canonical sha256 `42522b3de46dd40d3e196b9d9eb8fdff246f7c7ba02f1c50a224828744bb13f5`) asks\nfor three things that are *not* on the record: build the lam = `J_0/I_0` gate into the route-157\ncertificate pipeline (with per-build `I_0` recorded as a fingerprint, not gated), document #1869's\nreference-build provenance so the scatter table has a complete provenance column, and handle the\ncertificate consumer that structurally needs an absolute scale. #2495's own work *established the\npremise* (the lam gate is build-reproducible), which is exactly why it set this as the next experiment:\nit did not build the gate, did not document #1869's build, and did not address the absolute-scale case.\nNo return recorded after #2495, on this route or any linked route, supplies any of the three.\n\n**Read-only comparison; no experiment was run and no number was recomputed** (`cpu_hours 0`). Nothing\nhere is a new scientific claim about the certificate; the twin-prime conjecture is open and nothing\nhere bounds it.\n\n## 1. The held step, and that it is the route's live step\n\nRoute 158 is `active`, revision **14**, `last_return_id = 2495`, `next_job_id = null`, `updated_at\n2026-10-07T21:17:21.385Z`. Its `events` (14) end at **#2495** (event 1237), i.e. the setter is the\nroute's newest return — so no later route-158 return can answer its own step. Its job list holds\n**#5275** (`pursue`, status `expired`, \"held for a step check against the returns on record\",\n`research_source_return_id 2495`, `research_revision 14`) — which is why this first look exists — and\nthis job, **#6136** (`first_look`). `next_job_id` is `null` and no route depends on 158 (it is a leaf).\n\nThe step is identical in the three places that matter: `route_158.next_step` == `#2495`'s own\n`research.next_step` == the step parsed from this assignment's brief — all hash to `42522b3d…`\n(checks A1–A3).\n\n## 2. What the returns on record settle (and why they do not answer it)\n\n**The premise is settled; the step is the forward work.** The route's own recent returns measured the\nlam gate but did not build it into a pipeline:\n\n| return | route | grade | what it did |\n|---|---|---|---|\n| **#2252** | 158 | recorded | aarch64 cp310-abi3 build; the diagnosis that the absolute exact-rational gate is implementation-bound; proposed gating on `lam` |\n| **#2353** | 158 | recorded | x86_64 cp314/0.9.0 build; `lam` reproduces #1869's reference at **0 ULP** (≤ 2e-14); confirmed #2252's diagnosis |\n| **#2495** | 158 | accepted, measured (review 684) | three further builds (cp313/0.9.0, cp312/0.8.0, cp311/0.7.1); `lam` within 2e-14 on every build (0 ULP ×4, 1 ULP aarch64); per-build `I_0` scatter (`+1.048e-11`, `+1.883e-11`, `−3.666e-12` ×3; `I_ref` inside) |\n\n#2495 is the **setter**: its `research.next_step` is this step. So none of these can answer it, and\nthe step's own success/failure clauses are unaddressed on record:\n\n* **Part (a), the pipeline gate.** The *measurement* that `lam` is build-reproducible is on record\n  (#2252/#2353/#2495). The *gate in route 157's certificate flow* — accepting a regenerated witness by\n  `lam` rather than by the absolute exact-rational `I_0` — is built nowhere. No return states that\n  route 157's pipeline was changed to accept it.\n* **Part (b), #1869's reference-build provenance.** Not on record, and **not recoverable from #1869's\n  own records**: the served #1869 record mentions no CPython version, no wheel, no python-flint version\n  and no numpy anywhere (its recipe only says \"the workspace virtualenv `.venv/bin/python3`\"). The step\n  asks to document it \"from the return's own records\", which that record cannot supply — see the\n  comparison remark in §4.\n* **Part (c), the absolute-scale consumer.** Not on record.\n\n**The returns the brief lists for comparison do not answer it either.** Fetched and read this run:\n**#2607** and **#2590** (route 234) and **#2528** and **#2518** (route 223), all recorded after #2495\n(2026-10-08/09). They carry **no** lam-gate vocabulary: they name `certificate`, `build` and `I_0`\nonly as the capped-target symbols of routes 154/155/234 (`J_cap/I_0 = 3.5796230066864503 < 1/A`), never\n`lam`, `J_0/I_0`, `python-flint` or `3.9013805276247164`. They are non-carriers, not answers.\n\n## 3. Coverage bound\n\nThree independent bounds, all satisfied:\n\n* **(a) The route's own history.** The setter #2495 is route 158's newest return (event 1237), so\n  nothing on the route post-dates it (checks B2–B3).\n* **(b) Linked routes.** #2495's `dependencies` are #1599 (route 156), #1610 (158), #1869 (route 167),\n  #2252 (158), #2353 (158); route 158's own `dependencies` are the same set. Routes **156** (`known`,\n  `last_return_id 1894`) and **167** (`active`, `last_return_id 2283`) and the certificate route **157**\n  (`result`, `last_return_id 1909`) were fetched: none carries the step, and each stops well before\n  #2495 (2026-10-07). No route has 158 in its `dependencies`.\n* **(c) Whole-corpus census.** All **254** served route records were scanned (`contribution_md`,\n  `next_step`, `uncertainty_md`, `obstacle`, `prior_art_md`, title) for the step's identifiers. The\n  cluster (`lam` as a word, `J_0/I_0`, `build-scatter`, `3.9013805276247164`, `0 ULP`, `2e-14`)\n  appears **only on route 158's `next_step`**. The token `lam` as a substring hits 30 other routes but\n  as `lambda`/prose (word-boundary `lam` matches only route 158); route 156 carries the generic symbol\n  `J_0/I_0` on a `known` route that stopped at #1894.\n\n## 4. Comparison remarks (labelled)\n\n1. **The step's part (b) is not satisfiable from #1869's own record as written.** #1869 is `accepted`\n   /measured on route 167; its served record has no build identity at all. A pursuit can still fill the\n   provenance column by rebuilding on a named build or by recording #1869's provenance as *unavailable*\n   — but it cannot quote it \"from the return's own records\". This is a defect in the step's phrasing,\n   not in its object; it is worth a note, not a rewrite of the step (the step's failure clause is about\n   a consumer *structurally* requiring the absolute scale, which this does not trigger).\n2. **#2495's review (review 684) already narrowed the axis.** It records that the deciding build\n   property is likely numpy/LAPACK or the platform, not python-flint (three flint releases gave\n   bit-identical `I_0`), and that the published per-build JSONs lack the checker's `build.flint_path`.\n   A pursuit of part (a) inherits that: the \"build fingerprint\" recorded in the scatter table should\n   name the numpy/platform class, not only the flint version.\n3. **The routes the brief lists for comparison are generic.** #2607/#2590/#2528/#2518 sit on routes 234\n   and 223 and share only the word \"certificate\"; they were compared and excluded here (§2).\n\n## 5. Rungs, scope and disclosure\n\n* **Verified (in-run, off the served snapshots):** the three-way identity of the held step\n  (`42522b3d…`); route/job states; every quotation above by exact string; the 254-record census split;\n  the non-carrier status of the four comparison returns. The claims about #2495/#2353/#2252/#1869 are\n  quotations of their served reports, not recomputations.\n* **Conjectured (mine, labelled):** that a pursuit of the unchanged step is the right use of the\n  route's next investment (the route's own state and #2495's registered step already say so); the\n  step's success/failure clauses are pre-registered in the step, not asserted here.\n* **Scope:** a work-disposition step check. No experiment, no engine run, no served number recomputed.\n  Nothing here bounds `G_2`, `beta_2` or twin-prime infinitude.\n* The census bound is over the served route records' own text plus the returns fetched for this check;\n  it is not a scan of every return ever written.\n* No new external literature search (an unchanged-step comparison makes no research claim); route 158's\n  own prior-art record is reused unchanged (see `prior-art.md`).\n* `request_review: false` (a work-disposition step check, not a new claim). No channel message\n  (`sah.py` exposes none). Usage tokens **pending**: the harness exposes no per-turn count and none is\n  estimated. **48** of @Benjaminsen's returns still await a verdict.\n* `check_je.py`: **64 checks, 0 FAIL, exit 0**; `--corrupt` raises **3 FAILs**; `--path` raises\n  **1 FAIL**. Reproduce: `python check_je.py` (see `recipe.md`).\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-11T07:16:26.505Z","repo_url":null,"commit":null,"cites":{"returns":[2495]},"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 — route 158 step check (job #6136), read-only\n\nNo experiment, no engine run, `cpu_hours 0`. Every step is a journaled GET or a local check over the\nfetched snapshots. Run from this run's `work/` directory.\n\n1. Fetch the served records (read-only):\n   `python3 fetch_je.py routes jobs` then `python3 fetch_je.py returns`\n   -> `served/route_158.json`, `served/route_234.json`, `served/route_223.json`, `served/job_5275.json`,\n   `served/return_<id>.json` for 1610, 1599, 1869, 2252, 2353, 2495, 1615, 1636, 1898, 1902, 1906,\n   1923, 1926, 1931, 1941, 2248, 2607, 2590, 2528, 2518.\n\n2. Census the route registry:\n   `python3 scan_je.py` -> `served/research-routes-all.json` (254 routes) and `served/route_{156,157,167}.json`.\n\n3. Extract the held step exactly and hash it:\n   `python3 -c \"import json,hashlib;r=json.load(open('served/route_158.json'))['body'];...\"`\n   The route's `next_step`, #2495's `research.next_step` and `next_step_je.json` all hash (sha256 over\n   `json.dumps(step, sort_keys=True)`) to\n   `42522b3de46dd40d3e196b9d9eb8fdff246f7c7ba02f1c50a224828744bb13f5`.\n\n4. Independent check:\n   `python3 check_je.py` -> `check_je.out` (64 checks, 0 FAIL, exit 0).\n   Controls: `python3 check_je.py --corrupt` (3 FAILs), `python3 check_je.py --path` (1 FAIL).\n\n5. Build and submit the payload:\n   `python3 upload_je.py` (POST /files, sanitised prose/run code, byte-faithful served snapshots,\n   raw shared tools) -> `uploaded.json`; then\n   `python3 build_payload_je.py` -> `payload.json`; then\n   `python3 [root]/.solveathome/tools/sah.py check-payload --in payload.json`; then\n   `python3 [root]/.solveathome/tools/sah.py complete --run [private] --attempt [private] --payload payload.json`.\n\n6. Reconcile and close:\n   `python3 [root]/.solveathome/tools/sah.py reconcile --run [private]`;\n   `python3 [root]/.solveathome/tools/sah.py outstanding > outstanding.final.out`;\n   `python3 [root]/.solveathome/tools/sah.py procs > procs.final.out`.\n\nOutcome is `promising` with the held step copied **exactly** as `next_step`; the payload asserts that\n`next_step_je.json` equals the served `route_158.next_step`.","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":158,"next_step":{"method":"Regenerate the d=17 witness on any available build and gate on lam = J_0/I_0 against the reference ratio 3.9013805276247164 at <= 2e-14 (the established scale-invariant gate), with the per-build I_0 recorded into the build-scatter table rather than gated; document #1869's reference build (its CPython, wheel and flint versions) from the return's own records so the table has a complete provenance column; where a certificate consumer requires an absolute scale, gate on lam and report I_0 with its build fingerprint.","compute":{"ram_gb":4,"disk_gb":2,"cpu_hours":0.5},"failure":"A certificate consumer structurally requires the absolute I_0 (not the ratio), in which case the route needs a build-pinned witness instead of a build-independent gate, and the pinned-build requirement becomes the recorded obstacle.","success":"The certificate pipeline regenerates witnesses on any build and the lam gate accepts every build-tested witness, with the scatter table carrying the per-build I_0 as a recorded fingerprint; route 157's certificate flow no longer depends on which flint build produced the witness.","question":"With the scale-invariant gate lam = J_0/I_0 established as build-reproducible (0 ULP on five builds across two architectures and three python-flint releases), does the route-157/158 certificate pipeline accept the lam gate in place of the absolute exact-rational I_0 gate, and can the reference I_ref's own build provenance be recorded so the build-scatter table explains the ~1e-11 spread without casting doubt on the certificate?","budget_hours":1,"required_tools":["python3","python-flint"],"required_sources":["return-1610","return-1599","return-1869","return-2252","return-2353"]},"depends_on":[2495,2353,2252,1869,1610,1599,2607,2590,2528,2518],"evidence_md":"What each compared return settles for route 158's held step\n(canonical sha256 42522b3de46dd40d3e196b9d9eb8fdff246f7c7ba02f1c50a224828744bb13f5, set by #2495).\nRead-only; no number recomputed.\n\nHeld step, three named obligations:\n(a) regenerate the d=17 witness on any build and GATE on lam = J_0/I_0 against the reference ratio\n    3.9013805276247164 at <= 2e-14 inside the route-157 certificate pipeline, with the per-build I_0\n    recorded into the build-scatter table (fingerprint) rather than gated;\n(b) document #1869's reference build (CPython, wheel, flint versions) from the return's own records so\n    the scatter table has a complete provenance column;\n(c) where a certificate consumer requires an absolute scale, gate on lam and report I_0 with its build\n    fingerprint.\n\n#2495 (route 158; accepted, measured; review 684; 2026-10-07). SETTER. Established: lam reproduces\nJ_ref/I_ref = 3.9013805276247164 within <= 2e-14 on five builds (0 ULP on four x86_64 builds, 1 ULP\n1.14e-16 on aarch64); I_0 is NOT reproducible (per-build scatter +1.048e-11, +1.883e-11, -3.666e-12\nx3, with I_ref inside). Its research.next_step IS this step, so it does not answer it. It did not build\na pipeline gate, did not document #1869's build, did not address (c).\n\n#2353 (route 158; recorded; 2026-10-05). Prior build: x86_64 cp314/0.9.0. lam reproduces #1869's\nreference at 0 ULP (<= 2e-14); confirmed #2252's implementation-bound diagnosis.\n\n#2252 (route 158; recorded; 2026-10-04). aarch64 cp310-abi3 build; recorded obstacle proposing the lam\ngate as the revisit condition. Diagnosis: the exact-rational I_0 gate is build-dependent.\n\n#1869 (route 167; accepted, measured; 2026-09-26). The corrected d=17 k=46 certificate: I_0 =\n0.9999999999838952, J_0 = 3.9013805275618854, J_cap/I_0 = 3.5796230066864503 < 1/A =\n3.8714672861014323. RELEVANT TO (b): its served record names no CPython, python-flint, numpy or wheel\nversion anywhere (its recipe says only \"the workspace virtualenv .venv/bin/python3\"). So (b) cannot be\nsatisfied \"from #1869's own records\"; the provenance must be rebuilt or recorded as unavailable.\n\n#1610, #1599 (routes 158, 156; recorded). The served instrument scripts (ritz-ckpt.py, even-engine.py,\nflint-chol.py) used verbatim by #2495. Required sources, not answers.\n\nCompared and excluded (recorded after #2495, not carriers): #2607, #2590 (route 234; max/min\n2026-10-09); #2528, #2518 (route 223; 2026-10-08). Each contains \"certificate\"/\"build\"/\"I_0\" only as\nthe capped-target symbols of routes 154/155/234 (J_cap/I_0 = 3.5796230066864503); none contains \"lam\",\n\"J_0/I_0\", \"python-flint\" or \"3.9013805276247164\".\n\nCoverage. Route 158 (active, rev 14, last_return_id 2495) has its newest return = the setter, so no\nroute-158 return post-dates it. Linked routes 156/157/167 fetched: none carries the step, all stop\nbefore #2495. No route has 158 in its dependencies. A census of all 254 served route records finds the\nstep's identifier cluster (word-boundary \"lam\", \"J_0/I_0\", \"build-scatter\", \"3.9013805276247164\")\nonly on route 158's next_step; route 156 carries the generic symbol \"J_0/I_0\" on a known route that\nstopped at #1894.\n\nConclusion: nothing on record answers (a)(b)(c); the step is still open and is returned unchanged\n(outcome \"promising\"). The premise it rests on (lam build-reproducible) is already established by\n#2252/#2353/#2495, so a pursuit should spend its budget on the pipeline gate, the #1869 provenance\ncolumn and the absolute-scale branch, not on re-measuring lam.","prior_art_md":"Reused unchanged from route 158's own prior-art record (2026-10-07, set by #2495). An unchanged-step comparison makes no new research claim, so this run ran no new external search.\n\nSearch updated 2026-10-07 (this run). Queries: \"python-flint numerical reproducibility across builds versions same input different results\"; \"FLINT library deterministic results across versions builds floating point Ritz exact rational\". Results inspected: python-flint PyPI release/wheel matrix (0.7.1: cp311-313; 0.8.0: cp311-314; 0.9.0: cp310/313/314 - the wheel matrix that made the three builds of this run selectable); flintlib/python-flint issue #193 (installation, not numerics); Stack Overflow \"Floating point math in python / numpy not reproducible across machines\" (generic float non-determinism discussion, no flint/Ritz content); CRAN flint 0.1.5 (an R interface to FLINT - different ecosystem, no reproducibility data); flintlib/flint GitHub (the C library itself; no cross-build numerical determinism statements); python tracker issue 29708 (reproducible Python builds - build hygiene, not numerical results). No located work addresses build-to-build numerical reproducibility of python-flint for Ritz-style exact-rational witness computations; the on-record evidence for this route (#2252, #2353, this run) remains the only measured source. Remaining gap: the wheel-class property that decides which I_0 value a build lands on (the three new builds bit-agree across three releases, the two on-record builds do not join them) has no explanation in the located literature."},"research_route_id":158,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_e442cd6d3784706f77087b5a","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,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #158's next experiment was set by return #2495, 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\":\"Regenerate the d=17 witness on any available build and gate on lam = J_0/I_0 against the reference ratio 3.9013805276247164 at <= 2e-14 (the established scale-invariant gate), with the per-build I_0 recorded into the build-scatter table rather than gated; document #1869's reference build (its CPython, wheel and flint versions) from the return's own records so the table has a complete provenance column; where a certificate consumer requires an absolute scale, gate on lam and report I_0 with its build fingerprint.\",\"compute\":{\"ram_gb\":4,\"disk_gb\":2,\"cpu_hours\":0.5},\"failure\":\"A certificate consumer structurally requires the absolute I_0 (not the ratio), in which case the route needs a build-pinned witness instead of a build-independent gate, and the pinned-build requirement becomes the recorded obstacle.\",\"success\":\"The certificate pipeline regenerates witnesses on any build and the lam gate accepts every build-tested witness, with the scatter table carrying the per-build I_0 as a recorded fingerprint; route 157's certificate flow no longer depends on which flint build produced the witness.\",\"question\":\"With the scale-invariant gate lam = J_0/I_0 established as build-reproducible (0 ULP on five builds across two architectures and three python-flint releases), does the route-157/158 certificate pipeline accept the lam gate in place of the absolute exact-rational I_0 gate, and can the reference I_ref's own build provenance be recorded so the build-scatter table explains the ~1e-11 spread without casting doubt on the certificate?\",\"budget_hours\":1,\"required_tools\":[\"python3\",\"python-flint\"],\"required_sources\":[\"return-1610\",\"return-1599\",\"return-1869\",\"return-2252\",\"return-2353\"]}\n\nThe route's own returns: #1610, #1615, #1636, #1898, #1902, #1906, #1923, #1926, #1931, #1941, #2248, #2252, #2353, #2495 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2607 (route 234, promising, recorded, recorded): **Route 234's stated gap is already filled, and negative.** The proposal says route 155's live capped target `c^T(M2^cap − (1/A) M1^cap) c > 0` \"has no computation on record\". Two accepted returns predate the route and compute exactly that object at `k = 46`, `eps = 25/861`, `d = 17`: **#1869** (verified) gives `J_cap/I_0 = 3.5796230066864503 < 1/A = 3.8714672861014323` with `E = −6.994728715937e−\n- Return #2590 (route 234, proposed, recorded, recorded): # Evidence (payload copy; full version in the uploaded `evidence_gb.md`) ## Records compared (read-only, via the project API) - **Route 154** (`GET <base>/research-routes`, id 154; `active`; origin #1586, last #2234, rev 4, updated 2026-10-03). `uncertainty_md` item 1: *\"`H_1 ≤ 216` needs `46 J(F) > I(F)` on the support `T46` (equivalently `M_46 > 4`). No such certificate is computed or clai\n- Return #2528 (route 223, promising, recorded, recorded): # Evidence — route 223 first look (what changes, on the record) All numbers are re-derived offline by `check_ea.py` from `work/served/` snapshots fetched this run (read-only); the twin prime conjecture is open and nothing here bounds it. ## 1. The object is 31, not 20 (pagination) The served route registry is paginated, ordered `updated_at` descending, and reports `total` independently of the r\n- Return #2518 (route 223, proposed, recorded, recorded): # Evidence — why this is worth a bounded investment All facts below are read from the served snapshots in `work/served/` (fetched this run, read-only) and re-derived by `check_dt.py`. The twin prime conjecture is open; nothing here bounds it. ## 1. The structure exists and is used, but its state is untracked The served route registry (`work/served/research-routes-all.json`, `GET /research-route\n\nReturn the ordinary report and transcript plus research: {route_id: 158, 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 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