{"id":4170,"job_id":8542,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Report — job #8542 (explore, first look, route 291, lane `dir-558`): the two-anchor pricing rule, priced on the record\n\n**Outcome: `promising`.** Route 291's declared first look was executed on the served artifacts with no\nproducer re-run: the exact `d = 27` even-signature engine was rebuilt from the stored witness vectors and\nthe quadratic form was evaluated on the witness support block at both anchors. Every control passes\n(the served exact `I`, `J`, `Q_source`, `Q_standard` strings are reproduced exactly, and the served\n1024-bit Ritz values `eig_hp` are reproduced at their quoted digits).\n\n## 1. Headline\n\n**The register's metric is one scalar and one comparison.** With `M := J / I = c^T M2 c / c^T M1 c`\n(the engine's `M2` already carries the factor `k = 46`) the form is `Q_tau = I·(M − tau)` for **every**\nwitness, so nothing about a certificate is anchor-dependent except the position of the single tau-free\nscalar `M` relative to the anchors. Exactly:\n\n- `M > 1/A` ⇒ certifies at the source anchor; `M > 4` ⇒ certifies at the standard anchor;\n- the verdict is **convention-borne** (passes one anchor, fails the other) ⇔ `1/A < M < 4`;\n- `|Q_4| / Q_{1/A} > 1` ⇔ `M < (4 + 1/A)/2 = 10166/2583 = 3.935733643050716…`, the **anchors' midpoint**;\n- and identically `(4 − 1/A)·I = Q_{1/A} + |Q_4|`, i.e. `(gap/margin) = 1 + |Q_4|/Q_{1/A}`.\n\nMeasured exactly on the two served `d = 27` certificates (the record's own decisive scalars), with the\nserved rows as the control:\n\n| `eps` | `M = J/I` | margin `M − 1/A` | excess `4 − M` | `​|Q_4|/Q_{1/A}` | position |\n|---|---|---|---|---|---|\n| `25/861` (source rescaling) | 3.92021547305991 | +0.0487481869584776 | 0.07978452694008996 | **1.6366665** | inside `(1/A, 4)`, below the midpoint |\n| `79/1250` (recorded enlargement) | 3.9066362953689966 | +0.03516900926756421 | 0.09336370463100335 | **2.6547152** | inside `(1/A, 4)`, below the midpoint |\n\n`Q_{1/A} = +4.874818695369e-02 / +3.516900926679e-02` and\n`Q_4 = −7.978452693226e-02 / −9.336370462895e-02` — the served #2577 values, independently reproduced.\nSo the route's premise holds on its own object: the sign of both certificates is carried by the anchor,\nand the ratio exceeds 1 for both rows.\n\n## 2. New: the capped track is priced, and its one served row is anchor-robust\n\nRoute 291's contribution named the project's own open obligation — the capped-support certificate\n`M^{cap} > 1/A` — as the place where the convention had not been priced at all. That obligation is not\nempty on the record: **#1942** (accepted, final rung `measured`) builds the capped Gram pair\n`M2^cap = M2 + k·E_sym`, `M1^cap = M1 − Delta_sym` at `k = 46`, `eps = 25/861`, `d = 17` and re-optimises\nthe witness there, reporting `J_cap/I_cap = 3.8115713687001214` with `Q = −1.9296200187e-95` and the\nverdict `DOES NOT CERTIFY`.\n\nPriced by the rule above, that row is **outside the window and below both anchors**:\n`3.8115713687001214 < 1/A = 3.8714672861014323 < 10166/2583 < 4`. Its verdict is therefore\n**anchor-independent** (it fails at both), the first decisive scalar examined here that is not\nconvention-borne. Its deficit to the window floor is `0.059896` — about 4 × 10^4 times the row's\n7-significant-digit resolution, so the classification does not depend on the quoted precision (the three\nquoted numbers are mutually consistent to that precision: `J/I`, `J − (1/A) I` reproduce the quoted\nvalues).\n\nConsequences for the obligation, stated exactly rather than as prose:\n\n- Any capped witness with `M^{cap} ≤ 1/A` fails at both anchors (the #1942 situation);\n- any capped witness with `1/A < M^{cap} < 10166/2583` **passes at `1/A` and fails at `4`, and its margin\n is dominated by the convention** (ratio > 1) — this is the regime route 291 exists to price;\n- only `M^{cap} ≥ 4` is convention-free, and then the same witness also settles the standard anchor. So the\n cap obligation's own entry fee is the gap `4 − 1/A = 332/2583 = 0.128533` measured in `M` units, and the\n register's demand is that any capped certificate be quoted as `M^{cap}` with its distances to `1/A`, the\n midpoint and `4` — never as \"the sign passed\".\n\nThe experiment therefore **does not** build a capped witness: no cap optimum was recomputed here, and the\nserved support block is the witness-support truncation of the *uncapped* Gram pair (independently\nre-confirmed: the support-block and full-assembly certificates carry the same witness and equal exact\n`I`, `J`, `Q`). What is new is that the cap track's one existing number is classified, and the whole cap\nobligation has a price in the same units as the uncapped verdicts.\n\n## 3. The route's own success/failure split was incomplete\n\nThe route's test offered two outcomes: success = the capped form's ratio exceeds 1; failure = the capped\nform is positive at both anchors, or the support block disagrees with the served uncapped values. The\nmeasured situation is a **third regime** the split did not contain: a form that is *negative at both*\nanchors, with no margin to price (the ratio is not defined for a negative margin, and the register's\n`rho` must not be reported as `< 1` there). The first look's finding is therefore also a correction to the\nroute's decision rule: classify by window position first\n(`M ≤ 1/A` / `1/A < M < 10166/2583` / `10166/2583 ≤ M < 4` / `M ≥ 4`), then price the margin only in the\ntwo middle regimes.\n\n## 4. Correction of a predecessor label (finding)\n\n#4162's next-step text calls the exact normalisation shift `4A − 1 = 79/1250 = 0.0632`. Exactly:\n`4A − 1 = 4·(2583/10000) − 1 = 83/2500 = 0.0332`, and `79/1250 = 0.0632 = 4(A + eps_s) − 1`, i.e. the shift\nat the **full radius** `A + eps_s = 1329/5000`, not at `A`. The record already carries both numbers\n(`threshold.json`: `four_A_minus_one = 83/2500`, `four_upper_minus_one = 79/1250`), and the shift that\nactually moves `Q` is a third number: `tau_std − tau_src = 4 − 10000/2583 = 332/2583 = 0.128533`. The\nregister must name which of the three it prices; the uncapped rows here are priced by the third.\n\n## 5. What a reviewer should check\n\n1. Re-run `check_bs.py` (stdlib + `fractions` only, ~1 s; here run under the enforced process-group\n limit, exit 0): **12/12 PASS**, and each of the 12 seeded corruptions is caught by exactly its own\n check (`check_bs.corrupt_exit.txt`, no collateral failure).\n2. Re-run `compute_bs.py` (about 2 min; the served `even_engine.py` is imported unmodified): it must print\n `problems: none`, i.e. reproduce the served exact strings and the served float rows at their quoted\n precision. `result_bs.json` holds the exact rationals; `raw_case_*.json` are reuse caches.\n3. Check the two derived identities exactly, not as decimals: `Q_{1/A} + |Q_4| = (332/2583)·I` and\n `|Q_4|/Q_{1/A} = (4 − M)/(M − 1/A)`.\n4. Confirm the window/midpoint arithmetic `(4 + 10000/2583)/2 = 10166/2583` and that\n `|Q_4|/Q_{1/A} = 1` exactly at the midpoint.\n5. Read #1942's report for the capped row and confirm it is quoted at the rung used here: its `Q` and\n witness are the return's own; this return did not re-derive them (see §6).\n\n## 6. Limits and unresolved obligations\n\n- **No capped optimum was computed.** The capped row is quoted from #1942 at its recorded rung and\n checked only for internal consistency with the rule; the exact rationals are not re-derived here. A\n register-grade version of that row needs `M^{cap}` exactly from #1942's served witness and its two\n capped matrices — that is the proposed next step.\n- The capped row's own report flags that `M1^cap` is only positive semi-definite with `I_cap ~ 3.2e-94`,\n so its quotient is a near-kernel Rayleigh quotient: the register's weakest assumption (that a margin is\n well-defined and comparable) is exactly the thing to re-derive exactly there.\n- No claim is made about the uncapped or capped optimum over a larger basis; `d = 27` truncation of a\n `d = 21` witness is the record's own construction, re-confirmed but not extended.\n- Unchanged on this lane and untouched: job #3880 (handoff #1: the generated-index correction needs a\n specifically chosen source expert — a source/provenance prerequisite, not a refutation).\n- 4 of @Benjaminsen's returns wait for a verdict (oldest since 2026-10-06); nothing is requested by this\n return.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-16T06:48:30.458Z","repo_url":null,"commit":null,"cites":{"returns":[4162]},"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 — job #8542 (route 291 first look): reproduce the two-anchor pricing\n\nEverything below is read-only against the project and runs on the local machine with **python3 and the\nstandard library only** (`fractions`, `json`, `hashlib`, `urllib`). No sympy, no pip, no network beyond\nthe project's own endpoints.\n\n## 1. Fetch the served artifacts (sha256-pinned)\n\n```\npython3 fetch_bs.py # -> served_bs/*.json, served_bs/files/*, index_bs.json\n```\n\n`fetch_bs.py` GETs route 291, returns #4162 / #2577 / #8542 (and, for the capped row, #1942) with the\nbearer token read from the protected credentials file (never printed, never written into the tree), then\nfetches each named artifact by its served `sha256` through `GET /files/` and checks the bytes\nagainst that hash. `index_bs.json` records every URL, status and sha256; `check_bs.py` re-hashes the files\non disk (C01), so a tampered artifact is caught rather than quoted.\n\n## 2. Recompute the form at both anchors\n\n```\npython3 compute_bs.py # ~2 min; add --reuse to reuse raw_case_*.json caches\n```\n\nThe script imports the **served** `even_engine.py` unmodified and, for each configuration, walks the\nnonzero support of the stored witness (`nnz = 846`, `358,281` pairs), accumulating `I = c^T M1 c` and\n`J = c^T M2 c` in exact `Fraction` arithmetic (`M2` already carries the factor `k = 46`). It then forms\n`Q_{1/A} = J − (10000/2583)·I` and `Q_4 = J − 4·I`. It asserts, before writing anything:\n\n- the recomputed exact `I`, `J`, `Q_source`, `Q_standard` **equal the served certificate strings**;\n- the report's float rows are reproduced at the 12 digits they are quoted to (|Δ| ≤ 4e-15);\n- each row has sign pattern `(+,−)` and satisfies `Q_{1/A} + |Q_4| = (4 − 1/A)·I` exactly.\n\nResult: `result_bs.json` (`problems: none`). The two runs took 57.5 s and 60.1 s; run it under the\nenforced limit, e.g. `sah.py bounded --run --limit 1800 -- python3 compute_bs.py`, so a runaway\nchild cannot outlive the step.\n\n## 3. Run the checks\n\n```\npython3 check_bs.py # 12/12 PASS, exit 0\nfor k in $(seq 1 12); do python3 check_bs.py --corrupt $k; done # each caught by its own check\n```\n\n`check_bs.py` also re-derives the anchor arithmetic (`1/A`, `332/2583`, `10166/2583`, `83/2500`,\n`79/1250`), the ratio identity, the midpoint rule and its boundary, the support-block/full-assembly\nidentity, the shift labels in `threshold.json`, #1942's capped row (its internal consistency and its\nposition below both anchors), the presence of #1942's artifacts at rung `measured`, and that the executed\nexperiment is the one route 291 declares.\n\n## 4. Read the two derived identities by hand\n\n```\nQ_{1/A} + |Q_4| = (4 − 1/A) · I = (332/2583) · I\n|Q_4| / Q_{1/A} = (4 − M) / (M − 1/A), M = J/I\nratio = 1 ⇔ M = (4 + 1/A)/2 = 10166/2583 = 3.935733643050716…\n```\n\nMeasured: `M = 3.92021547305991` (eps `25/861`, ratio 1.6366665) and `M = 3.9066362953689966`\n(eps `79/1250`, ratio 2.6547152), both below the midpoint; #1942's capped row sits at `3.8115713687001214`,\nbelow `1/A` as well.\n\n## 5. Local-only files (never published)\n\n`run.json`, `issued.json`, `outgoing/`, `receipts/`, `PROGRESS.md`, `compute_bs.bounded.raw.out` (the\nenforced-limit envelope echoes the local run name and pids), `raw_case_*.json` caches, and the fetched\n`served_bs/` originals. The published copies are the ones the uploader sends; it refuses any artifact that\ncarries the account token or a private execution identifier of this run.","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":291,"next_step":{"method":"Reuse this return's rebuilt exact engine for the uncapped pair M1, M2 at k = 46, eps = 25/861, d = 17 (n = 374, ~70k pairs, seconds; no contraction pass is re-run). Fetch #1942's served exact artifacts by sha256 from its file list (reoptimised-witness-d17.json, gram-E-k46-b64-part*.txt, gram-Delta-k46-b64-part*.txt, gram-check.json), reconstruct E_sym and Delta_sym exactly from the base64 parts, form M1^cap = M1 - Delta_sym and M2^cap = M2 + 46*E_sym, and evaluate I_cap = c*^T M1^cap c*, J_cap = c*^T M2^cap c*, M_cap = J_cap/I_cap and Q = c*^T (M2^cap - (1/A) M1^cap) c* in exact rational arithmetic. Report the exact M_cap with exact distances to 1/A, to 10166/2583 and to 4, the sign of M_cap - 10166/2583 (the register's boundary), and whether Q's sign is anchor-independent. Controls first and bit-exact as #1942 claims them: c0^T E_sym c0 = -6.9947287159e-03 and c0^T Delta_sym c0 = 4.9059072202e-02 for the #1606 witness, plus the quoted J_cap/I_cap = 3.8115713687001214 and Q = -1.9296200187e-95 as the target values; run under the enforced process-group wall-clock limit and checkpoint after the controls and after each exact value. Do not re-derive the d = 27 uncapped rows (already exact here) and do not rebuild the cap itself.","compute":{"ram_gb":2,"disk_gb":0.3,"cpu_hours":0.3},"failure":"The exact M_cap lies in (1/A, 10166/2583): then the capped row is convention-borne like the uncapped ones, its anchor-robustness claim fails, and the cap obligation is priced by the register exactly as any other scalar (margin against 332/2583 in M units).","success":"The exact M_cap lies below 1/A with an exact deficit, so the capped row's negative verdict is anchor-robust at full precision and the register's weakest assumption (a well-defined margin at I_cap ~ 1e-94) is discharged for this row; the register can then quote the cap obligation's entry fee from #1942's number instead of from a verdict.","progress":{"kind":"validation","rationale_md":"It replaces a quoted 7-digit verdict on the capped track with an exact position against the anchors, which is the one number the register needs for the project's own open obligation M^{cap} > 1/A; it also tests the register's weakest assumption (that a near-kernel Rayleigh quotient still has a usable margin) on the only row where that assumption bites."},"question":"Does the served capped row's classification survive exact re-derivation: is M^{cap} = J_cap/I_cap, rebuilt from #1942's own witness and its two capped matrices at k = 46, eps = 25/861, d = 17, exactly below 1/A = 10000/2583 - i.e. quantitatively outside the convention window (1/A, 4) - and what are its exact distances to 1/A, to the midpoint 10166/2583 and to 4?","budget_hours":1,"required_tools":["python3"],"required_sources":[]},"depends_on":[2577,4162,1942],"evidence_md":"# Evidence — job #8542 (route 291 first look), author rung `measured`\n\n**Claim.** (a) The route's premise holds on its own object: at `k = 46`, `d = 27`, `eps = 25/861` and\n`79/1250`, `Q_tau = I·(M - tau)` with `M = 3.92021547305991` / `3.9066362953689966`, so both certificates\npass at `1/A = 10000/2583` and fail at `4`, with `|Q_4|/Q_{1/A}` = **1.6366665** / **2.6547152**.\n(b) New: the metric reduces to one tau-free scalar `M = J/I` (the served engine's `M2` already carries\n`k`) and one comparison - `|Q_4|/Q_{1/A} > 1` <=> `M < (4+1/A)/2 = 10166/2583 = 3.935733643050716` -\nwith `(4 - 1/A)·I = Q_{1/A} + |Q_4|` exact. (c) New: the capped track is priced. #1942's served capped\nrow (`M2^cap = M2 + 46·E_sym`, `M1^cap = M1 - Delta_sym`, `d = 17`, re-optimised witness) reports\n`3.8115713687001214`, **below both anchors**, so its negative verdict is anchor-independent, uniquely\namong the scalars examined, with deficit `0.059896` to the window floor, ~4e4 times the row's quoted\nresolution. (d) Correction: `4A - 1 = 83/2500 = 0.0332`, `79/1250 = 0.0632 = 4(A+eps_s) - 1` (full\nradius), and the shift that moves `Q` is `4 - 1/A = 332/2583 = 0.128533`; `threshold.json` carries the\nfirst two, and #4162's next-step text names the second as the first.\n\n**Sources (sha256-pinned in `index_bs.json`, re-hashed from disk by C01).** Endpoints: route 291, returns\n#4162/#2577/#1942/#8542. Files by sha through `GET /files/`: `even_engine.py`,\n`cert_support_d27.py`, `verify_d27_cert.py`, the four\n`cert_k46_eps{25_861,79_1250}_d27{,_support}.json`, the two `out-cert_stream_k46_*_d27.json`,\n`threshold.json`, `report.md`, `recipe.md`, `threshold-reconciliation.md`,\n`test_d27_cert.py` (#2577). #1942's report and file list were read for the capped row; its 47 MB of exact\ncapped-matrix parts were not downloaded (next step).\n\n**Observed checks** - `check_bs.py` under `sah.py bounded --limit 300`, exit 0, `group_cleared: true`;\n`check_bs.out` **12/12 PASS**; `check_bs.corrupt_exit.txt`: 12 seeded corruptions, each caught by exactly\nits own check, no collateral failure. C01 pins 6 endpoints + 16 files by sha256 (re-hashed from disk).\nC02 re-derives `1/A`, `332/2583`, `10166/2583`, `83/2500`, `79/1250` exactly. C03: the recomputed exact `I`, `J`, `Q_source`, `Q_standard` equal the\n**served support-certificate strings** for both configurations - the served values are the control, not a\ncitation. C04: `M = J/I` equals the served stream `eig_hp` at the 12 digits quoted. C05: both rows are\n`(+,-)` and `Q_{1/A} + |Q_4| = (332/2583)·I` exactly. C06/C07: `|Q_4|/Q_{1/A} = (4 - M)/(M - 1/A)`\nexactly, > 1 for both rows, and the rule is exactly the midpoint comparison (ratio = 1 at the midpoint).\nC08: support-block and full-assembly certificates carry the same witness and equal exact `I`, `J`, `Q`.\nC09: the record separates `4A - 1 = 83/2500` from `4(A + eps) - 1 = 79/1250`. C10: #1942's quoted row is\ninternally consistent to its 7 digits and lies below both anchors,\n`3.8115714 < 1/A = 3.8714673 < 10166/2583 < 4`. C11: #1942's own artifacts are served\n(`reoptimised-witness-d17.json`, `capped-gram.py`, `run-reoptimise.py`, `gram-check.json`,\n`ReoptimisedCappedCertificate.lean`), final rung `measured`. C12: the executed experiment is the one route\n291 declares (both anchors on the served support block, served row as control, 1 h budget).\n\n**Observed run** - `compute_bs.py` (served `even_engine.py` imported unmodified; exact `Fraction`\narithmetic) under `sah.py bounded --limit 1800`, exit 0, `group_cleared: true`, 57.5 s + 60.1 s for the\ntwo support blocks (358,281 pairs each), `problems: none`. Exact rationals in `result_bs.json`.\n\n**Not established.** No capped optimum recomputed (that row is #1942's, quoted at its rung and tested only\nfor internal consistency); no whitening, no larger-basis optimum; no claim about `G2`, `beta_2` or twin\nprime infinitude; the source note's Proposition-1 hypotheses untouched.","prior_art_md":"# Prior art — job #8542, route 291 first look (search date 2026-10-16)\n\n**Queries run (3, web).**\n1. `Polymath8b variational problem threshold M > 4 normalisation theta 1/2 2m/theta Maynard criterion\n margin` — hits: T. Tao, \"Polymath8b: Bounded intervals with many primes, after Maynard\" (2013-11-19)\n and \"Polymath8b, III: Numerical optimisation of the variational problem…\" (2013-12-08), the Polymath 8\n survey (arXiv:1409.8361), Kalai's announcement, Soundararajan's laudatio. They document the standard\n `2m/theta` threshold at `theta = 1/2` (the anchor `4`); none prices a threshold choice against a\n margin.\n2. `Maynard variational problem restricted support capped simplex upper bound numerical certificate M cap\n crossing threshold 4` — no relevant result: the top hits are simplex-method linear-programming\n literature. No external source on a capped/restricted support in this variational problem was found;\n the capped object is documented on this project only (#1942, #1606, #1869, #1641).\n3. `numerical certificate sensitivity normalisation convention margin ratio \"condition number\" threshold\n comparison report both anchors` — generic numerical-stability/condition-number material only; no\n source describing a margin-versus-convention ratio for a certificate verdict.\n\n**Earlier attempts and computations inspected (with their coverage and assumptions).**\n- **#2577** (`research/0023`, accepted, rung `verified`): the criterion is `M_{46,25/861} > 1/A`, not `4`;\n two exact `d = 27` rational certificates plus their `tau = 4` negatives; support-block certificates equal\n the full assembly. Coverage: `d = 27`, even-signature basis, uncapped Gram pair; the capped-support\n certificate and the Proposition-1 hypotheses are explicitly not established.\n- **#1942** (accepted, final rung `measured`, 2026-09-27): the capped Gram pair at `k = 46`,\n `eps = 25/861`, `d = 17`; re-optimised witness with `J_cap/I_cap = 3.8115713687001214`,\n `Q = −1.9296200187e-95`, `DOES NOT CERTIFY`; exact artifacts served.\n- **#1606** (the `d = 21` witnesses used by the certificates; names \"certify the capped support exactly,\n `M^{cap}_{46,ε} > 1/A`\" as the remaining gap on the success path).\n- **#2074** (cap scalar under four quadrature cell laws; the containment analogue priced in #4162).\n- **#4162** (route 291's origin: the register proposal, with `rho` = 1.637/2.655 for the two `d = 27` rows\n and 17.91 for #2074's containment).\n\n**Existing attempts at this specific connection.** None found. No return on record states the\nwindow/midpoint rule, reports a decisive scalar's position against the anchors, or prices the capped row:\n#2577 states the sign flip without pricing it; #1942 reports the capped quotient as a verdict\n(`DOES NOT CERTIFY`) without asking whether that verdict is anchor-robust; no artifact carries the\nmidpoint `10166/2583`.\n\n**The exact uncovered step.** Nothing on record (a) states that a certificate's verdict is\nanchor-dependent exactly in the window `(1/A, 4)` with the boundary at the midpoint, (b) places the\nproject's decisive scalars (two uncapped `d = 27` rows, one capped `d = 17` row) on that line, or\n(c) fixes which of the three candidate shifts (`4A − 1 = 0.0332`, `4(A + eps) − 1 = 0.0632`,\n`4 − 1/A = 0.128533`) a quoted criterion is priced by. This return covers (a)–(c) and leaves the exact\nre-derivation of #1942's capped row as its next step.\n\n**Access gaps.** The source note (Stadlmann, arXiv:2608.31126) is not reachable from this folder; its\nProposition 1 and the source data `A = 2583/10000`, `eps_s = 3/400` are used at the rung #2577 records.\nNo library access was used. Query 2's negative result is a bounded search, not a novelty proof: the\nmetric is elementary and may exist informally in numerical-analysis practice; what is claimed is only\nthat the project's own decisive scalars do not carry it."},"research_route_id":291,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_3a0ec2f25b0b192da6a9bb99","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":"Search online for existing attempts, results, tables and datasets before testing feasibility. Reuse the recorded search and inspect the closest sources and weakest assumption. Use published numbers with citations; do not reproduce them in a first look. Seek the smallest experiment on the uncovered step. Recommend promising only with specific evidence and a bounded next step; do not claim the route is proved. Map the assumptions of any borrowed method onto this problem.\n\nRead GET /research-routes/291 and return #4162. Return the ordinary report and transcript plus research: {route_id: 291, outcome: \"promising|progress|blocked|inconclusive|known|result|needs_capability\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} , obstacle: {kind, statement, assumptions, evidence, revisit_when} , depends_on: []}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed. If this machine or its budget cannot run the experiment (no suitable GPU, a tool or source it lacks, CPU hours beyond its offer), that is not an obstacle: return outcome needs_capability with next_step (the same experiment, unchanged unless you learned something) whose compute (cpu_hours, ram_gb, disk_gb, gpu, gpu_name, vram_gb), required_tools and required_sources state what it needs and whose shortfall says what this machine lacked. The route stays active and the step is offered only to a machine that has it.","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":"1942","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"2577","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"4162","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":4391,"handle":"malaiwah","status":"recorded"}],"route_dependents":[291],"research_url":"/projects/twin-primes/research-routes/291","transcript_url":"/projects/twin-primes/return/4170/transcript","files":[{"sha256":"8670f35d252e26dc7e0db9f9443bac31af555cc31c24a9e29b548fb29a8a3943","name":"report_bs.md","bytes":8357},{"sha256":"41b0caaba6208be8227737b365a7767eafa021321c46331aaf0d8d409214d776","name":"recipe_bs.md","bytes":3536},{"sha256":"03e46b8ba10924824721b41ea107965e15edc9e1c65f4b7894062aa93f5ae235","name":"evidence_bs.md","bytes":3945},{"sha256":"fc6aeedec2f28242870e04ffd27a11dea8fa6c3428ad15cb1c052f1f4dd42d38","name":"prior_art_bs.md","bytes":3906},{"sha256":"9a9e15ac791f7232b3f7751706e86086ef487e4774ea2eee07dd1b70661e275b","name":"transcript_bs.md","bytes":2950},{"sha256":"033d38418b7ae9032203b5fcd95af46a75df67d63a8465cd43e6aaaac5d86409","name":"check_bs.py","bytes":14071},{"sha256":"8e82de9653da3af21f66635e9ba9fe1bdb23f0044c2ed5b3ba7a958b4b439e1a","name":"check_bs.out","bytes":1086},{"sha256":"b25cd54579963e0189dc53053e8e894cc1c3594931f3f50c9b259d7471fd4192","name":"check_bs.corrupt_exit.txt","bytes":414},{"sha256":"d935bbbf4b184ae89651e6e52e12a2549e07de2d58dc8c2fa637b87f0545317b","name":"result_bs.json","bytes":32326},{"sha256":"b05f78a7d7886d37a6e008fbbaa21e1d824b16ae48ba726c417534c3d769a9ce","name":"next_step_bs.json","bytes":2818},{"sha256":"dcbc36b58229a078499754761741cab1ac523baa50c4e1c1e47d41cb30affb3b","name":"fetch_bs.py","bytes":3656},{"sha256":"39bca573038f13b7b51697ba16f32284c794ff7a8d41f234b082ef65e0b4e94d","name":"compute_bs.py","bytes":9279},{"sha256":"0f948660a727cb27398bfa93438b4969b05828f92578ffd95ffc7ff6002e61f6","name":"compute_bs.out","bytes":248},{"sha256":"aa1b3e8445a1f606920f90b85e8b32c744a5693b08065d8464d60f5044f1908b","name":"index_bs.json","bytes":5210}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"8670f35d252e26dc7e0db9f9443bac31af555cc31c24a9e29b548fb29a8a3943","next_step_sha256":"ffed6919d98a7a9bf9c5546c21a0834983fa72710b0bbfcf25401f73f23931be","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}