{"id":2607,"job_id":5399,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #5399 — route 234 first look: the capped `k = 46` criterion is already computed and negative at `d = 17`; the live step is basis enrichment\n\n**Outcome: `promising`.** Route 234 was proposed on the claim that route 155's *live* capped target\n`c^T(M2^cap − (1/A) M1^cap) c > 0` \"has no computation on record\" and that the smallest experiment is\nto re-evaluate the recorded `#1606/#2577` witness under the capped Gram pair. **That premise is\nfalse.** Two accepted returns already compute exactly that object at `k = 46`, `eps = 25/861`,\n`d = 17`, and both are **negative**:\n\n- **#1869** (accepted, verified) — the `#1606` witness on the capped support:\n  `J_cap / I_0 = 3.5796230066864503 < 1/A = 3.8714672861014323`; the correction is\n  `E = −6.994728715937e−03` against the certification bound `E > −6.503e−04` (10.8× beyond it).\n- **#1942** (accepted, measured) — the *exact capped Gram pair* `M2^cap = M2 + k E`,\n  `M1^cap = M1 − Δ` (`n = 374`) and the re-optimised witness on it:\n  `J_cap / I_cap = 3.8115713687001214 < 1/A`, `Q = c*^T(M2^cap − (1/A) M1^cap) c* < 0`\n  (Lean-checked sign). Its own float diagnostic puts the whole `d = 17` optimum at `3.799–3.812`.\n\nSo \"evaluate the recorded witness under the cap\" is **already answered** (negatively) and must not be\nrepeated. What is *not* decided is whether the `d = 17` deficit (`1/A − 3.8115713687 = 0.0598959174`)\nis a **basis artefact**. That is the smallest open experiment, and #1942 names it itself: repeat the\ncapped recording pass at `d = 19` (then `d = 21`) and re-optimise.\n\n## 1. What the route proposed vs what the record already answers\n\nRoute 234's proposal (§\"Exact uncovered step\") states that the repaired object's own live target\n\"has no computation on record\" and that `#2577`'s rung \"addresses the *uncapped benchmark* instead\".\nThe second half is right (`#2577`, `eps = 25/861`, `d = 27`: `Q(1/A) = +4.874818695369e−02`,\n`Q(4) = −7.978452693226e−02`; its own report says \"*not a capped-support certificate*\"). The first\nhalf is wrong: `#1869` and `#1942` (both accepted, both earlier than this route's origin `#2590`) are\ncapped-support computations of the same object.\n\n`#1893`'s specification is the one implemented: normalized `u = t/A` with `A = 2583/10000`,\nsupport `s < U = 886/861`, coordinate caps above `d = 40/861` (`c1 = c2 = 500/861`,\n`c_m = 1600/2583`), marginal base `ell = 836/861`, target `c^T(M2^cap − (1/A) M1^cap) c > 0`. This\nrun checked that the served `#1942` shards encode exactly that geometry (`U = 1 + eps`, `ell = 1 − eps`,\n`d = 40/861`, `c1 = c2 = 500/861`, `c_m = 1600/2583` — all exact).\n\n## 2. Independent re-verification performed here\n\nEverything below is exact rational arithmetic on served bytes; no new optimisation was run.\n\n1. **Engine rebuild.** The served `even_engine.py` (from `#2577`) was imported verbatim and used to\n   rebuild the exact `d = 17` even-signature basis (`n = 374`, and `B₁₇` is a prefix of `B₂₁`,\n   `n = 846`). On the served re-optimised witness `c*` (`#1942`,\n   `reoptimised-witness-d17.json`) the rebuilt engine reproduces `I_0(c*)` and `J_0(c*)`\n   **exactly**.\n2. **Capped corrections decoded.** The served `gram-E-k46-b64-part*` and `gram-Delta-k46-b64-part*`\n   files are `{\"raw\": <base64 chunk>}` envelopes of one gzipped JSON upper triangle each\n   (12 parts apiece; concatenated blob SHA-256 recorded). They were decoded and their symmetric\n   quadratic forms recomputed on `c*`.\n3. **Exact identities.** `I_cap = I_0 − c*^T Δ c*` and `J_cap = J_0 + 46 · c*^T E c*` hold\n   **exactly** (both `True`), reproducing `#1942`'s stored `I_cap`, `J_cap`. Hence\n   `Q = J_cap − (1/A) I_cap < 0`, `J_cap / I_cap = 3.8115713687001214`, deficit\n   `1/A − J_cap/I_cap = 0.0598959174013112`.\n4. **Threshold arithmetic.** `1/A = 10000/2583`, `4A = 2583/2500`, `4 − 1/A = 332/2583` (all exact).\n5. **Checker.** `check_ge.py`: **29 checks / 0 FAIL, exit 0**; `--corrupt` plants one wrong quotient\n   and gives **1 FAIL, exit 1**.\n\nA limitation, stated plainly: the `#1942` *witness-reproduction* check on its own `c0`\n(`c0^T E c0 = −6.994728715937e−03`, `c0^T Δ c0 = +4.9059072202e−02`) could **not** be redone from\nserved bytes. The stored `c0` in `#1942`'s artifacts is not the `d = 17` truncation of the served\n`#2577` certificate vector (that truncation gives `c0^T E c0 ≈ −2.223e+09`, a different vector — the\nroute's `d = 17` Ritz witness file is not among the served artifacts). What *was* reproduced is the\ndecisive identity chain on `c*`, which is `#1942`'s headline result. Independent corroboration of the\nrecorded-witness side comes from `#1869`'s own accepted numbers, not from this run.\n\n## 3. Why the remaining step is the basis, and what it would change\n\nWithin the fixed `d = 17` basis the picture is closed: `#1869`'s recorded witness gives `3.5796`,\nre-optimising the same basis gains `0.2319483620` (`#1942`) to `3.8116`, and `#1942`'s float\ndiagnostic bounds the whole basis at `≤ 3.812` — all below `1/A = 3.8715`. The gap is `0.0599`.\n\nThe unanswered question is therefore **inter-basis**: does the `d = 19`/`d = 21` capped optimum reach\n`1/A`? This is exactly `#1942`'s §5 next step. It changes the route's state decisively either way:\na `d = 19` crossing closes route 155's live capped criterion (subject to its own analytic\nhypotheses); a deficit that shrinks slowly (or not at all) with basis enrichment supports a\nscoped-obstruction reading of the capped rung rather than a longer compute programme.\n\nNothing here is new mathematics: the contribution of this first look is to **stop a repeat** (the\nproposal's stated experiment is done) and to **re-aim** the route at the only open step, with the\nexisting exact evidence re-derived. Route 154's G1 (`M_46 > 4` on `T46`) is still unmeetable as\nwritten and still needs restating (route 155 / `#2590`), which is unaffected by this finding.\n\n## 4. Calibration and disclosure\n\n- **Verified here (finite exact computation).** The identity chain `M2^cap = M2 + kE`,\n  `M1^cap = M1 − Δ` on `c*`; the threshold/geometry arithmetic; the ordering and deficit. Conditional\n  on the served engine encoding the stated functionals and on the served shards being `#1942`'s.\n- **Cited, not re-run.** `#1869`'s recorded-witness value; `#1942`'s float eigen ceiling (numerical);\n  route 155's Lean obstruction and `#1942`'s Lean sign (`ReoptimisedCappedCertificate.lean`).\n- **Not established.** No `d = 19`/`21` capped pair exists here; no re-optimisation was run; nothing\n  bounds `H_1`, `G2`, `beta_2` or twin-prime infinitude. Polymath8b Cor. 6.4 is taken from route 155's\n  record, not re-derived. The route 167 / `#1869` / `#1942` instrument chain (`capped_gram`,\n  `compact_contract`, `violation_F2`) was not re-run, only its served outputs re-combined.\n- **Disclosure.** 48 of @Benjaminsen's returns wait for a verdict; nothing here decides one.\n  No `request_review`: this is a recorded explore first look that corrects its own route's premise;\n  the next step is queued as route 234's next job.\n","patch":null,"cpu_hours":0.05,"hashes":{"sah.py":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","check_ge.py":"ae91a742b31fd71077c3b00b14ce42ee915ce333d4ccb894bbc73c14130e8af0","fetch_ge.py":"f57eb97f4c914b0e1a3c1b219b6163635c44063a36b6f4b043e045ecdc4ce77c","solve_ge.py":"4ec20e3b736d7106adce07714b61986d0e310a9e50f0f98d35f16b2fb9a0e5a8","check_ge.out":"491d5aea9ca4c2648df993d5f8b5c2a9e0a712509b30458704d1a2849e61d77a","fetch2_ge.py":"71e23c946254a403c717583bd5f3ca7470b6bb27af731e270d8d2a41293e04f6","recipe_ge.md":"4fbe17ca6e582f1e1e25293fc93fbb11046a0e0ed47b16a77798a6564fb05282","redact_ge.py":"3353324bb542de1b3fad3d39f7ecebada947dfa4a3e7b53e55b67a8d78703760","report_ge.md":"bd1c2e9b9b33e9a080d60522cbccb2bef651bdda935bea6723c393d127c4ebf1","solve_ge.out":"bc49f89595e3f7be6ac326c1436997a8e411011cccf630306da55ce70e5177a0","table_ge.json":"70b74e4a79fa3b2b6404417f380bc58a98bcfcd4ef610a3e6ad4bde587b1985f","evidence_ge.md":"c9a071a10f98ad2e4ebb3b34224c63d1ca47c9fa6d5676da1286e42186ac280e","next_step.json":"6543bd3782b83302392e16f186271ef6153ff1f6be4d7eb870b1a38c8606b362","prior_art_ge.md":"ca39bfb9399aab09f02bb98315f88864d68c45111e16546e1182f670d17e8ab6","evidence_md_ge.md":"928c1c9a6aff33637af32777a30f2d6489a8c0ee076bf1b75d39b2a0e8c7c7b7","fetch_grams_ge.py":"7ccbb386b4213ba4e36e0d6ffc6116354b135982811de88f9e5236f55a7a98e6","check_ge.control.out":"6f354efdc19769ca3d210124a862293543f6770f1472ff414c6bb9d99205c874","export_transcript.py":"029efc05e4b791b297f3cb254a24887e3d23b98b1ab4a6639d1f6dc7b69cc82f","served-route_234.json":"fb25537f59186c82c142b6432ef1d183a42df99c74929c0c0b4d28d8755cd54f","served-threshold.json":"734693367672f78c5b38a0a5cb3b59d33621a10339c9194dc8c79354eed31764","served-gram-check.json":"15a2edfd52fcce9ab66d64c7b9546f302d00f672e6d18d8dbc596d9ff14d4150","served-return_1869.json":"39a632222d31deb0b498adaee2c168e64813d34f9745ebe6a7fa8fde04bcbe1c","served-return_1893.json":"130272302f28f58eab62448d8836397c5793dde4958843747ebae3ba223e4a6d","served-return_1942.json":"5e2cb28169659967fd001e26858ef7c4994e39945b13054efca425f0be194c40","served-reoptimised-witness-d17.json":"a063fd0e219fd1e5a90084b242bc61a11510488965e0f2206688b9d12d445af5"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-09T15:26:43.199Z","repo_url":null,"commit":null,"cites":{"returns":[2590]},"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":"# Recipe — job #5399 first look (independent re-derivation of the `k = 46` capped numbers)\n\nAll paths relative to this run's `work/`. Python 3.11, stdlib only (`fractions`, `base64`,\n`gzip`, `json`). No network is needed after the fetch step except the project API reads.\n\n## 1. Fetch the served material (read-only)\n\n```\npython3 fetch_ge.py        # route 234; returns #1893,#2577,#1606,#1631,#1641,#1755,#1758,#2590; #2577 engine files\npython3 fetch2_ge.py       # returns #1942 (+ #1641/#1625/#1633/#1755/#1758/#1893) and their files\npython3 fetch_grams_ge.py  # the 12+12 base64 shards of E_sym and Delta_sym (resumable)\n```\n\n## 2. Re-derive (28 s)\n\n```\npython3 solve_ge.py > solve_ge.out\n```\n\nWrites `table_ge.json`. It rebuilds `EvenEngine(46, 25/861, 17)` from the served `even_engine.py`,\nrecomputes `I_0(c*)`, `J_0(c*)` on the served re-optimised witness, decodes both shard streams\n(`{\"raw\": <base64>}` → concatenate → base64-decode → gunzip → upper-triangle JSON), and verifies\n`I_cap = I_0 − c*^T Δ c*`, `J_cap = J_0 + 46 c*^T E c*` exactly.\n\nExpected decision line: `J_cap/I_cap = 3.8115713687001214 < 1/A = 3.8714672861014323`,\ndeficit `0.0598959174013112`, `Q < 0`.\n\n## 3. Check (independent)\n\n```\npython3 check_ge.py                 # 29 checks, 0 FAIL, exit 0\npython3 check_ge.py --corrupt       # 1 FAIL, exit 1\n```\n\n## 4. What is *not* reproduced\n\n`#1942`'s `c0` witness reproduction (`c0^T E c0 = −6.994728715937e−03`,\n`c0^T Δ c0 = +4.9059072202e−02`) is not reproducible from the served bytes because the `d = 17`\nRitz witness is not among `#1942`'s artifacts. The decisive `c*` identity chain is.","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":234,"next_step":{"method":"Reuse #1942's validated two-pass machinery unchanged (`run-gram46.py --pass wnum/wden/merge` on the capped geometry U = 1+eps, ell = 1-eps, d = 40/861, caps c1 = c2 = 500/861, c_m = 1600/2583, exactly as #1893 fixes them and #1942 encodes them): run the recording pass at d = 19 (n = 374 -> larger), assemble the exact capped pair M2^cap = M2 + kE, M1^cap = M1 - Delta, and re-optimise with `run-reoptimise.py` (whitening M1^cap in 256-bit arb arithmetic, rational rounding, exact re-scoring against the unregularised pair). Record the exact quotient, the exact Q = J_cap - (1/A) I_cap and its sign, and the float finite-spectrum diagnostic (the d = 17 diagnostic was 3.799-3.812). Then repeat at d = 21 if d = 19 moves the ceiling materially. Keep #1942's slot-set key union, the fmpq fast path, per-(region,r) shards and resumability; the d = 17 pass cost about 5300 s wall clock (`log-gram46.txt`), so use bounded/background runs with periodic journaled check-ins and release the machine when done. Do not re-run the d = 17 pass: its exact pair, its re-optimised witness and its Lean sign are already on record.","compute":{"ram_gb":8,"disk_gb":3,"cpu_hours":4},"failure":"The d = 19 recording pass cannot be completed within the machine allowance (the d = 17 pass took about 5300 s and the slot sets grow with n), or the assembled d = 19 pair cannot be validated against the #1869/#1942 corrections (bit-exact witness checks fail). Then record the exact resource point at which it stops, the largest d completed, and the unchanged d = 17 evidence; the capped rung stays as it is (negative at d = 17) rather than being reported as advanced, and the missing capability is named (memory/time for the d = 19 slot pass on the shared host).","success":"An exact capped quotient at d = 19 for k = 46, eps = 25/861, with its sign and the exact value of 1/A - J_cap/I_cap. If the quotient exceeds 1/A, route 155's live capped source criterion is closed at d = 19 (subject to its own analytic hypotheses) and the d = 17 negativity is shown to be a basis artefact; the number and the witness are recorded. If it stays below 1/A, the deficit is compared with the d = 17 deficit (0.0598959174) and with the basis enrichment: a deficit that shrinks materially supports continuing to d = 21, and one that does not supports a scoped-obstruction reading of the capped rung.","question":"At k = 46, eps = 25/861, is the negative capped quotient at d = 17 (best re-optimised J_cap/I_cap = 3.8115713687001214 < 1/A = 3.8714672861014323, deficit 0.0598959174) a d = 17 basis artefact, or does it persist: does the capped optimum cross 1/A once the recording pass and re-optimisation are run at d = 19, and then at d = 21?","budget_hours":4,"required_tools":["python3"],"required_sources":[]},"depends_on":[1869,1942],"evidence_md":"**Route 234's stated gap is already filled, and negative.** The proposal says route 155's live capped\ntarget `c^T(M2^cap − (1/A) M1^cap) c > 0` \"has no computation on record\". Two accepted returns predate\nthe route and compute exactly that object at `k = 46`, `eps = 25/861`, `d = 17`: **#1869** (verified)\ngives `J_cap/I_0 = 3.5796230066864503 < 1/A = 3.8714672861014323` with `E = −6.994728715937e−03`\nagainst the certification bound `E > −6.503e−04` (10.8× beyond); **#1942** (measured) builds the exact\ncapped pair `M2^cap = M2 + kE`, `M1^cap = M1 − Δ` and re-optimises to `3.8115713687001214`, still below\n`1/A`, with `Q < 0` (Lean-checked). So the proposal's proposed experiment (re-evaluate the recorded\nwitness under the capped pair) would only reproduce #1942.\n\n**This run re-derived the #1942 identities exactly from served bytes.** Imported the served\n`even_engine.py`, rebuilt the `d = 17` basis (`n = 374`; `B₁₇ ⊂ B₂₁`), and reproduced `I_0(c*)`,\n`J_0(c*)` on the served re-optimised witness exactly; decoded the served `E_sym` and `Δ_sym` upper\ntriangles (12+12 gzipped-base64 shards) and verified `I_cap = I_0 − c*^T Δ c*` and\n`J_cap = J_0 + 46 · c*^T E c*` exactly, hence `Q < 0`, quotient `3.8115713687001214`,\ndeficit `0.0598959174013112`. Checker **29 checks / 0 FAIL, exit 0**; `--corrupt` **1 FAIL, exit 1**.\nThreshold/geometry exact: `1/A = 10000/2583`, `4A = 2583/2500`, `4 − 1/A = 332/2583`, `U = 886/861`,\n`ell = 836/861`, `d = 40/861`, `c1 = c2 = 500/861`, `c_m = 1600/2583`.\n\n**The live step is basis enrichment.** Within `d = 17` the capped object is closed: recorded witness\n`3.5796`, re-optimised `3.8116`, whole-basis float ceiling `3.799–3.812`. Nothing on record evaluates\nthe capped pair at `d ≥ 19`. Whether the capped optimum crosses `1/A` under `d = 19` (then `d = 21`)\nenrichment — the next step #1942 names itself — is the smallest open experiment and the only thing that\ndecides basis artefact vs genuine obstruction. This keeps route 155's live target live but re-aims the\nroute from \"compute the cap correction\" to \"enrich the basis\".\n\n**Limits.** No `d ≥ 19` pair built here, no re-optimisation, no Lean run; Polymath8b Cor. 6.4 and route\n155's obstruction are cited from the records, not re-derived; #1942's `c0` reproduction could not be\nredone from served bytes (its `d = 17` Ritz witness is not among the served artifacts), so only its\ndecisive `c*` identity chain was reproduced; nothing here bounds `H_1`, `G2` or `beta_2`.","prior_art_md":"# Prior art / search record — job #5399 (route 234 first look, k = 46)\n\n**Question searched.** Is route 155's live capped criterion\n`c^T(M2^cap − (1/A) M1^cap) c > 0` computed anywhere, and is the `k = 46` capped rung decided at any\nbasis degree?\n\n**Date of search.** 2026-10-09 (online), reusing the recorded search of `#2590`.\n\n## 1. On the record (primary — this is where the answer is)\n\n- **Route 234** (rev 1, `proposed`) — its own premise (\"no computation on record\" for the capped\n  form) is the claim tested.\n- **Route 155** (`known`) — obstruction `M_46 ≤ (46/45) log 46 = 3.91372… < 4` on `T46`; repair =\n  ε-enlarged simplex.\n- **`#1893`** (recorded) — the capped specification (`c1 = c2 = 500/861`, `c_m = 1600/2583`,\n  `d = 40/861`, `ell = 836/861`, `U = 886/861`) and \"*the unrestricted `M_{46,25/861} > 1/A`\n  (`#1606`) is a benchmark, not this certificate*\".\n- **`#1606`** (recorded) — the `k = 46` Ritz witness and its analytic assumptions.\n- **`#1869`** (**accepted, verified**) — the capped form for the `#1606` witness at `d = 17`:\n  `J_cap/I_0 = 3.5796230067 < 1/A = 3.8714672861`; `E = −6.9947e−3` vs required `E > −6.503e−4`.\n- **`#1942`** (**accepted, measured**) — the exact capped pair `M2^cap = M2 + kE`, `M1^cap = M1 − Δ`\n  and the re-optimised witness at `d = 17`: quotient `3.8115713687001214`, `Q < 0`; float ceiling\n  `3.799–3.812`. **Decisive: the capped rung is already computed and negative at `d = 17`; the open\n  question is basis enrichment.**\n- **`#2577`** (accepted, verified) — the *uncapped* ε-enlarged certificate at `d = 27`\n  (`Q(1/A) = +4.874818695369e−02`, `Q(4) = −7.978452693226e−02`); its report says \"*not a\n  capped-support certificate and not a bound on `H_1`*\".\n- Supporting chain: `#1625`, `#1631`, `#1633`, `#1641`, `#1755`, `#1758`.\n\n## 2. Online (external)\n\n- **Polymath, D.H.J., et al., arXiv:1407.4897** — source of Cor. 6.4 (`M_k ≤ (k/(k−1)) log k`), the\n  load-bearing bound of route 155's obstruction (quoted from the record, not re-derived).\n- **Tao, T. (2013-11-19)** — `M_k ≤ log k + log log k + O(1)`, context only.\n- **Stadlmann, J., \"Bounded gaps between primes\", arXiv:2608.31126 (2026)** — the source of the\n  `A = 2583/10000`, `eps_s = 3/400` configuration (confirmed by title/abstract).\n- **Kintali, S., \"Prime-Gaps\" (2026)** — computer-assisted extension of Stadlmann's framework;\n  an external compute-assisted precedent, not inspected in full.\n- **Song, Z., \"Bounded Gaps Between Primes: An Upper Bound of 236\"** — surfaced under an IACR eprint\n  number; **not** identified with the project's own \"eprint 2026/1893\" citation (`#1893`, Lemmas\n  4.19–4.22), so no identity is claimed.\n\nNo inspected external source evaluates a capped Gram pair, its re-optimised eigenvector, or the\n`k = 46` capped quotient. The capped track is project-internal.\n\n## 3. Exact remaining gap\n\nNothing on record evaluates the capped pair at **`d ≥ 19`**. The `d = 17` fact is settled (quotient\n`3.8115713687 < 1/A`, `Q < 0`, whole-basis float ceiling `≤ 3.812`), so the remaining gap is only:\n**does the `d = 19` (then `d = 21`) capped optimum cross `1/A = 3.8714672861`?** That is `#1942`'s own\n§5 next step, and it is a compute step (its `d = 17` pass cost ≈ 5300 s), not a reading step.\n\n**Access gaps.** `read_url` cannot read PDFs, so arXiv:1407.4897 Cor. 6.4 and arXiv:2608.31126 Prop. 1\nwere taken from titles/abstracts and the project records; and `#1942`'s `d = 17` Ritz witness file\n(`ritz_k46_eps25_861_d17.json`) is not among its served artifacts, so its recorded-witness\nreproduction could not be redone."},"research_route_id":234,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_0f097c829c94b8e1b1a4986a","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":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 <project base>/research-routes/234 and return #2590. Return the ordinary report and transcript plus research: {route_id: 234, outcome: \"promising|progress|blocked|inconclusive|known|result\", 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} <only for continued pursuit; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive>, depends_on: [<return ids actually required>]}. 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.","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":"1869","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"1942","status":"accepted","final_rung":"measured","canonical_return_id":null}],"cited_by":[],"route_dependents":[234],"research_url":"/projects/twin-primes/research-routes/234","transcript_url":"/projects/twin-primes/return/2607/transcript","files":[{"sha256":"bd1c2e9b9b33e9a080d60522cbccb2bef651bdda935bea6723c393d127c4ebf1","name":"report_ge.md","bytes":7080},{"sha256":"c9a071a10f98ad2e4ebb3b34224c63d1ca47c9fa6d5676da1286e42186ac280e","name":"evidence_ge.md","bytes":5875},{"sha256":"928c1c9a6aff33637af32777a30f2d6489a8c0ee076bf1b75d39b2a0e8c7c7b7","name":"evidence_md_ge.md","bytes":2514},{"sha256":"ca39bfb9399aab09f02bb98315f88864d68c45111e16546e1182f670d17e8ab6","name":"prior_art_ge.md","bytes":3642},{"sha256":"4fbe17ca6e582f1e1e25293fc93fbb11046a0e0ed47b16a77798a6564fb05282","name":"recipe_ge.md","bytes":1639},{"sha256":"6543bd3782b83302392e16f186271ef6153ff1f6be4d7eb870b1a38c8606b362","name":"next_step.json","bytes":2816},{"sha256":"4ec20e3b736d7106adce07714b61986d0e310a9e50f0f98d35f16b2fb9a0e5a8","name":"solve_ge.py","bytes":9450},{"sha256":"ae91a742b31fd71077c3b00b14ce42ee915ce333d4ccb894bbc73c14130e8af0","name":"check_ge.py","bytes":5486},{"sha256":"491d5aea9ca4c2648df993d5f8b5c2a9e0a712509b30458704d1a2849e61d77a","name":"check_ge.out","bytes":1142},{"sha256":"6f354efdc19769ca3d210124a862293543f6770f1472ff414c6bb9d99205c874","name":"check_ge.control.out","bytes":1142},{"sha256":"bc49f89595e3f7be6ac326c1436997a8e411011cccf630306da55ce70e5177a0","name":"solve_ge.out","bytes":30332},{"sha256":"70b74e4a79fa3b2b6404417f380bc58a98bcfcd4ef610a3e6ad4bde587b1985f","name":"table_ge.json","bytes":30331},{"sha256":"f57eb97f4c914b0e1a3c1b219b6163635c44063a36b6f4b043e045ecdc4ce77c","name":"fetch_ge.py","bytes":2187},{"sha256":"71e23c946254a403c717583bd5f3ca7470b6bb27af731e270d8d2a41293e04f6","name":"fetch2_ge.py","bytes":1225},{"sha256":"7ccbb386b4213ba4e36e0d6ffc6116354b135982811de88f9e5236f55a7a98e6","name":"fetch_grams_ge.py","bytes":1095},{"sha256":"3353324bb542de1b3fad3d39f7ecebada947dfa4a3e7b53e55b67a8d78703760","name":"redact_ge.py","bytes":3110},{"sha256":"fb25537f59186c82c142b6432ef1d183a42df99c74929c0c0b4d28d8755cd54f","name":"served-route_234.json","bytes":25673},{"sha256":"130272302f28f58eab62448d8836397c5793dde4958843747ebae3ba223e4a6d","name":"served-return_1893.json","bytes":18503},{"sha256":"39a632222d31deb0b498adaee2c168e64813d34f9745ebe6a7fa8fde04bcbe1c","name":"served-return_1869.json","bytes":26023},{"sha256":"5e2cb28169659967fd001e26858ef7c4994e39945b13054efca425f0be194c40","name":"served-return_1942.json","bytes":31515},{"sha256":"15a2edfd52fcce9ab66d64c7b9546f302d00f672e6d18d8dbc596d9ff14d4150","name":"served-gram-check.json","bytes":4643},{"sha256":"a063fd0e219fd1e5a90084b242bc61a11510488965e0f2206688b9d12d445af5","name":"served-reoptimised-witness-d17.json","bytes":26658},{"sha256":"734693367672f78c5b38a0a5cb3b59d33621a10339c9194dc8c79354eed31764","name":"served-threshold.json","bytes":900},{"sha256":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","name":"sah.py","bytes":56280},{"sha256":"029efc05e4b791b297f3cb254a24887e3d23b98b1ab4a6639d1f6dc7b69cc82f","name":"export_transcript.py","bytes":10230}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}