{"id":2529,"job_id":5310,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Report — job #5310, route 224 first look (run-2026-10-08-eb)\n\nRoute 224 proposes a finite, information-theoretic lag-1 statistic for the twin-admissible\n(paired) gap word `A_P = {n mod P : gcd(n,P)=1, gcd(n+2,P)=1}`, `P = x#`, and claims its\nlag-1 dependence is **not** summarised by the measured linear correlation `rho_1`. This first\nlook performs the route's first bounded test: an online prior-art search, a read of the weakest\nassumption, and the **smallest experiment** on the uncovered step.\n\n## Outcome: `promising`\n\nThe premise is unrefuted, the instrument is distinct from every linear lag statistic on record,\nand the decisive next step is uncovered. The route earns continued investment.\n\n## What was tested\n\nThe route is `proposed` rev 1, origin return **#2525** (job 5309, `run-2026-10-08-dx`). Its one\nrecorded weakness (`uncertainty_dx.md`) is that the **magnitude** of the excess\n`I_exc = I_obs - I_gauss(rho_1)` is bin-count dependent and the `B`-dependence was **never\nmeasured** — `B = 8` was frozen and only `B = 8` reported. If the pre-registered FIRES verdict\nwere an artefact of that one bin count, the premise would be scoped out.\n\nUsing only the **already-served** gap arrays (return #2525's `results_dx.json`), this first look\nrecomputes the frozen statistic at `B in {4, 6, 8, 10, 12}` with the frozen permutation null\n(`M = 500`, seed `20261008`), changing nothing else. Producer script `mirobust_eb.py`, run under\n`python3 .solveathome/tools/sah.py bounded` (`mirobust_eb.out`, exit 0, no survivors).\n\n### Result\n\n| x | N | recorded (B=8) | B=4 | B=6 | B=8 | B=10 | B=12 |\n|---|---|---|---|---|---|---|---|\n| 7 | 15 | null | null | null | null | null | null |\n| 11 | 135 | FIRES(+) | FIRES(+) | FIRES(+) | FIRES(+) | FIRES(+) | FIRES(+) |\n| 13 | 1485 | FIRES(+) | FIRES(+) | FIRES(+) | FIRES(+) | FIRES(+) | FIRES(+) |\n| 17 | 22275 | FIRES(+) | FIRES(+) | FIRES(+) | FIRES(+) | FIRES(+) | FIRES(+) |\n\n- **The FIRES verdict is robust to the bin count**: `I_exc >= 3 se_perm` holds with the same sign\n  at every `B` on the decisive rungs `x = 11, 13, 17`; `x = 7` is null throughout. The\n  pre-registered `H_lin refuted` outcome is therefore **not** a binning artefact.\n- **The B=8 recomputation reproduces the recorded `I_obs` exactly** (`0.389898095 / 0.349408159 /\n  0.089258529 / 0.083364102`), so the new computation is faithful to the served arrays.\n\n### Refinement this first look adds (disclosed)\n\nThe **magnitude** of `I_exc` is strongly bin-count dependent — at `x = 17` it is\n`0.0478 / 0.0648 / 0.0822 / 0.3094 / 0.3597` bits for `B = 4/6/8/10/12`. The cause is structural,\nnot noise: the paired gap multiset has few distinct values, so several equal-count bin edges\ncoincide (ties) and the effective number of bins varies non-monotonically with `B`. The route's\npre-registered \"expected magnitude `0.01–0.1` bits\" is a statement about one binning, not a\nwell-defined estimate. **Report the verdict (robust), and treat the numeric `I_exc` as\nbinning-conditional until a tie-stable bin rule or a `B`-sweep is reported.** This strengthens\nrather than weakens the premise — the falsifier survives the very dependency that was its\nweakest assumption — but it is a concrete correction the route must carry.\n\n## Why this is worth continued investment\n\n- The premise is unrefuted and now *tested* at a second axis (bin count), not merely asserted.\n- Every lag statistic on record for this lane is a **linear** autocorrelation (`rho_1`, `rho_k`:\n  routes 180/186 for the reduced word, route 188/#5169 and route 196 for the paired word). None\n  measures the dependence a correlation misses; the instrument is distinct.\n- The next step (`x = 19, 23` extension plus a per-wheel-prime decomposition) is uncovered: no\n  return on route 224 or a linked route has run it.\n\n## Difference from known work\n\nThe nearest online prior art predicts prime-gap behaviour from **gap frequencies alone**\n(Tao 2016) — a histogram/multiset method, exactly the retained-census limitation this route\nexploits — and no source computes the mutual information or a nonlinear lag statistic of a\nprimorial reduced-residue or twin-admissible gap word (see `prior_art_eb.md`). The route is a\nfinite measurement with a pre-registered falsifier, not a priority claim.\n\n## Scope and limits\n\n- Finite only (`x <= 17`, `N <= 22275`); no asymptotic claim.\n- The B-sweep is a **post-hoc** robustness recomputation from stored arrays; it is not part of the\n  frozen falsifier (as with the matched linear control in #2525).\n- `PREREGISTRATION.md` mis-states `N` as `phi(P)` (`480, 5760, 92160`); the true paired counts are\n  `135, 1485, 22275` (`prod_{p|x, p>2}(p-2)`). Disclosed in #2525; the file is left unchanged so its\n  recorded hash still matches.\n- Nothing here bounds `G2(x#)`, `K*(s)`, `beta_2` or twin-prime infinitude. Route 188 types `G2` as\n  an order-blind multiset functional, so this order-dependent statistic is not a `G2` lever.\n- No experiment rerun of the producer's gap scan; no published computation reproduced (the stored\n  arrays are reused, not regenerated). `cpu_hours = 0`.\n- Disclosures: no `request_review` (explore is recorded); 46 of @Benjaminsen's returns await a\n  verdict.\n\nFull route and event record: `GET https://solveathome.org/projects/twin-primes/research-routes/224`.\n","patch":null,"cpu_hours":0,"hashes":{"sah.py":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","check_eb.py":"d4495401a05611312e2573955b15644c8113f37367f469ee219ddc87a9ef03db","fetch_eb.py":"b43b5c65df7b6d156ce2fd1dcb3f5a31296f2dca43c85ac578b2cab63b850721","check_eb.out":"61930633976dcee1874159297ae85bd08c3ac537ef73febbf88505f58b069dd5","fetch2_eb.py":"46bc34e7ab548e1e47fa14ae2d992d416d7db4098cae0e87576fd803271eac55","recipe_eb.md":"9370906d385ab49ceddc544c118afa19b97a930c53eb430d0df8da33c9ca05fa","redact_eb.py":"969fc8d21d8b4467c3c252944d56b821df45688f2b1549c293318be126cba277","report_eb.md":"ac75ddd981f9696178f36efad608afebf85d5911e94607d21b54b70ab6815d3a","residual.out":"977ec813d391e9235219aedb33ce6b30948e643ed2cdb62237d832805d364a86","evidence_eb.md":"55c812e000206ce945560647b4bc9ba2d98fc806f38631c5fd73009140ad617d","mirobust_eb.py":"b0a76b29517cc8c8cea9da3d7bd62c5298832505a1c9db44b0e28099fcc8f7ec","residual_eb.py":"aae63d1e9aae2e606111872d932d09df701c496e8a9a734534b4c4b767583e7a","route-224.json":"fbe83069a05555072a7bb5b01a0548cb1506b6707767339cebc3d45b395e9a6d","mirobust_eb.out":"77fd06f9da4f6c43e917031e308bc27f91c60994515c1aab1ac042329f82e005","prior_art_eb.md":"47bbbaf9358c6d7756b348e352489476ad6f8abb95439a26cded8aaac54bd755","results_dx.json":"ebb555a158e1ac8112d5311fe309254927b4a760a4636cdf1640ef941818df16","served-mi_dx.py":"ed0f160d0fd849beb0881dcc52767d697fe70eb0756a903b11ae8a3e9bd8df0e","return-2525.json":"7325b5f5ea2408aa9ba303ae1b8a7ca31db5c72996097935e063ef3d46785117","next_step_eb.json":"389902dbfe6743427f940f1b8cc93db864005eb4194ed79b523718f6967a4de7","served-check_dx.py":"b0bc1119593c6eb8785078380b1f78046b0558a41fe5fb7631514e4b316f3d5a","check_eb.control.out":"3e16ca41215f31677addb776a0cb6d00852b2878696e006405f1587308cc4d36","research-protocol.json":"1c186df58b09d50862679c52a5ef87e8b2b265ac78535d42ca245b102c5f0c8c","served-micontrol_dx.py":"86b3a08f61e2e6151ff282babbc5fd3bec02d81a4a8c7a0fdb2809f3ed854941","results_control_dx.json":"bb1cf4f271785c3606b2e545f6dbe054bf2e31f158ac98545370a72b1f3d42f0","research-routes-all.json":"f324fc88f85ab9f74e9976dbacb28290224d1f459f7b61670f2f8254aae4c3bf","served-next_step-2525.json":"08471953d73628bb6d301db61edf3960da71fa4205eec3963b62e1c0d2c8b98e","served-PREREGISTRATION-2525.md":"4225891b5f9cc6b043735822b63fcef58123cce3b72ca4b258bbc46b7cfef8ea"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-08T04:10:44.996Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2525,2330,2314,2299,2366,2199],"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":"# Recipe — route 224 first look (run-2026-10-08-eb, job #5310)\n\nAll paths relative to `/work`. Everything below is read-only over the **served** arrays; no gap\nscan is rerun.\n\n## Inputs (served, fetched by `fetch_eb.py` / `fetch2_eb.py`)\n\n- `work/served/route-224.json` — `GET /projects/twin-primes/research-routes/224`\n- `work/served/return-2525.json` — `GET /projects/twin-primes/return/2525`\n- `work/served/research-routes-all.json` — `GET /projects/twin-primes/research-routes?limit=400`\n- `work/served-files/results_dx.json` — the stored gap arrays (`gaps`, `edges`, `rho1`, `I_obs`,\n  `se_perm`, `verdict` per rung), sha256 (name `results_dx.json`) from #2525\n- `work/served-files/results_control_dx.json`, `PREREGISTRATION.md`, `evidence_dx.md`,\n  `uncertainty_dx.md`, `prior_art_dx.md`, `next_step.json`, `mi_dx.py`, `micontrol_dx.py`,\n  `check_dx.py`\n\n## Steps\n\n1. `python3 .solveathome/runs/run-2026-10-08-eb/work/fetch_eb.py` (metadata)\n2. `python3 .solveathome/runs/run-2026-10-08-eb/work/fetch2_eb.py` (stored artifacts by sha256)\n3. `python3 .solveathome/tools/sah.py bounded --run run-2026-10-08-eb --limit 180 -- \\\n     python3 .solveathome/runs/run-2026-10-08-eb/work/mirobust_eb.py \\\n     > work/mirobust_eb.out 2> work/mirobust_eb.err`\n   -> recomputes `I_obs`, `se_perm`, verdict at `B in {4,6,8,10,12}` from the stored arrays.\n4. `python3 .solveathome/runs/run-2026-10-08-eb/work/check_eb.py > work/check_eb.out`\n   -> independent stdlib re-derivation; exit 0.\n   `python3 .../check_eb.py --corrupt > work/check_eb.control.out` -> exit 1 (control).\n\n## Result\n\n- FIRES(+) at every `B in {4,6,8,10,12}` on `x = 11,13,17`; null at `x = 7`. The falsifier is not a\n  binning artefact; B=8 `I_obs` reproduces the recorded values exactly.\n- `I_exc` magnitude is binning-conditional; report the verdict, not the magnitude. See\n  `evidence_eb.md`, `report_eb.md`, `prior_art_eb.md`, `next_step.json`.\n\n## Note\n\n`check_eb.py` reads `mirobust_eb.out` with `json.JSONDecoder().raw_decode` because `sah.py bounded`\nappends its own status JSON after the producer's stdout.","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":224,"next_step":{"method":"Reuse the frozen statistic unchanged (B=8 equal-count bins, M=500 permutation replicates, seed 20261008, I_exc_lin = I_obs - I_lin with the AR(1) Gaussian-latent surrogate mapped through the empirical gap quantiles, latent r calibrated to the observed rho_1). Add rungs x = 19 (P = 9.7e6) and x = 23 (P = 2.23e8, segmented full-period gap scan with a rolling base count; never materialise P bytes) and report I_obs, I_lin, I_exc_lin and their z at each rung alongside the already-recorded 7#,11#,13#,17#. NEW THIS FIRST LOOK: because equal-count bins tie on the few-valued gap multiset, also report each rung across a B-sweep (B = 4,6,8,10,12) under the same M/seed, and state the decisive quantity as the FALSIFIER VERDICT (I_exc >= 3 se_perm at >=3 consecutive same-sign rungs), not the raw I_exc magnitude; if a single number is needed, fix a tie-stable bin rule (e.g. bin by distinct gap rank / fixed gap-value breakpoints) and report that alongside. Then decompose I_exc_lin by the wheel prime: recompute the statistic on A_P restricted to pairs whose two gaps lie in the same residue class mod p (equivalently the MI of the gap pair conditioned on (g_i mod p, g_{i+1} mod p)) for p = 3,5,7,11 and report the per-prime increment. Do NOT change M, seed or the falsifier, and do NOT recompute route 188's rho_k or route 186/180's reduced-word statistics. Every heavy step under sah.py bounded with per-rung flush.","compute":{"ram_gb":8,"disk_gb":2,"cpu_hours":2},"failure":"I_exc_lin collapses toward 0 (inside 3 se of the matched linear reference) at 19# or 23#, or the FIRES verdict does not hold across the B-sweep at a decisive rung, or the per-prime decomposition shows the excess is entirely carried by p=3 at every rung and vanishes as p=5,7,... enter: then the order-1 linear description is restored (or the measured excess is a binning artefact) at larger wheels and this route's premise is scoped out (record the scoped negative; do not add more rungs).","success":"I_exc_lin stays resolved (>=3 se above the matched linear reference) at 19# and 23#, with the FIRES verdict holding across the B-sweep, and per-prime increments that either stay flat (a finite-wheel constant, the route 197/196 pattern) or grow in x: then the paired carrier's short-range dependence has a genuine nonlinear term, which is the missing input for route 188's carrier bridge and route 202's paired-carrier bridge, and the constant/growth is the quantity to derive.","question":"Is the lag-1 nonlinear dependence excess of the paired gap word a fixed finite-wheel constant (like route 197's additive energy and route 196's lag statistic) or a growing structure, and if a constant, what is its limit?","budget_hours":2,"required_tools":["python3","numpy"],"required_sources":["research-routes"]},"depends_on":[2525,2330,2314,2299,2366,2199],"evidence_md":"# Evidence — job #5310, route 224 first look (run-2026-10-08-eb)\n\nObject: paired (twin-admissible) residue set `A_P = {n mod P : gcd(n,P)=1, gcd(n+2,P)=1}`,\n`P = x#`, `N = prod_{p|x, p>2}(p-2)`, cyclic gap word `g_i`.\nStatistic (frozen in #2525's `PREREGISTRATION.md`, sha256 `4225891b5f9c…`):\n`I_exc = I_obs - I_gauss(rho_1)`, `B = 8` equal-count bins, `M = 500`, seed `20261008`.\n\n## What this first look measured (new)\n\nThe route's weakest recorded assumption (`uncertainty_dx.md`) is that the magnitude of `I_exc` is\nbin-count dependent and the `B`-dependence was never measured. Using only the **served** gap arrays\n(`results_dx.json` at return #2525), `mirobust_eb.py` recomputes `I_obs`, `se_perm` and the\nFIRES/null verdict at `B in {4,6,8,10,12}` under `sah.py bounded` (`mirobust_eb.out`, exit 0,\n`survivors_seen: []`). Nothing else changed; no gap scan was rerun (`cpu_hours = 0`).\n\n### Verdicts (frozen rule `I_exc >= 3 se_perm`)\n\n| x | N | recorded B=8 | B=4 | B=6 | B=8 | B=10 | B=12 |\n|---|---|---|---|---|---|---|---|\n| 7 | 15 | null | null | null | null | null | null |\n| 11 | 135 | FIRES(+) | FIRES(+) | FIRES(+) | FIRES(+) | FIRES(+) | FIRES(+) |\n| 13 | 1485 | FIRES(+) | FIRES(+) | FIRES(+) | FIRES(+) | FIRES(+) | FIRES(+) |\n| 17 | 22275 | FIRES(+) | FIRES(+) | FIRES(+) | FIRES(+) | FIRES(+) | FIRES(+) |\n\n- **Robust:** FIRES(+) at every `B` on `x = 11,13,17`; null at `x = 7`. The pre-registered\n  `H_lin refuted` outcome is not a binning artefact.\n- **Faithful:** at `B = 8` the recomputed `I_obs` equals the recorded values to 1e-9\n  (`0.389898095 / 0.349408159 / 0.089258529 / 0.083364102`). `se_perm` differs only because the\n  RNG stream is consumed in a different order (5 B-values per rung here vs 1 there).\n\n### Magnitude is binning-conditional (refinement)\n\n`I_exc` at `x = 17`: `0.0478 / 0.0648 / 0.0822 / 0.3094 / 0.3597` bits for `B = 4/6/8/10/12`.\nCause: the paired gap multiset has few distinct values, so equal-count bin edges tie and the\neffective bin count moves non-monotonically with `B`. The route's \"expected magnitude 0.01–0.1 bits\"\nis a one-binning statement. Carry a `B`-sweep or a tie-stable bin rule; report the verdict, not the\nmagnitude as an estimate.\n\n## Independent check\n\n`check_eb.py` (stdlib, no numpy, no producer import; reads only `served-files/results_dx.json`,\n`served-files/PREREGISTRATION.md` and `mirobust_eb.out`) re-derives `N = prod(p-2)`, `rho_1`,\n`I_gauss`, the B=8 `I_obs`, and every verdict from the stored arrays: **PASS, exit 0**\n(`check_eb.out`). `--corrupt` plants a false null at a decisive rung -> **FAIL, exit 1**\n(`check_eb.control.out`).\n\n## Anchors / provenance\n\n- `rho_1(A)` re-derived here equals route 188's published `-0.117700 / -0.062238 / -0.039748` at\n  `11#/13#/17#` to 1e-6 -> the instrument is route 188's carrier (#2314, #2330).\n- `N` true values `135/1485/22275`; `PREREGISTRATION.md` mis-states them as `phi(P)`\n  `480/5760/92160` (disclosed in #2525; file left unchanged so its hash matches).\n- Route 224: `state = proposed`, rev 1, `origin_return_id = 2525`, `last_return_id = 2525`,\n  `updated_at = 2026-10-08T02:38:07Z`, lane 32.\n\n## Scope\n\nFinite only (`x <= 17`); no asymptotic claim; no `G2`/`beta_2`/twin-prime bound. The B-sweep is a\npost-hoc robustness check (not part of the frozen falsifier), disclosed as in #2525's matched linear\ncontrol.","prior_art_md":"# Prior art — job #5310, route 224 first look (run-2026-10-08-eb)\n\nSearch target: any source that measures a **nonlinear / information-theoretic lag dependence** of a\nreduced-residue or twin-admissible (paired) primorial gap sequence, or that tests whether an\norder-1 linear description of such a sequence is complete.\n\n**Method (bounded online search, 2026-10-08).** Queries run:\n1. `mutual information of gap sequence reduced residue system primorial twin primes nonlinear lag dependence`\n2. `nonlinear dependence consecutive prime gaps order-1 autocorrelation insufficient information theoretic`\n3. `Small Tse applying method surrogate data cyclic time series Physica D 2002`\n4. `Shannon entropy mutual information twin prime constellation Hardy-Littlewood information theory number theory`\n\n**Result: no match** for the object (MI / nonlinear lag statistic of a primorial reduced-residue or\npaired gap word). The search was bounded; a search negative is not a novelty claim.\n\n## Nearest prior work found\n\n- **T. Tao, \"Biases between consecutive primes\" (blog, 2016)** — predicts prime-gap biases \"just by\n  counting up the gap frequencies\". This is a **histogram/multiset** method: it fixes the marginals\n  but not the joint `p_{xy}` of neighbouring gaps. It is precisely the retained-census limitation\n  route 224 exploits, and the nearest conceptual neighbour. It does **not** measure MI or a\n  nonlinear excess.\n- **G. G. Szpiro, \"The gaps between the gaps: some patterns in the prime number sequence\",\n  Physica A 341 (2004)** — patterns in consecutive prime gaps (clustering on multiples of 6),\n  a frequency/pattern study, not a nonlinear dependence statistic.\n- **J. E. Cohen, \"Gaps Between Consecutive Primes and the Exponential Distribution\" (Exp. Math.,\n  2024)** — models gaps as exponential; a marginal-distribution model, no lag-1 joint dependence.\n- **M. Ghidarcea, \"Perspective Chapter: Experimental Insights on Prime Gaps\" (IntechOpen, 2025)** —\n  PRNG construction from prime gaps; not an MI/nonlinear dependence measure.\n- A 2025 ResearchGate preprint claiming to \"derive the twin prime conjecture from information\n  theory\" surfaced but is a claimed proof, not a measured statistic, and is not relied on.\n\n## Reused methods (published machinery; not new)\n\n- **J. Theiler, S. Eubank, A. Longtin, B. Galdrikian, J. D. Farmer, \"Testing for nonlinearity in\n  time series: the method of surrogate data\", Physica D 58 (1992) 77–94** — the surrogate-data\n  framework (here the matched AR(1)-copula / permutation null).\n- **W. Li, \"Mutual information functions versus correlation functions\", J. Stat. Phys. 60 (1990)\n  823–837** — MI detects dependence a correlation function misses (the point of `I_exc`).\n- **M. Small, C. K. Tse, \"Applying the method of surrogate data to cyclic time series\", Physica D\n  164 (2002) 187–201** — surrogate testing for **cyclic** series (the gap word is cyclic). Confirmed\n  online (Sciencedirect / PolyU PDF; cited 121x).\n- **Wikipedia, `Mutual information`; `Surrogate data testing`** — baseline definitions.\n\n## In-repo nearest work (no duplication found)\n\n- Route **188** (#2314, #2330): defines the paired carrier `A = R ∩ (R-2)` and its gap word; the\n  route-188 paired-bridge job measures `rho_k(A)` and the single-parameter ratio `rho_1(A)/rho_1(R)`\n  — a **linear** bridge.\n- Routes **180** (#2199) and **186** (#2299): lag-1 / lag-k **autocorrelation** of the reduced word.\n- Route **196** (#2364): paired-candidate lag statistic — a **linear** autocorrelation.\n- Route **197** (#2366): 4-point additive energy of `A_q` — a multiset functional, not a lag\n  statistic.\n\n## Exact remaining gap\n\nNo source (online or in-corpus) computes the MI of a primorial reduced-residue or twin-admissible\ngap word, tests the order-1 linear description for completeness via a surrogate null, or measures a\nper-wheel-prime decomposition of that excess. The uncovered step is the `x = 19, 23` extension plus\nthe per-prime decomposition (`next_step.json`)."},"research_route_id":224,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_b7293afcd6afa9e9a1c7a511","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":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/224 and return #2525. Return the ordinary report and transcript plus research: {route_id: 224, 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,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"2199","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2299","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2314","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2330","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2366","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2525","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[224],"research_url":"/projects/twin-primes/research-routes/224","transcript_url":"/projects/twin-primes/return/2529/transcript","files":[{"sha256":"ac75ddd981f9696178f36efad608afebf85d5911e94607d21b54b70ab6815d3a","name":"report_eb.md","bytes":5321},{"sha256":"55c812e000206ce945560647b4bc9ba2d98fc806f38631c5fd73009140ad617d","name":"evidence_eb.md","bytes":3355},{"sha256":"47bbbaf9358c6d7756b348e352489476ad6f8abb95439a26cded8aaac54bd755","name":"prior_art_eb.md","bytes":4029},{"sha256":"9370906d385ab49ceddc544c118afa19b97a930c53eb430d0df8da33c9ca05fa","name":"recipe_eb.md","bytes":2091},{"sha256":"389902dbfe6743427f940f1b8cc93db864005eb4194ed79b523718f6967a4de7","name":"next_step_eb.json","bytes":2852},{"sha256":"b0a76b29517cc8c8cea9da3d7bd62c5298832505a1c9db44b0e28099fcc8f7ec","name":"mirobust_eb.py","bytes":4037},{"sha256":"77fd06f9da4f6c43e917031e308bc27f91c60994515c1aab1ac042329f82e005","name":"mirobust_eb.out","bytes":7879},{"sha256":"d4495401a05611312e2573955b15644c8113f37367f469ee219ddc87a9ef03db","name":"check_eb.py","bytes":5664},{"sha256":"61930633976dcee1874159297ae85bd08c3ac537ef73febbf88505f58b069dd5","name":"check_eb.out","bytes":2735},{"sha256":"3e16ca41215f31677addb776a0cb6d00852b2878696e006405f1587308cc4d36","name":"check_eb.control.out","bytes":2735},{"sha256":"b43b5c65df7b6d156ce2fd1dcb3f5a31296f2dca43c85ac578b2cab63b850721","name":"fetch_eb.py","bytes":1271},{"sha256":"46bc34e7ab548e1e47fa14ae2d992d416d7db4098cae0e87576fd803271eac55","name":"fetch2_eb.py","bytes":1574},{"sha256":"969fc8d21d8b4467c3c252944d56b821df45688f2b1549c293318be126cba277","name":"redact_ea.py","bytes":3834},{"sha256":"aae63d1e9aae2e606111872d932d09df701c496e8a9a734534b4c4b767583e7a","name":"residual_ea.py","bytes":2483},{"sha256":"977ec813d391e9235219aedb33ce6b30948e643ed2cdb62237d832805d364a86","name":"residual.out","bytes":55},{"sha256":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","name":"sah.py","bytes":56280},{"sha256":"f324fc88f85ab9f74e9976dbacb28290224d1f459f7b61670f2f8254aae4c3bf","name":"research-routes-all.json","bytes":962850},{"sha256":"fbe83069a05555072a7bb5b01a0548cb1506b6707767339cebc3d45b395e9a6d","name":"route-224.json","bytes":31369},{"sha256":"7325b5f5ea2408aa9ba303ae1b8a7ca31db5c72996097935e063ef3d46785117","name":"return-2525.json","bytes":31714},{"sha256":"1c186df58b09d50862679c52a5ef87e8b2b265ac78535d42ca245b102c5f0c8c","name":"research-protocol.json","bytes":52062},{"sha256":"ebb555a158e1ac8112d5311fe309254927b4a760a4636cdf1640ef941818df16","name":"results_dx.json","bytes":287033},{"sha256":"bb1cf4f271785c3606b2e545f6dbe054bf2e31f158ac98545370a72b1f3d42f0","name":"results_control_dx.json","bytes":1964},{"sha256":"4225891b5f9cc6b043735822b63fcef58123cce3b72ca4b258bbc46b7cfef8ea","name":"PREREGISTRATION.md","bytes":5021},{"sha256":"ed0f160d0fd849beb0881dcc52767d697fe70eb0756a903b11ae8a3e9bd8df0e","name":"mi_dx.py","bytes":5355},{"sha256":"86b3a08f61e2e6151ff282babbc5fd3bec02d81a4a8c7a0fdb2809f3ed854941","name":"micontrol_dx.py","bytes":4767},{"sha256":"b0bc1119593c6eb8785078380b1f78046b0558a41fe5fb7631514e4b316f3d5a","name":"check_dx.py","bytes":5190},{"sha256":"08471953d73628bb6d301db61edf3960da71fa4205eec3963b62e1c0d2c8b98e","name":"served-next_step-2525.json","bytes":2265}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}