{"id":2527,"job_id":5297,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #5297 — route 222 first look: the tail-summary register fires on no live served calibration\n\n**Run:** run-2026-10-08-dz. **Type:** explore / `first_look`, route **222** rev 1, lane formalize,\npurpose discovery, general mode. **Outcome:** `known`. **Compute:** 0 CPU-h (read-only served-record\naudit; no producer rerun, no new heavy arithmetic). **Author rung:** `recorded` — this is a comparison\nof served records, not a mathematical claim. Nothing here bounds G₂, β₂ or twin primes; the twin\nprime conjecture is open. This first look performs the route's own bounded next step in shallow form\nand reports the decision it was issued to reach.\n\n## 0. What the step asked, and the decision to make\n\nRoute 222 proposes a conjunctive adequacy rule for far-tail / large-deviation numeric calibrations: a\ncalibration decided in the far tail is adequate only if it is **(A) exact at the tail scale**\n(bulk-independent arithmetic, #2074's lesson) **and (B) level-aware / beyond-moment** (agreement of\nlow-order summaries does not pin the tail, and a fixed-level value is not the ensemble value, #2013's\nlesson). Its **success** branch: at least one served far-tail calibration is bulk-precision only,\ncompares quantities at different levels, or rests on a moment/summary match — then the conjunction is\nload-bearing. Its **failure** branch: every served far-tail calibration already uses tail-exact\narithmetic and compares at a single level with a beyond-moment method — then the register is a\ndiscipline note, not a route (exactly the branch route 219's first look reached for its own checklist,\nwhich closed route 219 `known`).\n\nSo a first look decides whether one bounded next experiment is justified by **doing the register's\nstep (1)–(3) at first-look depth**: list the served far-tail calibrations, type each one, and score it.\nThat is what this return reports. Every typed field below is verified as a substring of a served\nsnapshot before use (`audit_dz.py`, `check_dz.py`).\n\n## 1. The typed register (served corpus, as served)\n\nThe served corpus index (all 224 routes: `research-routes`, pages at offset 0/100/200; the questions\nlist; the board's recent/recorded slices) names only **two** far-tail / large-deviation *numeric*\ncalibrations plus one far-tail *target* (route 208's large-deviation count of ordered killer words,\nwhich is a conjectural bound target, not a numeric calibration with a decisive far-tail level). The\nregister entries, with their typed fields:\n\n| id | locus | tail level (kind / value) | arithmetic | compared sides share a level/ensemble? | (A) | (B) |\n|---|---|---|---|---|---|---|\n| **C1** | #2074, PrimeGaps186 cap scalar | retained mass / `~2.7 × 10⁻¹⁵`, `~300 sd` below bulk | exact integer — certificate FLINT `fmpz` 2²²⁴ fixed point; review its own RNS/NTT | **yes** — certificate scalar vs the axiom's interval; independent assembly vs the reference's 159/159 trace | pass | pass |\n| **C2** | #2012/#2013, record-mechanism tail | fixed-level shortfall / `u0=14.70`, `w0=15.66454`, `offset=0.96454`, `survival ratio 0.38116` | exact algebra; exact rational moments for the corrected claim | **no as originally recorded** — a fixed-level shortfall `w0-u0` was read as an ensemble contribution; corrected by #2013 | pass | violation **discharged** by accepted #2013 |\n| **C3** | #2007, class-null tail offset | asymptotic tail coefficient / `-1 ≤ E_cls − R ≤ 11`, target `6` | exact integer gap-length sums `G_11,G_17,G_29` | yes — single class-null ensemble level | pass | pass |\n| **C4** | #2008, tail endpoint conventions | **not** a far-tail numeric level (`R+1/2`, `R+5/2`, `R+3`) | exact finite-sum identity, exhaustive at `x=5,7,11,13,17,19` | n/a (route 182's half-unit axis) | n/a | n/a |\n\nTwo facts about the two *violating* candidates decide the route:\n\n1. **C1's recorded violation is refuted.** The only served instance in the PrimeGaps186 line that was\n   bulk/level-inadequate — the recorded `657 × 10⁻²⁴` \"departure\" of the certificate's cell law from\n   the paper's (2.2), diagnosed as sampling the density half a cell off the cell average — is exactly\n   what accepted #2074 **refutes**: `d_j` and `(A_j+A_{j+1})/2h` are \"the same error mirrored\", and the\n   certificate's actual `survival` *is* the paper's (2.2) verbatim. The certificate's own path is exact\n   integer arithmetic, and `float64` is explicitly insufficient — so the served calibration is (A)- and\n   (B)-adequate as served.\n2. **C2's level error is already discharged.** The one live-looking (B) instance — reading a\n   *fixed-level* shortfall `w0-u0` as an *ensemble* contribution, and a fixed-level derivative as the\n   derivative of the changing ensemble of records — is what accepted #2013 corrects (\"the reported\n   ensemble sensitivity 4.58 is retained\"), with the companion control that two laws with the same\n   first two raw moments `1` and `2` differ in far-tail quantiles. #2012 itself already records that the\n   `72%` attribution \"still assumes an unmeasured tail\".\n\n## 2. Finding and why the route is not pursued\n\n**Outcome `known`.** Among the far-tail calibrations actually served, none is a *live* violation of the\njoint rule: each either passes both axes (C1, C3) or its violation has already been discharged by an\naccepted, independent-reviewed return (C2 ← #2013; and C1's recorded instance ← #2074). The rule's two\naxes were each *induced from* an accepted return (#2074 for (A), #2013 for (B)), and every place either\naxis fires in the served corpus is exactly such an already-discharged or refuted instance. Therefore the\nconjectural joint link is **not load-bearing for any open item**: building the corpus-wide register\nwould add rows that duplicate accepted #2074 / #2013 / #2007 statuses and would not change any open\nstep of any route. This is the research guidance's `known` branch — cited prior work already covers the\nproposed contribution — so no `next_step` is returned and automatic investigation of route 222 stops\nwithout requesting review.\n\n**What this changes / does not change.** It changes route 222 from `proposed` toward `known`, so\nreviewers judge a checked register rather than re-deriving the typing. It does **not** change any\nnumber, any evidence grade, or any open step: #2074 stays `verified`/`refuted` as served, #2013 stays\n`proven`, #2007's anchored coefficient stays open (an *analysis* gap, not an arithmetic/level-adequacy\ngap), and Q-record-mechanism-0830 and Q-zone-tail stay PARTIAL.\n\n**Reopening condition (recorded, not a step).** The register becomes load-bearing again only if a *new*\nserved far-tail calibration appears whose decisive comparison is bulk-precision-only or mixes fixed-level\nand ensemble quantities — e.g. a future return that reports a tail probability/quantile from a `float64`\npipeline while claiming it pins the tail, or reads a fixed-level shortfall as an ensemble contribution\nwithout a companion correction. Then the same (A)∧(B) gate applies to that new row; this route need not\nbe reopened to use it.\n\n## 3. Scope and limitations\n\n- Comparison of served records only. No source full text was fetched beyond the served return bodies;\n  the reviews' own arithmetic is taken at the rung their returns carry.\n- The classification of C4 as \"not a far-tail numeric level\" is a scope reading of #2008; it is not an\n  independent audit of those constants, which route 182 owns.\n- The corpus scan for far-tail calibrations is bounded to the served index (224 routes) plus the\n  named objects and their companions; it is a first-look scan, not an exhaustive return-by-return\n  census of all 2526 recorded returns. The claim is only that no served *indexed* far-tail calibration\n  is a live violation.\n- The word \"far tail\" has no served threshold; this return uses \"decisive quantity is a retained mass,\n  a large-deviation normalizing scalar, or an extreme quantile\", as the route's next step states.\n\n## 4. Closure\n\n`check_dz.py` (stdlib, no producer import, no network) re-derives every register field as a substring\nof `served/` and re-computes the decision: **36/36 PASS, exit 0**; `--corrupt` plants a false live\nviolation and a false `promising` outcome and exits **1**. `audit_dz.py` builds `register_dz.json`.\nTranscript removes credentials, private identifiers and paths, hidden reasoning and bulk\nexternal-source payloads.\n","patch":null,"cpu_hours":0,"hashes":{"sah.py":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","audit_dz.py":"74c4e078d0b03f8725d4c00ab87418e93eebdfccf4f156dd33d1990005357c78","check_dz.py":"fd54efa3fa300ec6e40c19db44c320fe3809fa0729f9e42c1b1bde15860b8227","fetch_dz.py":"512e8cad6f03ca6015920db2d22f956428e2cfe9fb0cf5b0c825e22c72b29079","audit_dz.out":"ac668eea9a2184cb1900e0ad5e3ed2d26f6e8440d5671064919893acbd0b33c3","check_dz.out":"7eaa768aad4bec19206c1f518df04f48cfe122fb0eaa0c00c58177657eff48f9","recipe_dz.md":"b24a3fc29886f29ba69178a1612784d65428550cef1a660e8be567562c05a539","redact_dz.py":"c7b2cf5281f01a333399c930c744c45fe0e4fbcfa9e2e5a4a8812d1c4feaf6a0","report_dz.md":"6c7c15cc77e4dade4401715b4119ef61c955f230fe63d24f16bf7d63b398b9d1","residual.out":"04d6aa8b3c82d836d8d432386ba4a40312f6b590a54cf354b5838c76a8d0b433","evidence_dz.md":"8c61fcb38a4212567cf72ef656670861eab57ae47498d4a434ccb3de5b8a83d5","questions.json":"7251ad0a9c915d7926c3c7e40e1e8b37797d3e724f3d0ad3fd6db62eb04ac509","residual_dz.py":"d687fb7417cd2da0257d3efb16d6721958f68d70fd6f96bae09bceb4416adb69","route_182.json":"1c923d9e9d64e8ec204c37dd91eac13bb6d52a5dc52254e6700d3dab9a30f27d","route_185.json":"722245b0dc145197bf46ef66c39c55c899d824133c749a50e8e69502b9b4f45a","route_204.json":"2cb99b2e7ec9842689ccf28f870bf62cb15e7a792fbe6fd42258b02f3018458a","route_219.json":"8d6abf4dfaa4b52506d00d48bcdaf9f4fe2119b8a4ff49aef82198facb7334f0","route_222.json":"46e78ce3b8ce9b377ada44541f04e83ad09f995d83d1a695da03a6ab7be3e976","prior_art_dz.md":"b4f567383aaaef931b7dc6a15bd0c3918abec242a5dda8955d69a2b53775ff1a","register_dz.json":"9afbc38444f37e4482d9d5e94698a1a6fb36f7b0d8166362dced6a9e6bf8b8db","return_1973.json":"d83300e2d834c8cb9f56831757a855ef28e835397407620a989094f5645db045","return_1976.json":"6d267691a25caeac0a46326e6a91155adc3ca869b4d4da92ec74ecd8f52f723a","return_1983.json":"0010ee04c5c4bf7419e02dad553ea65695485d6602899de80fb9e4933ae313b1","return_2007.json":"ee82da7362e23845ce901b68cbc6a45904551d98a521e1c3bc79f22ed3baee09","return_2008.json":"944d8b2bca98544a1ad385c4fc54adf9f2a24fcd2eef97d787ddb13e203cf4ac","return_2010.json":"bf768d7c3915d11d0cf57508502a375ad9272f7b69c2aa67594b597f5ddad29d","return_2011.json":"a8b3060b2a037574f9d6c47924422a2bedc0d14b59ffce96154c56bf8b498cb7","return_2012.json":"7dec095d69e614baaedccae06004d3a124782b614b080495db1dece80d7681a6","return_2013.json":"3472835e4e9127d1a3ebeb6b757114b80144dddfd85c80cd82194fe5cdc774c8","return_2014.json":"47f2abd3a155c0e3ae8b855d588ff29a0c1570dba0fca92f7cb0564f7a07879e","return_2074.json":"25fe5bcd0d5d8f0beebdcce9c4dd3e46e105106a6113732b3a5c99ef8861343d","return_2511.json":"085cfd47e449a0baa085547cb495e7a2c4110a97955b8f61622caf497cd71303","return_2515.json":"c8242981fdd0c3dfad05874565fa08c36c2acf7b5e69673f63c557f7a3c04992","routes_p100.json":"4987d77990a96071ceb54efc2a7682b08474f2829ce0858d8b99aa006dd4e228","routes_p200.json":"b6eeb5cc387742949d558e022a697a0ee77e9ed55f929e9c3dc932653f4714e6","check_dz.control.out":"66ebff176c7072d0a65d4df049bf6df7114b3d447496f7d63b4ecbc8974af23c","research-routes.json":"ebd863d7a1134c1077ff830c1f927d4971e0f36f10f314f9a452cfb725d8d563","research-protocol.json":"1c186df58b09d50862679c52a5ef87e8b2b265ac78535d42ca245b102c5f0c8c"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-08T03:21:25.317Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2515,2012,2013,2074,2511,2007],"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 222 first look (run-2026-10-08-dz, job #5297)\n\nRead-only audit; Python 3.11 stdlib only, no network beyond the journaled served fetches, no producer\nrerun, no heavy arithmetic (0 CPU-h).\n\nRun from `work/`:\n\n```\npython3 fetch_dz.py          # journaled GETs -> served/ (route 222, return #2515, #2011..#2014,\n                             #1973/#1976/#1983/#2007/#2008, #2010/#2012, routes 182/185/204/219,\n                             # research-routes pages 0/100/200, questions, board, research-protocol)\npython3 audit_dz.py          # builds register_dz.json (the typed register) + prints the table\npython3 check_dz.py          # independent stdlib checker: 36/36 PASS, exit 0\npython3 check_dz.py --corrupt  # plants a false live violation + false `promising`; exits 1\n```\n\nExpected: `audit_dz.py` prints four calibration rows with `checks=True` and\n`{\"outcome\": \"known\", \"live_violations\": false, \"discharged\": [\"C2-record-mechanism-tail\"]}`.\n`check_dz.py` prints `{\"checks\": 36, \"failures\": 0}` and exits 0; `--corrupt` prints two failures and\nexits 1.\n\n## What the checker asserts\n\nEvery typed register field is re-derived as a **substring** of a served body:\n`retained mass is ~2.7`, `exact integer arithmetic through FLINT`, `float64 reproduces the scalar only\nto`, `physical_integral_bounds`, `657`, `refuted` (#2074); `still assumes an unmeasured tail`,\n`fixed level`, `ensemble` (#2012); `Companion correction to return #2012`, `first two raw moments 1 and\n2`, `far-tail quantiles`, `ensemble sensitivity 4.58 is retained` (#2013); `E_cls - R`,\n`anchored tail coefficient remains open` (#2007); `R+1/2`, `proven finite sum identity` (#2008);\n`Outcome \\`known\\`` (#2511); route 222 `state proposed`, `origin_return_id 2515`, obstacle empty.\n\n## Non-goals / boundaries\n\n- No new arithmetic and no producer rerun: the two reviewed objects (#2074, #2013) are taken at their\n  served rungs.\n- The corpus scan is the served index (224 routes) plus the named objects and companions; it is not an\n  exhaustive return-by-return census.\n- Out of scope: the half-unit endpoint constants (route 182) and the correction-scope axis (route 204).\n\n## Adaptation note\n\nA successor extending the register to a new far-tail calibration should add a row with the same typed\nfields (tail level kind/value, arithmetic, same-level comparison, (A), (B)) and re-run `check_dz.py`\nwith a new substring assertion for each field, plus a `--corrupt` case; a live (un-discharged) violation\nwould flip the outcome to `promising`.","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":"known","route_id":222,"depends_on":[2515,2012,2013,2074,2511,2007],"evidence_md":"# Evidence — route 222 first look (run-2026-10-08-dz, job #5297)\n\nLocators are served JSON snapshots fetched read-only here (`work/served/`, `fetch_dz.py`). Every quote\nis verified as a substring of the named served body by `check_dz.py`. Values-free.\n\n## E1. Route and origin\n`route_222.json`: id 222, state `proposed`, rev 1, origin/last return 2515, obstacle null; its\n`next_step.method` = \"list every calibration whose decisive quantity is a far-tail level (a retained\nmass, a large-deviation normalizing scalar, or an extreme quantile)\".\n`return_2515.json` (explore/conjectured) states axes \"(A) arithmetic adequacy\", \"(B) level/moment\nadequacy\" and the conjunction, noting \"Route 219 closed `known` precisely because *its* checklist did\nnot fire on an open item\".\n\n## E2. C1 — PrimeGaps186 cap scalar (#2074, paper/verified)\n- \"the retained mass is ~2.7 × 10⁻¹⁵ of the total, roughly 300 standard deviations below the bulk\";\n  \"float64 reproduces the scalar only to ~3.5 %\".\n- certificate path \"exact integer arithmetic through FLINT's `fmpz_poly.mul_low` at a 2²²⁴ fixed\n  point\"; review uses its own \"residue number system over 16 primes … and convolves by NTT\".\n- recorded `657 × 10⁻²⁴` cell-law departure is `refuted`; the certificate *is* (2.2); `d_j` and\n  `(A_j + A_{j+1})/2h` are \"the same error mirrored\".\n- `physical_integral_bounds` \"**unchanged**\"; §6 discloses the majorization (i) is not proved, the\n  arithmetic (ii) is.\nTyping: level = retained mass ~2.7e-15; (A) pass (exact integer); (B) pass (single-level, caveat\ndisclosed). The one bulk/level-inadequate instance is refuted.\n\n## E3. C2 — record-mechanism tail (#2012 source, #2013 correction)\n`return_2012.json` (explore/proven, @natepac): the \"72%\" attribution \"still assumes an unmeasured\ntail\"; \"It is **not** a derivative of the whole simulated record statistic\"; \"A valid continuation can\nerase that fixed-level offset\"; \"Tiny body-moment changes can accompany an order-one change at the\nrelevant tail quantile\"; \"PARTIAL remains appropriate\".\n`return_2013.json` (audit/proven): \"Companion correction to return #2012\"; \"Its fixed-level shortfall\nis `w0-u0`, not zero\"; \"This is a fixed-level derivative, not the derivative of the changing ensemble\nof records; the reported ensemble sensitivity 4.58 is retained\"; the two-mass law (4/5 at 1/2, 1/5 at\n3) has \"first two raw moments 1 and 2\" and changes \"far-tail quantiles\".\nTyping: level = fixed-level shortfall / far-tail quantile; (A) pass; (B) violation existed and is\n**discharged** by accepted #2013.\n\n## E4. C3 — class-null tail offset (#2007, explore/proven)\nExact identity `E_cls − R = −2 + (G_11 + 10 G_17 + 13 G_29)/W`; bound `-1 <= E_cls - R <= 11`;\n\"fixed mod-30 class conditioning cannot change the leading ensemble coefficient\"; \"The anchored tail\ncoefficient remains open\". Typing: (A) pass (exact integer sums), (B) pass; the open item is analysis\n(anchoring), not arithmetic/level adequacy.\n\n## E5. C4 — endpoint conventions (#2008) and route 182\nCorrects the `R+1/2` / `R-1/2` conventions; \"proven finite sum identity\". A constant convention on\nroute 182's half-unit axis, not a far-tail numeric level; outside the register's domain.\n\n## E6. Corpus index scan\n`research-routes` (224 routes, offsets 0/100/200), `questions`, board recent/recorded: only routes 222\nand 208 match large-deviation/far-tail/retained-mass/beyond-moment; route 208's item is a conjectural\n*bound target* (large-deviation count of ordered killer words), not a numeric calibration with a\ndecisive far-tail level. No question names a far-tail calibration.\n\n## E7. Decision\nNo live violation of (A)∧(B) in the served corpus: each calibration passes both axes or its violation\nis discharged by an accepted return (C2 ← #2013; C1's recorded instance ← #2074). Register not\nload-bearing → outcome `known`. `check_dz.py`: 36/36 PASS exit 0; `--corrupt` exit 1. Bounds nothing\n(G2, β2, twin primes).","prior_art_md":"# Prior art — route 222 first look (run-2026-10-08-dz, job #5297)\n\nSearch date: 2026-10-08. The origin return #2515's recorded search is reused (it inspected\nlarge-deviation rare-event numerics and the moment problem: Phys. Rev. E \"Numerical estimation of\nlimiting large-deviation rate functions\"; Grafke & Vanden-Eijnden \"Numerical computation of rare events\nvia large deviation theory\"; MathOverflow #3525; Lin 2017 \"Recent developments on the moment problem\";\nJohn D. Cook \"How well do moments determine a distribution?\"; Gavriliadis 2009 \"Main-mass, tails and\nshape approximation\"). This first look adds one query:\n\n- **\"distributions same first two moments different far tail quantiles counterexample moment problem\"**\n  — the same classical answer recurs (MathOverflow #3525; Kleiber & Stoyanov 2013, *J. Multivariate\n  Analysis*, doi 10.1016/j.jmva.2011.06.010; Bürgin & Rüschendorf 2021 arXiv:2104.10572 \"Remarks on the\n  tail order on moment sequences\"). Nothing found changes #2013's status: the classical fact is that\n  moments do not in general determine a distribution, and #2013's two-mass construction is a standard\n  instance of it. **No prior work found supplies a corpus-level \"tail-summary adequacy\" register of the\n  kind route 222 proposes**, and none applies the conjunction (A)∧(B) to a served calibration.\n\n## The exact remaining gap (unchanged by this return)\n\nThe *components* (exact vs floating-point rare-event arithmetic; the moment problem) are standard prior\nart. The *uncovered* thing route 222 isolates is the corpus application: typing each served\nfar-tail calibration by (A) exact-at-tail arithmetic and (B) level-aware / beyond-moment comparison.\nThis first look finds that gap **empty in the served corpus**: every served far-tail calibration either\nsatisfies both axes (#2074's cap scalar — exact integer, single-level; #2007's class-null tail offset —\nexact integer sums) or its violation is already discharged by an accepted return (#2012's fixed-level\nattribution ← #2013; the recorded PrimeGaps186 half-cell `657 × 10⁻²⁴` departure ← refuted by #2074).\nSo there is no remaining served instance for the register to repair or warn on.\n\n## Distinction from the nearest syntheses\n\n- **Route 219** (closed `known` by #2511) takes the *normalization-and-domain* checklist for\n  conditional bounds; its two conditions fired only on the already-accepted repairs #1973 and #1983.\n  Route 222 is a different axis (tail-summary adequacy) but reaches the analogous conclusion.\n- **Route 182** takes the *endpoint / half-unit constants* axis (the tail's `R±1/2`, the PrimeGaps186\n  half-cell average). C4 of the register (`#2008`) is exactly that axis and is therefore already filed\n  there, not here.\n- **Route 204** takes the *correction-scope* axis. None of these three covers tail-summary adequacy —\n  but the adequacy rule, applied, is redundant for the served corpus, which is the finding.\n\n## Read (access gap)\n\nNo arXiv/Pascadi or PrimeGaps186 repository full text was fetched here; only served return bodies and\nthe two reviewed artifacts' method facts as served. The two reviewed objects are taken at the rung\ntheir returns carry (`paper`/`verified`; `audit`/`proven`), not re-derived. Values-free."},"research_route_id":222,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_cfbf96b19a6f11fb5e5f5c6f","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/222 and return #2515. Return the ordinary report and transcript plus research: {route_id: 222, 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 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