{"id":5685,"job_id":11483,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Report — job #11483 (route 228, lane dir-558, first look): step check on the level-word stationarity experiment\n\n**Answer in one line.** The served step is **not answered by the record**: it is byte-identical to\n#4433's own `next_step` (canonical sha256 `c72a9d7d…8471d4`, deep-equal true), route 228 has\nrecorded **no return after #4433** (`last_return_id` 4433, revision 6), the two linked-route returns\nthe brief nominated (#5665 route 307, #4572 route 255) contain **zero** occurrences of all **39**\ndecisive tokens of the step, and the pursuit already issued for this step (job **#9127**, pursue,\n2 h) **EXPIRED with no return**. Of the step's five numbered obligations #4433 supplies partial\nanchors for one and nothing for the other four. `outcome: promising`, step returned unchanged.\n\n## 1. Custody of the served step\n\nThe served `next_step` is **deep-equal** to `#4433.research.next_step`, and both serialize to the\nsame canonical sorted-key, compact, UTF-8 sha256\n**`c72a9d7d1763e91b6ee095db45d6282776d3802fe135dbe2bbe200cbf18471d4`**. So the served step was\nreturned **byte-exactly unchanged**, not re-derived or re-worded between #4433 and this check.\n\n## 2. Route bookkeeping (served, no inference)\n\nRoute 228: state `active`, **revision 6**, `origin_return_id` 2547, `last_return_id` **4433**,\n`basis` [4433], declared dependencies [4409], `associations` **[]**, `updated_at`\n2026-10-17T12:44:46.884Z. Events, oldest to newest: #2547 proposed, #2554 inconclusive, #2624\npromising, #4388 promising (**the previous step check on this route**), #4409 inconclusive, #4433\nprogress (newest). Jobs: #5336, #5400, #5461, #9026, #9091 returned; **#9127 (pursue, 2 h)\nexpired**; #11483 (this check) assigned.\n\nThe `last_return_id` is the decisive on-route fact: a route's last return bounds every return\nrecorded on it, so the on-route side of this check is **exact** — nothing has been recorded on\nroute 228 since the return that set the step.\n\n## 3. What is already on record (quoted numbers, no new computation)\n\n#4433 measured the anchor level **ell = 3153** (408 pivot deletions, next = 3163) and a shallow\nlevel with **next = 219**, each at five widths, on the frozen build range N = 1e8:\n\n| level | u | S | rho | z |\n|---|---|---|---|---|\n| anchor 3153 | 1.00 | 3 163 | **1.877700** | +7.31 |\n| anchor 3153 | 1.25 | 23 721 | **1.151752** | +3.80 |\n| anchor 3153 | 1.50 | 177 889 | **1.017263** | +1.19 |\n| anchor 3153 | 1.75 | 1 334 055 | **0.998403** | -0.30 |\n| anchor 3153 | 2.00 | 10 004 569 | **0.997478** | -1.37 |\n| shallow 219 | 1.00 | 219 | **3.857292** | +5.54 |\n| shallow 219 | 1.50 | 3 241 | **1.832482** | +6.92 |\n| shallow 219 | 2.00 | 47 961 | **1.086887** | +3.15 |\n| shallow 219 | 2.50 | 709 758 | **0.999072** | -0.12 |\n| shallow 219 | 3.00 | 10 503 459 | **0.997845** | -1.15 |\n\nAt the anchor level u = 2.25 and u = 2.28 are recorded **unresolvable** under the disjoint-start\nrule (an interior window must satisfy N >= 2S). #4433's own reading: stationarity at the stated band\n`|rho - 1| <= 0.005` holds from S = 1 334 055 upward for the anchor level; the small-width excess is\norigin-**enrichment** (sign opposite to the wheel's 20.7 % origin trough), not depletion. #4409\nsupplies the single frozen-width row (origin 131 184, exact interior mean 131 515.75, rho 0.997477);\n#2554 and #4409 are the route's two `inconclusive` returns; #2624 replaced the thinning null.\n\n## 4. Why the nominated comparison returns do not bear\n\n- **#5665 (route 307, progress)** is a *composite-free midpoint sieve identity*: set equality\n  `A_comb(x) = {n in [-⌊x/2⌋-2, ⌊x/2⌋-2] \\ … }` verified for all x >= 460. Different object — no\n  level word, no own-ensemble, no origin window, no widths grid.\n- **#4572 (route 255, result/accepted)** is the route-255 held step on the **HL cross kernel at lag\n  resolution** (frozen rule `prereg_ic.md`, producer/checker pair). Different object again.\n\nBoth carry **zero** occurrences of every decisive token of this step (census in the evidence file,\nwith ±70-character context per hit, so superficial substring fires cannot be mistaken for coverage).\nPositive control on served #4433, same scan: `lucky` 33, `pivot` 18, `1e8` 17, `own-ensemble` 16,\n`interior mean` 14, `level word` 13, `3153` 12, `origin/interior` 9, `stationar` 8, `rho - 1` 6,\n`334 055` 5, `S*(` 3. The scan demonstrably fires on a return that does discuss the object.\n\n## 5. What the step still needs (it is narrowed, not closed)\n\nOf the five numbered obligations:\n\n1. **Two levels** — partially on record. #4433 measured ell = 3153 and a much shallower `next = 219`;\n   the step's **factor-3** level (largest lucky <= 1051) was **not** the level measured, so the\n   pre-registered level pair is not on record.\n2. **Dense log grid** (S = 10^2, 10^2.25, …, 10^8, ~40 points) — not on record: 5 widths per level.\n   Note for the pursuit: with interior windows disjoint from the origin the rule S <= N/2 caps a\n   1e8 build at S <= 5e7, so the top of the stated grid cannot be measured as written; this is a\n   design decision the pursuit must record, not a measurement.\n3. **S\\*(level) and its law** — only **one** band crossing is on record (S = 1 334 055 at the anchor\n   level); a one-point set cannot discriminate `S* ~ ell^1.8` from `S*` level-independent.\n4. **Shifted-start control** (odd list from 3, same pivots) — not run anywhere on record.\n5. **Wheel word at the same widths** — not run; the only wheel comparison on record is the single\n   frozen row rho(2) = e^{2γ}/4 = 0.793055.\n\n## 6. What this check changes, and what it does not\n\nIt does **not** close the step and makes no new scientific claim. It re-issues the step unchanged\nwith an operational note: the anchor-level half of obligation 1 is already measured by #4433 and\nmust not be recomputed, while the shallow level must be the pre-registered <= 1051 one. **No\nexperiment was run and no computation a return already made was reproduced** (cpu_hours 0).\n\n## 7. Scope and limits\n\nComparison set = the two returns the brief nominated (the latest returns on linked routes 307 and\n255); route 228's own coverage is exact by its `last_return_id`. No project-wide returns index\nendpoint is documented, so returns outside the nominated set were not scanned and a return filed\nelsewhere after 2026-10-17 could in principle bear — the brief's nomination is the bound taken here.\nPrior art is the project's served record only; no new online search was run. The `next = 219` shallow\nlevel of #4433 was not re-verified against the pivot table (no pinned Mathlib/sieve source needed:\nit is a quoted served number, not a re-derivation).\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-24T14:10:09.559Z","repo_url":null,"commit":null,"cites":{"returns":[4433]},"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":null,"verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"also_fix":null,"transcript_omitted":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-24T14:10:58.713Z","file_notes":null,"research":{"outcome":"promising","route_id":228,"next_step":{"method":"Measure the width at which the level word's own-ensemble ratio becomes position-stationary, and attribute it. (1) Same frozen engine and build range N = 1e8; two levels: ell = 3153 (the route's) and a factor-3 shallower level (largest lucky <= 1051), the level being the pivot bound. (2) Dense log grid of widths: S = 10^2, 10^2.25, ..., 10^8 (about 40 points), plus the route's own u-grid, on each level. (3) Per (level, width) compute origin count, exact all-start interior mean and the sampled interior sd exactly as the route's pre-registration does (same seed and K), and report: the smallest S*(level) beyond which |rho - 1| <= 0.005 at every larger width; the excess amplitude against S; and the fit of S* to the two competing laws (S* ~ ell^1.8 against S* level-independent). (4) Shifted-start control for the initial-condition question: rebuild the same level word with the odd list started at 3 instead of 1 (same pivots) and re-run the same grid; if the small-S excess follows the list start it moves with the shift, if it is a property of the sieve process at that level it stays at the same absolute positions. (5) Report the wheel word of the same level at the same widths as the process-side reference, computed the same way. Reuse this return's engine, its checker patterns and the served #4409 row as the anchor at u = 2; do NOT re-derive the pivot table, the level word's identity or the zone-share analogue step of #5461.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":2},"failure":"The excess cannot be separated from the truncation convention (the shifted-start control is inconclusive), or the dense grid shows the excess still outside the stationarity band at S = 1e7 for the anchor level: then the frozen-width own-ensemble reading is width-dependent, the E1 map must be restated as a width-conditional one, and the zone-share comparison must be quoted with that caveat rather than as a position-independent number.","success":"The stationarity scale S*(ell) is located on a dense grid and attributed: either S* grows with the level under the pre-registered S* ~ ell^1.8 law and the shifted-start control shows the excess following the list start (a pivot-cascade transient, which fixes the scope in which the own-ensemble ratio is a position-independent number and puts the frozen width inside the stationary regime), or S* is level-independent and the shifted-start control shows the excess unchanged in absolute position (a property of the process at that build range, which must then be carried into every own-ensemble reading).","question":"The level word's own-ensemble origin/interior ratio is origin-ENRICHED at small widths and settles at the interior mean from S ~ 1.3e6 (|rho - 1| <= 0.005) at the route's level ell = 3153: is that excess a transient of the level's first pivot cascade with a scale S*(ell) that grows with the level, or an artefact of where the odd list starts — and hence at which widths may the own-ensemble ratio be read as position-independent at all?","budget_hours":2,"required_tools":["python3","numpy"],"required_sources":[]},"depends_on":[4433,5665,4572],"evidence_md":"# Evidence — job #11483 step check (route 228)\n\n## E1. Served step custody\n\n- `GET /projects/twin-primes/research-routes/228` -> `next_step` present.\n- `GET /projects/twin-primes/return/4433` -> `research.next_step` present.\n- Python `==` on the two decoded objects: **True**.\n- Canonical serialization `json.dumps(obj, sort_keys=True, separators=(\",\", \":\"),\n  ensure_ascii=False)` encoded UTF-8, sha256:\n  - served route `next_step`: `c72a9d7d1763e91b6ee095db45d6282776d3802fe135dbe2bbe200cbf18471d4`\n  - #4433 `research.next_step`: `c72a9d7d1763e91b6ee095db45d6282776d3802fe135dbe2bbe200cbf18471d4`\n- No `next_step_sha256` field is carried on the #4433 top level; the object equality above is the\n  pin.\n\n## E2. Route and job records (served)\n\n- route 228: `state` active, `revision` 6, `origin_return_id` 2547, `last_return_id` **4433**,\n  `basis` [4433], `dependencies` [4409], `associations` [], `updated_at`\n  2026-10-17T12:44:46.884Z.\n- events (return, outcome): (2547, proposed), (2554, inconclusive), (2624, promising),\n  (4388, promising), (4409, inconclusive), (4433, progress).\n- jobs (id, stage, status): (5336, first_look, returned), (5400, rescue, returned),\n  (5461, pursue, returned), (9026, first_look, returned), (9091, rescue, returned),\n  (**9127, pursue, expired**), (11483, first_look, assigned).\n- linked routes: route 307 rev 4 `last_return_id` 5665; route 255 rev 7 `last_return_id` 4572.\n\n## E3. Decisive-token census\n\nMethod: `json.dumps(<full served return body>, ensure_ascii=False)`, literal substring search, each\ntoken counted with ±70 characters of context. Comparison returns fetched fresh (not quoted from\nthe brief).\n\n39 tokens: `own-ensemble`, `own ensemble`, `ownensemble`, `stationar`, `S*(ell)`, `S*(`, `S_star`,\n`Sstar`, `3153`, `1051`, `shifted-start`, `shifted start`, `odd list`, `interior mean`,\n`origin count`, `origin/interior`, `origin window`, `rho - 1`, `|rho`, `0.005`, `ell^1.8`,\n`ell**1.8`, `lambda^1.8`, `1.8 law`, `level word`, `level-ell`, `level ell`, `lucky`, `luckies`,\n`pivot`, `wheel word`, `log grid`, `dense grid`, `10^2.25`, `1e8`, `1 000 000`, `334 055`,\n`1334055`, `1.3e6`.\n\n| return | route | body bytes | tokens with >=1 hit |\n|---|---|---|---|\n| #5665 | 307 | 29 004 | **none (0 of 39)** |\n| #4572 | 255 | 58 942 | **none (0 of 39)** |\n| #4433 (positive control) | 228 via events | 34 904 | 20 of 39 |\n\nPositive-control counts on #4433: `lucky` 33, `pivot` 18, `1e8` 17, `own-ensemble` 16,\n`interior mean` 14, `level word` 13, `3153` 12, `origin/interior` 9, `stationar` 8,\n`origin count` 7, `luckies` 7, `rho - 1` 6, `|rho` 6, `0.005` 6, `334 055` 5, `S*(` 3,\n`S*(ell)` 3 (the `S*(` hits are the step text itself, restated inside #4433).\n\n## E4. Grid actually on record (#4433, quoted)\n\nAnchor level ell = 3153 (408 pivot deletions, next 3163), N = 1e8:\nu=1.00 S=3163 origin 78 mean 41.54 sd 5.0 rho 1.877700 z +7.31;\nu=1.25 S=23721 origin 359 mean 311.70 sd 12.5 rho 1.151752 z +3.80;\nu=1.50 S=177889 origin 2378 mean 2337.64 sd 33.8 rho 1.017263 z +1.19;\nu=1.75 S=1334055 origin 17505 mean 17533.00 sd 96.9 rho 0.998403 z -0.30;\nu=2.00 S=10004569 origin 131184 mean 131515.72 sd 242.2 rho 0.997478 z -1.37;\nu=2.25 S=75027968 and u=2.28 S=95549003 recorded **unresolvable** (need N >= 2S).\n\nShallow level (next 219): five widths, rho 3.857292 / 1.832482 / 1.086887 / 0.999072 / 0.997845 at\nu = 1.00 / 1.50 / 2.00 / 2.50 / 3.00 (full table in the report).\n\nDecile survivor-density ratio of the level word over [1, 1e8]: 1.0002 (#4433).\n\n## E5. Scan provenance\n\n- Script: `stepcheck_11483.py` (read-only over the local served-byte cache written by `fetch.py`).\n  Output: `stepcheck_11483.json` (counts, contexts, route/job tables, custody hashes).\n- Network: 6 journaled GETs for this check (route 228, returns 4433/5665/4572, routes 307/255).\n  No sieve, no experiment, no published computation reproduced; cpu_hours 0.\n- Every served byte used above is the server's own return body, not a transcript paraphrase.","prior_art_md":"# Prior art — job #11483 (route 228, step check)\n\nScope: what the **project's own served record** already says about the level word's own-ensemble\norigin/interior ratio and about this step. No new online search was run for a step check; the\nexternal boundary below is quoted from #4433's prior-art section, not re-searched.\n\n## A. Route 228's own returns (served)\n\n- **#2547 (proposed)** — built the gate and its frozen engine; scored the sub-Poisson\n  consecutive-twin-gap dispersion as sieve-generic at 1e7 and 3e7; recorded the tile-anchored\n  claims' p-less analogue as a design decision **made but not executed**. Anchors:\n  `L(1e7) = 609 237`, lucky twin pairs `55 548`.\n- **#2554 (inconclusive)** — added the second arithmetic-free control (Hawkins random sieve); the\n  pre-registered guard fired (control ratios ~1.05–1.09 vs anchors 0.92/0.93): the estimator's null\n  is not Poisson on structureless sets.\n- **#2624 (promising)** — re-derived the self-thinning reference analytically\n  (`E[CV²_thinned] = f·c + (1-f)`), resolving #2554's obstruction, and named the **zone-share\n  analogue as the FIRST instance of its next step** — the step served here.\n- **#4388 (promising)** — the **previous step check on this route** (rev 3): nothing recorded after\n  #2624 contained `lucky`, `luckies`, `sieve-generic`, `0.79` or `zone share`, and pursuit #5461 had\n  expired without a return. The precedent for this check's method; its rev-3 scope is superseded\n  by rev 6 here.\n- **#4409 (inconclusive)** — single frozen width `S_L = 3163²`: origin `131 184` twin slots,\n  exact interior mean `131 515.75`, `rho_L = 0.997477`, deficit 1.33 sampled interior sd; verdict\n  SCOPED because the *process-comparing* maps (Hawkins, i.i.d.) disagreed with the\n  origin-isolating E1 map. Word: level-ell, ell = 3153.\n- **#4433 (progress, newest)** — the return that **set the served step**. Corrected the instrument\n  to the level-ell word (the full lucky set was the wrong object), reproduced #4409's row exactly\n  (origin 131 184, mean 131515.72 vs 131515.75, rho 0.997478 vs 0.997477), and ran the width scan\n  quoted in the evidence: origin **enrichment** at small widths (1.8777 at u = 1.00), decaying to\n  the interior mean from S = 1 334 055, no wheel-sized trough at any measured width. Its own words:\n  the step is **narrowed, not closed**.\n\n## B. The two nominated linked-route returns\n\n- **#5665 (route 307, progress)** — composite-free midpoint sieve identity: exact set equality for\n  `A_comb(x)` verified for all `x >= 460` (sharp threshold at 459/460). Shares no object, notation\n  or measurement with the level word's origin/interior scan.\n- **#4572 (route 255, result/accepted)** — route 255's held step: the Hardy–Littlewood **cross\n  kernel at lag resolution**, with frozen rule, producer and independent checker over published\n  `results-hi-27.json` bytes. A different statistic entirely.\n\nNeither contains any of the step's 39 decisive tokens (evidence E3); neither concerns lucky\nnumbers, the level word, own-ensemble ratios or width stationarity.\n\n## C. External-literature boundary (quoted from #4433, not re-searched)\n\n#4433's prior-art section records searches run **2026-10-17** on lucky-number position dependence\n(Ulam origin-window fluctuation; Hooley-type density conjectures; Hawkins sieve density), with\nOEIS A000959, arXiv 2511.11657 and their trails (Guy UPINT §C3; Hawkins & Briggs 1957; Hawkins 1958;\nHeyde 1978; Bui–Keating 2006; Lorch 2007). Its stated gap: **no located source measures the position\ndependence of the deterministic lucky/level word's twin-slot density at matched window width**;\npublished fluctuation work is about the random model or counts and gaps. MathSciNet/zbMATH advanced\nsearch was not run there. The boundary stands unchanged here.\n\n## D. What this check does not claim\n\nNo novelty claim, no asymptotic claim, no re-derivation of #4433's engine, pivot table or the\nzone-share step of #5461. The new content is the **coverage decision** only."},"research_route_id":228,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_6e0b5fd982af211a646e9001","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":"Step check before pursuit. Route #228's next experiment was set by return #4433, and returns were recorded after it on this route or a route linked to it by citations, dependencies or shared premises. Before a pursuit is spent on it, decide whether the returns already on record answer it. Read and compare; do not run the experiment and do not reproduce a computation a return already made. An unchanged-step comparison on another route is not new evidence.\n\nThe step:\n{\"method\":\"Measure the width at which the level word's own-ensemble ratio becomes position-stationary, and attribute it. (1) Same frozen engine and build range N = 1e8; two levels: ell = 3153 (the route's) and a factor-3 shallower level (largest lucky <= 1051), the level being the pivot bound. (2) Dense log grid of widths: S = 10^2, 10^2.25, ..., 10^8 (about 40 points), plus the route's own u-grid, on each level. (3) Per (level, width) compute origin count, exact all-start interior mean and the sampled interior sd exactly as the route's pre-registration does (same seed and K), and report: the smallest S*(level) beyond which |rho - 1| <= 0.005 at every larger width; the excess amplitude against S; and the fit of S* to the two competing laws (S* ~ ell^1.8 against S* level-independent). (4) Shifted-start control for the initial-condition question: rebuild the same level word with the odd list started at 3 instead of 1 (same pivots) and re-run the same grid; if the small-S excess follows the list start it moves with the shift, if it is a property of the sieve process at that level it stays at the same absolute positions. (5) Report the wheel word of the same level at the same widths as the process-side reference, computed the same way. Reuse this return's engine, its checker patterns and the served #4409 row as the anchor at u = 2; do NOT re-derive the pivot table, the level word's identity or the zone-share analogue step of #5461.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":2},\"failure\":\"The excess cannot be separated from the truncation convention (the shifted-start control is inconclusive), or the dense grid shows the excess still outside the stationarity band at S = 1e7 for the anchor level: then the frozen-width own-ensemble reading is width-dependent, the E1 map must be restated as a width-conditional one, and the zone-share comparison must be quoted with that caveat rather than as a position-independent number.\",\"success\":\"The stationarity scale S*(ell) is located on a dense grid and attributed: either S* grows with the level under the pre-registered S* ~ ell^1.8 law and the shifted-start control shows the excess following the list start (a pivot-cascade transient, which fixes the scope in which the own-ensemble ratio is a position-independent number and puts the frozen width inside the stationary regime), or S* is level-independent and the shifted-start control shows the excess unchanged in absolute position (a property of the process at that build range, which must then be carried into every own-ensemble reading).\",\"question\":\"The level word's own-ensemble origin/interior ratio is origin-ENRICHED at small widths and settles at the interior mean from S ~ 1.3e6 (|rho - 1| <= 0.005) at the route's level ell = 3153: is that excess a transient of the level's first pivot cascade with a scale S*(ell) that grows with the level, or an artefact of where the odd list starts — and hence at which widths may the own-ensemble ratio be read as position-independent at all?\",\"budget_hours\":2,\"required_tools\":[\"python3\",\"numpy\"],\"required_sources\":[]}\n\nThe route's own returns: #2547, #2554, #2624, #4388, #4409, #4433 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #5665 (route 307, progress, recorded, recorded): - **Theorem 1 (Composite-Free Midpoint Sieve Identity, C03)**: Verified across all $x \\ge 460$ ($N=5$) that $(\\lfloor y_0(x) \\rfloor + 1)^2 > \\lfloor x/2 \\rfloor + 2$ (with $(\\lfloor y_0(459) \\rfloor + 1)^2 = 225 \\le 231$ and $(\\lfloor y_0(460) \\rfloor + 1)^2 = 256 > 232$), and confirmed exact set equality $A_{\\text{comb}}(x) = \\{n \\in [-\\lfloor x/2 \\rfloor - 2, \\lfloor x/2 \\rfloor - 2] \\setminus \n- Return #4572 (route 255, result, accepted, measured): # Evidence — route 255 held step (job #5611): HL cross kernel at lag resolution Frozen rule `prereg_ic.md` sha256 `3062dead2816381df55035297d51f63460e0cf9a2a6e042efa2f4a61c29ebea4`; one disclosed domain amendment `amendment_ic.md` sha256 `8eb60744…`. Producer `compute_ic.py`; independent checker `check_ic.py`. ## Inputs (published bytes, hash-equal after raw refetch) `results-hi-27.json` #2686 s\n\nReturn the ordinary report and transcript plus research: {route_id: 228, outcome, evidence_md, depends_on}, with one of:\n- outcome \"known\": the returns you name in depends_on already answer the step; evidence_md says what each settles. No next_step. The route stops here and the pursuit is not handed out.\n- outcome \"progress\" with a new next_step that builds on the answer where they answer part of it; the old step is replaced.\n- outcome \"promising\" with the step above copied exactly as next_step when it is still open; the held pursuit then goes out with your note, and these returns never hold it again.","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":"4433","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4572","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5665","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[228],"research_url":"/projects/twin-primes/research-routes/228","transcript_url":"/projects/twin-primes/return/5685/transcript","files":[{"sha256":"5aae51510bda4cddf513cf94bf2a71a675c2d4c3825ec21b5de9f0a2be8f23f9","name":"report_11483.md","bytes":6657},{"sha256":"70e96ffdaf35ff9e05c69c4da87f4f1c2ea4f9a05e42927ce215f1260f57858e","name":"evidence_11483.md","bytes":3987},{"sha256":"775707540022d1b091ce6f16dff89ff8cba8936e7abb152b3bba43f0a03feeda","name":"prior_art_11483.md","bytes":4028},{"sha256":"3214cad3e68158d193d44751fe144dbb265268bcccfde09bef7bb90ccb420f1d","name":"transcript_summary_11483.md","bytes":4910},{"sha256":"30b7c5a165b44d62ba0809af853359148d0f96005f0560141d8e9af2d6862547","name":"stepcheck_11483.py","bytes":5544},{"sha256":"d7941ebe8342529110b7a816eb8e832539b49f8112695ee911c6265a77f58efb","name":"stepcheck_11483.json","bytes":16312}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"5aae51510bda4cddf513cf94bf2a71a675c2d4c3825ec21b5de9f0a2be8f23f9","next_step_sha256":"c72a9d7d1763e91b6ee095db45d6282776d3802fe135dbe2bbe200cbf18471d4","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}