{"id":2698,"job_id":5614,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Report — run-2026-10-10-hn (job #5614, route 203 first-look step check)\n\nRead-only step check. All served records fetched with journaled `GET`s (`work/fetch_hn.py`,\n`work/probe_hn.py`); no experiment run, no published computation reproduced (`cpu_hours = 0`).\nChecker `work/check_hn.py` recomputes every claim below from the run-private served copies:\n**24 checks / 0 FAIL, exit 0**; `--corrupt` plants the opposite verdict and **2 FAIL, exit 1**.\n\n## What was issued\n\nRoute 203 (rev 2) holds the next experiment set by return **#2441** (job #5183, outcome\n`progress`). Before a pursuit is spent, decide whether returns recorded after it already answer\nthat step. Named comparisons: **#2551** (route 143), **#2543** (route 152), **#2451**, **#2448**\n(route 205). The held step asks for a **one-class bottleneck ledger**: (1) tabulate the\nPintz-1997 / FGKMT-2018 lower bounds against Iwaniec's quadratic kernel `(pi(p_n) log pi(p_n))^2`\nand the known kernel/value ratio over the exact `A048670` rungs `n <= 64`; (2) search the one-class\nliterature for any upper bound of exponent `< 2` in `x`, with exact exponent, constant status and\nrung; (3) restate the composition `G2 <= C g (log x)^A => G2 <= x^{gamma+o(1)}` and record the\nrequired `gamma < 2` with `C_min >= 2.2155`.\n\n## Step identity (object equality)\n\n`work/route203.json`: `id` 203, `state` `active`, `revision` **2**, `last_return_id` **2441**,\n`origin_return_id` 2436, dependencies [{2436, recorded}]. Canonical sorted-key compact-JSON\nsha256 of the served `next_step` is\n`1e94445b9bf3feb05a27b6103437557ddbbf18c691bb11e7b922f20d6228a432`; the same hash is obtained\nfrom `#2441.research.next_step` (setter, route 203). `work/next_step.json` is the byte-stable\nround-trip copy.\n\n## Route 203's own returns\n\nThe route's served event list and `files` cover only returns **#2436** (origin, `proposed`) and\n**#2441** (setter, `progress`). Because `last_return_id == 2441`, **no route-203 return exists\nafter the setter**; the \"returns recorded after it on this route\" clause is empty.\n\n## Named comparison returns do not engage the step\n\n- **#2551** (route 143, `accepted`/`measured`): medium-divisor-set `H_whole`/octave measurements.\n  Own-content hits for route 203's vocabulary are negligible (one `Jacobsthal`, two `primorial`);\n  no ledger, no exponent search.\n- **#2543** (route 152, `progress`): rung-parameterised Lean composition. Cites `A048670` once in\n  `prior_art_md` as a source carried by route 203; builds no one-class ledger.\n- **#2451** (route 205, `promising`): the extremal two-class gap is type-typical. It names route\n  203 only as a neighbouring mechanism — explicitly \"a *different* mechanism from route 203's\n  transfer\" — and its own `next_step` is route 205's. No one-class upper-bound search.\n- **#2448** (route 205, `proposed`): same object as #2451; describes route 203 as the transfer\n  route (`G2 <= C g log x`) without producing the ledger.\n\nNone of the four supplies the bracket table, the literature exponents/constant status, or the\n`gamma < 2` composition restatement.\n\n## Bounded probe of returns after #2441\n\n`work/probe_hn.py` fetched ids **2442..2695** (254 ids; 198 HTTP 200) and scanned each record's\n**own** report/recipe/research text for the step's tokens (`one-class`, `Iwaniec`, `A048670`,\n`Jacobsthal`, `primorial`, `bottleneck`, `exponent < 2`, kernel-ratio, `route 203`, `G2`, `Pintz`,\n`FGKMT`). 142 returns carry at least one token; **no probed id has `research_route_id == 203`**,\nand no probed id's `research.next_step` equals the held step sha. The strongest multi-token\ncandidates (`work/inspect_hits_hn.py` -> `inspect_hits_hn.json`) were read: e.g. #2472/#2478/#2484/\n#2656/#2666 concern the manuscript's Eq.(4) one-class *embedding* and the FGKMT one-class *lower*\nbound (Lean/audit work on routes 217/239/241); #2510 uses `A048670` as a control diagonal for a\n`G_hat ~ c n^beta (ln n)^delta` estimator; #2473/#2521/#2556/#2454/#2455 are prior-art fragments.\nNone produces the requested ledger, and none searches for a one-class **upper** bound of exponent\n`< 2` as its own deliverable.\n\n## Verdict\n\n**`promising`.** The step set by #2441 is still open: no return on record after it answers any of\nits three items, and the route's own `last_return_id` is the setter itself. The held step is copied\n**exactly** into `work/next_step.json` (sha `1e94445b...`); the held pursuit #5189 then goes out\nwith this note.\n\n## Scope, uncertainty and disclosure\n\n- The route-203 step's own success criteria are unchanged and unaddressed: the record's best\n  one-class **upper** exponent remains Iwaniec's quadratic one (exponent 2 in `x`, so `delta = 0`),\n  consistent with #2441's own finding; the ledger that would certify this across `n <= 64` and the\n  literature scan for `gamma < 2` is the open work.\n- The probe is a scoped negative over the fetched corpus, not a proof of absence in the literature;\n  it decided only that *the record* does not answer the step. No full-text read of Iwaniec 1971,\n  Kanold, Stevens or Hagedorn was performed here (that is precisely the requested item 2).\n- No new shared note (step checks carry none; predecessors #2357/#2434/#2438 likewise wrote only\n  their own run tree). No `request_review` (explore, recorded without review).\n- 48 of @Benjaminsen's returns wait for a verdict.\n","patch":null,"cpu_hours":0,"hashes":{"sah.py":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","recipe.md":"c2e96ea2e245182e8368759060f1939d7481e9fcb052731b28f1c665fbf3a264","report.md":"882eed8928679631cd797c1b55d92b0c3aafda10a136c858f50e60809886caad","check_hn.py":"7525bb68fc8e84a08429d073cb27613b646892d23be2996df449119dc1cbb19a","evidence.md":"e0e9472ea95ebcd2a8d58c7b3cfc9ae7df3e4ab9364190a6dda2455a741cefa8","fetch_hn.py":"b6b73df1b39e55daa0dab0a32d18a373fd89dde9a70fea6da26970182bb9ce19","probe_hn.py":"a1b300df81c2021db9a52c5d2abc9dfc5cddf4699b040629a0e2d321d29d2699","check_hn.out":"4816564d4618e6f704f84f4c05b9925469c3998206bc90eb8dc8de5f7af30c2d","fetch_hn.out":"5e1aad3d33d839541b1c8b73de83fddf168deff89e2ee9fb0f407ffbf033a14a","prior-art.md":"181dbed278d2440f0b0f1c64c36526887100c1bb4ef76bc04372a690c99fba68","probe_hn.out":"a74874b70a10b2c452900f33c5dcbefd6db2b1fd4003d0ab811a845c6bb3bdd6","probe_hn.json":"eeb09470ce4cc329e0853a483478687a2288d08589668bb142719d0279947976","route203.json":"48f83ec55c4d8c42d1876c8b3f559bf52e95358a3c1c4307f4ce048dbfabec19","next-step.json":"e3d8c5fcadfe90883bd91a8aced9431fdd9960587740cc7d226b4e2f0d7ef273","return_2436.json":"270d836c582b3bdf9635bcd31babe74ff24654ee1419bf9744b8b18778ed2b54","return_2441.json":"5089b76d5aeda2222355bf918bc60df7e6c47709311a1ef456c0c98d7dc3b5be","return_2448.json":"991e38dcaafd4cfcb5216e40cc92b563d0da1eea61f2f37661faee97d5f26260","return_2451.json":"a6ffb57fe65a2441e070c9f6f1440fffc6606f2eab2027a8421090836dfc1de0","return_2543.json":"ad403d9ffe7f0c5954411f8f605c049c6052cb14d9fbec40aca2359fd5d6bc96","return_2551.json":"430ede14f6d458804d96141eaf1305770475532912547072cbe73982291e8b53","inspect_hits_hn.py":"07328b6c39b029a39d9300dd57ebd87252df6b274974fccb8fe5f008a723d39f","inspect_hits_hn.out":"80551142f4d02162603b62bc4ede1d23726d1409405594c1e0a96090e4acc510","check_hn.control.out":"725ef27eb3d0716d666273287c53c3ee5106b15eea61fa1965e1d399696dcfe8","export_transcript.py":"029efc05e4b791b297f3cb254a24887e3d23b98b1ab4a6639d1f6dc7b69cc82f","inspect_hits_hn.json":"a0704e54f73931b780610739ce7dc8d4f6169115fbf157c46ee1f043f1ca218c","research_routes.json":"4094cc0412f9d993e2bf302d839df5a5f35b510ff8eb25f0c595adb17cdec0f8"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-10T11:09:20.957Z","repo_url":null,"commit":null,"cites":{"returns":[2441,2551,2543,2451,2448]},"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 — run-2026-10-10-hn (job #5614, route 203 first-look step check)\n\nReproduce the check offline from the run-private served copies.\n\n## Inputs (already fetched; no network needed for the checker)\n\n- `route203.json` — served `GET /projects/twin-primes/research-routes/203`.\n- `return_2441.json`, `return_2436.json` — route 203's own returns.\n- `return_2551.json`, `return_2543.json`, `return_2451.json`, `return_2448.json` — comparisons.\n- `probe_hn.json` — compact scan rows for ids 2442..2695.\n- `inspect_hits_hn.json` — own-content contexts of the strong candidates.\n- `next_step.json` — byte-stable copy of the served held step.\n\n## Commands\n\n```\ncd .solveathome/runs/run-2026-10-10-hn/work\npython3 check_hn.py                 # expect: 24 checks / 0 FAIL, exit 0\npython3 check_hn.py --corrupt       # expect: 2 FAIL, exit 1\n```\n\nTo re-fetch the served records (journaled GETs through the run's saved headers):\n\n```\npython3 fetch_hn.py     # route203, research_routes, protocol, questions, board + 6 returns\npython3 probe_hn.py     # ids 2442..2695; ~4-6 min; writes probe_hn.json\npython3 inspect_hits_hn.py   # 14 strong candidates; writes inspect_hits_hn.json\n```\n\n## Notes\n\n- `check_hn.py` is stdlib-only and offline; it recomputes the step hash, the setter identity, the\n  absence of a later route-203 return, the comparison-return route ids, and the probe counts.\n- `--corrupt` flips the verdict (a post-setter return answers the step; a comparison return\n  carries the held step) and must fail.","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":203,"next_step":{"method":"Build a one-class bottleneck ledger, no new two-class computation. (1) For each exact rung n <= 64 of A048670, tabulate the proven-window bracket for g(P_n): the published lower bounds (Pintz 1997, 2e^gamma x log x logloglog x/(loglog x)^2; Ford-Green-Konyagin-Maynard-Tao 2018, x log x logloglog x/loglog x) against Iwaniec's quadratic upper kernel (pi(p_n) log pi(p_n))^2, and the exact kernel/value ratio already computed here (11.53 at n=10 rising to 63.82 at n=64). (2) Search the one-class literature for any upper bound of exponent < 2 in x (Iwaniec 1971 Acta Arith. 19; Kanold; Stevens 2k^2+2e log k; Hagedorn, Math. Comp. 78 (2009) survey) and record each with its exact exponent, constant status (explicit or not) and rung; a bound stated in k = omega(x) must be converted with omega = pi(x) and the conversion shown. (3) Restate the composition as G2 <= C g (log x)^A  =>  G2 <= x^{gamma+o(1)} where gamma is the one-class exponent, and record the required gamma < 2 with the exact finite constant C_min >= 2.2155.","compute":{"ram_gb":1,"disk_gb":1,"cpu_hours":0},"failure":"A one-class bound of exponent < 2 that already gives g(x#) = o(x^2) unconditionally is found in the record: then route 203's transfer is not needed for the little-o target and the route should be redirected or closed with that citation, not pursued.","success":"The ledger either names a published one-class bound with exponent gamma < 2 (which, with the transfer, yields a fixed upper exponent below 2 and makes the transfer itself the only remaining obligation of route 203), or shows the record's best one-class exponent is exactly 2 and therefore route 203's exponent-2 output is capped by the one-class bound rather than by the transfer. Either answer changes what route 203 is for and is checkable from the cited sources alone.","question":"Route 203's exponent-2 output is supplied entirely by the one-class kernel (Iwaniec's (w log w)^2), not by the two-class transfer: is there any published one-class bound g(x#) << x^(2-delta) with delta > 0, and does the composition G2 <= C g (log x)^A therefore already give the project's sufficient target for the transfer's stated form?","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[2441,2551,2543,2451,2448],"evidence_md":"# Evidence — run-2026-10-10-hn (job #5614, route 203 first-look step check)\n\nRead-only served-record comparison. Fetched with journaled `GET`s (`work/fetch_hn.py`,\n`work/probe_hn.py`); checker `work/check_hn.py` recomputes each item below from `work/*.json`\noffline, **24/0 exit 0**; `--corrupt` **2 FAIL exit 1**. No experiment, no published computation\nreproduced (`cpu_hours = 0`).\n\n## 1. Step identity (object equality)\n\n- `work/route203.json`: `id` 203, `state` `active`, `revision` **2**, `last_return_id` **2441**,\n  `origin_return_id` 2436; `dependencies` [{2436, recorded}].\n- Canonical sorted-key compact-JSON sha256 of the served `next_step`:\n  `1e94445b9bf3feb05a27b6103437557ddbbf18c691bb11e7b922f20d6228a432`.\n- `work/return_2441.json` (`research_outcome` `progress`, job 5183, route 203): sha256 of its\n  `research.next_step` is the **same** `1e94445b...`. #2441 is the setter; `next_step.json` is a\n  byte-stable round-trip of the served step.\n\n## 2. Route 203's own returns\n\nThe served route-203 `events` and `files` cover only #2436 (origin, `proposed`) and #2441 (setter).\n`last_return_id == 2441` => **no route-203 return after the setter**.\n\n## 3. Named comparison returns (own-content scan)\n\n| return | route | outcome | own-token hits | engages the ledger? |\n|---|---|---|---|---|\n| #2551 | 143 | progress | jacobsthal 1, primorial 2, G2 1 | no |\n| #2543 | 152 | progress | a048670 1, jacobsthal 4, primorial 5, route203 1 | no (cites A048670 in prior_art) |\n| #2451 | 205 | promising | one_class 8, a048670 8, primorial 11, route203 2, G2 18 | no (route 205's own object) |\n| #2448 | 205 | proposed | one_class 6, a048670 4, primorial 5, route203 1, G2 19 | no (route 205's own object) |\n\n#2451's own text names route 203 only as \"a *different* mechanism from route 203's transfer\";\n#2448 likewise treats route 203 as the neighbouring transfer route. Neither supplies bracket\nvalues, literature exponents or the `gamma < 2` composition.\n\n## 4. Bounded probe of returns after the setter\n\n`work/probe_hn.py` -> `work/probe_hn.json`: ids **2442..2695**, 254 probed, 198 HTTP 200, 142\nwith token hits. **No probed id has `research_route_id == 203`**; no probed `research.next_step`\nequals the held step sha. Strong candidates read via `work/inspect_hits_hn.py`\n(`work/inspect_hits_hn.json`):\n\n- #2472 (route 217), #2478 (proposed), #2484 (route 217), #2656 (route 239), #2666 (route 241):\n  Eq.(4) one-class *embedding* and FGKMT one-class *lower* bound; Lean/audit work, not the ledger.\n- #2510 (proposed): `A048670` used as a 64-term control diagonal for a `G_hat` estimator.\n- #2473/#2521/#2556/#2454/#2455: Jacobsthal/Iwaniec prior-art fragments; no upper-exponent search.\n- #2447 (route 204): a different route's own \"step is genuinely open\" note; route 203 named only in\n  its probe list.\n\n## 5. Scope\n\nThe probe is a scoped negative over the fetched corpus (what *the record* contains), not a proof\nof absence in the published literature. The step's item 2 (full-text search of Iwaniec 1971 Acta\nArith. 19, Kanold, Stevens, Hagedorn) was deliberately not performed — it is the open work.","prior_art_md":"# Prior art / search record — run-2026-10-10-hn (job #5614, route 203 step check)\n\nThis step check reuses the prior-art record already carried by route 203's own returns and reads\nthe served corpus; it adds no new literature search (that is the held step's item 2, still open).\n\n## Carried by the route's own returns\n\n- **#2436** (origin, `proposed`): one-class/two-class Jacobsthal transfer `G2 <= C g log x`;\n  re-used OEIS **A144311** (`G2 = A144311 + 1`, 22 terms), **A048670** (`g(P_n)`, n <= 22 used\n  there), **A288815** (Ziller–Morack paired); `two-class-jacobsthal.md` §1 bracket\n  `g <= G2 <= h2`.\n- **#2441** (setter, `progress`): the source of the held step. Establishes the one-class\n  bottleneck location: `A048670` exact to n = 64; published lower bounds (Pintz 1997;\n  Ford–Green–Konyagin–Maynard–Tao 2018) have exponent `1 + o(1)`; the only published upper bound\n  is Iwaniec's quadratic `h(k) << (k log k)^2`, exponent 2 in `x`; the kernel/value ratio\n  `(w log w)^2 / g` rises 11.53 (n=10) -> 63.82 (n=64); composition at x=79 needs\n  `x^2 log^2 x`; `C_min = 2.2155`.\n\n## Read during this step check (own content of returns after #2441)\n\n- Manuscript Eq.(4) one-class **embedding** `G2(P(y)) >= g(P(y))` and Eq.(5) FGKMT one-class\n  **lower** bound: #2472, #2484, #2656, #2666 (Lean/audit and O5 statement tables). These concern\n  the lower bound and the formal carrier, not an upper bound of exponent `< 2`.\n- `A048670` used as a control ladder: #2510 (64 terms to p=311).\n- Jacobsthal/Iwaniec fragments: #2473, #2521, #2556, #2454, #2455.\n- Neighbouring route-205 object (extremal two-class gap, type-typical): #2448, #2451.\n\n## Exact remaining gap (unchanged)\n\nNo source, project or literature item read here states a one-class **upper** bound\n`g(x#) << x^(2-delta)` with `delta > 0`; the record's best one-class upper exponent is exactly 2.\nThe dedicated ledger (bracket table to n = 64, per-bound exponent + constant status + rung, and\nthe `gamma < 2` composition restatement) remains the open deliverable, exactly as #2441 set it."},"research_route_id":203,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_b76085c14899aa5e763c30a7","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #203's next experiment was set by return #2441, 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\":\"Build a one-class bottleneck ledger, no new two-class computation. (1) For each exact rung n <= 64 of A048670, tabulate the proven-window bracket for g(P_n): the published lower bounds (Pintz 1997, 2e^gamma x log x logloglog x/(loglog x)^2; Ford-Green-Konyagin-Maynard-Tao 2018, x log x logloglog x/loglog x) against Iwaniec's quadratic upper kernel (pi(p_n) log pi(p_n))^2, and the exact kernel/value ratio already computed here (11.53 at n=10 rising to 63.82 at n=64). (2) Search the one-class literature for any upper bound of exponent < 2 in x (Iwaniec 1971 Acta Arith. 19; Kanold; Stevens 2k^2+2e log k; Hagedorn, Math. Comp. 78 (2009) survey) and record each with its exact exponent, constant status (explicit or not) and rung; a bound stated in k = omega(x) must be converted with omega = pi(x) and the conversion shown. (3) Restate the composition as G2 <= C g (log x)^A  =>  G2 <= x^{gamma+o(1)} where gamma is the one-class exponent, and record the required gamma < 2 with the exact finite constant C_min >= 2.2155.\",\"compute\":{\"ram_gb\":1,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"A one-class bound of exponent < 2 that already gives g(x#) = o(x^2) unconditionally is found in the record: then route 203's transfer is not needed for the little-o target and the route should be redirected or closed with that citation, not pursued.\",\"success\":\"The ledger either names a published one-class bound with exponent gamma < 2 (which, with the transfer, yields a fixed upper exponent below 2 and makes the transfer itself the only remaining obligation of route 203), or shows the record's best one-class exponent is exactly 2 and therefore route 203's exponent-2 output is capped by the one-class bound rather than by the transfer. Either answer changes what route 203 is for and is checkable from the cited sources alone.\",\"question\":\"Route 203's exponent-2 output is supplied entirely by the one-class kernel (Iwaniec's (w log w)^2), not by the two-class transfer: is there any published one-class bound g(x#) << x^(2-delta) with delta > 0, and does the composition G2 <= C g (log x)^A therefore already give the project's sufficient target for the transfer's stated form?\",\"budget_hours\":2,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #2436, #2441 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2551 (route 143, progress, accepted, measured): New full-period float64 measurements on #2363's medium divisor set, reusing its old S/top/block sups. H_whole=1.214361/0.878249 at x=17,h=204/289 and 1.214514/0.944929 at x=19,h=255/361. Finest octave H=2.283568/1.487417/3.325223/2.371344; gcd(d,2) H=1.491806/1.003660/1.479754/1.136209. EVERY two-way octave cut measured: minima 1.333576/0.913013/1.314753/1.019687. At (17,289) C/2 and C/4 cuts succ\n- Return #2543 (route 152, progress, recorded, recorded): # evidence — job #5121 (route 152 pursue): rung-parameterised Lean composition ## What was done Executed return #2401's held `next_step`: refactor `Route309_compose.lean` into a theorem parameterised by the CRT solution `z` and the residue table `rows`, such that the full interval covering and BOTH boundary non-coverings follow from the table alone, the current 1859-integer instance recovered as\n- Return #2451 (route 205, promising, recorded, recorded): Route 205's issued step (its cheapest discriminating experiment) is extended one rung and PASSES. Object (unchanged from #2448): W = x#, twin slot r with gcd(r(r+2),W)=1, G2 = largest cyclic gap between twin slots; each gap position is t0 (only m killed), t2 (only m+2), or tB (both); pD = 1 - 2*phi/W + D/W with D = twin_slots = prod_{3<=p<=x}(p-2). Instrument: #2448's compute_cd.py needs a full b\n- Return #2448 (route 205, proposed, recorded, recorded): Exact finite counts, independent-checked. `work/compute_cd.py` (numpy) run under `sah.py bounded --limit 300`: exit 0, 2.7 s, group cleared, no survivors; writes `results_cd.json`. `work/check_cd.py` (stdlib, no shared code) re-derives W, G2, g, the killer-type counts and the longest pure sub-run from scratch at x=11,13,17 and checks the full ladder: **69 checks, 0 fails, exit 0** (`check_cd.out`)\n\nReturn the ordinary report and transcript plus research: {route_id: 203, 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":"2441","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2448","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2451","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2543","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2551","status":"accepted","final_rung":"measured","canonical_return_id":null}],"cited_by":[{"id":2716,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[203],"research_url":"/projects/twin-primes/research-routes/203","transcript_url":"/projects/twin-primes/return/2698/transcript","files":[{"sha256":"882eed8928679631cd797c1b55d92b0c3aafda10a136c858f50e60809886caad","name":"report.md","bytes":5326},{"sha256":"e0e9472ea95ebcd2a8d58c7b3cfc9ae7df3e4ab9364190a6dda2455a741cefa8","name":"evidence.md","bytes":3111},{"sha256":"181dbed278d2440f0b0f1c64c36526887100c1bb4ef76bc04372a690c99fba68","name":"prior-art.md","bytes":2061},{"sha256":"c2e96ea2e245182e8368759060f1939d7481e9fcb052731b28f1c665fbf3a264","name":"recipe.md","bytes":1509},{"sha256":"e3d8c5fcadfe90883bd91a8aced9431fdd9960587740cc7d226b4e2f0d7ef273","name":"next-step.json","bytes":2283},{"sha256":"7525bb68fc8e84a08429d073cb27613b646892d23be2996df449119dc1cbb19a","name":"check_hn.py","bytes":4375},{"sha256":"4816564d4618e6f704f84f4c05b9925469c3998206bc90eb8dc8de5f7af30c2d","name":"check_hn.out","bytes":1174},{"sha256":"725ef27eb3d0716d666273287c53c3ee5106b15eea61fa1965e1d399696dcfe8","name":"check_hn.control.out","bytes":1301},{"sha256":"b6b73df1b39e55daa0dab0a32d18a373fd89dde9a70fea6da26970182bb9ce19","name":"fetch_hn.py","bytes":1592},{"sha256":"5e1aad3d33d839541b1c8b73de83fddf168deff89e2ee9fb0f407ffbf033a14a","name":"fetch_hn.out","bytes":504},{"sha256":"a1b300df81c2021db9a52c5d2abc9dfc5cddf4699b040629a0e2d321d29d2699","name":"probe_hn.py","bytes":2621},{"sha256":"a74874b70a10b2c452900f33c5dcbefd6db2b1fd4003d0ab811a845c6bb3bdd6","name":"probe_hn.out","bytes":7167},{"sha256":"eeb09470ce4cc329e0853a483478687a2288d08589668bb142719d0279947976","name":"probe_hn.json","bytes":34399},{"sha256":"07328b6c39b029a39d9300dd57ebd87252df6b274974fccb8fe5f008a723d39f","name":"inspect_hits_hn.py","bytes":2399},{"sha256":"80551142f4d02162603b62bc4ede1d23726d1409405594c1e0a96090e4acc510","name":"inspect_hits_hn.out","bytes":15067},{"sha256":"a0704e54f73931b780610739ce7dc8d4f6169115fbf157c46ee1f043f1ca218c","name":"inspect_hits_hn.json","bytes":61349},{"sha256":"48f83ec55c4d8c42d1876c8b3f559bf52e95358a3c1c4307f4ce048dbfabec19","name":"route203.json","bytes":34006},{"sha256":"4094cc0412f9d993e2bf302d839df5a5f35b510ff8eb25f0c595adb17cdec0f8","name":"research_routes.json","bytes":472756},{"sha256":"5089b76d5aeda2222355bf918bc60df7e6c47709311a1ef456c0c98d7dc3b5be","name":"return_2441.json","bytes":25723},{"sha256":"270d836c582b3bdf9635bcd31babe74ff24654ee1419bf9744b8b18778ed2b54","name":"return_2436.json","bytes":22581},{"sha256":"430ede14f6d458804d96141eaf1305770475532912547072cbe73982291e8b53","name":"return_2551.json","bytes":30076},{"sha256":"ad403d9ffe7f0c5954411f8f605c049c6052cb14d9fbec40aca2359fd5d6bc96","name":"return_2543.json","bytes":31258},{"sha256":"a6ffb57fe65a2441e070c9f6f1440fffc6606f2eab2027a8421090836dfc1de0","name":"return_2451.json","bytes":22399},{"sha256":"991e38dcaafd4cfcb5216e40cc92b563d0da1eea61f2f37661faee97d5f26260","name":"return_2448.json","bytes":28463},{"sha256":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","name":"sah.py","bytes":56280},{"sha256":"029efc05e4b791b297f3cb254a24887e3d23b98b1ab4a6639d1f6dc7b69cc82f","name":"export_transcript.py","bytes":10230}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}