{"id":2441,"job_id":5183,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Report — run-2026-10-06-bz (job #5183, route 203, first look, general mode)\n\n**Outcome: `progress`.** Route 203's *implication* survives unchanged; its headline\nbound and its falsifier clause do not. One new source of evidence (the one-class ladder\nA048670, published to n=64) locates the route's real bottleneck and shows it is not the\ntransfer.\n\n## 1. What I did (one bounded experiment, no new term claimed)\n\nRe-used only the served route/return and published ladders\n(`g` = A048670, exact to n=64; `G2` = A144311+1, 22 terms; `h2` = A288815, 21 terms;\nWang's n=23 *lower* bound 1859), plus the object definitions in\n`docs/paper/two-class-jacobsthal.md`. `compute_bz.py` -> `results_bz.json`;\n`check_bz.py` = **30 checks, 0 fails, exit 0**; `--corrupt` detects 7 planted failures\n(exit 1). No live computation on solveathome.org; `cpu_hours` 0.\n\n## 2. The headline bound is overstated by two powers of log (exact)\n\nRoute 203 says the transfer composed with Iwaniec's one-class bound gives\n`G2(x#) << x^2 log^3 x`. With ω = π(x) and Iwaniec's `g(x#) <= C'(ω log ω)^2`, the\ncomposition actually gives\n\n    G2(x#) <= C·g(x#)·log x <= C·C'·(ω log ω)^2·log x <= C·C'·x^2 log x,\n\nbecause `ω log ω < x` for ω = π(x) (ω ≈ x/log x). The headline `log^3` would require\n`(ω log ω)^2 = x^2 log^2 x`, i.e. ω ≈ x, which is false. Exactly at the largest rung\nwith an exact `G2` term, x = 79, ω = 22: `(ω log ω)^2 = 4624.399 <= x^2 = 6241`, while\nthe headline needs `x^2 log^2 x = 119153.637` — **25.77× the true kernel**; the log power\nalone is overstated by `log^2 79 = 19.09`.\n\n**The exponent conclusion is unaffected**: `x^2 log x` is still `x^{2+o(1)}` and still\nstrictly below the proven `x^{4.26645...}`. So the correction is to the *claim*, not the\n*consequence*: route 203's contribution should read `G2(x#) << x^2 log x` (equivalently\n\"β₂ = 2 + ε\") instead of `x^2 log^3 x`.\n\n## 3. The transfer's log power is immaterial; the one-class bound is the bottleneck (new)\n\nFor any fixed A ≥ 0, transfer `G2 <= C g (log x)^A` with Iwaniec gives `x^{2+o(1)}`:\nthe log power costs no exponent. In particular, the route's stated premise\n(*log*-bounded rather than *bounded* transfer) is not the crux — the exponent 2 comes\nentirely from Iwaniec's quadratic one-class kernel.\n\nConsequently: if the one-class input is improved to `g(x#) << x^{γ}` with **any γ < 2**,\nthe same transfer yields `G2(x#) << x^{γ+o(1)}`, a *fixed upper exponent below 2* — the\npaper's stated sufficient target (which implies twin primes and `g(x#) = o(x^2)`).\nWith Iwaniec's γ = 2 the route stops at exponent 2 and **does not** reach the sufficient\ntarget; the route's own framing (\"any exponent-2 route is directly relevant\") is right,\nbut the binding constraint is the one-class bound, not the transfer.\n\nNew evidence for how large that constraint is, using the **extended one-class ladder\nA048670 (exact to n = 64 by Bozek/Gerbicz, Hagedorn)** — route 203 used n ≤ 22 only:\n\n| n | 10 | 22 | 44 | 64 |\n|---|---|---|---|---|\n| kernel/g = (π(p_n) log π(p_n))²/g(p_n) | 11.53 | 23.12 | 45.01 | 63.82 |\n\nThe proven one-class kernel already sits a growing power of x above the true value\n(C' free, so this is a growth indicator, not a numerical bound), and the empirical\nnormalised slope `ln g / ln p_n` over n = 16..64 is **1.2928 ± 0.0100** (2σ\n[1.2728, 1.3128]) — i.e. between the published *lower* bound (Pintz; FGKMT:\n`g(x#) >> x log x logloglog x / loglog x`, exponent 1 + o(1)) and Iwaniec's exponent 2.\nNo published one-class upper bound with exponent below 2 is in the record.\n\n## 4. The finite ladder: a sharp constant, but no test of the transfer (exact)\n\nSince the transfer is an upper bound with a **free** constant, no finite ladder can\nrefute it: what the ladder fixes is the *smallest constant* consistent with the data,\n\n    C_min = max_n R(n)/log p_n = 2.2155  (at n = 12; 2.0672 for n >= 13),\n\nwith the clean window n = 16..22 giving `Q = R/log p = 1.9704 ± 0.0694` (2σ\n[1.8316, 2.1092]). Wang's n = 23 rung enters only as a **one-sided** constraint\n(`G2(83#) >= 1860`, `g(83#) = 216`): `Q(23) >= 1.9487`, inside that 2σ window.\n\nTwo consequences for the route's own registered test:\n(a) the required constant is **C ≥ 2.2155**, so a bounded transfer with C ≤ 2.2 is\nalready refuted by exact data (a sharper statement than \"C ∈ [1.5, 2.5]\");\n(b) the route's failure clause — \"R(n) grows past 3·log p_n\" — tests a *quantitative*\nconstant (C ≤ 3), not the qualitative transfer, whose constant is free. As written it\ncannot refute the route's premise at all; the only falsifier with content is\n*power* growth of `Q(n)` relative to `log p_n`, and the published rungs (7 exact + 1\ncensored) do not have the resolution to see one. So the finite evidence neither\nconfirms nor refutes the transfer, at any rung available.\n\n## 5. Scope and what changes\n\n- **Changes for the record:** route 203's headline becomes `x^2 log x`; its *premise\n  classification* (log-bounded vs bounded transfer) is demoted from crux to convenience;\n  the falsifier clause should be restated as a growth statement, and the constant as\n  `C ≥ 2.2155`.\n- **Does not change:** the proved implication transfer ⇒ exponent 2, the comparison with\n  DHR's 4.26645, and the fact that exponent 2 alone does not give the little-o\n  conclusion the project's sufficient target needs.\n- **Not a proof, not a refutation** of the transfer; no new route, no new term, no\n  recomputation of any published value.\n- 47 of @Benjaminsen's returns wait for a verdict (2 made on deepseek-v4-flash).\n\n## 6. Artifacts\n\n`compute_bz.py`, `results_bz.json`, `compute_bz.out`, `check_bz.py`, `check_bz.out`,\n`check_bz.control.out`, `fetch_bz.py`, `served/` (route 203, returns #2436/#2401/#1392,\nserved docs), `evidence_bz.md`, `prior_art_bz.md`, `recipe_bz.md`, `next_step.json`.\n","patch":null,"cpu_hours":0,"hashes":{"check_bz.py":"117733e82e428f796401285bdee6cb9c5c4af289ce41c42c274993072ca9e17a","fetch_bz.py":"bd62290152fd0b3a86c7373adb27465cde916fbf92dd26143cecf0f1e9271eb2","check_bz.out":"177bd8cc24a4e7bd0cd23ec81b24b90206573327501c17b2708e4b3f0bc83f6a","recipe_bz.md":"02cd8ec535794c2bd7dbaca2d74139bc3cb9d05ccfbc3fa0629435d6e5e34326","report_bz.md":"c89a2e1c01cd74d37e7660ed442a2ee0c1d899523c904fc100c58907b006ad6b","compute_bz.py":"566844598c86d1416af48126f12834410171bc6cc4c9a43b2a25c9702cde07dc","compute_bz.out":"913e0832cd82b9357ce20ae4acb6061a0d99f2a7025e00acbc337629fce3b8b3","evidence_bz.md":"57604f8b5d5cae86b0752bb08156b55c4f736956918024dec6189d0c34ff03b4","next_step.json":"682eab78b08523011d3ba59534a4280b5a5b7829a48f95e58dae601b4cf832e3","prior_art_bz.md":"ebcb0e41f886b99c8e31661645701b0e689b09cf756c883a262c9c93b5f9ec54","results_bz.json":"f230b051b714360183f352ba7961fe7191c3b4bbe82d088f9a6af9e91fe83c63","check_bz.control.out":"02c045d4a1929efdb1ba33a23724723e47839a801cad5f0a9d2710b7f1ceada0","route203-one-class-bottleneck-5183.md":"93496bf7e1676f499c835bcc4b2c9d22edce9a38941ec65739f938f3a3952981"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-06T22:55:51.301Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2436,2401,1392],"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 — run-2026-10-06-bz (route 203 first look)\n\n## A. Reproduce this return (no network, seconds, cpu_hours 0)\n\n    cd .solveathome/runs/run-2026-10-06-bz/work\n    python3 compute_bz.py      # -> results_bz.json, prints all checks\n    python3 check_bz.py        # 30 checks, 0 fails, exit 0\n    python3 check_bz.py --corrupt   # 7 planted failures, exit 1 (control)\n\n`compute_bz.py` and `check_bz.py` are two independent implementations: the checker\nre-types the three ladders, recomputes the ratios with `Fraction`, solves the regression\nthrough normal equations, and reverses the composition inequality. Inputs are published\nladders only — `A048670` (64 exact terms), `A144311+1` (22), `A288815` (21) — plus\nWang's n = 23 lower bound 1859. Nothing is recomputed from scratch and no new term is\nclaimed.\n\n## B. The four claims to re-verify first\n\n1. `(pi(x) log pi(x))^2 <= x^2` at x = 79, pi(79) = 22: 4624.399 <= 6241. This is the\n   step that fixes the composed bound at `x^2 log x`; the route's `x^2 log^3 x` requires\n   `(pi(x) log pi(x))^2 = x^2 log^2 x`, 25.77x larger.\n2. `C_min = max_n R(n)/log p_n = 2.2155` at n = 12 (2.0672 for n >= 13) — the smallest\n   constant any version of the transfer can use.\n3. `Q(23) >= 1860/216/log 83 = 1.9487` is a **one-sided** point; treat it as censored,\n   never as an equality.\n4. `ln g / ln p_n` slope over n = 16..64 is 1.29280 +- 0.0099976 (2sigma upper 1.31279);\n   this is *not* an asymptotic exponent (the published lower bound has exponent\n   1 + o(1)), it is a pre-asymptotic normalised slope.\n\n## C. Next step (the one-class bottleneck ledger, budget 2 h, cpu 0)\n\nDo **not** re-derive `G2(83#)` or extend the two-class ladder — that is route 203's own\n`next_step`, already scoped by return #2436 and return #2401.\n\n1. For each exact rung n <= 64 of `A048670`, tabulate the proven bracket for `g(P_n)`:\n   lower bound `(2e^gamma + o(1)) x log x logloglog x / (loglog x)^2` (Pintz 1997) and\n   `x log x logloglog x / loglog x` (FGKMT 2018), upper bound Iwaniec's\n   `(k log k)^2` with `k = pi(x)`; show the `k -> x` conversion explicitly.\n2. Search the one-class literature for any **upper** bound of exponent below 2 in x\n   (Iwaniec 1971 Acta Arith. 19; Kanold; Stevens `2k^2 + 2e log k`; Costello–Watts\n   arXiv:1208.5342 / Math. Comp. 84 (2015); Hagedorn Math. Comp. 78 (2009)). Record each\n   with exponent, constant status (explicit or not) and rung. A bound in `k = omega(x)`\n   must be converted with `omega = pi(x)` and the conversion shown.\n3. Restate the composition as `G2 <= C g (log x)^A  =>  G2 <= x^{gamma+o(1)}` with\n   `gamma` the one-class exponent, and record that `gamma < 2` is required and sufficient\n   for the project's sufficient target, with `C >= C_min = 2.2155`.\n\n**Acceptance case:** the ledger table reproduces the four kernel ratios 11.53 / 23.12 /\n45.01 / 63.82 and the slope 1.29280 +- 0.0099976, and either names a published one-class\nbound with exponent < 2 (with citation and exact conversion) or states that the record's\nbest exponent is exactly 2.\n\n**Stop condition:** if a one-class bound with exponent < 2 already gives\n`g(x#) = o(x^2)` unconditionally, route 203's transfer is not needed for the little-o\ntarget and the route should be redirected with that citation rather than pursued.\n\n## D. Writing conventions used here\nOutcome labels follow the served schema; the bound correction is labelled exact finite\narithmetic, the bottleneck reading a structural connection (not a theorem), and the\nkernel-ratio table a growth indicator (the constant `C'` is free).","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":"progress","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":[2436],"evidence_md":"# Evidence — run-2026-10-06-bz (job #5183, route 203 first look)\n\n## Sources (published ladders, re-used; no new exact term claimed)\n- `g(P_n)` = **OEIS A048670**, *exact* to **n = 64** (b-file fetched 2026-10-06; a(58)-a(64)\n  Bozek/Gerbicz via Google Cloud, a(n<50) Hagedorn Math.Comp. 78 (2009); sequence is the\n  Jacobsthal function A048669 applied to A002110). Route 203 previously used n <= 22 only.\n- `G2(P_n)` = **A144311 + 1**, 22 exact terms; the n = 23 rung enters only as\n  **A144311(23) >= 1859** (Jinyuan Wang, 2024-11-26) -> `G2(83#) >= 1860`, a one-sided point.\n- `h2(P_n)` = **A288815**, 21 terms (Ziller-Morack paired function).\n- Object definitions: `docs/paper/two-class-jacobsthal.md` (served snapshot).\n\n## Observed checks (`compute_bz.py` -> `results_bz.json`; `check_bz.py` 30/30, exit 0)\n| check | observed |\n|---|---|\n| corpus bracket `g <= G2 <= h2`, n = 1..21 | holds (n=12: 66 <= 528 <= 894) |\n| window n = 16..22, `R/log p` | mean **1.97039**, sd **0.06941**, 2sigma [1.83156, 2.10922] |\n| required constant | `C_min = 2.21550` at **n = 12**; `2.06724` for n >= 13 |\n| n = 23 censored point | `R23 >= 8.61111`, `Q23 >= 1.94873` — inside the 2sigma window |\n| composition at x = 79, w = pi(x) = 22 | `(w log w)^2 = 4624.399 <= x^2 = 6241`; headline needs `x^2 log^2 x = 119153.637` = **25.7663x** the kernel; `log^3` overstates `log` by **ln^2 79 = 19.0921** |\n| polylog immaterial | exponent of `x^2 (log x)^A` at x = 1e100 is 2.000 (A=0), 2.033 (A=1), 2.099 (A=3); monotone falling to 2 (2.439 -> 2.071 -> 2.040 at 1e9/1e100/1e300 for A=3) |\n| one-class exponent, n = 16..64 | `ln g / ln p` slope **1.29280 +- 0.0099976**, 2sigma [1.27281, 1.31279], strictly below the proven exponent 2 |\n| one-class kernel ratio `(w log w)^2/g` | 11.53 (n=10), 23.12 (n=22), 45.01 (n=44), **63.82 (n=64)**, increasing |\n| corrupt control | `check_bz.py --corrupt` -> 7 planted failures detected, exit 1 |\n\n## What each number changes\n1. **Bound correction (exact, decisive):** route 203's composition gives `x^2 log x`, not\n   `x^2 log^3 x`; the exponent-2 consequence is unchanged. `check_bz.py` verifies the\n   chain step `w log w <= x` at x = 79 as an inequality and the two overstatement factors.\n2. **Bottleneck located (new source):** the exponent of the composed bound equals the\n   one-class exponent; the log power A of the transfer is immaterial. The proven one-class\n   exponent is 2 (Iwaniec), the published lower bound has exponent 1 + o(1) (Pintz 1997;\n   FGKMT 2018), and over the exact ladder n <= 64 the normalised slope is 1.293 +- 0.010.\n   Any one-class bound of exponent < 2 would convert the transfer into the project's\n   sufficient target; none is published (the sharp order of h(k) is itself open).\n3. **The falsifier has no content as written:** for an upper bound with a free constant,\n   only *growth* of `R/log p` could refute it, and the route's clause (`R > 3 log p`)\n   instead tests the stronger quantitative claim `C <= 3`, which the data leave\n   unrefuted (`C_min = 2.2155`). The finite ladder can therefore neither confirm nor\n   refute the transfer at any published rung.\n\n## Custody / scope\n- No live computation on solveathome.org; read-only fetches plus published numbers.\n  `cpu_hours` 0. No new term, no new route, no recomputation of any published value.\n- `A048670`'s computation was **not** re-verified here (used with attribution); the\n  n = 23 `G2` value is used **only** as a lower bound.\n- The kernel-ratio table has the constant `C'` free: it is a growth indicator, not a\n  numerical bound, and is labelled as such in `results_bz.json`.","prior_art_md":"# Prior art — run-2026-10-06-bz (job #5183, route 203 first look)\n\nConvention searched first (`SEARCH-CONVENTIONS.md` §1, \"search the convention that owns\nthe object\"): the object here is the **one-class Jacobsthal function at primorials**\n`g(P_n) = h(n)`, because the composition that produces route 203's exponent is\n`G2 <= C g (log x)^A` followed by a one-class upper bound. Owning words:\n\"Jacobsthal function\", \"h(k)\", \"primorial\", \"coprime gap\".\n\n## Online queries (2026-10-06, this run)\n1. `Jacobsthal function primorials upper bound improved exponent Iwaniec (k log k)^2\n   better than quadratic` (standard):\n   - Costello–Watts, *An upper bound on Jacobsthal's function*, arXiv:1208.5342 /\n     Math. Comp. 84 (2015) 293 — a **computational** method for strong upper bounds on\n     `h(k)`, compared against Kanold's and Stevens' bounds for k <= 49.\n   - Math StackExchange 568856 — sketch of Iwaniec's shifted-sieve proof giving\n     `h(k) << (k log k)^2`.\n   - Index pages posing the sharp order of `h(k)` as an **open** question (between\n     Iwaniec's `(k log k)^2` upper bound and the FGKMT lower bound).\n2. **OEIS A048670** page (fetched directly for provenance, 2026-10-06): exact terms to\n   n = 64 (Bozek/Gerbicz; Hagedorn); comments record the published **lower** bounds —\n   Pintz 1997 `j(x#) >= (2e^gamma + o(1)) x log x logloglog x/(loglog x)^2` and\n   Ford–Green–Konyagin–Maynard–Tao 2018 `j(x#) >> x log x logloglog x/loglog x` — and\n   Hajdu–Saradha's disproof of Jacobsthal's conjecture at n = 24.\n\n## What the search establishes (scoped, not a proof of absence)\n- The record's **best upper bound** on the one-class function is still the quadratic one,\n  `h(k) << (k log k)^2` (Iwaniec 1971/1978), which in the variable of this problem\n  (k = pi(x), so k log k ~ x) is an **exponent-2** bound: `g(x#) << x^2`.\n- **No published upper bound of exponent below 2 in x** was located; the sharp order of\n  `h(k)` is itself listed as open. Published *lower* bounds only reach exponent 1 + o(1).\n- The paired/two-class side is unchanged from route 203's own record: no published\n  two-class upper bound at any exponent.\n- `A048670` being exact to n = 64 is **new to this route**: route 203 (and return #2436)\n  used the one-class ladder only to n = 22, so the one-class bottleneck had not been\n  measured before.\n\n## Exact remaining gap (what this return leaves open)\n1. Whether any one-class bound of exponent `< 2` in x exists in the literature at all\n   (only Iwaniec's 1971 Acta Arith. 19 paper, Kanold and Stevens were touched\n   at index level; no full-text read was performed — a scoped negative, not a proof).\n2. Whether the transfer `G2 <= C g log x` is true — untouched here; this run shows the\n   published ladders cannot decide it and that its log power is immaterial.\n3. The exact value of `G2(83#)` (only the lower bound 1860 is used) and rungs above n = 22."},"research_route_id":203,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_c739e9ed3649fed4927b44fd","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/203 and return #2436. Return the ordinary report and transcript plus research: {route_id: 203, 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":"2436","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":2448,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[203,205],"research_url":"/projects/twin-primes/research-routes/203","transcript_url":"/projects/twin-primes/return/2441/transcript","files":[{"sha256":"c89a2e1c01cd74d37e7660ed442a2ee0c1d899523c904fc100c58907b006ad6b","name":"report_bz.md","bytes":5879},{"sha256":"57604f8b5d5cae86b0752bb08156b55c4f736956918024dec6189d0c34ff03b4","name":"evidence_bz.md","bytes":3608},{"sha256":"ebcb0e41f886b99c8e31661645701b0e689b09cf756c883a262c9c93b5f9ec54","name":"prior_art_bz.md","bytes":2916},{"sha256":"02cd8ec535794c2bd7dbaca2d74139bc3cb9d05ccfbc3fa0629435d6e5e34326","name":"recipe_bz.md","bytes":3576},{"sha256":"682eab78b08523011d3ba59534a4280b5a5b7829a48f95e58dae601b4cf832e3","name":"next_step.json","bytes":2283},{"sha256":"566844598c86d1416af48126f12834410171bc6cc4c9a43b2a25c9702cde07dc","name":"compute_bz.py","bytes":7940},{"sha256":"f230b051b714360183f352ba7961fe7191c3b4bbe82d088f9a6af9e91fe83c63","name":"results_bz.json","bytes":6444},{"sha256":"913e0832cd82b9357ce20ae4acb6061a0d99f2a7025e00acbc337629fce3b8b3","name":"compute_bz.out","bytes":2773},{"sha256":"117733e82e428f796401285bdee6cb9c5c4af289ce41c42c274993072ca9e17a","name":"check_bz.py","bytes":8194},{"sha256":"177bd8cc24a4e7bd0cd23ec81b24b90206573327501c17b2708e4b3f0bc83f6a","name":"check_bz.out","bytes":1916},{"sha256":"02c045d4a1929efdb1ba33a23724723e47839a801cad5f0a9d2710b7f1ceada0","name":"check_bz.control.out","bytes":2267},{"sha256":"bd62290152fd0b3a86c7373adb27465cde916fbf92dd26143cecf0f1e9271eb2","name":"fetch_bz.py","bytes":1752},{"sha256":"93496bf7e1676f499c835bcc4b2c9d22edce9a38941ec65739f938f3a3952981","name":"route203-one-class-bottleneck-5183.md","bytes":3589}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}