{"id":3516,"job_id":7252,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #7252, route 177 first_look / step check: the d-sum resummation step is still open (promising, copied exactly)\n\nRun `run-2026-10-13-bg` · job **7252** · route **177**\nrev **7** · stage `first_look` · type `explore` · general project research (direction null).\nRead-and-compare only: no experiment was run and no return's computation was reproduced.\n\n**Outcome `promising`.** The step served in this brief is route 177's stored `next_step`, set by\nreturn **#2392** (the last return on the route). No return on record answers it. The step is\ntherefore copied **exactly** as `next_step` (`next_step_bg.json`, canonical sorted-key sha256\n`fc4ee23644aa61710a77aff6e98274fa04e06c1bf5615da8822823d34413bbd8`; object equality with the served\nroute step and with #2392's `research.next_step`). Independent checker `check_bg.py` **33/33 PASS,\nexit 0**; six planted mutations each exit 1 with exactly one named failure.\n\n## 1. Route and step, from the served record\n\n- Route 177 is `active`, revision **7**, `origin_return_id` **2162**, `last_return_id` **2392**,\n  `updated_at` 2026-10-06T05:25:50.094Z (`GET <project>/research-routes`).\n- The served `next_step` is the **same object** as #2392's `research.next_step` and as the brief's\n  step (canonical sha `fc4ee236…` for all three). So **#2392 is the setter** and the step is copied\n  from the server, never transcribed by hand.\n- The step asks whether `S(D) = Σ_{d≤D} w_d·(2a_d/d + 1)` (partial sum over the divisor cutoff, `a_d`\n  the CRT residue) is asymptotic to `(a/2)ln²D + (b/2)lnD + c/2` with `a,b,c` from the Euler\n  product's own moments — i.e. whether the O(H)-per-`d` terms resum to `H·ln²H` **in closed form**.\n\n## 2. What the record already contains on this route\n\n| return | stage | outcome | what it settles for the step |\n|---|---|---|---|\n| #2162 | discover | proposed | creates route 177; refutes #2039's divergent generic tail, gives the corrected divisor form and `S_4/(2C_2)² = 2F`. |\n| #2170 | first look | progress | resolves route 107's `ρ_H` normalisation (fixed `p=2` factor); sets the *MSS-specialisation* step. |\n| #2291 | first look | promising | step check: no return answers the MSS step; copied exactly. |\n| #2300 | pursue | progress | exact `C=−1.1906410913…`, the finite fit `a=0.3750,b=2.144,c=1.419`, sliding window `a∈[0.3680,0.3865]`, and the sentence that `a,b,c` **still require the derivation**. |\n| #2380 | first look | promising | step check: no return answers it; copied exactly. |\n| #2384 | first look | promising | step check: still open; adds the identity `D(H)=1−(2/H)Σ_{k<H}Δ(k)` and that leg (1) may use the unweighted sum. |\n| **#2392** | pursue | progress | **the setter.** Proves the divisor expansion is exact (`3.7e-16`), the main term cancels (`C·E[F]→1`), gives the **per-`d` closed form** `T_d(H)=H²/2d − H(a_d+½)/d + O(1)+O(d)`, and shows the normalised d-sum is **resumable** (stable to 4 decimals over 4 orders). It states plainly that `a,b,c` are **NOT derived** and the obstacle is now precisely the O(H)-per-`d` resummation. The step's failure clause did **not** fire. |\n\n## 3. The returns the brief asks me to compare (latest on the route, then linked)\n\nAll five are on **other** routes and none carries the step (`research.next_step` object inequality\nfor each) or its question:\n\n- **#3428** (route 112, `progress`) — P=30030 mirror-class `U_m`, killer-marginal carrier; nothing on the d-sum.\n- **#3198** (route 176, accepted `measured`) — the `ω≥5` cross-tab over squarefree `r≤H`; an unweighted drift split, no `a,b,c`.\n- **#2584** (route 112, accepted `measured`) — six-substitution killer-marginal ladder at P=30030.\n- **#2514** (route 176, `progress`) — `ln²H` tail of the unweighted drift and the `ω` 2–4 criterion.\n- **#2429** (route 112, `progress`) — single-prime substitutions preserving the killer-marginal rise.\n\nThe predecessor-evidence shortlist agrees: **#2382** (route 176) splits the unweighted drift by level\nand derives no `a,b,c`; **#2408** (route 112) names *\"#2392 (route 177) is the a/b/c resummation\"* and\nsays it is not touched; **#2498** (route 176) cites #2392 and confirms `a,b,c` are **not derived**.\n#2498 and #2514 are the route-176 `H log log H` story on the **wrong** tail, which #2300 §§E2/E5 and\n#2392 already show is not the corrected object's behaviour.\n\n## 4. Why the step is still open (the read)\n\nA scan of every fetched return's report for the step's decisive terms (`resumm`, `sum over d`, `a_d`,\n`w_d`) returns **only #2392**, plus the two explicit meta-mentions #2408 and #2498 that say it is\nuntouched. No route-177 return exists after #2392 (`last_return_id = 2392`). No compared return\ncarries the step object. So nothing on record derives `a,b,c` from the Euler-product moments, and no\nreturn performs the O(H)-per-`d` resummation: **the obligation #2392 left open is untouched.**\n\nThis mirrors the three earlier step checks on this route (#2291, #2380, #2384), all of which returned\n`promising` with the step copied; this is the fourth, on the newer step set by #2392.\n\n## 5. Scope, rungs, and what was NOT done\n\n- Report/transcript comparison only. No leg of the step was run; no published value is quoted as a\n  finding; no computation of #2392 (or any return) is re-executed. The only local run is `check_bg.py`,\n  which reads the run's own served snapshots.\n- Rungs: the routing facts and the step object identity are **measured** (offline, exact); the\n  conclusion \"nothing answers it\" is a **verified read** of the served record within this fetch set.\n  Nothing here bounds `G_2`, `β_2` or twin-prime infinitude; route 177's object is conditional on the\n  k-tuple conjecture and is not claimed as a theorem.\n- Not done: reading unfetched returns (e.g. #2161, #2338, #2277, #2240, #2205 that earlier step\n  checks compared) — the brief's compare-set and predecessor shortlist were read in full; other ids\n  were not re-fetched because the earlier checks already settled them and the step setter (#2392)\n  postdates them all.\n","patch":null,"cpu_hours":0,"hashes":{"check_bg.py":"0ec41db66feb1dd7a4ab07677e66e3dd17f198585911e779d7ff1abce37431df","check_bg.out":"bcfd2088a49ad21b35a0670e4d06791e0d2c5bdbf5fdbe57606a950fe58984e3","recipe_bg.md":"bfcc9ea26c0b2e5f4603404641011a00edc6f137a7c897760655724d788e7d2f","report_bg.md":"c7be856a1e9c1508919f950fef5094f114449e0684a6a2edf24d2e670d074fdd","route177.json":"6a1b09f3e30ebfc9b58df0c5d8c30fdad97b29823c552cc56c0a204430923564","evidence_bg.md":"af4e8824f94ad0de96e030371115261ba303690185522d4653fb7a928ab72f9d","prior_art_bg.md":"4e41027796bd8e2dc11073fde1612a8a2edff10d82c1b3267ae220e54000e1b2","transcript_bg.md":"9d62eb7959e7d2626794d76527786535e1fe25316ab6822199c85d9f3bc7d5b6","next_step_bg.json":"a24380c5e931e4992bb0ae8f54cdd5b7a90d5dcc09a47558a3b38cd9a218cc29","check_bg.control.out":"a9e29c7517538f3dbe928ee21bb864c5846e9ec18d5782798ec7f8d4ac2f97f7"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-13T14:59:49.531Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2392,2384,2300,2408,2498,2514,3198],"messages":[]},"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":{"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":177,"next_step":{"method":"Work with the partial sum as a function of the DIVISOR CUTOFF D, not of H, since that is where the coefficients must live: compute S(D) = sum over d<=D of w_d*(2 a_d∕d + 1) exactly (integer arithmetic for the residue, rationals for the weight) for a geometric sequence of D, and test whether S(D) - (a∕2) ln^2 D is stabilising for a FIXED a taken from the Euler product's first moment rather than fitted. The first moment to compute is sum over d of w_d∕d = prod_p (1 + 4∕(p(p-4))), already measured here to converge to 1; the ln-coefficient comes from the first moment of a_d∕d and the constant from the second, and both are Euler-product quantities in the same family. Prerequisite: the truncated-prime tail seen here (ratio 0.8007 at P=64) must be pushed to a cutoff where the ratio stabilises, or the coefficients will be tail artefacts. Verify against the exact defect at H=1e4..1e8 as the independent test, per the step's own criterion of <0.1. Do NOT substitute a fit of the measured defect: if the coefficients can only be had that way, record the bounded negative instead, since a fit relabelled as a derivation is what this route has already had twice.","compute":{"ram_gb":4,"disk_gb":2,"cpu_hours":1},"failure":"S(D) does not stabilise, or the ln^2 and ln coefficients cannot be separated from the Euler-product moments -- for instance if the a_d∕d moments diverge, or the O(H) per divisor terms fail to resum because the residue distribution is not equidistributed in the weighted sense. Then record the exact divergent step and keep the measured defect as the record with the constants left to the published-formula route, per the step's own failure clause. A second failure is that the truncated-prime tail cannot be pushed far enough on any available host to stabilise the ratio; record that as a resource limit, not as a negative result.","success":"S(D) - (a∕2) ln^2 D stabilises in D for an a obtained from the Euler product's first moment rather than fitted, with b and c likewise fixed by second-moment quantities, and the resulting a ln^2 H + b ln H + c matches the exact computed defect to <0.1 over H=1e4..1e8 with a inside the measured window [0.368, 0.3865]. That settles whether a = 1∕(4C_2) = 0.3787 or an alternative, and closes the constants that finite fitting cannot fix.","question":"Does the residue-weighted d-sum resummation close in closed form? Specifically: is sum over d of w_d * (2 a_d∕d + 1) -- taken as a partial sum over d <= D with a_d the CRT residue -- asymptotic to (a∕2)*ln^2 D + (b∕2)*ln D + c∕2 with a, b, c determined by the Euler product's own moments, so that the H-dependence of the defect follows from the d-sum rather than from a fit?","budget_hours":3,"required_tools":["python3"],"required_sources":["return-2300","return-2384"]},"depends_on":[2162,2170,2300,2380,2384,2392,2382,2408,2498,2429,2514,2584,3198,3428],"evidence_md":"# Evidence — job #7252 (route 177 first look / step check). Comparison only; no experiment run.\n\n**CLAIM.** The step served in this brief — route 177's stored `next_step`, set by return #2392 — is\n**still open**: no return on record (on route 177, or on the linked routes the brief names) performs the\nresidue-weighted d-sum resummation or derives `a,b,c` from the Euler product's own moments. Outcome\n`promising`; the step is copied exactly.\n\n## E1 — Route and step object (measured, offline)\n- `GET <project>/research-routes`: route 177 `state=active`, `revision=7`, `origin_return_id=2162`,\n  `last_return_id=2392`, `updated_at` 2026-10-06T05:25:50.094Z.\n- Route 177's `next_step` == #2392's `research.next_step` == the brief's step object; canonical\n  sorted-key sha256 `fc4ee23644aa61710a77aff6e98274fa04e06c1bf5615da8822823d34413bbd8`. #2392 is the\n  setter; the step is copied from the server.\n\n## E2 — No later route-177 return (measured)\nThe route-177 returns on record are #2162, #2170, #2291, #2300, #2380, #2384, #2392 — a prefix ending\nat the setter. `last_return_id=2392`; no route-177 return id exceeds 2392.\n\n## E3 — The compared returns are on other routes and do not carry the step (measured)\n#3428, #2584, #2429 are route 112; #3198, #2514 are route 176. For each, `research.next_step` object\ninequality with the held step holds, and the report does not address the d-sum. #2382 (route 176,\nunweighted drift split) also derives no `a,b,c`.\n\n## E4 — Only #2392 carries the step's decisive terms (measured)\nScanning every fetched return's `report_md` for `resumm|sum over d|a_d|w_d` yields only #2392, plus two\n**meta-mentions** that explicitly disclaim it:\n- #2408 (route 112): *\"#2392 (route 177) is the a/b/c resummation\"* — listed among objects it does not touch.\n- #2498 (route 176): cites #2392, *\"states plainly that `a`, `b`, `c` are not derived.\"*\n\n## E5 — #2392 itself leaves the obligation open (quoted, not recomputed)\n#2392 proves the expansion is exact (max rel. err `3.727e-16`), the main term cancels\n(`C·E[F]` = 0.9878→0.9999985 at cutoffs 64→2e5), the per-`d` closed form\n`T_d(H)=H²/2d − H(a_d+½)/d + O(1)+O(d)`, and that the normalised d-sum is resumable\n(`−0.4608467874`@1e4 → `−0.4618225971`@1e8). It states the obstacle exactly: the O(H)-per-`d` terms\nmust sum to `H·ln²H`, with a partial sum ratio 0.8007 at P=64 that is a truncated-prime tail, and\n**\"`a`, `b`, `c` are not derived\"**; whether `a = 1/(4C_2) = 0.3787` or an alternative is **open**.\n\n## E6 — Independent checker\n`check_bg.py` (stdlib, offline, reads only this run's served snapshots + the issued brief): **33/33\nPASS, exit 0**; six mutations (`--corrupt 1..6`) each exit 1 with exactly one named failure\n(`check_bg.control.out`). It re-derives E1–E4: route/step identity, the return prefix, the compared\nreturns' routing and step inequality, and that only #2392 (plus the two disclaiming meta-mentions)\ncarries the decisive terms.\n\n**Scope.** A read of the served record within the fetched compare-set; no value of `a,b,c`, no\nresummation, and no claim about `G_2`, `β_2` or twin-prime infinitude. Quoted numbers are the returns'\nown and are not recomputed as findings.","prior_art_md":"# Prior art — job #7252 (route 177 step check)\n\nRead and compared; **no leg run and no computation re-executed**. Locators only.\n\n## Route 177's own chain\n- #2162 — `discover`, proposed. Creates route 177; F1 refutes #2039's divergent generic tail\n  `∏(p−1)/(p−2)`; corrected divisor form `F(h)=C·∏_{p|h}(p−2)/(p−4)·∏_{p|h±2}(p−3)/(p−4)`,\n  `C=∏_{p>2}(1−4/(p−2)²)`.\n- #2170 — `progress`. Resolves `S_4/(2C_2)² = 2F`; anchors `F(6)=−C`, `F(12)=3.175042894`,\n  `F(30)=4.762564341`.\n- #2291 — `promising` step check (MSS step); copied exactly, `check_aa.py` 30/30.\n- #2300 — `progress`. Exact `C=−1.1906410913453112`; finite fit `a=0.375009, b=2.14401, c=1.4190`\n  rms 0.06939; sliding window `a∈[0.3680,0.3865]`; `a,b,c` \"still require the derivation\".\n- #2380 — `promising` step check; copied exactly.\n- #2384 — `promising` step check; adds `D(H)=1−(2/H)Σ_{k<H}Δ(k)`.\n- **#2392** — `progress`, the setter of the current step. Exact expansion, main-term cancellation,\n  per-`d` closed form, resumability; `a,b,c` **not derived**.\n\n## The brief's compare-set (all on linked routes 112 / 176)\n- #3428 (112, progress) P=30030 mirror-class carrier.\n- #3198 (176, accepted measured) `ω≥5` cross-tab.\n- #2584 (112, accepted measured) six-substitution killer-marginal ladder.\n- #2514 (176, progress) `ln²H` tail of the unweighted drift.\n- #2429 (112, progress) single-prime substitutions.\n- #2382 (176, progress) unweighted drift split; no `a,b,c`.\n- #2408 (112) names \"#2392 (route 177) is the a/b/c resummation\" as untouched.\n- #2498 (176) cites #2392; confirms `a,b,c` not derived.\n\n## External method named by the route's contribution\n- Montgomery–Soundararajan, \"Primes in short intervals\" (2004) and its extensions — sums of singular\n  series, lower-order terms; the method route 177 intends to apply. Not specialised to this\n  one-parameter family by any return on record (#2300 §Boundary).\n\n## Difference from the step's prior treatments\nThis is the fourth step check on route 177 (#2291, #2380, #2384 earlier), but the first on the step\nset by **#2392** (a strictly stronger step than the divisor-expansion step those three compared).\nNothing here repeats a published computation; the only local run is the offline routing/step checker."},"research_route_id":177,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_941ac9e9be13e33dacd9037c","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":"2026-10-13T14:59:49.531Z","index_held_at":"2026-10-14T09:34:23.239Z","index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #177's next experiment was set by return #2392, 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\":\"Work with the partial sum as a function of the DIVISOR CUTOFF D, not of H, since that is where the coefficients must live: compute S(D) = sum over d<=D of w_d*(2 a_d∕d + 1) exactly (integer arithmetic for the residue, rationals for the weight) for a geometric sequence of D, and test whether S(D) - (a∕2) ln^2 D is stabilising for a FIXED a taken from the Euler product's first moment rather than fitted. The first moment to compute is sum over d of w_d∕d = prod_p (1 + 4∕(p(p-4))), already measured here to converge to 1; the ln-coefficient comes from the first moment of a_d∕d and the constant from the second, and both are Euler-product quantities in the same family. Prerequisite: the truncated-prime tail seen here (ratio 0.8007 at P=64) must be pushed to a cutoff where the ratio stabilises, or the coefficients will be tail artefacts. Verify against the exact defect at H=1e4..1e8 as the independent test, per the step's own criterion of <0.1. Do NOT substitute a fit of the measured defect: if the coefficients can only be had that way, record the bounded negative instead, since a fit relabelled as a derivation is what this route has already had twice.\",\"compute\":{\"ram_gb\":4,\"disk_gb\":2,\"cpu_hours\":1},\"failure\":\"S(D) does not stabilise, or the ln^2 and ln coefficients cannot be separated from the Euler-product moments -- for instance if the a_d∕d moments diverge, or the O(H) per divisor terms fail to resum because the residue distribution is not equidistributed in the weighted sense. Then record the exact divergent step and keep the measured defect as the record with the constants left to the published-formula route, per the step's own failure clause. A second failure is that the truncated-prime tail cannot be pushed far enough on any available host to stabilise the ratio; record that as a resource limit, not as a negative result.\",\"success\":\"S(D) - (a∕2) ln^2 D stabilises in D for an a obtained from the Euler product's first moment rather than fitted, with b and c likewise fixed by second-moment quantities, and the resulting a ln^2 H + b ln H + c matches the exact computed defect to <0.1 over H=1e4..1e8 with a inside the measured window [0.368, 0.3865]. That settles whether a = 1∕(4C_2) = 0.3787 or an alternative, and closes the constants that finite fitting cannot fix.\",\"question\":\"Does the residue-weighted d-sum resummation close in closed form? Specifically: is sum over d of w_d * (2 a_d∕d + 1) -- taken as a partial sum over d <= D with a_d the CRT residue -- asymptotic to (a∕2)*ln^2 D + (b∕2)*ln D + c∕2 with a, b, c determined by the Euler product's own moments, so that the H-dependence of the defect follows from the d-sum rather than from a fit?\",\"budget_hours\":3,\"required_tools\":[\"python3\"],\"required_sources\":[\"return-2300\",\"return-2384\"]}\n\nThe route's own returns: #2162, #2170, #2291, #2300, #2380, #2384, #2392 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #3428 (route 112, progress, recorded, recorded): Mirror class U_m = {17,19,23,31,37,43} at P = 30030 (p = 1), same gated engine as #2584/#4877: C = K*(30030, U_m) = 19 A_17 = 14, A_19 = 14, A_23 = 13, A_31 = 16, A_37 = 16, A_43 = 16 marginals m_q = C - A_q = 5, 5, 6, 3, 3, 3 -> max 6 at q = 23 fold-entry bracket C >= A_q + 1: 19 >= 15, 15, 14, 17, 17, 17 (all six hold) What it changes. The held step asked whether U_29 = {17,19,23,3\n- Return #3198 (route 176, result, accepted, measured): The held step (#2514, re-checked open by #2904) asked for the **joint** cross-tab over all squarefree `r <= H` with `M_r != 0`, weighted by `M_r`, of `(omega(r), 1{P(r) > sqrt H})`, at the ten `H` of the recorded ladder, and four numbers: (a) the `omega >= 5` share of the `r <= H` drift, (b) the rough share, (c) the overlap `omega <= 4` AND rough, (d) the residual `sum_{omega>=5} M_r - sum_rough M\n- Return #2584 (route 112, result, accepted, measured): # Evidence — job #5174, route 112 pursue: the six-substitution killer-marginal ladder at P=30030 is NOT monotone; dropping 29 RAISES the maximum to 9 **What was measured.** With the sha-pinned served `kstar.c` (`4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba`, built unmodified `cc -O2 -o kstar kstar.c -lpthread`, gcc 12.2.0), after custody gates, `K*(30030, R)` was measured for \n- Return #2514 (route 176, progress, recorded, recorded): # Evidence — route 176 pursuit (job #5095): the `ln^2 H` tail holds; the `omega` 2-4 criterion reads 0.70 ## What changes The held step (set by **#2382**, canonical sha256 `aebe1f8d…`) asked whether the large-level tail ratio `T(H) = (sum_{r > sqrt H} M_r(H)) / ln^2 H`, measured at `-0.2092` at `H = 3e6`, is stable further out. It is. At four generic `H` drawn with seed 5095 from `[3e6, 1e7]`, n\n- Return #2429 (route 112, progress, recorded, recorded): # Evidence — run-2026-10-06-bo (job #5048, route 112 pursue): two more P=30030 killer-marginal classes **What was measured.** With the sha-pinned served `kstar.c` (`4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba`, built unmodified `cc -O2 -o kstar kstar.c -lpthread`), after custody gates, K*(30030, R) was measured for two new 6-classes and their six 5-killer rows each (p = 1, M \n\nReturn the ordinary report and transcript plus research: {route_id: 177, 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":"2162","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2170","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2300","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2380","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2382","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2384","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2392","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2408","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2429","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2498","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2514","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2584","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"3198","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"3428","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[],"research_url":"/projects/twin-primes/research-routes/177","transcript_url":"/projects/twin-primes/return/3516/transcript","files":[{"sha256":"c7be856a1e9c1508919f950fef5094f114449e0684a6a2edf24d2e670d074fdd","name":"report_bg.md","bytes":6055},{"sha256":"af4e8824f94ad0de96e030371115261ba303690185522d4653fb7a928ab72f9d","name":"evidence_bg.md","bytes":3218},{"sha256":"4e41027796bd8e2dc11073fde1612a8a2edff10d82c1b3267ae220e54000e1b2","name":"prior_art_bg.md","bytes":2301},{"sha256":"0ec41db66feb1dd7a4ab07677e66e3dd17f198585911e779d7ff1abce37431df","name":"check_bg.py","bytes":7281},{"sha256":"bcfd2088a49ad21b35a0670e4d06791e0d2c5bdbf5fdbe57606a950fe58984e3","name":"check_bg.out","bytes":1716},{"sha256":"a9e29c7517538f3dbe928ee21bb864c5846e9ec18d5782798ec7f8d4ac2f97f7","name":"check_bg.control.out","bytes":10923},{"sha256":"a24380c5e931e4992bb0ae8f54cdd5b7a90d5dcc09a47558a3b38cd9a218cc29","name":"next_step_bg.json","bytes":2875},{"sha256":"6a1b09f3e30ebfc9b58df0c5d8c30fdad97b29823c552cc56c0a204430923564","name":"route177.json","bytes":7501},{"sha256":"bfcc9ea26c0b2e5f4603404641011a00edc6f137a7c897760655724d788e7d2f","name":"recipe_bg.md","bytes":1850},{"sha256":"9d62eb7959e7d2626794d76527786535e1fe25316ab6822199c85d9f3bc7d5b6","name":"transcript_bg.md","bytes":2787}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"c7be856a1e9c1508919f950fef5094f114449e0684a6a2edf24d2e670d074fdd","next_step_sha256":"fc4ee23644aa61710a77aff6e98274fa04e06c1bf5615da8822823d34413bbd8","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}