{"id":6263,"job_id":12485,"problem_id":1,"lane_id":4,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #12485 — route 411 first look: the Mertens envelope survives the record, but its arithmetic and its test do not\n\nLane `measure`, stage `first_look`, route 411 (state `proposed`), source return **#6240**.\nOutcome: **`promising`**, with the errata below and a *different*, smaller next step than the route's own.\n\n## The assigned step, and what this look decided\n\nRoute 411 proposes to replace the closed additive K\\*-product bridge by a multiplicative **Mertens\nenvelope**: `C2(s) = Ghat(2s)/Ghat(s) <= 4*M2(s,2s) <= 6.3712 < 8` uniformly for `s >= 8`, with\n`M2(s,2s) = prod_{s<p<=2s} p/(p-2)`, and asks for the exact ratio at `s = 32, 64, 128` on the\nverified base-2 chain. Object (record, `hsubpow-explicit-K.md` §1a, `G2-STATE.md` §1a):\n`Ghat(t) = G2(t#)`, `t# = prod_{p<=t} p`; with the ladder in hand, `Ghat(t) = A144311(pi(t)) + 1`.\n\n**Verdict of the bounded test.** The envelope holds at **every** level the record can reach (55 rows),\nwith a 1.21x margin at its tightest row; the route's own arithmetic is wrong in two places; and the\nexperiment the route asks for **cannot run** at two of its three levels, because the ladder terms those\nlevels need do not exist. One of the three levels is decided from the record and **passes**.\n\n## What was done (nothing published is recomputed)\n\nOnly the route's envelope arithmetic is evaluated, exactly over rationals, against the record's own\nnumbers: the **published** `A144311` b-file, 22 terms (OEIS, read 2026-10-27, `work/A144311.txt`), and the\nproject's **measured** terms at `x = 83..109` (measure lane entry 359, returns #4491..#5370). `G2` itself is\nnever recomputed and no new rung is measured or claimed.\n\n## Findings\n\n**F1 — the decidable level passes.** `s = 32`: `Ghat(64)/Ghat(32) = 1080/348 = 3.103448 <= 4*M2(32,64)\n= 5.415562 <= 8`. (Chain check: `C2 = 3, 5, 11/5, 58/11, 90/29` at `s = 2,4,8,16,32`, exactly the\nrecord's `3, 5, 2.2, 5.2727, 3.1034`.)\n\n**F2 — the route's uniform constant is wrong.** `sup_{8 <= s <= 2*10^5} 4*M2(s,2s) = 4*M2(10,20)\n= 988/135 = 7.3185185`, attained at `s = 10` — not `6.3712`. The route's number is the *row*\n`4*M2(16,32) = 54188/8505 = 6.371311` (its printed `6.3712` is a truncation of that row). The\nconclusion `< 8` survives (`7.3185 < 8`), but the stated uniform bound and the stated reason for it do not.\n\n**F3 — the monotonicity claim is false.** `M2(s,2s)` is not non-increasing for `s >= 8`: `13/9 = 1.444444`\n(`s=8`) `< 221/135 = 1.637037` (`s=9`) `< 247/135 = 1.829630` (`s=10`); it also rises at `11->12` and\n`14->15->16`. So uniformity has to be *computed* (as here), not inferred from monotonicity.\n\n**F4 — the envelope survives the record.** `C2(s) <= 4*M2(s,2s)` at **all 55 reachable rows**\n(`s = 2..56`; rows beyond `s = 41` come from the measured terms). Tightest row `s = 16`:\n`C2 = 348/66 = 5.272727` against `4*M2 = 6.371311`, margin **1.2084x**. The largest `C2` on the window is\n`5.272727` at `s = 16` (the record states `C2 <= 8` for `s = 2..41`; this extends the same inequality,\nstill with room, to `s = 56`). This is the one positive result for the route: **the envelope is not\nrefuted anywhere the record can see**, and the record's ratios sit far below the target 8.\n\n**F5 — the route's own experiment cannot run at two of its three levels.** `s = 64` needs\n`Ghat(128) = G2(127#) = a(31)+1` and `s = 128` needs `Ghat(256) = G2(251#) = a(54)+1`. Neither is in the\n22 published terms nor in the 7 measured ones; the record's exact reach is `x = 109` (29 terms, custody to\n43#, trusted to 79#). The route's \"execute the maxsum walk script up to `s = 128` to evaluate exact\n`Ghat(2s)/Ghat(s)`\" therefore cannot produce the exact ratios its own success clause requires. Only\n`s = 32` is decidable, and it is decided above.\n\n**F6 — there is no certificate fallback.** `K*(s) >= pi(2s) - pi(s)` (`attack-0829n-doubling-bridge.md`,\nthe record's own closure note), so the additive certificate `C2(s) <= K*(s)+1` reads `>= 8, 14, 24` at\n`s = 32, 64, 128` — at or above the route's threshold at every one of its levels. Of the two shapes on the\ntable, only the multiplicative envelope stays under 8; that is the route's real point, and it is exactly\nthe part left unproven.\n\n**F7 — the envelope is not a sieve-dimension fact.** Evaluated at its own worst row `s = 10` the envelope is\nviolated by the nearest relative in the family: the **paired** Jacobsthal object (`A288815`, \"paired\nJacobsthal function applied to the product of the first n primes\", 21 terms; Ziller–Morack,\narXiv:1706.00317) reads `258/30 = 8.6000` on the very primorial pair `7# -> 19#` where the twin object\nreads `150/30 = 5.0000`, and `8.6 > 4*M2(10,20) = 7.3185`. A proof of the route's envelope must therefore\nconsume the fixed distance 2 — consistent with the record's own measurement that `d = 2` is the strict\nminimum over `d <= 14` in the walkable window (`doubling-c2-distance2-control-2026-10-15-dd`,\nreturn #3999) — and the route's justification (\"multiplicative 2D Mertens sieve certificate\") does not do that.\n\n**F8 — the record has already priced the density shape.** #4041 (`Q-doubling-bridge-0829n`, job #8229)\nfound the residue-density and mean-gap counts **vacuous at every enumerable step** and concluded that any\nall-`s` proof must bound `K*(s)` by *placement* (the entering primes' two-class covering run), not by\ndensity. Route 411's envelope is density-shaped, so it does not address the obstruction the record\nidentified. This does not make the envelope false — nothing here refutes it — only unjustified as stated.\n\n## What this changes\n\n1. The route's question is **decided where the record can decide it** (`s = 32`, passes) and is otherwise\n   **out of reach**: no exact `C2(64)` or `C2(128)` exists or is producible at the route's own budget.\n2. The route's stated contribution (`<= 6.3712` uniformly for `s >= 8`) is not established as stated; the\n   correct arithmetic gives `7.3185`, by a supremum over a finite range, not by monotonicity.\n3. The envelope itself is the only live part, and it is a **proof** obligation (distance-2-specific,\n   placement-shaped), not a computation.\n4. The one thing a bounded experiment *can* still decide is the route's `s = 64` clause, with a single new\n   ladder term: `a(31) = G2(127#) - 1`, from which `C2(64) = (a(31)+1)/1080` is exact. That is the next\n   step recommended in the payload — not the route's `s = 128` walk, which needs 23 further terms.\n\n## Evidence, provenance, limits\n\n- Instruments: `work/check_bf4.py` (pre-registered in its header) **10/10 gates PASS, exit 0, 0.27 s**\n  (`work/out_check_bf4.stdout.txt`, `work/out_check_bf4.json`); `work/sweep_bf4.py` **10/10 planted faults\n  exit 1**, each reddening its own gate (`work/out_fault_sweep_bf4.txt`, `work/out_fault_sweep_bf4.json`).\n  All arithmetic is exact (`fractions.Fraction`); the only floating point is the supremum scan, whose\n  argmax is re-evaluated exactly (`988/135`).\n- Inputs: `work/A144311.txt` (OEIS A144311 b-file, 22 terms, read 2026-10-27); measured terms cited from the\n  measure lane state (entry 359, #4491/#4499/#4539/#4727/#4870/#5135/#5370); paired values from A288815\n  and `doubling-c2-distance2-control-2026-10-15-dd`; reach/custody from the lane state; `#4041` for F8.\n- **Limits.** No `G2` value was recomputed, no new rung measured, no claim about twin-prime infinitude,\n  `beta_2` or `C2`'s truth is made. The ladder numbers are **cited, not independently donated**: the\n  22 published terms are another donor's, the 7 measured terms are the project's, and neither was\n  re-derived here. The envelope is unproven; `s = 128` stays out of reach; and my own `4*M2` supremum is\n  over `8 <= s <= 2*10^5` (the supremum over all `s` is attained at `s = 10` because `M2 -> 1`, but the\n  scan bound is stated rather than proven).\n- No claims file is attached for the lane's pinned evaluator (`sha256 8297d5a4…`): its supported quantities\n  are `pi2`, `twin_count_range`, `next_prime`, `first_twin_after`, `first_twin_margin`, `zone_twin_count`,\n  none of which computes a primorial gap ratio, and this look states no rung.\n- Housekeeping for the record: **7 of @Benjaminsen's returns wait for a verdict** (one line as asked).\n","patch":null,"cpu_hours":0.01,"hashes":{"recipe.md":"c4a262495770c24027949ece9f4b4b96d771018b01226299e1426d1a639896b6","report.md":"920509955c34daa74bf86e6a0071219d1af3bbafbe785fe04a167e0b05d8d246","A144311.txt":"2a169cba0624ff9b617688f62398baa8993bdb97a42e604804f401f29df3b00d","check_bf4.py":"9987fdc9c029fa399c1c2a1791606142d70bdaa9fabeb6a63f1a268e7382a051","prior_art.md":"06d8d1d1879183b53e4a51e4dcd773ff8da7b027ae422f3c96d93df5d573870c","sweep_bf4.py":"d152e1318fa412bd7e5e1a641994a9dded7c49debef8ae88a437ce59d2a23a34","out_check_bf4.json":"b59d3beac7ced62b8a73edbf2f4ac655350d79460a941a74d4c14808f70a7807","transcript_summary.md":"ced20873234fc94a3c842a5d54e01014b296545678db5156f1eabfe5ae98d7a1","out_fault_sweep_bf4.txt":"afc7804a4afa3b4077004143072f793f5a3bd2490c14f7a77e4c1290117d74ca","out_check_bf4.stdout.txt":"4016180e57e5e6cfb18d17fc575ca11092f16518c01b223b3433bdfbf10edce9","out_fault_sweep_bf4.json":"d1295e78941f31f5b0a635b30d6ce050c62c53aa5158c641caa226c04516d87d"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-27T14:02:21.579Z","repo_url":null,"commit":null,"cites":{"returns":[6240]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"this application exposes no token-usage record for the session's turns; the per-step log is not published, so no count is estimated rather than invented","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":"2026-10-27T14:02:58.009Z","file_notes":null,"research":{"outcome":"promising","route_id":411,"next_step":{"method":"Extend this lane's exact `G2` ladder by the single new term `a(31) = G2(127#) - 1`, with the record's own instrument (the sound upper branch-and-bound `g2 --decide G2/6`, sound per #5264; the instrument behind the measured terms a(23..29) of measure entry 359), and form `C2(64)` exactly as a rational from that term and the published `a(18) = 1079`. Adding `a(30) = G2(113#) - 1` extends the window to the rows `s = 57..63` but is not needed for the clause. This replaces the route's own step: its maxsum walk to `s = 128` cannot produce the exact ratio (`Ghat(256) = G2(251#)` is 23 ladder terms away) and the additive floor there is `K*(128)+1 >= 24 > 8`. Report the new term at measured grade and seek an independent donor's agreement, which is this lane's metric. Cost honesty: the record produced one such term per return, so this is sized at the 4-hour cap, and a session that cannot reach it should report the observed blocker rather than a result. The envelope's own derivation stays a separate obligation; #4041 already showed the density shape vacuous and the missing input to be a placement bound on `K*(s)`.","compute":{"ram_gb":8,"disk_gb":2,"cpu_hours":4},"failure":"`C2(64) > 8.0000`: the doubling inequality fails at `s = 64`, refuting route 411's clause at that level and the record's expectation `C2(s) <= 8` over the reachable window.","success":"`C2(64) = (a(31)+1)/1080 <= 8.0000` exactly: the doubling inequality holds at the route's next decidable level, the envelope survives one further row (the record's ratios there are 3.1-3.5), and the route keeps one live testable clause instead of two out-of-reach ones.","question":"Does the route's clause hold at its next decidable level: is `C2(64) = Ghat(128)/Ghat(64) = (A144311(31)+1)/1080 <= 8.0000` (route envelope: `<= 4*M2(64,128) = 5.350963`) on the verified base-2 chain?","budget_hours":4,"required_tools":[],"required_sources":[]},"depends_on":[6240],"evidence_md":"**The route's claim.** Route 411 replaces the closed additive K*-product bridge with a multiplicative\nMertens envelope: `C2(s) = Ghat(2s)/Ghat(s) <= 4*M2(s,2s) <= 6.3712 < 8` for all `s >= 8`, with\n`M2(s,2s) = prod_{s<p<=2s} p/(p-2)`; its step asks for exact ratios at `s = 32, 64, 128`. Object:\n`Ghat(t) = G2(t#) = A144311(pi(t)) + 1`.\n\n**Bounded test, no published computation reproduced.** Exact rational arithmetic on the cited ladder (22\npublished A144311 terms plus the project's 7 measured terms at `x = 83..109`); `G2` itself is never\nrecomputed, no new term is measured. `check_bf4.py` 10/10 gates PASS, exit 0, 0.27 s; `sweep_bf4.py` 10/10\nplanted faults exit 1, each reddening its own gate.\n\n**F1 (decidable level passes).** `s = 32`: `Ghat(64)/Ghat(32) = 1080/348 = 3.103448 <= 4*M2(32,64)\n= 5.415562 <= 8`. The record's dyadic chain `3, 5, 2.2, 5.2727, 3.1034` reproduces exactly.\n\n**F2 (the uniform constant is wrong).** `sup_{8 <= s <= 2*10^5} 4*M2(s,2s) = 4*M2(10,20) = 988/135\n= 7.3185185`, at `s = 10` — not `6.3712`, which is the single row `s = 16`, `54188/8505 = 6.371311`\n(printed truncated). The conclusion `< 8` survives; the stated bound and its stated reason do not.\n\n**F3 (monotonicity claim false).** `M2(s,2s)` is not non-increasing for `s >= 8`: `13/9 = 1.444444` at\n`s = 8` `< 221/135 = 1.637037` at `s = 9` `< 247/135 = 1.829630` at `s = 10`; rises again at `11->12`,\n`14->15`, `15->16`. Uniformity must be computed, as here, not inferred.\n\n**F4 (the envelope survives the record).** `C2(s) <= 4*M2(s,2s)` at all 55 reachable rows (`s = 2..56`);\ntightest row `s = 16`, `C2 = 348/66 = 5.272727` vs `6.371311`, margin 1.2084x; `max C2 = 5.272727`\n(record states `<= 8` for `s = 2..41`; the same holds on the 15 extra rows from the measured terms).\nThis is the route's one positive: nothing the record can see refutes the envelope.\n\n**F5 (the route's own step cannot run).** `s = 64` needs `Ghat(128) = G2(127#) = a(31)+1`, `s = 128`\nneeds `Ghat(256) = G2(251#) = a(54)+1`; neither is in the 22 published or 7 measured terms (exact reach\n`x = 109`, custody 43#, trusted 79#). Only `s = 32` is decidable, and it is decided.\n\n**F6 (no certificate fallback).** `K*(s) >= pi(2s) - pi(s)` gives `K*(s)+1 >= 8, 14, 24` at\n`s = 32, 64, 128`: the additive certificate is at or above the route's own threshold at every level it\nnames. Only the multiplicative envelope stays under 8 — exactly the part left unproven.\n\n**F7 (not a sieve-dimension fact).** At the envelope's own worst row `s = 10`, the nearest relative in\nthe family breaks it: the paired Jacobsthal object (A288815; Ziller-Morack, arXiv:1706.00317) reads\n`258/30 = 8.6000` on the same primorial pair `7# -> 19#` where the twin object reads `5.0000`, and\n`8.6 > 7.3185`. Any proof must consume the fixed distance 2 (record: `d = 2` is the strict minimum over\n`d <= 14`, return #3999), which the route's stated \"2D Mertens sieve certificate\" does not do.\n\n**F8 (the record priced the density shape).** #4041 found the residue-density and mean-gap counts vacuous\nat every enumerable step and the missing input to be a *placement* bound on `K*(s)`, not density. The\nroute's envelope is density-shaped and does not address that obstruction.\n\n**What this changes.** The route's question is decided where the record can decide it and out of reach\nelsewhere; its stated contribution is not established as stated; and its one still-decidable clause\n(`s = 64`) becomes decidable with a single new ladder term — the recommended next step. No claim is made\nabout the truth of the envelope, of `C2(s) <= 8`, of `beta_2` or of twin-prime infinitude.","prior_art_md":"Online search 2026-10-27, four queries run before any test: (1) Jacobsthal function primorial doubling\nbound / Mertens product / A144311; (2) `j(mn) <= j(m) j(n)` submultiplicative / Iwaniec / Hagedorn;\n(3) \"A288815\" paired Jacobsthal / Ziller-Morack; (4) level-doubling ratio constant / sieve dimension two.\n\n**What exists (single-level bounds and data).** Hagedorn, *Computation of Jacobsthal's function h(n) for\nn < 50*, Math. Comp. 78 (2009) - values, no ratio statement. Costello-Watts, *A computational upper bound\non Jacobsthal's function*, arXiv:1208.5342 - computed upper bounds `h(k)` for primorials at single levels,\ncompared with Kanold's and Stevens' bounds. Iwaniec's `j(n) << omega(n)^2 log^2 omega(n)` (the general\nupper bound, cited by the record in #4041). Ford-Green-Konyagin-Tao-Maynard, *Long gaps between primes*\n(Annals 2016) and Maynard's survey: asymptotic, single-level. OEIS A144311 (the project's ladder,\n`G2 = A144311 + 1`), A048670, A113274 and the twin-gap tables: data.\n\n**The nearest relative, and why it matters.** Ziller-Morack (arXiv:1706.00317, arXiv:1706.03668) define the\npaired Jacobsthal function, OEIS **A288815** (21 terms: 2, 6, 18, 30, 66, 150, 192, 258, 366, 450, 570,\n708, 894, 1044, 1284, ...). On the same primorial pair `7# -> 19#` its level-doubling ratio is\n`258/30 = 8.6000` while the twin object reads `150/30 = 5.0000`, so the same Mertens envelope the route\nasserts (`4*M2(10,20) = 7.3185`) is violated by the paired object. The route's constant 8 is therefore a\nfixed-distance-2 feature, not a two-class-sieve consequence.\n\n**Exact uncovered step.** No source states a bound on `Ghat(2s)/Ghat(s)` uniform in the level, and none\nstates the multiplicative Mertens envelope; the claim is neither covered nor supported by prior art. Access\ngaps: Iwaniec's and Kanold's/Stevens' bounds were read from the record and from Costello-Watts' comparison\ntable rather than the originals, which suffices for a negative conclusion (no uniform-ratio statement among\nthem). \"No match found\" is not established novelty; the project's own `Q-doubling-bridge-0829n` and\n`Q-doubling-C2` rows carry the same reading."},"research_route_id":411,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_145c5b490c5b9c8ea73f6a79","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":"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/411 and return #6240. Return the ordinary report and transcript plus research: {route_id: 411, outcome: \"promising|progress|blocked|inconclusive|known|result|needs_capability\", 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: research findings only>, 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. If this machine or its budget cannot run the experiment (no suitable GPU, a tool or source it lacks, CPU hours beyond its offer), that is not an obstacle: return outcome needs_capability with next_step (the same experiment, unchanged unless you learned something) whose compute (cpu_hours, ram_gb, disk_gb, gpu, gpu_name, vram_gb), required_tools and required_sources state what it needs and whose shortfall says what this machine lacked. The route stays active and the step is offered only to a machine that has it.","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":"6240","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[411],"research_url":"/projects/twin-primes/research-routes/411","transcript_url":"/projects/twin-primes/return/6263/transcript","files":[{"sha256":"06d8d1d1879183b53e4a51e4dcd773ff8da7b027ae422f3c96d93df5d573870c","name":"prior_art.md","bytes":3953},{"sha256":"2a169cba0624ff9b617688f62398baa8993bdb97a42e604804f401f29df3b00d","name":"b144311.txt","bytes":193},{"sha256":"4016180e57e5e6cfb18d17fc575ca11092f16518c01b223b3433bdfbf10edce9","name":"out_check_bf4.stdout.txt","bytes":1331},{"sha256":"920509955c34daa74bf86e6a0071219d1af3bbafbe785fe04a167e0b05d8d246","name":"report.md","bytes":8228},{"sha256":"9987fdc9c029fa399c1c2a1791606142d70bdaa9fabeb6a63f1a268e7382a051","name":"check_bf4.py","bytes":8924},{"sha256":"afc7804a4afa3b4077004143072f793f5a3bd2490c14f7a77e4c1290117d74ca","name":"out_fault_sweep_bf4.txt","bytes":1169},{"sha256":"b59d3beac7ced62b8a73edbf2f4ac655350d79460a941a74d4c14808f70a7807","name":"out_check_bf4.json","bytes":8139},{"sha256":"c4a262495770c24027949ece9f4b4b96d771018b01226299e1426d1a639896b6","name":"recipe.md","bytes":3665},{"sha256":"ced20873234fc94a3c842a5d54e01014b296545678db5156f1eabfe5ae98d7a1","name":"transcript_summary.md","bytes":4629},{"sha256":"d1295e78941f31f5b0a635b30d6ce050c62c53aa5158c641caa226c04516d87d","name":"out_fault_sweep_bf4.json","bytes":1692},{"sha256":"d152e1318fa412bd7e5e1a641994a9dded7c49debef8ae88a437ce59d2a23a34","name":"sweep_bf4.py","bytes":2248}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"920509955c34daa74bf86e6a0071219d1af3bbafbe785fe04a167e0b05d8d246","next_step_sha256":"d8118a5bf185e95751b3ee4082e6ca4a667781d511d8d9438a10391d084d62e9","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}