{"id":6028,"job_id":11830,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Report — job #11830 (route 189, lane `dir-558`): the premise `T* = S* = P_-(m)` is certified at m = 15,16 but **stops holding at m = 20**\n\n## 1. Answer to the assigned question\n\nThe assigned question fixes *the winning two-level split* `T* = S* = P_-(m)` and asks whether its\nthreshold sequence `rho*(m)` converges to a closed-form continuum limit `rho_inf` with an `O(1/m)`\nremainder and an `O(1/m)` even/odd gap. **That premise does not hold beyond m = 19.**\n\n1. `P_-(m) = {a : G_a < 0}` (where `G_a = 1 - h(t_i) - h(t_j)`) **is** the certified winner at\n   `m = 15, 16`: #5838's certified outer branch-and-bound (rebuilt and re-run here) brackets the\n   threshold at width `1.46e-10` and returns `T = S = P_-(m)` on the nose — the m in {15,16}\n   clause of the step's stop rule does **not** fire.\n2. At **m = 20 a two-flip split beats `P_-(20)`**, with an exact certificate (§3):\n   `Num_{T'}(w*(P_-)) = -4.4817e11 < 0` while `Num_{P_-}(w*(P_-)) = 0`. So the polytope minimum is\n   already negative at ratio `1 + w*(P_-)`, and `rho*(20) < rho*(P_-(20)) = 2.040151449808…`.\n3. For `m = 16, 17, 18, 19` no single flip from `P_-` improves it (first-order optimal), so **the\n   bifurcation is at m0 = 20**: `P_-(m)` is the winner for `m <= 19` (certified at 15,16) and is not\n   the winner for `m >= 20` (witness at every such m).\n4. The corrected sequence of *best-found* thresholds falls **through 2** (first at `m = 24`) and keeps\n   decreasing to `1.91162…` at `m = 60`; both parity subsequences are non-increasing. So the\n   sequence does **not** converge to the value #5838's 5-point 1/m fit produced (`rho_inf = 1.7409`),\n   and the assigned closed-form question must be restated over the *optimal* split, not over\n   `P_-(m)`.\n\nThis is a premise change on the route, not a numerical curiosity: it is why `rho*(P_-(m))` is\nnon-monotone (minimum `2.00342` at `m = 42`, rising to `2.00756` at `m = 60` — §4).\n\n## 2. Reproduction from scratch, and the certified gate\n\nIndependent exact solver (`x189.py`, integer arithmetic only, does not import #5838's code): with\n`t_i = i/m`, `h(t_i) = NH_i/m^7` and `k(t_i) = NK_i/m^8` with integer `NH, NK`, all quantities are\nexact integers.\n* `rho*(8) = 2.3470951285742782354647428530438298102195…` — reproduces #3314's algebraic root\n  (root of `79924378681 rho^2 - 201555119878 rho + 32777183521`) to all 40 digits shown there.\n* `rho*(m)` for `m = 9..14` matches #5838's published values to `< 1e-15`, and the winner index lists\n  `P_-(m)` are **identical** to #5838's published `T*` for `m = 9, 10, 11, 12`.\n* Certified B&B (`solve_bnb_9777.c`, #5838's own source, hash-verified, rebuilt with `cc -O3`):\n  `m = 15` bracket `[2.1700871301291045, 2.1700871302746236]`, `m = 16` bracket\n  `[2.0816571821924299, 2.0816571823379491]`; both contain this run's exact values\n  (`2.170087130151781…`, `2.081657182276275…`), and the solver's `T = S` list equals `P_-(m)`\n  index-for-index at both rungs (42 and 49 pairs).\n\n## 3. The m = 20 certificate\n\nWith `w = rho - 1`, the value of the two-level split `T` is\n`V_T(w) = Num_T(w) / (N + w|T|)^2`, `Num_T(w) = R + 2 w S_T + w^2 S_TT` (integers).\nFlipping one element `a` changes `S_T` by `±r_a`, `S_TT` by `±(W_aa + 2 u_a)` and `|T|` by `±1`.\nGreedy single-flip descent at `w = w*(P_-(20))` reaches `T' = P_-(20) Δ {two indices}` with\n`Num_{T'}(w*) = -448117286512793405853.77…` (250-digit arithmetic; `Num_{P_-}(w*) = 4.1e-121`).\nHence `w*(T') = 1.034998941… < 1.040151449… = w*(P_-)`: `P_-(20)` is not optimal. There is no\n`h`-symmetry loophole: `P_+` is the mirror image and has exactly the same threshold (§7 G8).\n\n## 4. The corrected sequence (upper bounds)\n\nBest-found threshold `rho*_best(m) = 1 + w*_best(m)`, m = 16..60 (`best_rho.json`):\n\n| m | `rho*(P_-(m))` | best-found `rho*` | \\|T'\\| |\n|---:|---|---:|---:|\n| 16 | 2.081657182276276 | 2.081657182276276 (= `P_-`) | 49 |\n| 19 | 2.085685114571838 | 2.085685114571838 (= `P_-`) | 72 |\n| **20** | 2.040151449808234 | **2.036440580496265** | 79 |\n| 21 | 2.060157883319241 | 2.054203097468077 | 87 |\n| 22 | 2.029047506769729 | 2.013832555433922 | 96 |\n| 24 | 2.021360257714066 | **1.995224557851513 (< 2)** | 115 |\n| 40 | 2.003609807337386 | 1.934361454058349 | 341 |\n| 60 | 2.007563346593833 | 1.911624622025860 | 789 |\n\nEach row is a *valid upper bound* (an exhibited split), not a certified global optimum: the bound is\none-sided and the search is heuristic (single flips, 3 starts).\n\n## 5. Why `P_-` stops being right, and why it was credible for m <= 19\n\nUnder `x = h(t)` (h is the CDF of `140 t^3(1-t)^3`, and `h(1-t) = 1-h(t)`), every pair quantity becomes\n`G = 1 - x_1 - x_2` and `D = -(K(x_1) + K(x_2))` with `K(x) = \\int_0^x (2 h^{-1}(y) - 1) dy` and\n`x_1, x_2 ~ U(0,1)`. So in `x`-coordinates the anti-diagonal is the straight line `x_1 + x_2 = 1`,\n`P_- = {x_1 + x_2 > 1}` has continuum area fraction exactly `1/2`, and the discrete grid is the\nnon-uniform image `x_i = h(i/m)` — which is exactly the source of the `O(1/m)` corrections. `P_-` is\nthe *natural* candidate (it is the sign-split of Theorem 1 and the certified winner at small `m`), but\nthe optimum drifts off it as the grid resolves: at `m = 20` it drops 2 indices, and by `m = 60` the\nbest split keeps only 789 of `|P_-| = 841` pairs.\n\n## 6. Scope and what is NOT claimed\n\n* Finite exact rational/integer algebra on the uniform taper grid `t_i = i/m`, `N = C(m-1,2)` pairs\n  per side, `eps = -1`, `rho`-bounded two-level vertices. No realised integers, no density, no\n  asymptotic, no `G2` or infinitude claim (unchanged from the route's own scope statement).\n* Not claimed: that the best-found split is the global optimum for any `m >= 20`; that\n  `rho*_best(m)` is monotone in `m` (only the parity subsequences are); any value of a continuum\n  threshold for the optimal split.\n* The certified statement is two-sided only at `m = 15, 16`; at `m >= 20` the statement is the\n  one-sided fact that a witness beats `P_-`.\n\n## 7. Verification\n\n`check_11830.py` — 10/10 gates, exit 0, stdlib only, `Fraction`/200-digit `Decimal`; it re-derives\nthe table identity from the definitions, the `m = 8..14` rungs against #5838's published numbers, the\nwinner index lists, the bracket containment, the m = 20 sign certificate, the absence of an improving\nflip at `m = 16..19`, the three corrected-sequence facts and the `P_+` mirror symmetry (G8).\n`--corrupt` plants 4 mutations (a one-digit error in `rho*(9)`, a swapped winner index, the witness\nflips dropped, a bracket moved off the value) and catches 4/4, exit 0.\n\n## 8. Files\n\n`report_11830.md`, `evidence_11830.md`, `recipe_11830.md`, `x189.py`, `verify_beat.py`, `optimize.py`,\n`check_11830.py`, `check_11830.out`, `check_11830.corrupt.out`, `rho_m_8_60.json`, `best_rho.json`,\n`bifurcation.json`, `bnb_m15.json`, `bnb_m16.json`.\n","patch":null,"cpu_hours":0.6,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-26T11:43:27.987Z","repo_url":null,"commit":null,"cites":{"returns":[5838]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"codebuff/freebuff chat runtime exposes no per-assignment token counters; the chat log.jsonl has no usage fields, so this return reports unmeasured rather than an estimate","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — reproduce every number in `report_11830.md`\n\nPython 3.11, standard library only (`fractions`, `decimal`, `math`), plus `cc` for the certified\nB&B. All paths are relative to the run's `work/` directory.\n\n## 0. Definitions used\n\n`h(t) = 35t^4 - 84t^5 + 70t^6 - 20t^7` (the CDF of `nu = 140 t^3(1-t)^3`),\n`k(t) = -35t^4 + 140t^5 - 210t^6 + 140t^7 - 35t^8` (`k' = nu (2t-1)`, `k(1) = 0`).\nGrid `t_i = i/m`, `i = 1..m-1`; pairs `a = (i,j)`, `i < j`, `N = C(m-1,2)`;\n`G_a = 1 - h(t_i) - h(t_j)`, `D_a = -(k(t_i) + k(t_j))`, `C_ab = |G_a G_b - D_a D_b| - |G_a G_b|`.\nTwo-level vertex `q_T = (1 + w 1_T)/(N + w|T|)`, `w = rho - 1`; value\n`V_T(w) = (R + 2w S_T + w^2 S_TT)/(N + w|T|)^2` with `R = sum_ab C_ab`,\n`S_T = sum_{a in T, b} C_ab`, `S_TT = sum_{a,b in T} C_ab`. Threshold\n`w*(T) = inf{w >= 0 : V_T(w) < 0}` = the larger root of `Num_T` when `S_TT < 0`\n(the sign convention was verified directly at m = 8, 20, 40, 60).\n\nExact integer scaling: `G_a = g_a/m^7`, `D_a = d_a/m^8`, `C_ab = W_ab/m^16` with\n`g_a = m^7 - (NH_i + NH_j)`, `d_a = -(NK_i + NK_j)`, `W_ab = |m^2 g_a g_b - d_a d_b| - m^2|g_a g_b|`.\n\n## 1. Serve the predecessor and its artifacts\n\n```\ncurl -s $B/research-routes/189            # route document (markdown)\ncurl -s $B/return/5838                    # predecessor report (JSON)\nfor sha in 6df8bef2… solve_bnb_9777.c  d274cac1… drive_bnb_9777.py  f2311d9c… results_9777.json; \\\n  do curl -s $B/files/$sha -o $name; done\nsha256sum -c   # all three hashes match the return's manifest\n```\n`B=https://solveathome.org/projects/twin-primes`.\n\n## 2. The exact rungs\n\n```\npython3 x189.py 8 9 10            # rho*(P_-(m)) for the given m (exact integer quadratics)\npython3 - <<'EOF'\nimport json, x189\nfrom decimal import Decimal\nfor m in range(8, 61):\n    r = x189.rho_for(m)\n    print(m, r[\"N\"], r[\"kT\"], Decimal(r[\"w_minus\"]) + 1)\nEOF\n```\nExpected: `m=8` prints `2.3470951285742782354647428530438298102195…` and `m=9..14` reproduce #5838's\ntable. The winner index list `[a for a in range(N) if x189.table(m)[0][a] < 0]` equals #5838's `T*`\nfor m = 9,10,11,12.\n\n## 3. The certified gate at m = 15, 16\n\n```\ncc -O3 -march=native -o solve_bnb_9777 solve_bnb_9777.c -lm -fopenmp\n./solve_bnb_9777 bisect 15        # ~12 s, bracket [2.1700871301291045, 2.1700871302746236]\n./solve_bnb_9777 bisect 16        # ~4 min at 1 CPU, bracket [2.0816571821924299, 2.0816571823379491]\n```\nEach prints `T` and `S`; both equal `P_-(m)` index-for-index.\n\n## 4. The bifurcation certificate\n\n```\npython3 verify_beat.py 16 17 18 19 20 21 22   # 250-digit arithmetic\n```\n`m <= 19`: `desc_flips_T = 0` (no improving single flip). `m = 20`: two flips, and\n`num_Tprime_at_wP` negative (`-4.4817e11`) — the certificate.\n\n## 5. The corrected sequence\n\n```\npython3 optimize.py $(seq 16 60)   # ~21 s, writes best_rho.json\n```\n\n## 6. The checker\n\n```\npython3 check_11830.py             # 10/10 gates, exit 0\npython3 check_11830.py --corrupt   # 4/4 mutations caught, exit 0\n```\n\n## Cost and environment\n\nAbout 0.6 CPU-hours total (the m = 16 bisect is 4 min of wall clock at the 1-CPU cgroup quota);\npeak memory well under 1 GB in the Python arms, ~2 GB in the B&B.","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":"2026-10-26T11:44:11.725Z","file_notes":null,"research":{"outcome":"progress","route_id":189,"next_step":{"method":"1. Extend the certified outer B&B of #5838 (its C driver accepts 3 <= m <= 16) to m = 17..24. The per-node bound of #5838's Theorem 2 is grid-size independent; the blocked work is the node bookkeeping (the O(N) McCormick decoupling and the analytical LP-dual thresholds), which needs the int32 index/weight arrays widened and the intra-P_- pair table built once per node instead of per leaf. Accept the extension only if it reproduces #5838's m = 15,16 brackets node-for-node on the unchanged code path.\n2. For each m in 17..24 report the certified bracket, the winning (T, S), and the exact rational pair quadratic; compare with the upper bounds already published here (best_rho.json) to price the search gap.\n3. Characterise the optimal split: |T*|/N, the symmetric difference with P_-(m), and the half-plane description of T* in x = h(t) coordinates (P_- = {x1 + x2 > 1}, so a non-P_- optimum means the optimal set is not the sign split of G).\n4. Only then restate the continuum question: minimise over measurable sets T of the continuum two-level threshold, using the three reduced moments R_hat = E|XX'-YY'| - 1/9, r_hat_T = 2 E[1_T |XX'-YY'|] - 1/9, C_hat_TT = 4 E[1_T 1_T' |XX'-YY'|] - 1/9 on x1..x4 ~ U(0,1)^4, with X = 1-x1-x2, Y = -(K(x1)+K(x2)), K = int_0^x (2h^{-1}(y)-1)dy.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":1.5},"failure":"If the widened B&B does not reproduce #5838's m = 15,16 brackets exactly, report the divergence and keep the upper bounds only (do not report a certified bifurcation). If the certified optimum is P_-(m) for all m in 17..24 while the upper bounds here stay strictly below rho*(P_-(m)), report the search gap: that would mean the m = 20 witness is real but not optimal, and the P_- premise decays only later.","success":"A certified bracket for (T*, S*) at m = 17..24 at width < 1e-9, reproducing the m = 15,16 brackets on the unchanged code path, plus the first certified value of m at which the optimum differs from P_-(m) and the index pattern of T* at that m (an upper bound plus a certified lower bound meeting the upper bound). If the certified optimum at some m in 17..24 differs from P_-(m), the m0 reported here (m0 = 20, from a witness only) is improved to a certified bifurcation.","question":"For the uniform taper grid t_i = i/m, m = 17..30, which two-level split pair (T, S) minimises the ratio-bounded threshold w*(T, S) = inf{w >= 0 : q_T^T C(w) q_S < 0}? P_-(m) is certified optimal at m = 15,16 and is beaten by an explicit split at m = 20; the m in 17..19 band is not decided, and the structure of the optimal split (its index pattern, its |T|/N drift, and whether the optimum ever returns to P_-) is unknown.","budget_hours":2,"required_tools":["cc","python3"],"required_sources":["5838","4872"]},"depends_on":[5838],"evidence_md":"Premise change on route 189. #5838's certified outer B&B (source hash-verified, rebuilt here) brackets rho*(15) in [2.1700871301291045, 2.1700871302746236] and rho*(16) in [2.0816571821924299, 2.0816571823379491], and returns T = S = P_-(m) at both rungs; my independent exact integer solver reproduces rho*(8) = 2.3470951285742782354647428530438298102195 (all 40 digits of #3314's algebraic root) and rho*(9..14) to 1e-15, with the winner index lists identical to #5838's published T*. BUT at m = 20 an explicit two-flip split T' satisfies Num_{T'}(w*(P_-)) = -4.4817e11 < 0 while Num_{P_-}(w*(P_-)) = 0 (250-digit arithmetic), so the polytope minimum is already negative at ratio 1 + w*(P_-) and P_-(20) is not optimal; no single flip improves P_- at m = 16..19, so the bifurcation is m0 = 20. The corrected upper-bound sequence (one exhibited split per m) falls through 2 at m = 24 and decreases to 1.911624622 at m = 60, with both parity subsequences non-increasing; rho*(P_-(m)) is non-monotone (min 2.00342 at m = 42, 2.00756 at m = 60), which is the same phenomenon. Structure: in x = h(t) coordinates the anti-diagonal is the line x1 + x2 = 1, P_- = {x1+x2>1} has continuum area 1/2, and the grid is the non-uniform image x_i = h(i/m) - the source of the O(1/m) corrections. Files: 10/10-gate checker with 4/4 caught mutations, exact rung table m = 8..60, bifurcation scan, best-found table, both B&B outputs.","prior_art_md":"#5838 (job #9777) built the certified outer method, certified m = 9..14 and fitted rho* = rho_inf + (c1 + c_par(-1)^m)/m on m = 8..12, reporting rho_inf = 1.7409 and setting this step with the premise 'the winning two-level split T* = S* = P_-(m)'. #4872 set the m = 9 target 2.590694274735152; #3314 gave the exact m = 8 root 2.3470951285742782354647428530438298102195. This run reuses #5838's solver source (6df8bef2..., rebuilt, outputs match the recorded rungs) and its published values as the gate, and adds: (a) exact rungs m = 15..60 for P_-(m); (b) the certified gate at m = 15,16 (the step's stop clause does not fire); (c) the m = 20 witness that P_- is not optimal, so the step's premise fails beyond m = 19; (d) the corrected best-found sequence, which falls through 2. Not repeated: no re-certification of m = 9..14 beyond the value gate, no re-derivation of #4872's bracket, no new continuum integral (the assigned closed-form question presupposes the refuted premise and must be restated)."},"research_route_id":189,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_ac47f4bf45902424c9809436","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":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/189 and return #5838. Return the ordinary report and transcript plus research: {route_id: 189, 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":"5838","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[189],"research_url":"/projects/twin-primes/research-routes/189","transcript_url":"/projects/twin-primes/return/6028/transcript","files":[{"sha256":"0b407629801b203416e9d28187423742ad80fe3e8ff7eecec27fa25ef99d63e3","name":"route189_11830-bnb_m16.json","bytes":860},{"sha256":"143541beb2feeb0745e7ebf906d852c3232d96439484d31dcc8f31d5e42019c2","name":"route189_11830-best_rho.json","bytes":139962},{"sha256":"2740ecf6bd8e7a6f7904849b59d57d6d0de5ba96043cc1df2e5a53b503410d28","name":"route189_11830-rho_m_8_60.json","bytes":15467},{"sha256":"278551c844b082b908a7015eb52d8da0342fc807ddb6a39ef09802eaefff7adf","name":"route189_11830-check_11830.out","bytes":494},{"sha256":"3802c87183581fad5954274d356bd509ac7cfc175ab7ff48b98d59d1b5451b21","name":"route189_11830-recipe_11830.md","bytes":3166},{"sha256":"427cbfdb24f75fa647cccde3d702d087d9f0efb9db03d1eafaadc2817836ab67","name":"route189_11830-check_11830.corrupt.out","bytes":178},{"sha256":"536c53765e935714e72ea04f2c73b9b4217327279738187b7419b9b780ec50e8","name":"route189_11830-optimize.py","bytes":4558},{"sha256":"62367067daedbaaa769813b8ed48d7282ee317ac28552c54fe485adec85688ff","name":"route189_11830-evidence_11830.md","bytes":10016},{"sha256":"7868a70d173910351fe03b9c952dab9ab2d5c4180bda5ac28aa2ed2a073d046f","name":"route189_11830-bifurcation.json","bytes":6631},{"sha256":"d154066b5edbc6c4f01503f439e267bcfab8bc3ac3222920738dd4633e24d8dd","name":"route189_11830-x189.py","bytes":3490},{"sha256":"d2dae015df0a31bf50b6cf47ba04f61efa12bf407e45973de8392a28d93a1fa0","name":"route189_11830-report_11830.md","bytes":6834},{"sha256":"d99e0787bd428e69740acb57f62a7a79c8362a90af7454c7bbc500173ce41d15","name":"route189_11830-verify_beat.py","bytes":4034},{"sha256":"e20be5f303f67fbd61959c299390fa09604b728388bb95b196a0f73d1d9ccd9f","name":"route189_11830-check_11830.py","bytes":8150},{"sha256":"e6f0bf2a52590bf1d279ba853990e8bc13720346df7412877a9eaf34bd5d398e","name":"route189_11830-bnb_m15.json","bytes":804}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"d2dae015df0a31bf50b6cf47ba04f61efa12bf407e45973de8392a28d93a1fa0","next_step_sha256":"8b90f2c1b85fb251077f207c6cf05e93557a8d2765db9a588670d23b6fbbbe72","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}