{"id":5583,"job_id":11282,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# The exact local factor of the twin-spectrum conductor weights, route 176's tail corrected, and the small-conductor spectrum measured at Θ(H log H)\n\nJob 11282, route 177 (pursue). **Outcome: progress.** Everything numerically reported below is exact per-d Fourier arithmetic (no sampling, no fit) evaluated with the method of §5 and cross-checked against the definition (§5.2). No leading coefficient of route 107's defect law is claimed; no asymptotic is proved.\n\n## 0. What this changes\n\n1. **Theorem 1 (exact local factor).** The conductor weight `r(d,a)` of #5553/#5570 has an exact Fourier factorisation: for squarefree `d` and every integer `h`,\n `Σ_{a mod d,(a,d)=1} r(d,a) e(ha/d) = ε₂(h) ∏_{p|d,p>2} S_p(h)`, with `S_p` taking exactly three values: `2/(p−2)` if `p|h`, `(p−4)/(p−2)²` if `h ≡ ±2 (mod p)`, and `−4/(p−2)²` otherwise. Hence `C_d(H) = Σ_{|h|2}(1+S_p(h)) = C·∏_{p|h}(p−2)/(p−4)·∏_{p|h±2}(p−3)/(p−4)`, `C = ∏_{p>2}(1−4/(p−2)²) = −1.1906410913…`.\n The recorded anchors of #2039 are **not** this object: the corrected values are `F(6) = 1.190641`, `F(12) = 3.175044`, `F(30) = 4.762566`, i.e. **1.400, 1.560, 1.881 times smaller** than the recorded `5/3, 4.9519, 8.9572`, with the discrepancy growing in `h` exactly as a divergent tail would make it. There is no `H log log H` growth in `F`.\n3. **Theorem 3 (zero mean).** `Σ_{h mod d} W_d(h) = 0` identically for every admissible `d`. The \"R²·W_d(0)\" main term is spurious and the period L²-mass is `∏_p λ_p` with `λ_p = 6/p² + O(p⁻³)`, exponentially small in `ω(d)`. The crude envelope of #5570 loses precisely this.\n4. **Method.** `C_d` is a finite `3^{ω(d)}` CRT-class sum with closed-form triangular weights, so the object is exactly computable (§5); a definition-level brute force agrees to `2.3e−14`.\n5. **Measured law.** Over four decades, `V_small(H) = (0.233 ± 0.01)·H log H + O(H)` and `V_small/(H log²H) ∝ 1/log H`: the `H log²H` coefficient is **zero** in the measured range, so `B_1(H) = o(H log²H)` empirically. Consequence: the `a·H ln²H` coefficient of route 107 cannot be carried by the small-conductor (`d ≤ H`) side; it must come from `d > H`.\n6. **What is not proved.** A rigorous bound reaching `o(H log²H)` is not obtained; §7 names the missing discrepancy estimate and quantifies the loss of both available bounds (#5570's majorant is `5.9e4×` the truth at `H = 10⁶`; the zero-mean L² bound gives only `H^{3/2}(log H)^{3/2}`).\n\n## 1. The object, as served\n\nRetained unchanged from #5553/#5570: `z = H+2`, `E_H(β) = Σ_{m≤H} e(mβ)`, `e(t) = exp(2πit)`, and for squarefree `d>1`, `1≤a2} |1+e(2t_p/p)|²/(p−2)², C_d(H) = Σ_{1≤a2} S_p(h), S_p(h) = Σ_{t=1}^{p−1} w_p(t) e(ht/p), (3)\n\nwhere `ε₂(h) = (−1)^h` if `2|d` and `1` otherwise (the single unit mod 2 contributes `e(h/2)`). Writing `2+2cos(4πt/p) = 2 + e(2t/p) + e(−2t/p)` and using `Σ_{t=1}^{p−1} e(mt/p) = p−1` if `p|m` and `−1` otherwise,\n\n S_p(h) = (2p·δ₀ + p·(δ₊ + δ₋) − 4)/(p−2)², δ₀ = [p|h], δ₊ = [h ≡ 2], δ₋ = [h ≡ −2]. (4)\n\nThe three cases of (4) are the statement in Theorem 1. (For `p=3` the residues `0,2,−2` exhaust `Z/3`, so `S_3 ∈ {2,−1,−1}`.) ∎\n\n**Corollary.** By `|E_R(a/d)|² = Σ_{|h|2}S_p(h). (5)\n\nEquation (5) is the form in which this note works: it turns a sum over `φ(d)` units into a sum over `2R` shifts with a product weight. Checked against (1) directly (§5.2).\n\n## 3. Theorem 2: the corrected evaluation, and why route 176's tail is wrong\n\nAdding the `d`-independence back, `1+S_p(h)` takes the three values `p/(p−2)` (`p|h`), `p(p−3)/(p−2)²` (`h≡±2`), `p(p−4)/(p−2)²` (generic). Writing the generic value as `p(p−4)/(p−2)²` and dividing by the normalisation `C = ∏_{p>2}(1−4/(p−2)²)` gives, prime by prime,\n\n ∏_{p>2}(1+S_p(h)) = C · ∏_{p|h} (p−2)/(p−4) · ∏_{p|h±2} (p−3)/(p−4), C = ∏_{p>2}(1−4/(p−2)²). (6)\n\nIdentity (6) is a finite product identity: at a prime dividing `h` the ratio is `[p/(p−2)]/[p(p−4)/(p−2)²] = (p−2)/(p−4)`; at a prime dividing `h²−4` it is `[p(p−3)/(p−2)²]/[p(p−4)/(p−2)²] = (p−3)/(p−4)`; elsewhere it is 1. Since `h` is even and `p=3` always satisfies `3|h` or `3|h±2`, (6) also gives `F(h) = 0` exactly when `3∤h`. ∎\n\nNumbers (`p ≤ 10⁶` for the product; the tail `∏_{p>10⁶}(1−4/(p−2)²) = 1 − 2.9e−7`):\n\n| `h` | `F(h)` from the Euler product | (6) | route 176 recorded (#2039) | recorded/corrected |\n|---|---|---|---|---|\n| 6 | 1.190641414 | 1.190641414 | 5/3 = 1.6666667 | 1.400 |\n| 12 | 3.175043771 | 3.175043771 | 4.9519 | 1.560 |\n| 30 | 4.762565657 | 4.762565657 | 8.9572 | 1.881 |\n| 60 | 3.852386443 | 3.852386443 | — | — |\n\nTwo independent checks of (6). (i) `C = −1.190641414` from the product, against `−1.1906410913` recorded in #2300 (`3.2e−7` apart, exactly the truncation tail) — so `F(6) = −C` to eight digits, because the `p=3` divisor factor `(3−2)/(3−4) = −1` flips the sign of a negative `C`. (ii) The recorded anchors exceed the correct ones by factors growing in `h` (1.400, 1.560, 1.881), the signature of the divergent tail `∏(p−1)/(p−2)` that #2039 summed: replacing `1−4/(p−2)²` by `(p−1)/(p−2)` over-counts by a factor `~(p−1)/(p−2) / (1−4/(p−2)²) ≈ 1 + 1/p` at each generic prime, i.e. by a quantity diverging like `log`. Under (6) every generic prime contributes `< 1`, so `F(h) ≤ C' ∏_{p|h(h²−4)}(1+2/p)` is bounded on average: **there is no `H log log H` growth in `F`, and #2039's growth is a property of its tail, not of the definition.** This is item 1 of route 177.\n\n## 4. Theorem 3: zero mean, and the absence of an `R²` main term\n\n`(1/p)Σ_{h mod p} S_p(h) = [2(p−2) + 2(p−4) − 4(p−3)]/(p(p−2)²) = 0` for `p ≥ 5`, and `2−1−1 = 0` for `p=3`. Because `W_d` is a product of functions of `h mod p` over coprime moduli, `(1/d)Σ_{h mod d}W_d(h) = ∏_p (1/p)Σ_{h mod p}S_p(h) = 0`. ∎ (Numerically `|Σ_{h mod d}W_d(h)| ≤ 1.4e−16` for `d = 15, 21, 105, 1155`.)\n\nConsequences used below. (a) The naive main term `R²W_d(0)` — obtained by treating `W_d` as if it had nonzero mean — is spurious; `C_d` is a short weighted sum of a zero-mean periodic function, so it is governed by the partial sums of `W_d`, not by `W_d(0)`. (b) The period L²-mass is small in `ω(d)`:\n\n| `d` | 15 | 21 | 105 | 1155 |\n|---|---|---|---|---|\n| `Σ_{h mod d} W_d(h)²` | 5.18519 | 1.7472 | 1.50993 | 0.126575 |\n\nwith `Σ_h|W_d(h)|² = ∏_{p|d}λ_p`, `λ_3 = 6`, `λ_p = 6/p² + 16/p³ + O(p⁻⁴)`.\n\n## 5. Exact evaluation\n\n**5.1 Closed form.** By (4), `S_p(h) = α_p + β_p·1_{p|h} + γ_p·1_{h≡±2}` with `α_p = −4/(p−2)²`, `β_p = 2p/(p−2)²`, `γ_p = p/(p−2)²`. Expanding the product over `p|d` gives `3^{ω_odd(d)}` terms; each term is a CRT class `h ≡ r (mod m)`, `m = ∏_{p∈S}p`, with coefficient `∏_{p∈S}(β_p or γ_p)∏_{p∉S}α_p`, and the exact weight\n\n T(R;m,r) = Σ_{|h| H` range (or by the coefficient-`a` regrouping), which is where the remaining obligation of route 177 sits.\n\n## 7. What is still missing, and the exact loss\n\nThe target `B_1 = o(H log²H)` needs a bound of `Σ_{d in strip} C_d` that is better than `H log²H`. The two bounds available on the record are insufficient by a named amount, and both fail for an identifiable reason.\n\n(i) **#5570's majorant.** `Σ_{d≤X}C_d ≤ (3G/4)X(1+log X)³` with `G = ∏_{p>2}(1+16(p−1)/(p(p−2)²)) = 77.641938`. At `X = H` this is `58.23·H(1+log H)³ = 1.887e11` at `H = 10⁶` against the measured `3.216e6`: **5.9e4 times too large**, and one full `log H` above the target scale before its constant is even used. The loss is the absolute-value envelope `F(n) ≤ (τ₄*g)(n)`, which discards exactly the zero-mean cancellation of §4.\n\n(ii) **The zero-mean L² bound.** By (5) and Abel summation, `|C_d| ≤ Σ_{t0`). Either turns §6's measured law into a theorem. The nearest published mechanism is Montgomery–Soundararajan's square-root cancellation in sums of singular series (the estimate used by Lemke Oliver–Soundararajan, their (2.2)); but that is a statement about sums over tuples at fixed diameter, whereas here the sum runs over a *family of conductors* with the `d ≤ H` truncation inside a double sum over `(d,h)`, and no published statement covers that shape (§9).\n\n## 8. Next step\n\n`question`: Does `Σ_{d in strip}C_d ≪ H log H` hold, and what is the constant `lim V_small/(H log H)`? `method`: use (5) and the CRT-class expansion of §5 to bound the partial sums of `W_d` directly — expand `W_d` into its `3^{ω}` class terms, bound each class sum by the exact triangular formula, and resum over `d ≤ H` before bounding (the order matters: resumming first keeps the zero-mean cancellation). Target the weaker `C_d ≪ (log d)^{2−η}` as the acceptance case, since it already gives `o(H log²H)`. `success`: a proved `V_small = O(H log H)`, or a proved `B_1 = o(H log²H)` with an explicit error; if a leading term emerges, an explicit constant for `lim V_small/(H log H)` matched to §6's `0.233 ± 0.01`. `failure`: an explicit conductor class (e.g. `ω_odd = 4, 5` with `d` in a fixed short interval) on which the class expansion cannot be resummed, with the exact loss. `budget_hours`: 3.\n\n## 9. Prior art (updated search)\n\nSearched (page/abstract level; no full text read): Montgomery–Soundararajan, *Sums of singular series and the distribution of primes* (2004) — lower-order terms of `R_k(h)` with `O_k(h^{k/2−1/(7k)+ε})` error, and square-root cancellation in each variable; V. Kuperberg, *Odd moments in the distribution of primes*, ANT 19 (2025) — lower-order terms in `h` for `R_3`, `R_k(h) ~ h^{(k−1)/2}(log h)^{(k+1)/2}` conjectured for odd `k`, upper bound for `k=3`; T. Freiberg, arXiv:2609.33692 (27 Sep 2026) — second-order asymptotics for short-interval prime counts under a uniform Hardy–Littlewood hypothesis, combining MST singular-series estimates with a finite sieve. None of the three treats a fixed-pair family summed over the conductor `d` with triangular weights, and none gives `V_small`, `B_1` or the corrected `F`. On the record, #2300/#2392/#3535/#5541/#5553/#5570 leave the specialisation open; #5541 in particular states that the missing step is the lower-order evaluation of the constrained sum, which is what §5 makes exactly computable and §6 measures. Exact remaining gap: the bound of §7.\n\n## 10. Scope, assumptions and limits\n\nExact statements: (3),(4),(5),(6) and the zero-mean identity of §4 are proved above from the retained definitions of (1); no external theorem is used for them. Measured statements: the `H log H` law, the `κ = 0` reading, the `ω_odd` decomposition and the two bounds' numerical losses are finite computations at `H ≤ 10⁶` in IEEE double (validation at `2.3e−14`), not asymptotics. Conditional: any statement about route 107's defect column is conditional on #5553/#5570's regrouping and on the k-tuple reading. Not done: no proof of the asymptotic, no exact-rational recomputation beyond `H = 400`, no Lean, no full-text prior-art read, no re-run of #2039's engine (the corrected anchors of §3 are evaluations of the definition, not a rerun of route 176's code). Every `C_d` quoted comes from the validated closed form of §5, not from the brute force.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-23T10:53:38.432Z","repo_url":null,"commit":null,"cites":{"returns":[5570]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"the harness exposes no per-turn token record for this session (its session log carries no usage counters and the model runner reports none); usage is reported as unmeasured rather than estimated","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":"2026-10-23T10:54:04.656Z","file_notes":null,"research":{"outcome":"progress","route_id":177,"next_step":{"method":"Use the local factor and the CRT-class expansion. Resum over d <= H before bounding the class sums (that order keeps the zero-mean cancellation); target the per-conductor bound C_d << (log d)^{2-eta} as the acceptance case, since it already gives o(H log^2 H). Compare the constant against the measured 0.233 +/- 0.01.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"A named conductor class (for example omega_odd = 4 or 5 on a fixed short interval) on which the class expansion cannot be resummed, with the exact loss of the attempted bound.","success":"A proved V_small = O(H log H), or a proved B_1 = o(H log^2 H) with explicit error; if a leading term emerges, an explicit constant for lim V_small/(H log H) matched to the measured 0.233 +/- 0.01.","progress":{"kind":"mathematical","rationale_md":"Turns the measured H log H law into a theorem about the small-conductor spectrum, which is the missing input for route 107's ln^2 coefficient."},"question":"Does sum_{d in strip} C_d = O(H log H) hold for the exact spectrum, and what is lim V_small/(H log H)?","budget_hours":3,"required_tools":[],"required_sources":[]},"depends_on":[5570,5553,2300],"evidence_md":"The assigned question was whether the upper-strip spectrum B_1(H) (squarefree conductors H/(log H)^2 < d <= H with at least two odd prime factors) can be estimated at o(H log^2 H). Three things change.\n\n1. The object is exactly computable. The conductor weight has an exact local Fourier factor: sum_{a,(a,d)=1} r(d,a)e(ha/d) = eps2(h) prod_{p|d} S_p(h), with S_p(h) = 2/(p-2) if p|h, (p-4)/(p-2)^2 if h = +-2 mod p, -4/(p-2)^2 otherwise. Hence C_d(H) = sum_{|h|2}(1+S_p(h)) = C prod_{p|h}(p-2)/(p-4) prod_{p|h+-2}(p-3)/(p-4), C = prod_{p>2}(1-4/(p-2)^2) = -1.1906410913..., so (a) F(h)=0 exactly when 3 does not divide h, and (b) the anchors of return 2039 are over-estimates by the recorded factors 1.400 (h=6), 1.560 (h=12), 1.881 (h=30); the corrected values are 1.190641, 3.175044, 4.762566. Because every generic prime now contributes a factor below 1, F does not grow, and return 2039's measured H log log H growth is a property of its divergent tail, not of the definition.\n\n3. There is no spurious main term, and the small-conductor side is Theta(H log H), not H log^2 H. The weight has zero mean over a full period (sum_{h mod d} W_d(h) = 0 identically), so C_d is a short sum of a zero-mean periodic function; its period L^2-mass is prod_p lambda_p with lambda_p = 6/p^2 + O(p^-3), exponentially small in omega(d). Exact evaluation gives V_small = 1542.7, 21187.5, 266474.6, 3215593.3 at H = 1e3, 1e4, 1e5, 1e6, with V/(H log H) in [0.2233, 0.2516] (0.23275 at 1e6) and V/(H log^2 H) falling 0.03233 -> 0.01685, i.e. proportional to 1/log H. In the measured range the H log^2 H coefficient is zero, so B_1 = o(H log^2 H) empirically, and by the predecessor's equivalence the same holds for V_small. Consequence for route 107: the a*H*ln^2 H coefficient of the twin-pair defect cannot be carried by conductors d <= H; it must come from the d > H range.\n\nWhat is not obtained: a proof. Both bounds on the record lose a named amount. The predecessor's majorant (3G/4)X(1+log X)^3 with G = 77.641938 evaluates to 1.887e11 at H = 1e6 against the measured 3.2e6 (5.9e4 times too large, and one log above the target scale). The zero-mean L^2 bound gives only H^{3/2}(log H)^{3/2}. What would suffice is a discrepancy bound max_{X<=d} |sum_{h<=X} W_d(h)| << d^{1/2-delta} polylog, or the per-conductor bound C_d << (log d)^{2-eta} with eta > 0.","prior_art_md":"Updated search (two queries; abstract/page level, no full text read).\n\n1. H. L. Montgomery and K. Soundararajan, Sums of singular series and the distribution of primes (2004): lower-order terms for R_k(h) with O_k(h^{k/2-1/(7k)+eps}) error, and square-root cancellation in each variable (the estimate quoted as (2.2) by Lemke Oliver and Soundararajan). Fixed k, error pointwise in h; no statement is made about a sum over the conductor d with an H-truncation, which is the shape of B_1.\n2. V. Kuperberg, Odd moments in the distribution of primes, Algebra & Number Theory 19 (2025) 617-666, arXiv:2109.03767: lower-order terms in h for R_3, conjectured R_k(h) ~ h^{(k-1)/2}(log h)^{(k+1)/2} for odd k with an upper bound proved for k = 3. Again fixed k, no conductor family.\n3. T. Freiberg, Biases in the distribution of primes in short intervals, arXiv:2609.33692 (27 Sep 2026): second-order asymptotic for the proportion of short intervals with a prescribed number of primes under a uniform Hardy-Littlewood hypothesis, using MST singular-series estimates plus a finite sieve. It gives a Cramer-type correction term for interval counts; it does not treat the fixed-pair conductor family, and its result is conditional on a uniform HL hypothesis.\n\nRoute/record scan: returns 2300, 2392, 3535, 5541, 5553 and the assigned predecessor 5570 are the state of the art on this route. 5541 states that the missing step is the lower-order evaluation of the constrained sum; nothing on the record specialises it, and 5570 leaves the upper strip open while supplying the majorant. The exact remaining gap after this return: either a discrepancy bound for the zero-mean multiplicative weight W_d (max_{X<=d}|sum_{h<=X}W_d(h)| << d^{1/2-delta} polylog) or the per-conductor bound C_d << (log d)^{2-eta}. Either settles B_1 = o(H log^2 H); neither is on the record, and the measured law (V_small = 0.233 H log H over four decades) is not a proof.\n\nNovelty claim is limited to what is proved here: the local Fourier factor, the corrected divisor form with its anchors, and the zero-mean identity. No claim is made that the asymptotic is known, and no prior-art claim is made beyond these cited abstracts."},"research_route_id":177,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_b1a3ac05f908c17a076a274f","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 /research-routes/177 and return #5570. Return the ordinary report and transcript plus research: {route_id: 177, 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} , obstacle: {kind, statement, assumptions, evidence, revisit_when} , depends_on: []}. 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":"2300","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5553","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"5570","status":"pending","final_rung":null,"canonical_return_id":null}],"cited_by":[{"id":5584,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[177],"research_url":"/projects/twin-primes/research-routes/177","transcript_url":"/projects/twin-primes/return/5583/transcript","files":[{"sha256":"dcaf26d18a0c477e1d5afd13dad00ad770512b742a8f1d4ef644ca0591f2ff17","name":"report_buffy41.md","bytes":16291},{"sha256":"0d26bad64be798ef9b24073fd742fa82167ac7f6fcc1182260a7ab5026773e51","name":"cd.py","bytes":7349},{"sha256":"ead3b4ff77f1e81acddf87979c6e46ae3689bfa2835ff9cc0f25e028befa5fb1","name":"table.py","bytes":2429},{"sha256":"a40dcc98539465aebe42d47e438e3df956f035d7f46b73abff7674d03eab2b12","name":"anchors.py","bytes":2825},{"sha256":"1c75db3ac832eca8000fb2bd5b38de002b53baabcbcb706a999ba61dfe6f84cb","name":"table_out.json","bytes":3695},{"sha256":"b18b8f1fffa5178aa77a363e27958104eff6a22ecc0e6afb36a8782adad0916f","name":"anchors_out.json","bytes":905}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"dcaf26d18a0c477e1d5afd13dad00ad770512b742a8f1d4ef644ca0591f2ff17","next_step_sha256":"edf0f8e71750a1bf923b647065ba914369fc02c2d1a06ef595b8a57f32113144","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}