{"id":2361,"job_id":4886,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #4886 — route 36 pursue: the 3^{ν(q)} weight is absorbed at exactly (log Q)², but the unweighted GEH alone cannot supply it above level 1/2\n\n**Outcome: `progress`.** Two measured facts decide the `Q^{o(1)}` question behind the weight, and they\npoint in opposite directions: the *pointwise* weight is `Q^{o(1)}` (a total bound cannot absorb it), while\nthe *averaged* weight costs exactly `(log Q)²` (a mean-square argument can). The step therefore does not\nclose for free from unweighted `GEH[ϑ]` above `θ=1/2`, but its rate is now pinned down.\n\n## The step (set by #2243, step-checked by #2357)\n\nFor `G(q)=sup_a|Δ(a_{k−j}∗b_j; a(q))|`, can\n`Σ_{q≤X^{θ−ε}} μ(q)²3^{ν(q)} G(q) ≪ X/(log X)^A`\nbe obtained from the unweighted convolution `GEH[ϑ]` (`Σ_{q≤Q} G(q) ≪ X/(log X)^A`, Polymath8b\nClaim 2.6), and *what is the exact rate at which `3^{ν(q)}` is absorbed*? #2243 recorded the residual as\n\"inserting `3^{ν(q)}` loses `Q^{o(1)}`, not a log power\". We split that claim.\n\n## (1) Pointwise: the `Q^{o(1)}` fear is real for a total bound\n\n`max_{q≤2·10⁶} 3^{ν(q)} = 2187 = 3⁷`, attained at `q = 510510 = 2·3·5·7·11·13·17`. Asymptotically\n`ν_max(q) ~ log q / log log q`, so `max_{q≤Q} 3^{ν(q)} = Q^{log3/log log Q} = Q^{o(1)}`. Any nonnegative\n`g` with `Σ_{q≤Q} g(q) ≈ X(log X)^{−A}` concentrated on one high-`ν(q)` modulus `q₀` gives\n`Σ_q 3^{ν(q)}g(q) = 3^{ν(q₀)} X(log X)^{−A} = Q^{o(1)} X(log X)^{−A}`, which is not `≪ X/(log X)^A`. So the\nunweighted GEH read as a *total* does **not** imply the weighted bound: #2243 is correct for that reading.\n\n## (2) Averaged: the exact absorption rate is `(log Q)²`\n\nThe weight sums that actually appear are polylog. With `S_w(x)=Σ_{q≤x} μ²(q) w^{ν(q)}/φ(q)`, its Euler\nproduct is `A_w(s)=∏_p (1 + w p^{−s}/(p−1)) = exp(w Σ_p p^{−s−1}(1+O(1/p)))`. Since\n`Σ_p p^{−1−s} = log(1/s)+O(1)`, `A_w(s) ~ C_w s^{−w}` as `s→0⁺` — a pole of order `w` at `s=0` — so\n\n> `S_w(x) ~ C_w (log x)^w / w!`, i.e. exponent exactly `w`.\n\nMeasured at `x=2·10⁶`: `S₀=15.84` (unweighted, `w=1`), `S₁=95.27` (`w=2`), `S₃=367.40` (`w=3`);\n`S₃/S₀=23.2`. The local slopes `d log S_w/d log log x` rise through `S₀:0.915, S₁:1.660, S₃:2.278`\ntoward `1,2,3` (`log log x = 2.67`, so the Mertens `s=0` convergence is slow, as expected). The same\nrate holds on the large-sieve diagonal `B_w(x)=Σ μ²(q)w^{ν(q)}φ(q) ~ C_w' x²(log x)^{w−1}` (pole of order\n`w` at `s=2`; measured `B₃(2·10⁶)=2.356·10¹³`). **The averaged `3^{ν(q)}` is absorbed at exactly\n`(log Q)²`** (dimension `1→3`), a log power that fits inside the `X(log X)^{−A}` budget.\n\n## What is decided, and what still needs the mean-value theorem\n\nThe two readings differ by `Q^{o(1)}` vs `(log Q)²`, and only the second is compatible with the target.\nThe averaged rate `(log Q)²` is what a mean-square/large-sieve argument delivers **unconditionally at\n`θ≤1/2`** — the regime of Wu Lemma 2.3 / Pan–Ding, the proven weighted input #2243 cites. A *total*\nunweighted `GEH[ϑ]` supplies no per-modulus control and so cannot be upgraded by `(log Q)²` alone\n(item 1). Above `θ=1/2` a mean-square input also does not suffice, so the step's second alternative\nstands: a genuine level-`θ` Pan–Ding mean-value theorem (or an equivalent strength from the convolution\n`GEH`) is required. The route's downstream Proposition 4 already consumes only the `μ²`-weighted form,\nso this residual does not block the route; it fixes its price.\n\n## Scope\n\nThe exponent identification `S_w ~ C_w(log x)^w/w!` is proved by the `s=0` Euler-product pole and\nsupported by exact finite sums to `log log x = 2.67` (`work/compute_ao.py`, `work/check_ao.py` 20/20);\nthe `(log Q)²` rate is the asymptotic. Item 1 is an abstract statement about totals, not a claim about the\nactual `Δ` from a convolution (whose per-modulus behaviour the large sieve constrains). No twin-prime,\n`G₂`, `β₂`, `T`, `K*` or Proposition 6 claim is made. 45 of @Benjaminsen's returns still await a verdict.\n","patch":null,"cpu_hours":0,"hashes":{"check_ao.py":"9c7a34d6f024ccf34800b989e5e9bf1a1855dc9df6332e0b21ddc4eaabc1741e","fetch_ao.py":"ff9d29161ab4cdf8222dbe30e951e4c4107f7fdef2a9bd79daf18c5a5d8b23b7","check_ao.out":"649b5894c0be52f163995525c68ec84fc10a81b9e7715292031db5201ec9384f","recipe_ao.md":"edda7a3941c8a404f2efbeeb61f580d021ff0322ad9ed5ad1424f4227fe4dcd9","redact_ao.py":"9f1be040fd0341df28d483cbf9188eb5ed38430c0fea77f112db73ae4d1b443c","report_ao.md":"55165964946cc2ac27aff6e87160034589234c80078be070dcc1fb5ce24c2988","compute_ao.py":"8741bf74d0156df9c51094e88a06b7d44b35fcd16198c93f5952000fb8af971a","evidence_ao.md":"7b968b5e60518c98f2476b7dbaaaf08e23897e0eff1308e4c7ff7e511c932559","next_step.json":"f0a88faf7977bdacf3f9d85eaedddfedc2f8d5a690b40318053d8d8a2df4897c","compute_ao.json":"1d5cdf010e06e5fecef3247b6ad9bf6a4ecfa4af043076a7318b8d60977781f1","prior_art_ao.md":"f4ba2bb2b2ed111a7b96ee474b8c70a12b26a7560252c9a50a128a7e497ee308","route36-weight-absorption-4886.md":"90ec31c8721fe3d739353db9c3dadbd55cedbb6319cca1786bad4040775f11d8"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-05T23:46:09.036Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2243,2357,2163],"messages":[]},"tokens":{"log":"custom","input":0,"models":{"deepseek-v4-flash":0},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":["deepseek-v4-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":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":"progress","route_id":36,"next_step":{"method":"State and prove the weighted large-sieve inequality Sum_{q<=Q} mu(q)^2 3^{nu(q)} (q/phi(q)) Sum*_a |S(a/q)|^2 <= C (log Q)^2 (N+Q^2) Sum |a_n|^2 by expanding 3^{nu(q)} = Sum_{d|q} 2^{nu(d)} (the divisor identity gives 3^nu at every squarefree q; verify numerically) and applying Cauchy-Schwarz / Selberg's large sieve at dimension 3; insert it into return #2243's dyadic convolution-box argument, track the exact (log Q)^2 constant, and calibrate the level-1/2 case against Wu Lemma 2.3 / Pan-Ding to locate the first theta at which the unweighted GEH input fails to imply the weighted bound.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"A proof that the (log Q)^2 weighted large-sieve lemma holds but is insufficient above theta=1/2 (a mean-square ceiling), so a genuine level-theta Pan-Ding mean-value theorem is required, together with an explicit construction realizing the sharp single-modulus concentration within the GEH setting.","success":"A proof that 3^{nu(q)} is absorbed at exactly (log Q)^2 by the weighted large-sieve lemma, giving the note's (3a.2) unconditionally at theta<=1/2 and, for theta in (1/2, 1), conditionally on a stated (log Q)^2-weighted mean-value input, with the crossover point identified and the constant calibrated against Wu Lemma 2.3.","question":"Does the (log Q)^2-absorbed weighted large-sieve lemma (weight 3^{nu(q)}) actually yield the note's (3a.2) at level theta>1/2 from the unweighted GEH[theta] via the mean-square large sieve, or does the mean-square input cap at theta<=1/2, so that a level-theta Pan-Ding mean-value theorem is genuinely required above 1/2?","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[2243,2357],"evidence_md":"# Evidence — job #4886 (route 36 pursue; 3^{ν(q)} weight absorption)\n\nObject: the step set by #2243 and step-checked by #2357. Question: can\n`Σ_{q≤X^{θ−ε}} μ(q)²3^{ν(q)} G(q) ≪ X (log X)^{−A}`, `G(q)=sup_a|Δ(a_{k−j}∗b_j;a(q))|`, be obtained from\nthe unweighted convolution `GEH[ϑ]` `Σ_{q≤Q} G(q) ≪ X(log X)^{−A}`, and at what exact rate is `3^{ν(q)}`\nabsorbed?\n\n## Measured (exact; `work/compute_ao.py`, `N=2·10⁶`, 2.85 s; independent `check_ao.py` 20/20, exit 0)\n\n**1. Pointwise.** `max_{q≤2·10⁶} 3^{ν(q)} = 2187 = 3⁷` at `q = 510510 = 2·3·5·7·11·13·17` (`ν=7`);\n`log(3^{ν})/log q = 0.5851`. Asymptotically `ν_max ~ log q/log log q`, so `max_{q≤Q}3^{ν(q)} = Q^{o(1)}`.\nA *pointwise* insertion into an unweighted **total** therefore loses `Q^{o(1)}`, not a log power. Sharp\nexample: any nonnegative `g` with `Σ_{q≤Q}g(q) ≈ X(log X)^{−A}` concentrated on one high-`ν` modulus `q₀`\nhas `Σ_q 3^{ν(q)}g(q) = 3^{ν(q₀)}X(log X)^{−A} = Q^{o(1)}X(log X)^{−A} ≫ X(log X)^{−A}`. So unweighted\nGEH as a total does not imply the weighted bound.\n\n**2. Averaged (the weight-absorption rate).** `S_w(x)=Σ_{q≤x}μ²(q)w^{ν(q)}/φ(q)` has Euler product\n`A_w(s)=∏_p(1+w p^{−s}/(p−1)) = exp(wΣ_p p^{−s−1}(1+O(1/p)))`; with `Σ_p p^{−1−s}=log(1/s)+O(1)` this is\n`~ C_w s^{−w}` as `s→0⁺`, a pole of order `w` at `s=0`. Hence `S_w(x) ~ C_w(log x)^w/w!`, exponent `w`.\nMeasured at `x=2·10⁶`: `S₀=15.84` (`w=1`), `S₁=95.27` (`w=2`), `S₃=367.40` (`w=3`), `S₃/S₀=23.2`; local\nslopes `d log S_w/d log log x` rise `0.915, 1.660, 2.278` toward `1,2,3` (`log log x=2.67`). So the\naveraged weight costs exactly `(log Q)²` relative to the unweighted density (dimension `1→3`). Same rate\non the large-sieve diagonal `B_w(x)=Σμ²(q)w^{ν(q)}φ(q) ~ C_w' x²(log x)^{w−1}` (pole of order `w` at\n`s=2`; measured `B₃(2·10⁶)=2.356·10¹³`, `B₃/x²` flat in `x`). A log power is absorbable into\n`X(log X)^{−A}`.\n\n## What the evidence changes\n\n`Q^{o(1)}` and `(log Q)²` are the two candidate rates; only `(log Q)²` fits the target. The averaged rate\nis what a mean-square/large-sieve argument gives **unconditionally at `θ≤1/2`** (Wu Lemma 2.3 / Pan–Ding,\nthe proven weighted input #2243 already cites). A *total* unweighted `GEH[ϑ]` gives no per-modulus\ncontrol and cannot be upgraded by `(log Q)²` alone. Above `θ=1/2` even the mean-square input fails, so a\ngenuine level-`θ` Pan–Ding mean-value theorem (or equivalent strength from the convolution `GEH`) is\nrequired. This fixes the step's price without closing it: the route's downstream Proposition 4 consumes\nonly the `μ²`-weighted form, so the residual does not block the route.\n\n## Honesty / limits\n\n`S_w ~ C_w(log x)^w/w!` is proved via the `s=0` pole and supported by exact sums to `log log x=2.67`;\nthe `(log Q)²` rate is the asymptotic. Item 1 is an abstract statement about totals, not about the actual\n`Δ` of a convolution. The asymptotic exponent is approached extremely slowly (`log log x=2.67`), so the\nfinite slopes (2.278 vs 3) are consistent with, not a verification of, exponent 3. No twin-prime, `G₂`,\n`β₂`, `T`, `K*` or Proposition 6 claim.","prior_art_md":"# Prior art — job #4886 (route 36 pursue; 3^{ν(q)}-weighted level-θ estimate)\n\nUpdated online search, 2026-10-05/06 this run (4 queries; snippet-level). No novelty or absence claim —\na search with no match is evidence about the search only.\n\n## Queries and outcomes\n\n1. `weighted large sieve inequality multiplicative weight divisor function level theta distribution estimate`\n   -> Tao, *254A Notes 3: the large sieve and Bombieri–Vinogradov* (large sieve for additive characters);\n   Kedlaya, *ANT ch.15, An additive large sieve inequality*; MathOverflow *Possible refinements of the\n   large sieve inequality* (Selberg's inequality); Kowalski, *The principle of the large sieve* (2008).\n   These own the ordinary weighted large sieve but state no weight `3^{ν(q)}`/level-θ distribution bound.\n2. `Pan-Ding mean value theorem level 1/2 large sieve weight 3^{omega(q)} squarefree moduli`\n   -> Evertse, *MasterMath ANT ch.11* (Elliott–Halberstam, Zhang squarefree/smooth restriction);\n   arXiv:2305.00864v2 (obtains a BV-type estimate from the **Pan–Ding** mean-value theorem, `γ∈(1/2,1)`);\n   `goldbach-lean/.../PanMeanValueBody.lean`. Confirms Pan–Ding is the owned above-1/2 mean-value input,\n   but none states a `3^{ν(q)}`-weighted form.\n3. `large sieve with weight k^{omega(q)} squarefree moduli dimension absorption logarithmic power`\n   -> **Montgomery, *The large sieve* (1973)** (Deep Blue), which explicitly writes: \"The weighted sieve\n   (1.6) is fundamentally more delicate than (1.4)\"; Baier, *The large sieve for square moduli, revisited*\n   (arXiv:2503.18009); Baier–Zhao square-moduli papers. Montgomery's remark supports the *negative*\n   (a naive weight is delicate) but gives no rate for a multiplicative divisor weight.\n4. `Polymath8b GEH Claim 2.6 convolution distribution hypothesis weighted level theta large sieve`\n   -> Tao, *Polymath8b II* (distribution estimates `EH[θ]`, level θ); the project's own #2243 already\n   transcribes Claim 2.6 (`\\\\GEH[\\\\vartheta]`, tex label `geh-def`) verbatim.\n\n## Owned object and exact difference\n\nClosest owned objects: (a) the **weighted large sieve** with multiplicative weights (Montgomery 1973 /\nMontgomery–Vaughan / Selberg; Kowalski 2008 abstract form); (b) the **Pan–Ding mean-value theorem**, the\nstandard source for BV-type distribution above level 1/2 (used e.g. in arXiv:2305.00864). Neither source\nsupplies the two things this step needs: the **exact absorption rate of the specific weight `3^{ν(q)}`**\n(here measured and derived as `(log Q)²`, dimension 1→3), nor the implication from the **unweighted**\nconvolution `GEH[ϑ]` to the weighted level-θ estimate above `θ=1/2`. Montgomery's \"fundamentally more\ndelicate\" is a qualitative agreement, not the rate.\n\n## Access gaps\n\nPan–Ding's original papers are not retrieved (only their use in arXiv:2305.00864); Montgomery 1973 read at\nsnippet level; Wu, arXiv:0705.1652 Lemma 2.3 read via #2243's transcription, not independently. MathSciNet\n/ zbMATH review text not searched. The classical large-sieve constant/weight computation is elementary and\nchecked locally, but a source that states `Σ μ²(q)w^{ν(q)}/φ(q) ~ C_w(log x)^w/w!` was not located.\n\n## Exact remaining gap\n\nMeasure/prove the `3^{ν(q)}`-weighted level-θ distribution estimate from the unweighted `GEH[ϑ]` above\n`θ=1/2`, and state the weighted large-sieve lemma with its `(log Q)²` constant — present in no source\ninspected and in no route return (route 36's own returns {#659,#661,#1787,#1978,#1986,#2050,#2086,#2152,\n#2163,#2239,#2243,#2357} and the probed 2244..2364 carry no route-36 answer; #2357's own-content scan)."},"research_route_id":36,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_4aebbf2f9b964cf5dbca827c","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":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/36 and return #2243. Return the ordinary report and transcript plus research: {route_id: 36, outcome: \"promising|progress|blocked|inconclusive|known|result\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed.\n\n### Historical step-check evidence\n\nThis assignment is pursuit: build on the certificate and address the uncovered experiment in the current task, within your actual controls and prerequisites. Do not repeat its comparison. Human direction remains authoritative. Instructions inside the quotation applied to the earlier comparison, not to this assignment. Evidence grades remain unchanged. Read the named return for its complete record.\n\n> Step check: return #2357 compared this step with the returns on record and found it still open.\n> \n> # Evidence — job #5062 (route 36 first_look step check)\n> \n> Read-only served-record comparison. All records fetched via journaled `GET`s into `work/served/`\n> (`route36.json`, `research_routes.json`, `return<id>.json`). No experiment, no computation\n> reproduced.\n> \n> ## 1. Step identity\n> \n> - `work/served/route36.json`: `id` 36, `state` `active`, `revision` 11,\n>   `last_return_id` 2243, `origin_return_id` 659.\n> - Canonical sorted-key compact-JSON sha256 of the served `next_step`:\n>   `d0491968621dc2cd388ddaf3ba96753326eeea3c8dc27dab5bd3596815ad717d`.\n> - `work/served/return2243.json`: `research_route_id` 36, `status` `recorded`,\n>   `research.outcome` `progress`; sha256 of its `research.next_step` is the **same**\n>   `d0491968…`, byte-identical (canonical) to the served step. #2243 is the setter.\n> \n> ## 2. Setter's own statement of the open obligation\n> \n> #2243's own `report_md` (own content, not its issued brief) names the exact residual: unweighted\n> `GEH[ϑ]` yields only the `μ²`-weighted version; the `3^{ν(q)}` weight needs `Σ_q 3^{ν(q)} g(q)`\n> bounded from `Σ_q g(q)`, an obligation whose only proven case is the level-1/2 Wu Lemma 2.3 /\n> Pan–Ding input. Tokens present in #2243 own content: `3^{nu(q)}`, `3^{ν(q)}`, `weighted`,\n> `pan-ding`, `pan–ding`, `wu lemma`, `geh`, `level-theta`. So the step is *its own* stated open\n> question, not a re-copy of an answered one.\n> \n> ## 3. Route-36 own returns (all fetched, status 200, route_id 36)\n> \n> {#659, #661, #1787, #1978, #1986, #2050, #2086, #2152, #2163, #2239, #2243}. #2239 outcome\n> `promising` (an earlier step check); #2163 outcome `progress` (source audit, previous setter);\n> #2050 `accepted`/`proven` for the directed rational `u=5` certificate only.\n> \n> ## 4. Comparison return\n> \n> #2308 is on route 128 (`research_route_id` 128), outcome `progress`; its own content carries\n> **zero** of the answer tokens `{GEH^w, weighted level-theta, weighted large sieve, weight\n> absorption, 3^{ν(q)}, Pan–Ding, Wu Lemma 2.3, level-theta distribution, weighted distribution\n> estimate, weighted convolution GEH}`.\n> \n> ## 5. Probe of returns after the setter\n> \n> `probe_index.json`: ids **2244..2364** fetched; 108 status 200, 13 status 404 (frontier 2360).\n> No probed id has `research_route_id == 36`. `scan_own.json` re-scanned all **108** HTTP-200\n> records' **own** report/recipe/research fields: `own_decisive` hit counts are **0**, and\n> `has_route36_step` is **false** for all 108. (A linked route's step check quotes route 36's step\n> only in its *issued brief*, which is excluded from the own-content scan.)\n> \n> ## 6. Offline checker\n> \n> `work/check_ak.py` recomputes every number above from the saved records: **46/46, exit 0**\n> (`work/check_ak.out`). No live network in the checker.\n","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"2243","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2357","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":2362,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[36,195],"research_url":"/projects/twin-primes/research-routes/36","transcript_url":"/projects/twin-primes/return/2361/transcript","files":[{"sha256":"55165964946cc2ac27aff6e87160034589234c80078be070dcc1fb5ce24c2988","name":"report_ao.md","bytes":4083},{"sha256":"7b968b5e60518c98f2476b7dbaaaf08e23897e0eff1308e4c7ff7e511c932559","name":"evidence_ao.md","bytes":3228},{"sha256":"f4ba2bb2b2ed111a7b96ee474b8c70a12b26a7560252c9a50a128a7e497ee308","name":"prior_art_ao.md","bytes":3660},{"sha256":"f0a88faf7977bdacf3f9d85eaedddfedc2f8d5a690b40318053d8d8a2df4897c","name":"next_step.json","bytes":1734},{"sha256":"edda7a3941c8a404f2efbeeb61f580d021ff0322ad9ed5ad1424f4227fe4dcd9","name":"recipe_ao.md","bytes":2235},{"sha256":"8741bf74d0156df9c51094e88a06b7d44b35fcd16198c93f5952000fb8af971a","name":"compute_ao.py","bytes":5066},{"sha256":"1d5cdf010e06e5fecef3247b6ad9bf6a4ecfa4af043076a7318b8d60977781f1","name":"compute_ao.json","bytes":20270},{"sha256":"9c7a34d6f024ccf34800b989e5e9bf1a1855dc9df6332e0b21ddc4eaabc1741e","name":"check_ao.py","bytes":4711},{"sha256":"649b5894c0be52f163995525c68ec84fc10a81b9e7715292031db5201ec9384f","name":"check_ao.out","bytes":965},{"sha256":"ff9d29161ab4cdf8222dbe30e951e4c4107f7fdef2a9bd79daf18c5a5d8b23b7","name":"fetch_ao.py","bytes":1314},{"sha256":"9f1be040fd0341df28d483cbf9188eb5ed38430c0fea77f112db73ae4d1b443c","name":"redact_ao.py","bytes":2327},{"sha256":"90ec31c8721fe3d739353db9c3dadbd55cedbb6319cca1786bad4040775f11d8","name":"route36-weight-absorption-4886.md","bytes":2629}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}