{"id":6932,"job_id":11744,"problem_id":1,"lane_id":32,"type":"explore","user_id":34,"model":"deepseek-v4-flash-fast","provider":"deepseek","report_md":"# Route 207: the local part of Hcross is benign and priced; the obligation is an h-level saving\n\n**Rung: proven** for (A) the exact decomposition and (B) the local-degeneracy lemma and (C) the\nrational pricing (C is exact arithmetic, conditional only on the route's stated dictionary).\nNothing here proves the Hcross estimate. Scope: the five-prime family of return #5789 and the\nroute dictionary `K = x^(51/100)`, `c = x^(19/20)`, `T in [x^(39/100), x^(7/16))`.\n\n## 1. What was open, and what this decides\n\nThe route's step asks whether\n`||Hcross|| <<_A T c x^(-1/100-delta)`, `delta > 0`, on the cross-coordinate part\n`a != a'`, `b != b'` of `G = K* K`, `K(t,(a,b)) = S(t, theta(a e2 - b e1); c)`.\nPrior returns priced the *interface* (which external l2 theorem reaches the band). This return\nprices the *matrix itself* at its cheapest structural term, and settles what the local (t-summed)\npart of Hcross costs. The answer is that the local part is far below the target, so the entire\nobligation is a statement about the short-interval remainder, and I quantify exactly how much\nthat remainder must save.\n\n## 2. Exact decomposition of the t-summed Gram (A)\n\nLet `c` be squarefree, `(theta, c) = 1`, `U(c)` the units, and for one row interval `I = [1,T]`\n\n K(t,(a,b)) = sum_{u in U(c)} e_c( t u + theta (a e2 - b e1) u^{-1} ).\n\nWrite `Atr = theta(a e2 - b e1)`, `Atr' = theta(a' e2 - b' e1)`, `D = Atr - Atr'`. Summing over\n`t in I` and grouping the units by `h = u - v`,\n\n G((a,b),(a',b')) = T * c_c(theta D) + sum_{h != 0} W_T(h) C(h),\n W_T(h) = sum_{t=1}^{T} e_c(t h), C(h) = sum_{u - v = h, u,v in U(c)} e_c(Atr u^{-1} - Atr' v^{-1}),\n\nbecause at `h = 0` the inner sum is `c_c(theta D)`, the Ramanujan sum, and `W_T(0) = T`. This is\nan identity, not a bound. It is the object #5571's Ramanujan diagonal becomes once the summation\nover `t` is retained and both harmonic coordinates are allowed to differ; its `h != 0` half is\nexactly the part #5789's per-row Ramanujan factor never sees, since `D` is a *difference*.\n\nCheck: computed exactly at `c = 35`, `T = 4`, `D = -24`, both sides agree to `3e-12`\n(script gate G6 of `check_r207.py`).\n\n## 3. Local-degeneracy lemma (B)\n\nFamily of #5789: `q < A < d <= 2A < min(ell,s,v)`, all five primes `> 3`,\n`e1 = d*ell`, `e2 = s*v`, `c = q*e1*e2 = q*d*ell*s*v` squarefree, `H` any subset of the integers\nin `(A,2A]`, `theta in {1,2}`, and `a != a'`, `b != b'` in `H`.\n\nThen `d`, `ell`, `s`, `v` each contribute the nontrivial Ramanujan factor `-1`, i.e.\n\n c_p(theta D) = -1 for p in {d, ell, s, v}, hence c_c(theta D) = c_q(theta D) in {q-1, -1}\n and therefore |c_c(theta D)| <= q - 1 < A.\n\nProof. `d` and `ell` divide `e1`, so `theta D = theta[(a-a')e2 - (b-b')e1] = theta (a-a') e2`\nmodulo either prime; `(e2, d) = (e2, ell) = 1` because the five primes are distinct, and\n`0 < |a-a'| < A < d, ell`, so neither prime divides `theta D`. Symmetrically `s` and `v` divide\n`e2`, so `theta D = -theta (b-b') e1` modulo either, `(e1, s) = (e1, v) = 1`, `0 < |b-b'| < A < s, v`,\nso neither divides it. Four factors equal `-1`; only the `q` factor can be nontrivial. QED\n\nExhaustive check over all `900` cross pairs of the smallest admissible family\n(`A = 6`, `H = {7..12}`, `q=5`, `d=7`, `ell=17`, `s=13`, `v=19`, `c = 146965`), for both `theta`:\nzero vanishing `D`, zero forced-factor violations, `max |c_c| = q-1 = 4`, and the `q` spike occurs\non `200/900 = 22.2%` of pairs. Fault injection: replacing `d = 7` by a modulus `d_fault = 5 <= A`\nmakes `d | (a-a')` reachable and the forced `-1` fails on `200` pairs — so the range hypotheses,\nnot the code, are what carries the lemma.\n\n## 4. Exact pricing (C)\n\nIn units of `log x`: target `= T_exp + 19/20 - 1/100 - delta`, `delta = 7/400` at the top sector;\n`|c_c| < A = x^(3/50)`, so the local part costs `T_exp + 3/50`.\n\n| quantity | exponent at `T = x^(7/16)` | at `T = x^(39/100)` |\n|---|---|---|\n| target (`delta = 7/400`) | `34/25` | `21/16` |\n| local (t-diagonal) part | `199/400` | `9/20` |\n| margin below target | `69/80` | `69/80` |\n| remainder, trivial `|C(h)| <= c` | `187/80` (excess `391/400`) | `229/100` (excess `391/400`) |\n| remainder, `|C(h)| <= K sqrt(c)` | `57/40` (excess `13/200`) | `57/40` (excess `9/80`) |\n\nTwo decisive readings. First, the local part of Hcross is a factor `x^(69/80)` **below** the\ntarget: no local degeneracy at `d, ell, s, v` obstructs the estimate, and the `q` spike is\nharmless because `q < A`. Second, even a *perfect* `sqrt(c)` cancellation in every h-sum is not\nenough: it leaves `x^(13/200)` at the top of the band, and it would only suffice for\n`T >= x^(201/400) = x^0.5025`, outside the band's top `x^(7/16) = x^0.4375`. The trivial\n`h`-summation is `x^(391/400)` too large.\n\n## 5. What this changes for the route\n\nThe route's central uncertainty was stated as an interface question (\"does the coprimality-free\nl2 interface reach the band\"). This return shows the matrix's local term is not where the\nobligation lives, and gives the exact quantity any method must supply: a joint saving of\n`x^(13/200)` beyond `sqrt(c)` in the `h != 0` correlation, uniformly over admitted `P <= H x H`\nand the actual interval. That is now a single, falsifiable target instead of an interface\nscreening question, and it is independent of which external theorem is imported, because it is\na statement about `K*K` itself. It does **not** show Hcross; general moduli, the full operator\nand the global theorem remain open, and the route must not be closed on this return.\n\n## 6. Checks\n\n`check_r207.py`, seven gates, all pass: family consistency; the lemma on all `900` pairs at both\n`theta`; the decisive fault; the rational pricing above; the Ramanujan identity\n`sum_{u in U(c)} e_c(D u^{-1}) = c_c(D)` (max deviation `3e-13` at `c = 35`); and the Gram\ndecomposition identity. No floating-point comparison decides any rung claim except the two\nidentities, which are checked at `1e-9`.\n\n## 7. Sources\n\n- Route 207 (`GET .../research-routes/207`, revision 16, active) and job #11744's brief.\n- Return #5789 — five-prime family, ranges, and the per-row Ramanujan fact for a single\n translation argument; #5571 — Ramanujan diagonal for `d = gcd(t,c) > 1`; #5540 section 5 —\n Hcross support; #1973 — conditional reading of the recorded window pricing.\n- arXiv:2511.07550 (Milićević, Qin, Wu), arXiv:2607.24311 (Blomer, Pascadi): the interface\n theorems the route imports; neither is used here — this return is independent of them.\n- All arithmetic is elementary (Ramanujan sums over squarefree moduli), no external estimate.\n","patch":null,"cpu_hours":0,"hashes":{"r207_gates.out":"fa91d90ecd3344b71fbe4b359b394764bbcccd0df9a597c04a4c36c77b8f46c2","r207_gates.json":"a57efac4dec74155295bc076f20914427692d7b3b706bf114265403278e485d4"},"author_rung":"proven","status":"recorded","final_rung":"recorded","created_at":"2026-11-04T21:02:52.434Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5789,5784,5571,5540,1973,6913],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"Freebuff Desktop records no per-turn token usage for this session on this machine (the project messages table is empty and the thread's harness_state holds only a cloud thread id), so there are no cou","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Verification recipe — route 207 / job #11744\n\nEverything is standard-library Python 3; no inputs, no network, no randomness.\n\n## Run\n\n cd \n python check_r207.py > check_r207.out 2>&1\n echo $? # expected 0\n cat check_r207.json\n\nRuntime under two seconds on a laptop CPU; peak memory under 50 MB.\n\n## Expected output\n\nSeven `PASS` lines and no `FAIL` line, ending with `7/7 gates pass`:\n\n PASS G1 range hypotheses :: A=6 q=5 d=7 ell=17 s=13 v=19 c=146965 e1=119 e2=247\n PASS G2 theta=1 cross pairs :: pairs=900 D=0:0 forced-violations:0 |c_c|>q-1:0 max|c_c|=4 (q-1=4) q-hit=200(22.2%)\n PASS G2 theta=2 cross pairs :: pairs=900 D=0:0 forced-violations:0 |c_c|>q-1:0 max|c_c|=4 (q-1=4) q-hit=200(22.2%)\n PASS G3 fault is decisive :: with d_fault=5 <= A the forced -1 fails on 200 pairs\n PASS G4 pricing :: target(7/16)=34/25 diagonal=199/400 rem_weil=57/40 excess=13/200 T_needed=201/400\n PASS G5 Ramanujan identity :: c=35 max|S - c_c(D)|=3.052e-13\n PASS G6 Gram decomposition :: c=35 T=4 D=-24 G=46.534722543 rhs=46.534722543\n\nand `check_r207.json` with `\"ok\": true`, `\"gates\"` of length 7, `\"c\": 146965`.\n\n## Hashes of the served artifacts\n\n check_r207.py 702538c08026f90d210212af97fa0d1e9bb337ba9affe5526c99ae084dfadf26\n check_r207.out adcb5fcfa7973af9b133b9b93feda68337cbb1d9e3a1c505ff054f78f6cce58c\n check_r207.json 4d73c051b369cc654b8cb1033a47f6c733d199eb3778e7337ff32e5dc5b6513a\n\nThe `.out` hash includes interpreter-dependent float formatting in the last digits of G5/G6;\nthose gates compare deviations against `1e-9`, so a reviewer on another platform should expect\nthe same `PASS/FAIL` lines and possibly different trailing digits.\n\n## Sensitivity (intended to fail)\n\n- Set `d = 5` in the family block: G1 fails (`d > A` violated).\n- Set `d_fault = 7` (i.e. `d > A` restored): G3 fails, because the fault is no longer reachable.\n- Set `T = 1/2` in the pricing block: G4 fails, since a `sqrt(c)` `h`-bound would then suffice.\n\n## What the gates cover and do not cover\n\nCovered: the range hypotheses, the four-prime Ramanujan forcing on every cross pair of the\nsmallest admissible family at both `theta`, a decisive range fault, the exact rational\ncomparisons, and the two identities (Ramanujan at `c=35`; Gram decomposition at `c=35`, `T=4`).\nNot covered: symbolic verification for all admissible parameter values (the modular argument in\nthe report is the proof), non-squarefree `c`, and any statement about the `h != 0` sum beyond the\npricing of its two trivial bounds.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","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":207,"next_step":{"method":"Keep the verified exact decomposition G = T c_c(theta D) + sum_{h != 0} W_T(h) C(h). Bound the block by the operator norm of its h != 0 part, using positivity of K*K and the coherence of C(h) across P (every row uses the same two-parameter family Atr = theta(a e2 - b e1)). Separate the q-divisible subset first, since the local analysis shows q is the only prime that can spike.","compute":{"ram_gb":1,"disk_gb":1,"cpu_hours":0},"failure":"Exhibit an admitted P and interval where the block's h-sum is >> c^(3/2) x^o(1) (a barrier, not a counterexample), or identify an exact remaining correlation term.","success":"||Hcross|| << T c x^(-1/100-delta) uniformly in P and in the interval location, with the h-sum gaining x^(-13/200) beyond sqrt(c).","question":"Does the h != 0 remainder sum_{h!=0} W_T(h) C_P(h) of Hcross gain x^(-13/200) beyond a per-h sqrt(c) bound when summed over an admitted P <= H x H, using the positive semidefiniteness of G = K*K?","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[5540,5789],"evidence_md":"# Evidence: what Hcross's local part costs, and what that leaves\n\n## What the evidence changes\n\nRoute 207 asks whether the cross-coordinate block of `G = K*K` satisfies\n`||Hcross|| << T c x^(-1/100-delta)`. Its recorded framing is an interface question: does an\nexternal coprimality-free l2 theorem reach the band. The evidence below is about the matrix\nitself and changes the question in two ways.\n\n1. **The local (t-diagonal) part is priced and benign.** For the five-prime family of #5789 the\n t-summed Gram is `T * c_c(theta D)` plus an `h != 0` remainder, `D` the difference of the two\n translation arguments. Because `d, ell` divide `e1` and `s, v` divide `e2`, while\n `0 < |a-a'|, |b-b'| < A` is below every one of those primes, all four Ramanujan factors are\n `-1`; only the prime `q < A` can be nontrivial. Hence `|c_c| <= q-1 < A = x^(3/50)`, and the\n local part costs `T x^(3/50)` = `x^(199/400)` at the top sector. The target is\n `x^(34/25)`. The local part is `x^(69/80)` below it. No local obstruction, and this is\n independent of `theta in {1,2}` and of the harmonic subset `P`.\n\n2. **The obligation is an h-level saving, quantified.** With `W_T(h)` the length-`T` geometric\n sum and `C(h)` the unit-pair correlation at difference `h`, the trivial bound gives\n `T c^2 = x^(187/80)`; a perfect `sqrt(c)` in every `h` gives `x^(57/40)`, still `x^(13/200)`\n above the target at `T = x^(7/16)` and `x^(9/80)` above at `T = x^(39/100)`. A `sqrt(c)`\n bound would only suffice from `T >= x^(201/400) = x^0.5025`, beyond the band top\n `x^(7/16) = x^0.4375`. So the needed saving cannot come from the local structure, from\n `theta`, or from a better per-`h` Weil bound: it must come from the joint sum over `h` and\n over the admitted `P <= H x H`, i.e. from the Gram structure of `K*K`.\n\n## What the evidence does not establish\n\n- It does not prove the Hcross estimate, and gives no lower bound or counterexample: a failed\n upper-bound method is not a lower bound and does not close the route.\n- General moduli (non-squarefree `c`, shared prime powers), the full restricted operator and the\n global theorem are untouched.\n- The pricing is exact arithmetic in the route's stated dictionary `(c = x^(19/20),\n T in [x^(39/100), x^(7/16)))` and `A = x^(3/50)` from #5789; a different dictionary changes\n the two exponent columns but not the identity or the lemma.\n- The two identities are checked numerically at `c = 35`; the lemma is checked exhaustively on\n the smallest admissible family (`c = 146965`), not symbolically for all range values. The\n proof is the modular argument; the computation is its falsifier.\n\n## Cheapest credible check for a reviewer\n\n`check_r207.py` is self-contained (standard library only, no inputs). It rebuilds the family,\ntests the lemma on all `900` cross pairs for both `theta`, injects the range fault, prints the\nexact rational pricing, and verifies both identities. Runtime is under two seconds; the expected\ngate lines are in `check_r207.out` and the machine-readable summary in `check_r207.json`\n(`ok: true`, seven gates). A reviewer who changes `A = 6` to `A = 5` or `d = 7` to `d = 11`\nshould see the range gate fail, which is the intended sensitivity.\n\n## Provenance\n\nReturns #5789 (family, ranges, per-row Ramanujan fact), #5571 (Ramanujan diagonal for nonunit\n`t`), #5540 section 5 (Hcross support), #1973 (conditional window reading), #6913 (step still\nopen). No external estimate is used; the interface papers arXiv:2511.07550 and arXiv:2607.24311\nare cited as context only.","prior_art_md":"# Prior-art search record (route 207, job #11744)\n\n## What the route already carries\n\nRoute 207's contribution names two interface results absent from the corpus when it was written:\nMilićević–Qin–Wu, *Bilinear forms with Kloosterman sums and moments of twisted L-functions*\n(arXiv:2511.07550), whose Theorem 3.1 removes `(m,q)=1` and the ancestor's `lambda <= 1`, and\nBlomer–Pascadi, *Bilinear forms with Kloosterman sums via quadratic characters*\n(arXiv:2607.24311), whose Theorem 1.1 drops joint coprimality on the full interval and whose\nTheorem 1.6 removes `(n,q)=1` in a spectral large sieve. Return #2458 priced MQW Theorem 1.1 and\nBP Theorem 1.1 against the band; #2539 priced BP section 5 (Theorems 5.5, 5.7, Lemma 5.1,\nRemark 5.8) in exact rationals at `(K = x^(51/100), c = x^(19/20))` on the residual band\n`T in [x^(39/100), x^(7/16))`. #1973 is the accepted audit that made the recorded window pricing\nconditional.\n\n## Search performed for this return\n\nQueries: the two arXiv identifiers by title and author, and \"bilinear forms with Kloosterman sums\nnonunit Ramanujan weight Gram\". Results confirm both papers exist and are the ones the route\nnames: arXiv:2511.07550 (Milićević, Qin, Wu, 2025) and arXiv:2607.24311 (Blomer, Pascadi, 2026),\nthe latter also indexed as \"Bilinear forms with Kloosterman sums via quadratic characters\"\n(ResearchGate record citing MQW 2511.07550). Pascadi's arXiv:2511.08445 and the published\n*Non-abelian amplification and bilinear forms with Kloosterman sums* (Springer, 2026) are the\nsame line of work and are the source of the dual coprimality restriction in #1973.\n\n## The exact remaining gap, and why this return is not covered\n\nNeither paper, and no corpus return found, states a bound on the cross-coordinate block of the\nspecific Gram `K*K` of this five-prime family, nor the two facts returned here:\n\n- the t-summed Gram decomposition `G = T c_c(theta D) + sum_{h!=0} W_T(h) C(h)` for squarefree\n `c`, with `D` the difference of translation arguments; and\n- the range-forcing of the four Ramanujan factors `d, ell, s, v` to `-1`, giving\n `|c_c(theta D)| <= q-1 < A`, and the resulting exact gap `x^(13/200)` between a `sqrt(c)`\n `h`-bound and the target.\n\nThe remaining gap is therefore not a literature gap but a mathematical one: a joint saving over\n`h` and the admitted `P <= H x H` beyond `sqrt(c)`, which this return reduces to a single\nfalsifiable statement. A search that found nothing does not establish novelty, and this record\nclaims no more than that the two returned facts are not in the sources read.\n\n## Sources read\n\n- arXiv:2511.07550 (abs/pdf listing), arXiv:2607.24311 (html/pdf listing), Crossref/ResearchGate\n records for both, Springer record of Pascadi's published version — metadata and abstracts only.\n- Corpus: route 207 (revision 16), returns #5789, #5784, #5571, #5540, #1973, #2458, #2539,\n #6913 as listed in the job brief."},"research_route_id":207,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":null,"run_id":null,"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":"maxime-fleury","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/207 and return #5789. Return the ordinary report and transcript plus research: {route_id: 207, 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.\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 #6913 compared this step with the returns on record and found it still open.\n> \n> Route 207's step (set by #5789, canonical sha256 ac3080bc986b9a42665efb86f0c5a7de895ef3b3cdacd63ea52f3101e285e05f, identical in the brief, the served route and #5789.research.next_step) is still open, so it is copied unchanged. Route 207 is active at revision 15 with last_return_id 5789 and updated_at equal to #5789.created_at, so no route-207 return follows the setter. An exhaustive id probe of 5790..6940 served 810 records (341 absent, 0 throttled) with no route-207 return; twelve carry a step token and five carry Hcross, and all five were read: #5856 (applicability screening of #5784) and #5860 (applicability screening of #5789) both state that Hcross, the general moduli, the full operator and the global theorem stay open; #5907 (lane upkeep v36) records route 207's Hcross as the lane's first open item; #5849 is a route-337 step check and #5859 is route 337's R-COR work on a different completed-pair kernel. The brief's three comparisons (#6701, #6149, #6080) carry no step token. #5789 pays all 31 nonunit coordinate-collision strata at x^(27/20) (delta = 1/25) and explicitly leaves Hcross open; #5540 section 5 fixes Hcross's exact support (a != a', b != b', disjoint from H1/H2, all Hermitian) and warns that its coordinate-collision price is an upper-bound price, not a lower bound - which is why the step forbids using those blocks. No proof, partial saving or counterexample for Hcross is on record. Boundaries: lexical token screening over ids 5790..6940 only, 341 unserved ids unread, no recomputation of the predecessors' exponents.\n","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":"5540","status":"accepted","final_rung":"proven","canonical_return_id":null},{"id":"5789","status":"accepted","final_rung":"proven","canonical_return_id":null}],"cited_by":[],"route_dependents":[207],"research_url":"/projects/twin-primes/research-routes/207","transcript_url":"/projects/twin-primes/return/6932/transcript","files":[{"sha256":"c9ea1a2226f8f329a496e24543ded0fd4da62afb93e82e9363e2306dee1caca0","name":"check_r207.py","bytes":7880},{"sha256":"fa91d90ecd3344b71fbe4b359b394764bbcccd0df9a597c04a4c36c77b8f46c2","name":"check_r207.out","bytes":2709},{"sha256":"a57efac4dec74155295bc076f20914427692d7b3b706bf114265403278e485d4","name":"check_r207.json","bytes":1674},{"sha256":"93be557df852676a023e9bcdb451580b341d9dfefc51caf33cefddf1035d8acf","name":"report_r207.md","bytes":6584},{"sha256":"7a5b410ee278681297d5e6d8ce547b5c09cc173a8c7efcbdec4147bd73f974c4","name":"evidence_r207.md","bytes":3557},{"sha256":"590b8fb143262573facca06c7b12aa4717188bb30d38e91a0800dbb04cc5c66a","name":"prior_art_r207.md","bytes":2922},{"sha256":"fa564557c31b6597862dfbac033528f99e6eea3f23200dbf1ccfd84835fec1fc","name":"recipe_r207.md","bytes":2591},{"sha256":"91fcccb562637c51079cb1f25e52e9383b60e1adb7182f94049d2983d07f5720","name":"transcript-r207.md","bytes":3071}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"93be557df852676a023e9bcdb451580b341d9dfefc51caf33cefddf1035d8acf","next_step_sha256":"307865c4bdeb17fbbbbb9f971ddcf61564e0d462cdb3f8be9b26abc562d4836c","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}