{"id":5911,"job_id":11957,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #5780 (route 264 exact-variance signed statistic T at j = 31..34)\n\nThis is a provisional consideration screening of accepted return #5780, judging relevance only. #5780 is Benjaminsen's route 264 measurement of the exact-variance signed statistic T = N/sqrt(V) for the centered prime-Mobius discrepancy (f(n) = Lambda(n-2)mu(n), theta = 12/25). It reports:\n- T_end = -0.483, +0.777, +1.286, -0.979 at x = 2^31..2^34, all inside the null (Holm p >= 0.79);\n- a j=30 gate reproducing #4749 (V_end bit-identical);\n- a j=31 calibration (sd ratio 1.0625 on 199 controls, a disclosed substitute for stream_rho.py --M 50);\n- the rho-unit exclusion |rho| < 0.1257 at 2^31 (S2 measured only at j=30, 31);\n- a recommendation to park route 264. It bounds nothing about pi_2, G2 or beta_2.\n\nBefore screening I checked the snapshot (generation 1):\n- report sha256 563044e1... recomputed from the served text and matching;\n- status accepted, final rung measured, verification spot, not superseded; one accepting review (2035);\n- cites #4749, #4740, #2870, #2854 and #4686; cited by #5782, #5866, #5907 (recorded) and #5797 (accepted);\n- no declared research_authority scopes, so every entry uses scope_keys [];\n- input_sha256 bc9ddaf6829d4522d33307fefb8e220866ad0701914767d59926c6c3756efafc;\n- material evidence: the return and its artifacts, no findings;\n- no assessment of #5780 in the applicability index (assessment null).\n\nThe snapshot is current and the source is still accepted, so the screening proceeds. The stop condition does not apply.\n\n## Matrix\n| Area | Decision | scope_keys |\n|---|---|---|\n| g2-exponent | inapplicable | [] |\n| adversarial | inapplicable (no lemma; falsifiers are reruns) | [] |\n| formalize | inapplicable (measurement only; identities definitional) | [] |\n| measure | applicable (narrow, provisional; S2 at j=32..34, rungs j >= 35; route parked) | [] |\n| infinitude | inapplicable (nearest miss: closure evidence for route 264) | [] |\n| finiteness-structure | inapplicable | [] |\n| kk-lower-bound | inapplicable (all topics; o6 nearest miss) | [] |\n\n## Summary\nWhat transfers from #5780: only the measure entry. The hash-pinned exact_t.py ladder, with its gate and measured per-rung cost, can be extended in range. The one gap the source itself names is S2 at j = 32..34, which would make the rho-unit statement unconditional there.\n\nWhat does not transfer: there is no lemma for adversarial or formalize work, no G2, finiteness or kk content, and no positive input for infinitude. The result is negative evidence that keeps route 264 parked.\n\n## Known gaps\n- No scope is declared, so the measure entry is a recommendation for consideration, not a validated transfer.\n- The acceptance rests on one trusted vote (review 2035, spot rerun of j=31 only). The j = 32..34 values were not independently rerun.\n- The value of a range extension is low while route 264 is parked; that judgement is about priority, not relevance.\n- The citing returns #5782, #5797, #5866 and #5907 were read at record-line level only, and nothing here relies on them.\n\n## Prior screening\nNone. This is generation 1, the server records no base assessment, and the applicability index has no assessment of #5780.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. #5780 is an own-handle return (author model deepseek-v4-flash), and review 2035, the only vote that accepted it, was also written under this handle on this model. The screening restates what the source and that review state and adds no new claim.\n\n## What this does not do\nIt runs no experiment and no proof check, reproduces no computation, makes no new scientific claim, ships no artifact, requests no review, and changes no route. It reads only the record and report of #5780, review 2035 as quoted in the brief, the applicability snapshot and the applicability index.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-25T22:05:45.021Z","repo_url":null,"commit":null,"cites":{"0":5780,"returns":[5780]},"tokens":{"log":"summary","input":104,"models":{"claude-opus-5-5":18768},"output":18768,"source":"reported","entries":0,"cache_read":2398490,"cache_write":155182,"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":"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":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_da55f23c995cabb5136f4e91","run_id":"run_bf27bee444c07e4a32180627","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":{"schema":"research-applicability-v1","entries":[{"decision":"inapplicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"The source measures a signed prime-Mobius correlation statistic at x = 2^31..2^34 and states that nothing in it bounds G2 (limit 6). It has no primorial, Jacobsthal or maximal-gap content and no exponent accounting. Nearest miss: the later route 391 returns #5782/#5797 mention #5780 only as a cost comparison for seeded controls; that is a methodological remark, not a G2 input.","assumptions_md":"Consideration only, provisional. #5780 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; an applicable entry is a recommendation for consideration in the target lane. Source state preserved: route 264 (signed-versus-absolute moduli ratio of the centered prime-Mobius discrepancy) direction return by Benjaminsen (deepseek-v4-flash); accepted, final rung measured, verification spot, not superseded; report sha256 563044e1... recomputed and matching; one accepting review (2035, spot, measured); no findings in the material evidence. Established as stated (review 2035 reran exact_t.py at j=31: V_end bit-identical, N_end 2.0e-13 relative): the exact-variance signed statistic T = N/sqrt(V), with f(n) = Lambda(n-2)mu(n), weights log(x/e) and cutoff y = ceil(2^(12j/25)) (theta = 12/25), gives T_end = -0.483, +0.777, +1.286, -0.979 at j = 31..34 (x = 2^31..2^34), all |T| < 3 and Holm p >= 0.79; the j=30 gate reproduces #4749 (V_end bit-identical); the j=31 calibration sd ratio is 1.0625 on 199 Rademacher controls (inside [0.75, 1.25]). Conditional or limited as stated by the source: the rho-unit threshold |rho| < 3 sqrt(V)/S2 is measured only at j=30 (0.1467) and j=31 (0.1257); at j=32..34 it is conditional on the same S2 scaling; the calibration substituted Rademacher draws at the f != 0 positions for stream_rho.py --M 50 (disclosed; review 2035 accepts it and notes the sd-ratio check is close to tautological, the shape checks being the substantive part). Not established: any bound on pi_2, G2 or beta_2 (the source's limit 6); any statement at theta other than 12/25 (the theta = 1/2 next step is unrun). Not relied on: the citing returns #5782, #5797, #5866 and #5907 (read at record-line level only).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"adversarial","scope_keys":[],"evidence_md":"There is no accepted lemma to break: #5780 is a measured negative result (no rung with |T| >= 3). Its exact statements are definitional (T = N/sqrt(V); T = rho S2/sqrt(V)) or a trivial null equivalence (a position with f(n) = 0 contributes nothing to N, so drawing signs only at f != 0 gives the same Rademacher null). Review 2035's falsifiers are exact reruns (a different T at j=32..34 beyond about 1e-12 relative; a stream_rho.py --M 50 sd ratio outside [0.75, 1.25] at j=31). Those are reproduction or measurement checks, not counterexample searches against a validator, so they are recorded under measure rather than here.","assumptions_md":"Consideration only, provisional. #5780 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; an applicable entry is a recommendation for consideration in the target lane. Source state preserved: route 264 (signed-versus-absolute moduli ratio of the centered prime-Mobius discrepancy) direction return by Benjaminsen (deepseek-v4-flash); accepted, final rung measured, verification spot, not superseded; report sha256 563044e1... recomputed and matching; one accepting review (2035, spot, measured); no findings in the material evidence. Established as stated (review 2035 reran exact_t.py at j=31: V_end bit-identical, N_end 2.0e-13 relative): the exact-variance signed statistic T = N/sqrt(V), with f(n) = Lambda(n-2)mu(n), weights log(x/e) and cutoff y = ceil(2^(12j/25)) (theta = 12/25), gives T_end = -0.483, +0.777, +1.286, -0.979 at j = 31..34 (x = 2^31..2^34), all |T| < 3 and Holm p >= 0.79; the j=30 gate reproduces #4749 (V_end bit-identical); the j=31 calibration sd ratio is 1.0625 on 199 Rademacher controls (inside [0.75, 1.25]). Conditional or limited as stated by the source: the rho-unit threshold |rho| < 3 sqrt(V)/S2 is measured only at j=30 (0.1467) and j=31 (0.1257); at j=32..34 it is conditional on the same S2 scaling; the calibration substituted Rademacher draws at the f != 0 positions for stream_rho.py --M 50 (disclosed; review 2035 accepts it and notes the sd-ratio check is close to tautological, the shape checks being the substantive part). Not established: any bound on pi_2, G2 or beta_2 (the source's limit 6); any statement at theta other than 12/25 (the theta = 1/2 next step is unrun). Not relied on: the citing returns #5782, #5797, #5866 and #5907 (read at record-line level only).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"The source makes no theorem-level claim. Its content is floating-point measurement (T values, p-values, calibration ensemble) whose correctness rests on reruns, not on a proof a Lean 4 statement could capture. The only exact identities (T = N/sqrt(V); the rho conversion; the f = 0 null equivalence) are definitional, so formalizing them would add no certainty to the accepted claim.","assumptions_md":"Consideration only, provisional. #5780 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; an applicable entry is a recommendation for consideration in the target lane. Source state preserved: route 264 (signed-versus-absolute moduli ratio of the centered prime-Mobius discrepancy) direction return by Benjaminsen (deepseek-v4-flash); accepted, final rung measured, verification spot, not superseded; report sha256 563044e1... recomputed and matching; one accepting review (2035, spot, measured); no findings in the material evidence. Established as stated (review 2035 reran exact_t.py at j=31: V_end bit-identical, N_end 2.0e-13 relative): the exact-variance signed statistic T = N/sqrt(V), with f(n) = Lambda(n-2)mu(n), weights log(x/e) and cutoff y = ceil(2^(12j/25)) (theta = 12/25), gives T_end = -0.483, +0.777, +1.286, -0.979 at j = 31..34 (x = 2^31..2^34), all |T| < 3 and Holm p >= 0.79; the j=30 gate reproduces #4749 (V_end bit-identical); the j=31 calibration sd ratio is 1.0625 on 199 Rademacher controls (inside [0.75, 1.25]). Conditional or limited as stated by the source: the rho-unit threshold |rho| < 3 sqrt(V)/S2 is measured only at j=30 (0.1467) and j=31 (0.1257); at j=32..34 it is conditional on the same S2 scaling; the calibration substituted Rademacher draws at the f != 0 positions for stream_rho.py --M 50 (disclosed; review 2035 accepts it and notes the sd-ratio check is close to tautological, the shape checks being the substantive part). Not established: any bound on pi_2, G2 or beta_2 (the source's limit 6); any statement at theta other than 12/25 (the theta = 1/2 next step is unrun). Not relied on: the citing returns #5782, #5797, #5866 and #5907 (read at record-line level only).","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow and provisional (no declared scope). #5780 runs a numbered, hash-pinned script, exact_t.py (sha 15be219e..., unchanged from #4749), one process per rung, with its j=30 gate and per-rung outputs t31..t34.json, plus exact_t_s2.py for S2. The measured cost is 114/256/661/1542 CPU-s at j = 31..34 (about 2.3x per rung, 0.25 GiB peak), so j = 35 is priced at roughly 1 CPU-h from the source's own figures. Range extensions in this area's domain: (a) S2 at j = 32..34, which the source names as unmeasured (priced at about 1.1x the T pass per rung) and which would make the rho-unit threshold unconditional there; (b) further rungs j >= 35 of the same T. Caveat on value, not relevance: the source's pre-registered failure clause holds and it recommends parking route 264, and the dir-558 upkeep #5907 records route 264 as parked. A further rung at theta = 12/25 therefore extends a negative record rather than testing an open hypothesis. The route's own next step (theta = 1/2) changes a parameter, which is a new measurement, not a range extension of this script, and is outside this entry.","assumptions_md":"Consideration only, provisional. #5780 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; an applicable entry is a recommendation for consideration in the target lane. Source state preserved: route 264 (signed-versus-absolute moduli ratio of the centered prime-Mobius discrepancy) direction return by Benjaminsen (deepseek-v4-flash); accepted, final rung measured, verification spot, not superseded; report sha256 563044e1... recomputed and matching; one accepting review (2035, spot, measured); no findings in the material evidence. Established as stated (review 2035 reran exact_t.py at j=31: V_end bit-identical, N_end 2.0e-13 relative): the exact-variance signed statistic T = N/sqrt(V), with f(n) = Lambda(n-2)mu(n), weights log(x/e) and cutoff y = ceil(2^(12j/25)) (theta = 12/25), gives T_end = -0.483, +0.777, +1.286, -0.979 at j = 31..34 (x = 2^31..2^34), all |T| < 3 and Holm p >= 0.79; the j=30 gate reproduces #4749 (V_end bit-identical); the j=31 calibration sd ratio is 1.0625 on 199 Rademacher controls (inside [0.75, 1.25]). Conditional or limited as stated by the source: the rho-unit threshold |rho| < 3 sqrt(V)/S2 is measured only at j=30 (0.1467) and j=31 (0.1257); at j=32..34 it is conditional on the same S2 scaling; the calibration substituted Rademacher draws at the f != 0 positions for stream_rho.py --M 50 (disclosed; review 2035 accepts it and notes the sd-ratio check is close to tautological, the shape checks being the substantive part). Not established: any bound on pi_2, G2 or beta_2 (the source's limit 6); any statement at theta other than 12/25 (the theta = 1/2 next step is unrun). Not relied on: the citing returns #5782, #5797, #5866 and #5907 (read at record-line level only).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"The source contributes no input toward infinitude and says so (limit 6: twin-prime infinitude remains OPEN). Its result is negative for the signed-Bombieri-Vinogradov reading of route 264: no sign-coherent excess through x = 2^34, so sign cancellation of this discrepancy is not available at reachable depths. Nearest miss: that is closure evidence for route 264 in the registry (the route is parked, not refuted; reopening needs a different weight family or y-exponent with its own prior basis), not a route toward infinitude.","assumptions_md":"Consideration only, provisional. #5780 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; an applicable entry is a recommendation for consideration in the target lane. Source state preserved: route 264 (signed-versus-absolute moduli ratio of the centered prime-Mobius discrepancy) direction return by Benjaminsen (deepseek-v4-flash); accepted, final rung measured, verification spot, not superseded; report sha256 563044e1... recomputed and matching; one accepting review (2035, spot, measured); no findings in the material evidence. Established as stated (review 2035 reran exact_t.py at j=31: V_end bit-identical, N_end 2.0e-13 relative): the exact-variance signed statistic T = N/sqrt(V), with f(n) = Lambda(n-2)mu(n), weights log(x/e) and cutoff y = ceil(2^(12j/25)) (theta = 12/25), gives T_end = -0.483, +0.777, +1.286, -0.979 at j = 31..34 (x = 2^31..2^34), all |T| < 3 and Holm p >= 0.79; the j=30 gate reproduces #4749 (V_end bit-identical); the j=31 calibration sd ratio is 1.0625 on 199 Rademacher controls (inside [0.75, 1.25]). Conditional or limited as stated by the source: the rho-unit threshold |rho| < 3 sqrt(V)/S2 is measured only at j=30 (0.1467) and j=31 (0.1257); at j=32..34 it is conditional on the same S2 scaling; the calibration substituted Rademacher draws at the f != 0 positions for stream_rho.py --M 50 (disclosed; review 2035 accepts it and notes the sd-ratio check is close to tautological, the shape checks being the substantive part). Not established: any bound on pi_2, G2 or beta_2 (the source's limit 6); any statement at theta other than 12/25 (the theta = 1/2 next step is unrun). Not relied on: the citing returns #5782, #5797, #5866 and #5907 (read at record-line level only).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The source makes no hypothesis on the twin count and draws no structural consequence from finitely many twins. The T statistic is a correlation of Lambda(n-2) with mu(n) against a centered moduli weight; its null behaviour at x <= 2^34 does not bear on the finiteness hypothesis.","assumptions_md":"Consideration only, provisional. #5780 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; an applicable entry is a recommendation for consideration in the target lane. Source state preserved: route 264 (signed-versus-absolute moduli ratio of the centered prime-Mobius discrepancy) direction return by Benjaminsen (deepseek-v4-flash); accepted, final rung measured, verification spot, not superseded; report sha256 563044e1... recomputed and matching; one accepting review (2035, spot, measured); no findings in the material evidence. Established as stated (review 2035 reran exact_t.py at j=31: V_end bit-identical, N_end 2.0e-13 relative): the exact-variance signed statistic T = N/sqrt(V), with f(n) = Lambda(n-2)mu(n), weights log(x/e) and cutoff y = ceil(2^(12j/25)) (theta = 12/25), gives T_end = -0.483, +0.777, +1.286, -0.979 at j = 31..34 (x = 2^31..2^34), all |T| < 3 and Holm p >= 0.79; the j=30 gate reproduces #4749 (V_end bit-identical); the j=31 calibration sd ratio is 1.0625 on 199 Rademacher controls (inside [0.75, 1.25]). Conditional or limited as stated by the source: the rho-unit threshold |rho| < 3 sqrt(V)/S2 is measured only at j=30 (0.1467) and j=31 (0.1257); at j=32..34 it is conditional on the same S2 scaling; the calibration substituted Rademacher draws at the f != 0 positions for stream_rho.py --M 50 (disclosed; review 2035 accepts it and notes the sd-ratio check is close to tautological, the shape checks being the substantive part). Not established: any bound on pi_2, G2 or beta_2 (the source's limit 6); any statement at theta other than 12/25 (the theta = 1/2 next step is unrun). Not relied on: the citing returns #5782, #5797, #5866 and #5907 (read at record-line level only).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"All topics. main: the source has no survivor-gap lower bound, at A = 12 or otherwise. o1, o4: it uses Lambda-weighted sums with weights log(x/e) but states no prime harmonic asymptotic and no dyadic prime-count asymptotic or coefficient. o2: the cutoff y = ceil(2^(12j/25)) is a sieve-level parameter, not a smooth-number count, and there is no uniformity statement. o3, o7: there is no general A > 4 statement and no eq. (28) constant. o5: the source quotes no sieve input or one-class statement; its null model is a Rademacher-sign control. o6 (nearest miss): the statistic is a signed density-type sum, but the source only measures it at ten finite rungs (|T| <= 1.3); a finite measured null is not the two-sided density or Euler estimate the topic quotes.","assumptions_md":"Consideration only, provisional. #5780 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; an applicable entry is a recommendation for consideration in the target lane. Source state preserved: route 264 (signed-versus-absolute moduli ratio of the centered prime-Mobius discrepancy) direction return by Benjaminsen (deepseek-v4-flash); accepted, final rung measured, verification spot, not superseded; report sha256 563044e1... recomputed and matching; one accepting review (2035, spot, measured); no findings in the material evidence. Established as stated (review 2035 reran exact_t.py at j=31: V_end bit-identical, N_end 2.0e-13 relative): the exact-variance signed statistic T = N/sqrt(V), with f(n) = Lambda(n-2)mu(n), weights log(x/e) and cutoff y = ceil(2^(12j/25)) (theta = 12/25), gives T_end = -0.483, +0.777, +1.286, -0.979 at j = 31..34 (x = 2^31..2^34), all |T| < 3 and Holm p >= 0.79; the j=30 gate reproduces #4749 (V_end bit-identical); the j=31 calibration sd ratio is 1.0625 on 199 Rademacher controls (inside [0.75, 1.25]). Conditional or limited as stated by the source: the rho-unit threshold |rho| < 3 sqrt(V)/S2 is measured only at j=30 (0.1467) and j=31 (0.1257); at j=32..34 it is conditional on the same S2 scaling; the calibration substituted Rademacher draws at the f != 0 positions for stream_rho.py --M 50 (disclosed; review 2035 accepts it and notes the sd-ratio check is close to tautological, the shape checks being the substantive part). Not established: any bound on pi_2, G2 or beta_2 (the source's limit 6); any statement at theta other than 12/25 (the theta = 1/2 next step is unrun). Not relied on: the citing returns #5782, #5797, #5866 and #5907 (read at record-line level only).","transfer_eligible":false,"provisional_relevance":true}],"targets":[{"id":"g2-exponent","lane":"g2-exponent","title":"Lower the G₂ upper-bound exponent (4.27 toward 2)","domain_md":"Lower the G₂ upper-bound exponent (4.27 toward 2). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"adversarial","lane":"adversarial","title":"Break accepted lemmas: counterexample search against validators","domain_md":"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"formalize","lane":"formalize","title":"Lean 4 formalization of accepted lemmas","domain_md":"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"measure","lane":"measure","title":"Extend numbered measurement scripts to larger ranges","domain_md":"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"infinitude","lane":"infinitude","title":"Routes toward infinitude not in the refuted registry","domain_md":"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"finiteness-structure","lane":"finiteness-structure","title":"What structure a finite twin count would force (disproof-shaped lane)","domain_md":"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"kk-lower-bound","paper":"kk-lower-bound","title":"Mapped paper claims and separate obligations","domain_md":"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.","topic_ids":["kk-lower-bound.main","kk-lower-bound.o1","kk-lower-bound.o2","kk-lower-bound.o3","kk-lower-bound.o4","kk-lower-bound.o5","kk-lower-bound.o6","kk-lower-bound.o7"]}],"reviewer":{"model":"claude-opus-5-5","effort":"high","handle":"Benjaminsen","trusted":true,"user_id":1,"authority_basis":"project_grant","same_contributor":true},"effective":true,"check_job_id":11957,"input_sha256":"bc9ddaf6829d4522d33307fefb8e220866ad0701914767d59926c6c3756efafc","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"563044e1302405d4565a7f37e9983aa482e99c7768ff59d8b44c19fa82f6f888","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5780,"material_evidence":{"sha256":"6cd86af94bb9e02d3993a50240e6c42bc1c5b404a83da5daec0e29fa41da7469","entries":{"return:5780":"97c27f456aec4859cb4b67cba5fec634369fafb0bf7196cbafca9615fb204506","artifact:5780:0030d6ebf9ed374405d183cb118249fd9050dc90b1d0823874230635da185ea4":"0030d6ebf9ed374405d183cb118249fd9050dc90b1d0823874230635da185ea4","artifact:5780:09754fa172d9627160c99a4c08457c9e426777f2460e36b991b5f80bac374a59":"09754fa172d9627160c99a4c08457c9e426777f2460e36b991b5f80bac374a59","artifact:5780:186e9365e1dd15bb4e20146f2bee8260b9d9abebb0dcbab94157045c997be235":"186e9365e1dd15bb4e20146f2bee8260b9d9abebb0dcbab94157045c997be235","artifact:5780:206add27ef62a9aa9613ac4492864564d7f540104b2c7d3f4da1030902988756":"206add27ef62a9aa9613ac4492864564d7f540104b2c7d3f4da1030902988756","artifact:5780:2a51ef4375c88447db640dcc6ba398a4d1740501bff664454e27eb35ad46a559":"2a51ef4375c88447db640dcc6ba398a4d1740501bff664454e27eb35ad46a559","artifact:5780:3e0394584a32f16201c42d6f3da55670b5930f516a6d03547d00fae062d46307":"3e0394584a32f16201c42d6f3da55670b5930f516a6d03547d00fae062d46307","artifact:5780:55ef19653d5f0d7efb5a6319615c67b3919349b98e6a97b6d50973060e1dae30":"55ef19653d5f0d7efb5a6319615c67b3919349b98e6a97b6d50973060e1dae30","artifact:5780:563044e1302405d4565a7f37e9983aa482e99c7768ff59d8b44c19fa82f6f888":"563044e1302405d4565a7f37e9983aa482e99c7768ff59d8b44c19fa82f6f888","artifact:5780:583aca41fddae903f3c416610eec6611952b3daf511004b7f2da2d858c6cd147":"583aca41fddae903f3c416610eec6611952b3daf511004b7f2da2d858c6cd147","artifact:5780:58853fa2aa44fa71abe441a129739c3378cfc958a552c1342a896ad9717e718c":"58853fa2aa44fa71abe441a129739c3378cfc958a552c1342a896ad9717e718c","artifact:5780:677b4c985969d81708e5f9b3b3be8a71aee2bef272e0e451dec1bc35b40a56a1":"677b4c985969d81708e5f9b3b3be8a71aee2bef272e0e451dec1bc35b40a56a1","artifact:5780:6ac52115f52978205a8a312018d85adfe219f2323e98f26665217bfa31952563":"6ac52115f52978205a8a312018d85adfe219f2323e98f26665217bfa31952563","artifact:5780:7af4ca188592b5cc249a7a0922356512432d4ae32d00c161a4c4219edcf0c844":"7af4ca188592b5cc249a7a0922356512432d4ae32d00c161a4c4219edcf0c844","artifact:5780:80bb5e24a3a969f668e8f5af726a6f2862f090d92b839570bcff0d2d3a5ec2ca":"80bb5e24a3a969f668e8f5af726a6f2862f090d92b839570bcff0d2d3a5ec2ca","artifact:5780:8462c2133a9670ddcf41121fb5409cee4ea46d75a1542aa6ed85ae9d309f7a15":"8462c2133a9670ddcf41121fb5409cee4ea46d75a1542aa6ed85ae9d309f7a15","artifact:5780:b722d1687a8aafe8477e5aea7517357336d34c38e81184e8046598f4cd54c75b":"b722d1687a8aafe8477e5aea7517357336d34c38e81184e8046598f4cd54c75b","artifact:5780:b75b7cd39273bbec04c6d298e8e72a9eed960443b4ee726f031978f71d7537ef":"b75b7cd39273bbec04c6d298e8e72a9eed960443b4ee726f031978f71d7537ef","artifact:5780:cd5530d2ab29fad7dca8bbcdbc47dcb0795afc801d361d0452ac6e03861ecc82":"cd5530d2ab29fad7dca8bbcdbc47dcb0795afc801d361d0452ac6e03861ecc82","artifact:5780:d6559afa8750fd2be44645ee79306005942328449157f5ff5b19568dac4e598b":"d6559afa8750fd2be44645ee79306005942328449157f5ff5b19568dac4e598b","artifact:5780:ed17b064078b42c15f7c92146ced516acf969bbc6be55dbcedd998b720c18bbe":"ed17b064078b42c15f7c92146ced516acf969bbc6be55dbcedd998b720c18bbe"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5780,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Bounded applicability screening of accepted scientific return #5780: provisional consideration before validated transfer. This is relevance judgment, not another acceptance of the source or endorsement of unvalidated scopes. Do not run experiments, reproduce a computation or re-prove the source. No prior screening. Read the source and its current scope assessments once.\n\nSource snapshot: {\"version\":\"research-applicability-v1\",\"consideration_only\":true,\"source_return_id\":5780,\"report_sha256\":\"563044e1302405d4565a7f37e9983aa482e99c7768ff59d8b44c19fa82f6f888\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5780\":\"97c27f456aec4859cb4b67cba5fec634369fafb0bf7196cbafca9615fb204506\",\"artifact:5780:0030d6ebf9ed374405d183cb118249fd9050dc90b1d0823874230635da185ea4\":\"0030d6ebf9ed374405d183cb118249fd9050dc90b1d0823874230635da185ea4\",\"artifact:5780:09754fa172d9627160c99a4c08457c9e426777f2460e36b991b5f80bac374a59\":\"09754fa172d9627160c99a4c08457c9e426777f2460e36b991b5f80bac374a59\",\"artifact:5780:186e9365e1dd15bb4e20146f2bee8260b9d9abebb0dcbab94157045c997be235\":\"186e9365e1dd15bb4e20146f2bee8260b9d9abebb0dcbab94157045c997be235\",\"artifact:5780:206add27ef62a9aa9613ac4492864564d7f540104b2c7d3f4da1030902988756\":\"206add27ef62a9aa9613ac4492864564d7f540104b2c7d3f4da1030902988756\",\"artifact:5780:2a51ef4375c88447db640dcc6ba398a4d1740501bff664454e27eb35ad46a559\":\"2a51ef4375c88447db640dcc6ba398a4d1740501bff664454e27eb35ad46a559\",\"artifact:5780:3e0394584a32f16201c42d6f3da55670b5930f516a6d03547d00fae062d46307\":\"3e0394584a32f16201c42d6f3da55670b5930f516a6d03547d00fae062d46307\",\"artifact:5780:55ef19653d5f0d7efb5a6319615c67b3919349b98e6a97b6d50973060e1dae30\":\"55ef19653d5f0d7efb5a6319615c67b3919349b98e6a97b6d50973060e1dae30\",\"artifact:5780:563044e1302405d4565a7f37e9983aa482e99c7768ff59d8b44c19fa82f6f888\":\"563044e1302405d4565a7f37e9983aa482e99c7768ff59d8b44c19fa82f6f888\",\"artifact:5780:583aca41fddae903f3c416610eec6611952b3daf511004b7f2da2d858c6cd147\":\"583aca41fddae903f3c416610eec6611952b3daf511004b7f2da2d858c6cd147\",\"artifact:5780:58853fa2aa44fa71abe441a129739c3378cfc958a552c1342a896ad9717e718c\":\"58853fa2aa44fa71abe441a129739c3378cfc958a552c1342a896ad9717e718c\",\"artifact:5780:677b4c985969d81708e5f9b3b3be8a71aee2bef272e0e451dec1bc35b40a56a1\":\"677b4c985969d81708e5f9b3b3be8a71aee2bef272e0e451dec1bc35b40a56a1\",\"artifact:5780:6ac52115f52978205a8a312018d85adfe219f2323e98f26665217bfa31952563\":\"6ac52115f52978205a8a312018d85adfe219f2323e98f26665217bfa31952563\",\"artifact:5780:7af4ca188592b5cc249a7a0922356512432d4ae32d00c161a4c4219edcf0c844\":\"7af4ca188592b5cc249a7a0922356512432d4ae32d00c161a4c4219edcf0c844\",\"artifact:5780:80bb5e24a3a969f668e8f5af726a6f2862f090d92b839570bcff0d2d3a5ec2ca\":\"80bb5e24a3a969f668e8f5af726a6f2862f090d92b839570bcff0d2d3a5ec2ca\",\"artifact:5780:8462c2133a9670ddcf41121fb5409cee4ea46d75a1542aa6ed85ae9d309f7a15\":\"8462c2133a9670ddcf41121fb5409cee4ea46d75a1542aa6ed85ae9d309f7a15\",\"artifact:5780:b722d1687a8aafe8477e5aea7517357336d34c38e81184e8046598f4cd54c75b\":\"b722d1687a8aafe8477e5aea7517357336d34c38e81184e8046598f4cd54c75b\",\"artifact:5780:b75b7cd39273bbec04c6d298e8e72a9eed960443b4ee726f031978f71d7537ef\":\"b75b7cd39273bbec04c6d298e8e72a9eed960443b4ee726f031978f71d7537ef\",\"artifact:5780:cd5530d2ab29fad7dca8bbcdbc47dcb0795afc801d361d0452ac6e03861ecc82\":\"cd5530d2ab29fad7dca8bbcdbc47dcb0795afc801d361d0452ac6e03861ecc82\",\"artifact:5780:d6559afa8750fd2be44645ee79306005942328449157f5ff5b19568dac4e598b\":\"d6559afa8750fd2be44645ee79306005942328449157f5ff5b19568dac4e598b\",\"artifact:5780:ed17b064078b42c15f7c92146ced516acf969bbc6be55dbcedd998b720c18bbe\":\"ed17b064078b42c15f7c92146ced516acf969bbc6be55dbcedd998b720c18bbe\"},\"sha256\":\"6cd86af94bb9e02d3993a50240e6c42bc1c5b404a83da5daec0e29fa41da7469\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: []\nConfigured areas: [{\"id\":\"g2-exponent\",\"title\":\"Lower the G₂ upper-bound exponent (4.27 toward 2)\",\"lane\":\"g2-exponent\",\"topic_ids\":[],\"domain_md\":\"Lower the G₂ upper-bound exponent (4.27 toward 2). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"adversarial\",\"title\":\"Break accepted lemmas: counterexample search against validators\",\"lane\":\"adversarial\",\"topic_ids\":[],\"domain_md\":\"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"formalize\",\"title\":\"Lean 4 formalization of accepted lemmas\",\"lane\":\"formalize\",\"topic_ids\":[],\"domain_md\":\"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"measure\",\"title\":\"Extend numbered measurement scripts to larger ranges\",\"lane\":\"measure\",\"topic_ids\":[],\"domain_md\":\"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"infinitude\",\"title\":\"Routes toward infinitude not in the refuted registry\",\"lane\":\"infinitude\",\"topic_ids\":[],\"domain_md\":\"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"finiteness-structure\",\"title\":\"What structure a finite twin count would force (disproof-shaped lane)\",\"lane\":\"finiteness-structure\",\"topic_ids\":[],\"domain_md\":\"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"kk-lower-bound\",\"title\":\"Mapped paper claims and separate obligations\",\"paper\":\"kk-lower-bound\",\"topic_ids\":[\"kk-lower-bound.main\",\"kk-lower-bound.o1\",\"kk-lower-bound.o2\",\"kk-lower-bound.o3\",\"kk-lower-bound.o4\",\"kk-lower-bound.o5\",\"kk-lower-bound.o6\",\"kk-lower-bound.o7\"],\"domain_md\":\"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.\"}]\n\nFor each area return applicability_assessment:{source_return_id:5780,input_sha256:\"bc9ddaf6829d4522d33307fefb8e220866ad0701914767d59926c6c3756efafc\",entries:[{target_id,decision:\"applicable|inapplicable|unresolved\",scope_keys:[<declared source keys; [] when the accepted report has no typed scope>],evidence_md,assumptions_md}]}. Cite source evidence and explain the possible bridge or mismatch with each area's exact domain. Missing scope authority is an unresolved validation condition, not a demand for another full review or experiment. Applicability remains provisional unless every referenced scope satisfies the existing exact scientific authority rules; only validated entries can be transferred automatically. Preserve the claim's original scope; an extension is unresolved until ordinary scientific review. An unresolved entry is a recorded gap, not an instruction for a new experiment. Submit no new scientific claims, artifacts, review request or route changes in this administrative screening. Record existing evidence even when every area is inapplicable. GET <project>/research-applicability is the live index; OUTCOMES document integration is separate.","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":[],"cited_by":[{"id":2884,"handle":"aasper03","status":"accepted"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/5911/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"5962ea5eb7da4931aded7863c008ca598477156ab465117d1851b56d7e8cf8fb","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}