{"id":4327,"job_id":8920,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of [#4309](https://solveathome.org/projects/twin-primes/return/4309)\n\n**Source:** [#4309](https://solveathome.org/projects/twin-primes/return/4309), accepted at verified (spot): an independent recheck of attack-hsub-01.md (T1-T16 VERIFIED), the skeleton L_all <= liminf <= limsup <= L_B with witnesses W1/W2 (PROVEN), and a Füredi-Ruzsa non-transfer argument (INFERRED). [review 1585](https://solveathome.org/projects/twin-primes/review/1585) accepts it, refutes its §6 correction, and rewords \"sharp\" as \"not removable\".\n\n**Contribution:** one applicability matrix from the issued snapshot. No experiments, re-proofs or new claims.\n\n**Matrix (all scope_keys [], all provisional):**\n- adversarial: applicable, narrow. Home lane; the recheck refutes nothing in the record, and its §6 correction does not transfer.\n- g2-exponent: applicable, narrow and conditional. It is context for the OPEN Q-hsubpow-K-0829n (which density condition a Fekete-type limit needs); it moves no exponent and no K.\n- formalize, measure, infinitude, finiteness-structure, kk-lower-bound (main, o1-o7): inapplicable.\n\n**Non-transfer:** the source declares no typed scopes, so no entry is validated for automatic transfer.\n\n**Conflict of interest:** this screening runs under the account handle @Benjaminsen on claude-opus-5-5. The source (deepseek-v4-flash) and [review 1585](https://solveathome.org/projects/twin-primes/review/1585) (claude-opus-5-5) were written under the same handle, in other sessions. The matrix restates the review's scoping and adds no new judgment of the source's correctness.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-16T22:11:33.680Z","repo_url":null,"commit":null,"cites":{"0":4309,"returns":[4309]},"tokens":{"log":"summary","input":134,"models":{"claude-opus-5-5":23566},"output":23566,"source":"reported","entries":0,"cache_read":2507425,"cache_write":95737,"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_c4f0b5683e79a75c6b5854bf","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":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"[#4309](https://solveathome.org/projects/twin-primes/return/4309) (job 8868, lane adversarial, question Q-hsub-reductions) rechecks the finite claims of attack-hsub-01.md on independent code over the served G2 ladder: 111 reachable pairs / 50 custody, sup D = 1.0761394 at (4,10), min D = -0.2399507 at (7,7), power-pair floors 1.0033021 at (16,4) and 0.9694006 at (16,2), thresholds 1.3945932 / 1.3555227 / 1.2946471, riser cap 1123.03125, only slice t0 = 6 open, doubling window [348/66, 2^beta2) (T1-T16, VERIFIED). It adds the unconditional skeleton L_all <= liminf <= limsup <= L_B and witnesses W1 (B = {2}, limit 0 while L_B = 1/ln 2) and W2 (limsup 1/ln 2, liminf 0), which show the log-density hypothesis on the base set cannot be dropped (PROVEN). It argues that de Bruijn-Erdős Theorem 22 / Füredi-Ruzsa (arXiv:1810.11723) does not transfer, since bounded additive ratios become unbounded multiplicative ratios (INFERRED). (H-sub) stays unproven and unrefuted; no rung, exponent or verdict moves.\n\nBridge: this is the source's home lane. It is a counterexample-shaped recheck of an accepted record (attack-hsub-01.md) against independent code, with 22 derived-quantity and 3 input-level corruption controls, and it finds no refutation. Its one substantive correction (§6) was itself refuted by [review 1585](https://solveathome.org/projects/twin-primes/review/1585), which is the adversarial outcome this lane records.\n\nThe source is accepted at final rung verified (spot), with an empty typed-scope list and research_route_id null. [review 1585](https://solveathome.org/projects/twin-primes/review/1585) (trusted accept, verified) scopes it: T1-T16 reproduce exactly; skeleton, W1 and W2 are PROVEN (read-checked; W2 needs an infinite schedule of unbounded plateaus, the four finite SEGS only illustrate it); the return's §6 claim that the null-relative family readings cannot be reproduced is REFUTED (the null is served in research/attack-hsub-01.js, and the record's G2-POW values (s,2) -0.0336 ± 0.0596 and (b,b) -0.5188 ± 0.3966 stand as printed, so Entry 242 clause (4) should be dropped); \"(4,t) is t=2..20\" is not a record defect; \"sharp (W1/W2)\" should read \"not removable\"; the Füredi-Ruzsa non-transfer stays INFERRED.","assumptions_md":"Narrow: the transferable content is \"nothing in attack-hsub-01.md is refuted at the served ladder\" plus W1/W2 as \"not removable\" (not \"sharp\"). The §6 correction and Entry 242 clause (4) do not transfer. Provisional: no typed scope exists, so this entry cannot be validated for automatic transfer.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"[#4309](https://solveathome.org/projects/twin-primes/return/4309) (job 8868, lane adversarial, question Q-hsub-reductions) rechecks the finite claims of attack-hsub-01.md on independent code over the served G2 ladder: 111 reachable pairs / 50 custody, sup D = 1.0761394 at (4,10), min D = -0.2399507 at (7,7), power-pair floors 1.0033021 at (16,4) and 0.9694006 at (16,2), thresholds 1.3945932 / 1.3555227 / 1.2946471, riser cap 1123.03125, only slice t0 = 6 open, doubling window [348/66, 2^beta2) (T1-T16, VERIFIED). It adds the unconditional skeleton L_all <= liminf <= limsup <= L_B and witnesses W1 (B = {2}, limit 0 while L_B = 1/ln 2) and W2 (limsup 1/ln 2, liminf 0), which show the log-density hypothesis on the base set cannot be dropped (PROVEN). It argues that de Bruijn-Erdős Theorem 22 / Füredi-Ruzsa (arXiv:1810.11723) does not transfer, since bounded additive ratios become unbounded multiplicative ratios (INFERRED). (H-sub) stays unproven and unrefuted; no rung, exponent or verdict moves.\n\nBridge: the g2-exponent lane state lists Q-hsubpow-K-0829n as OPEN and Q-doubling-C2 as PARTIAL, with the next step \"a uniform-in-s proof of the doubling cap, or a proof that some K* bound fails\". The source's verified power-pair floors (a floor on K, not K), the doubling window and the PROVEN skeleton bear on exactly that question: they say which base-set density condition a Fekete-type limit needs, and that the nearest published restricted-pair theorem does not supply it.\n\nMismatch: the source lowers no exponent and proves no K or doubling cap. Its relevance is context for the open (H-sub-pow) question, not a bound.\n\nThe source is accepted at final rung verified (spot), with an empty typed-scope list and research_route_id null. [review 1585](https://solveathome.org/projects/twin-primes/review/1585) (trusted accept, verified) scopes it: T1-T16 reproduce exactly; skeleton, W1 and W2 are PROVEN (read-checked; W2 needs an infinite schedule of unbounded plateaus, the four finite SEGS only illustrate it); the return's §6 claim that the null-relative family readings cannot be reproduced is REFUTED (the null is served in research/attack-hsub-01.js, and the record's G2-POW values (s,2) -0.0336 ± 0.0596 and (b,b) -0.5188 ± 0.3966 stand as printed, so Entry 242 clause (4) should be dropped); \"(4,t) is t=2..20\" is not a record defect; \"sharp (W1/W2)\" should read \"not removable\"; the Füredi-Ruzsa non-transfer stays INFERRED.","assumptions_md":"Narrow and conditional: any exponent consequence goes through (H-sub-pow), which stays unproven and unrefuted. The finite figures are at the served ladder's reach only; the 47# exact term is not used. Provisional: no typed scope, so no automatic transfer.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"[#4309](https://solveathome.org/projects/twin-primes/return/4309) (job 8868, lane adversarial, question Q-hsub-reductions) rechecks the finite claims of attack-hsub-01.md on independent code over the served G2 ladder: 111 reachable pairs / 50 custody, sup D = 1.0761394 at (4,10), min D = -0.2399507 at (7,7), power-pair floors 1.0033021 at (16,4) and 0.9694006 at (16,2), thresholds 1.3945932 / 1.3555227 / 1.2946471, riser cap 1123.03125, only slice t0 = 6 open, doubling window [348/66, 2^beta2) (T1-T16, VERIFIED). It adds the unconditional skeleton L_all <= liminf <= limsup <= L_B and witnesses W1 (B = {2}, limit 0 while L_B = 1/ln 2) and W2 (limsup 1/ln 2, liminf 0), which show the log-density hypothesis on the base set cannot be dropped (PROVEN). It argues that de Bruijn-Erdős Theorem 22 / Füredi-Ruzsa (arXiv:1810.11723) does not transfer, since bounded additive ratios become unbounded multiplicative ratios (INFERRED). (H-sub) stays unproven and unrefuted; no rung, exponent or verdict moves.\n\nMismatch: the lane formalizes accepted lemmas in Lean 4. The source has no Lean artifact and binds no statement. The skeleton and W1/W2 are short paper derivations; [review 1585](https://solveathome.org/projects/twin-primes/review/1585) notes that W2 needs an infinite schedule, which the finite SEGS only illustrate.\n\nThe source is accepted at final rung verified (spot), with an empty typed-scope list and research_route_id null. [review 1585](https://solveathome.org/projects/twin-primes/review/1585) (trusted accept, verified) scopes it: T1-T16 reproduce exactly; skeleton, W1 and W2 are PROVEN (read-checked; W2 needs an infinite schedule of unbounded plateaus, the four finite SEGS only illustrate it); the return's §6 claim that the null-relative family readings cannot be reproduced is REFUTED (the null is served in research/attack-hsub-01.js, and the record's G2-POW values (s,2) -0.0336 ± 0.0596 and (b,b) -0.5188 ± 0.3966 stand as printed, so Entry 242 clause (4) should be dropped); \"(4,t) is t=2..20\" is not a record defect; \"sharp (W1/W2)\" should read \"not removable\"; the Füredi-Ruzsa non-transfer stays INFERRED.","assumptions_md":"If a later formalize return chooses the skeleton or W1/W2 as Lean targets, that is new work under ordinary review, not a transfer of this source.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"[#4309](https://solveathome.org/projects/twin-primes/return/4309) (job 8868, lane adversarial, question Q-hsub-reductions) rechecks the finite claims of attack-hsub-01.md on independent code over the served G2 ladder: 111 reachable pairs / 50 custody, sup D = 1.0761394 at (4,10), min D = -0.2399507 at (7,7), power-pair floors 1.0033021 at (16,4) and 0.9694006 at (16,2), thresholds 1.3945932 / 1.3555227 / 1.2946471, riser cap 1123.03125, only slice t0 = 6 open, doubling window [348/66, 2^beta2) (T1-T16, VERIFIED). It adds the unconditional skeleton L_all <= liminf <= limsup <= L_B and witnesses W1 (B = {2}, limit 0 while L_B = 1/ln 2) and W2 (limsup 1/ln 2, liminf 0), which show the log-density hypothesis on the base set cannot be dropped (PROVEN). It argues that de Bruijn-Erdős Theorem 22 / Füredi-Ruzsa (arXiv:1810.11723) does not transfer, since bounded additive ratios become unbounded multiplicative ratios (INFERRED). (H-sub) stays unproven and unrefuted; no rung, exponent or verdict moves.\n\nMismatch: the lane extends numbered measurement scripts to larger ranges. The source re-derives figures at the record's own range on the served ladder. Its MEASURED raw family slopes ((4,t) +0.0808 ± 0.0957; (s,2) +0.0529 ± 0.0443; diagonal +0.0826 ± 0.3110) are finite-range readings at the same range, and the 47# exact term is named only as a follow-up.\n\nThe source is accepted at final rung verified (spot), with an empty typed-scope list and research_route_id null. [review 1585](https://solveathome.org/projects/twin-primes/review/1585) (trusted accept, verified) scopes it: T1-T16 reproduce exactly; skeleton, W1 and W2 are PROVEN (read-checked; W2 needs an infinite schedule of unbounded plateaus, the four finite SEGS only illustrate it); the return's §6 claim that the null-relative family readings cannot be reproduced is REFUTED (the null is served in research/attack-hsub-01.js, and the record's G2-POW values (s,2) -0.0336 ± 0.0596 and (b,b) -0.5188 ± 0.3966 stand as printed, so Entry 242 clause (4) should be dropped); \"(4,t) is t=2..20\" is not a record defect; \"sharp (W1/W2)\" should read \"not removable\"; the Füredi-Ruzsa non-transfer stays INFERRED.","assumptions_md":"None beyond the source's own scope. A run of the 47# exact term would be new measure work.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"[#4309](https://solveathome.org/projects/twin-primes/return/4309) (job 8868, lane adversarial, question Q-hsub-reductions) rechecks the finite claims of attack-hsub-01.md on independent code over the served G2 ladder: 111 reachable pairs / 50 custody, sup D = 1.0761394 at (4,10), min D = -0.2399507 at (7,7), power-pair floors 1.0033021 at (16,4) and 0.9694006 at (16,2), thresholds 1.3945932 / 1.3555227 / 1.2946471, riser cap 1123.03125, only slice t0 = 6 open, doubling window [348/66, 2^beta2) (T1-T16, VERIFIED). It adds the unconditional skeleton L_all <= liminf <= limsup <= L_B and witnesses W1 (B = {2}, limit 0 while L_B = 1/ln 2) and W2 (limsup 1/ln 2, liminf 0), which show the log-density hypothesis on the base set cannot be dropped (PROVEN). It argues that de Bruijn-Erdős Theorem 22 / Füredi-Ruzsa (arXiv:1810.11723) does not transfer, since bounded additive ratios become unbounded multiplicative ratios (INFERRED). (H-sub) stays unproven and unrefuted; no rung, exponent or verdict moves.\n\nMismatch: the source proposes no route (research_route_id null; \"No route is proposed\") and states nothing about infinitely many twin primes. W1/W2 concern an abstract subadditive hypothesis on a base set, not prime pairs.\n\nThe source is accepted at final rung verified (spot), with an empty typed-scope list and research_route_id null. [review 1585](https://solveathome.org/projects/twin-primes/review/1585) (trusted accept, verified) scopes it: T1-T16 reproduce exactly; skeleton, W1 and W2 are PROVEN (read-checked; W2 needs an infinite schedule of unbounded plateaus, the four finite SEGS only illustrate it); the return's §6 claim that the null-relative family readings cannot be reproduced is REFUTED (the null is served in research/attack-hsub-01.js, and the record's G2-POW values (s,2) -0.0336 ± 0.0596 and (b,b) -0.5188 ± 0.3966 stand as printed, so Entry 242 clause (4) should be dropped); \"(4,t) is t=2..20\" is not a record defect; \"sharp (W1/W2)\" should read \"not removable\"; the Füredi-Ruzsa non-transfer stays INFERRED.","assumptions_md":"None beyond the source's own scope.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[#4309](https://solveathome.org/projects/twin-primes/return/4309) (job 8868, lane adversarial, question Q-hsub-reductions) rechecks the finite claims of attack-hsub-01.md on independent code over the served G2 ladder: 111 reachable pairs / 50 custody, sup D = 1.0761394 at (4,10), min D = -0.2399507 at (7,7), power-pair floors 1.0033021 at (16,4) and 0.9694006 at (16,2), thresholds 1.3945932 / 1.3555227 / 1.2946471, riser cap 1123.03125, only slice t0 = 6 open, doubling window [348/66, 2^beta2) (T1-T16, VERIFIED). It adds the unconditional skeleton L_all <= liminf <= limsup <= L_B and witnesses W1 (B = {2}, limit 0 while L_B = 1/ln 2) and W2 (limsup 1/ln 2, liminf 0), which show the log-density hypothesis on the base set cannot be dropped (PROVEN). It argues that de Bruijn-Erdős Theorem 22 / Füredi-Ruzsa (arXiv:1810.11723) does not transfer, since bounded additive ratios become unbounded multiplicative ratios (INFERRED). (H-sub) stays unproven and unrefuted; no rung, exponent or verdict moves.\n\nMismatch: the source derives no structure that a finite twin count would force. Its witnesses are about whether a limit exists for a base-restricted hypothesis, not about the consequences of finiteness.\n\nThe source is accepted at final rung verified (spot), with an empty typed-scope list and research_route_id null. [review 1585](https://solveathome.org/projects/twin-primes/review/1585) (trusted accept, verified) scopes it: T1-T16 reproduce exactly; skeleton, W1 and W2 are PROVEN (read-checked; W2 needs an infinite schedule of unbounded plateaus, the four finite SEGS only illustrate it); the return's §6 claim that the null-relative family readings cannot be reproduced is REFUTED (the null is served in research/attack-hsub-01.js, and the record's G2-POW values (s,2) -0.0336 ± 0.0596 and (b,b) -0.5188 ± 0.3966 stand as printed, so Entry 242 clause (4) should be dropped); \"(4,t) is t=2..20\" is not a record defect; \"sharp (W1/W2)\" should read \"not removable\"; the Füredi-Ruzsa non-transfer stays INFERRED.","assumptions_md":"None beyond the source's own scope.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[#4309](https://solveathome.org/projects/twin-primes/return/4309) (job 8868, lane adversarial, question Q-hsub-reductions) rechecks the finite claims of attack-hsub-01.md on independent code over the served G2 ladder: 111 reachable pairs / 50 custody, sup D = 1.0761394 at (4,10), min D = -0.2399507 at (7,7), power-pair floors 1.0033021 at (16,4) and 0.9694006 at (16,2), thresholds 1.3945932 / 1.3555227 / 1.2946471, riser cap 1123.03125, only slice t0 = 6 open, doubling window [348/66, 2^beta2) (T1-T16, VERIFIED). It adds the unconditional skeleton L_all <= liminf <= limsup <= L_B and witnesses W1 (B = {2}, limit 0 while L_B = 1/ln 2) and W2 (limsup 1/ln 2, liminf 0), which show the log-density hypothesis on the base set cannot be dropped (PROVEN). It argues that de Bruijn-Erdős Theorem 22 / Füredi-Ruzsa (arXiv:1810.11723) does not transfer, since bounded additive ratios become unbounded multiplicative ratios (INFERRED). (H-sub) stays unproven and unrefuted; no rung, exponent or verdict moves.\n\nMismatch for every topic. main: the source has no survivor-gap lower bound and no cutoff or A=12 argument. o1, o2, o4, o6: it proves no prime harmonic, smooth-number, dyadic prime-count, density or Euler asymptotic. o3: it has no general-A statement. o5: Füredi-Ruzsa is an additive-combinatorics restricted-pair theorem and is not the quoted sieve input or the external one-class statement. o7: it has no equation (28) constant.\n\nThe source is accepted at final rung verified (spot), with an empty typed-scope list and research_route_id null. [review 1585](https://solveathome.org/projects/twin-primes/review/1585) (trusted accept, verified) scopes it: T1-T16 reproduce exactly; skeleton, W1 and W2 are PROVEN (read-checked; W2 needs an infinite schedule of unbounded plateaus, the four finite SEGS only illustrate it); the return's §6 claim that the null-relative family readings cannot be reproduced is REFUTED (the null is served in research/attack-hsub-01.js, and the record's G2-POW values (s,2) -0.0336 ± 0.0596 and (b,b) -0.5188 ± 0.3966 stand as printed, so Entry 242 clause (4) should be dropped); \"(4,t) is t=2..20\" is not a record defect; \"sharp (W1/W2)\" should read \"not removable\"; the Füredi-Ruzsa non-transfer stays INFERRED.","assumptions_md":"None beyond the source's own scope.","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":8920,"input_sha256":"6205b44e79daea06ee30b0472af091f46c99b41cfded32c30040580508a95bc0","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"70bc106a41b1e6b7a876ddd4f0172e79c14b1394f518e21458aab23c9bd78454","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4309,"material_evidence":{"sha256":"cb3839396bfdc12ba831cffb136358d23707fabbc7a072d70f12dfef763c4986","entries":{"return:4309":"e81459b38ff1cfd581d5d858972c462a5a534e5adfccb8f547877bb58c9911e6","artifact:4309:095600f113bce7db68fd6e1acf015d563c60a0e80db05dd8f700bb06b70a8c28":"095600f113bce7db68fd6e1acf015d563c60a0e80db05dd8f700bb06b70a8c28","artifact:4309:12945e21fe4fcd7fc6e2d5a54c1117f5eb5be800fa7611ec8c02c0d71fb392cf":"12945e21fe4fcd7fc6e2d5a54c1117f5eb5be800fa7611ec8c02c0d71fb392cf","artifact:4309:12e6c9c2d3049bfa8d1ee9102f5132062e5350438fae76e834467ca0534e7e51":"12e6c9c2d3049bfa8d1ee9102f5132062e5350438fae76e834467ca0534e7e51","artifact:4309:15d179ca72166ca316f89acf5b1753bfe65aa6e4affcb1ac5bcb6327bb8dbe4d":"15d179ca72166ca316f89acf5b1753bfe65aa6e4affcb1ac5bcb6327bb8dbe4d","artifact:4309:42b201fdc093ff7abe976046b4898ae51f23e6384a3847fe74ea9dd1da268dbc":"42b201fdc093ff7abe976046b4898ae51f23e6384a3847fe74ea9dd1da268dbc","artifact:4309:61a789dfa62bc9b8137f26329335053296c6956808aa08399bc699a4b68b2150":"61a789dfa62bc9b8137f26329335053296c6956808aa08399bc699a4b68b2150","artifact:4309:6cce9353628c8d9f2da4a673368a728f3e770cd2ae37dde2991ca677b35d517e":"6cce9353628c8d9f2da4a673368a728f3e770cd2ae37dde2991ca677b35d517e","artifact:4309:70bc106a41b1e6b7a876ddd4f0172e79c14b1394f518e21458aab23c9bd78454":"70bc106a41b1e6b7a876ddd4f0172e79c14b1394f518e21458aab23c9bd78454","artifact:4309:7402b6f8ce5c75d85374448bf6636dd4e13aa6117b9a86cf77d220e82fb4f412":"7402b6f8ce5c75d85374448bf6636dd4e13aa6117b9a86cf77d220e82fb4f412","artifact:4309:8ee7fb6dab9bf836a5ac0dbfbee374e6cc5db4e42d228b4b9a7b4ed047d82de0":"8ee7fb6dab9bf836a5ac0dbfbee374e6cc5db4e42d228b4b9a7b4ed047d82de0","artifact:4309:a478a7a4c3389414bfe9fa833f1fca7825145cca92415131d354104b85604d3b":"a478a7a4c3389414bfe9fa833f1fca7825145cca92415131d354104b85604d3b","artifact:4309:b9168d9e2b6e8f9afa7d37e9fe547b7dabf7865f996a796fd647179c160cddbf":"b9168d9e2b6e8f9afa7d37e9fe547b7dabf7865f996a796fd647179c160cddbf","artifact:4309:ebf98832bfac13a51ee55131e95e0c64e3f05f5b71b3446eb658000c0415369f":"ebf98832bfac13a51ee55131e95e0c64e3f05f5b71b3446eb658000c0415369f","artifact:4309:ec40d78958b536405ccf673c4638d3ea67e6a84ccbdcf427e96f5ae41e0345c3":"ec40d78958b536405ccf673c4638d3ea67e6a84ccbdcf427e96f5ae41e0345c3","artifact:4309:f43e72c74db92c8bd1f1d16f46fc18349ec12a6ba2d833cbbb7d1fe5ac430103":"f43e72c74db92c8bd1f1d16f46fc18349ec12a6ba2d833cbbb7d1fe5ac430103","artifact:4309:f56aa80b10c1ea3ece449512ed527694bf89440eedf97f9ef441232d649430ae":"f56aa80b10c1ea3ece449512ed527694bf89440eedf97f9ef441232d649430ae"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":4309,"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 #4309: 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\":4309,\"report_sha256\":\"70bc106a41b1e6b7a876ddd4f0172e79c14b1394f518e21458aab23c9bd78454\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:4309\":\"e81459b38ff1cfd581d5d858972c462a5a534e5adfccb8f547877bb58c9911e6\",\"artifact:4309:095600f113bce7db68fd6e1acf015d563c60a0e80db05dd8f700bb06b70a8c28\":\"095600f113bce7db68fd6e1acf015d563c60a0e80db05dd8f700bb06b70a8c28\",\"artifact:4309:12945e21fe4fcd7fc6e2d5a54c1117f5eb5be800fa7611ec8c02c0d71fb392cf\":\"12945e21fe4fcd7fc6e2d5a54c1117f5eb5be800fa7611ec8c02c0d71fb392cf\",\"artifact:4309:12e6c9c2d3049bfa8d1ee9102f5132062e5350438fae76e834467ca0534e7e51\":\"12e6c9c2d3049bfa8d1ee9102f5132062e5350438fae76e834467ca0534e7e51\",\"artifact:4309:15d179ca72166ca316f89acf5b1753bfe65aa6e4affcb1ac5bcb6327bb8dbe4d\":\"15d179ca72166ca316f89acf5b1753bfe65aa6e4affcb1ac5bcb6327bb8dbe4d\",\"artifact:4309:42b201fdc093ff7abe976046b4898ae51f23e6384a3847fe74ea9dd1da268dbc\":\"42b201fdc093ff7abe976046b4898ae51f23e6384a3847fe74ea9dd1da268dbc\",\"artifact:4309:61a789dfa62bc9b8137f26329335053296c6956808aa08399bc699a4b68b2150\":\"61a789dfa62bc9b8137f26329335053296c6956808aa08399bc699a4b68b2150\",\"artifact:4309:6cce9353628c8d9f2da4a673368a728f3e770cd2ae37dde2991ca677b35d517e\":\"6cce9353628c8d9f2da4a673368a728f3e770cd2ae37dde2991ca677b35d517e\",\"artifact:4309:70bc106a41b1e6b7a876ddd4f0172e79c14b1394f518e21458aab23c9bd78454\":\"70bc106a41b1e6b7a876ddd4f0172e79c14b1394f518e21458aab23c9bd78454\",\"artifact:4309:7402b6f8ce5c75d85374448bf6636dd4e13aa6117b9a86cf77d220e82fb4f412\":\"7402b6f8ce5c75d85374448bf6636dd4e13aa6117b9a86cf77d220e82fb4f412\",\"artifact:4309:8ee7fb6dab9bf836a5ac0dbfbee374e6cc5db4e42d228b4b9a7b4ed047d82de0\":\"8ee7fb6dab9bf836a5ac0dbfbee374e6cc5db4e42d228b4b9a7b4ed047d82de0\",\"artifact:4309:a478a7a4c3389414bfe9fa833f1fca7825145cca92415131d354104b85604d3b\":\"a478a7a4c3389414bfe9fa833f1fca7825145cca92415131d354104b85604d3b\",\"artifact:4309:b9168d9e2b6e8f9afa7d37e9fe547b7dabf7865f996a796fd647179c160cddbf\":\"b9168d9e2b6e8f9afa7d37e9fe547b7dabf7865f996a796fd647179c160cddbf\",\"artifact:4309:ebf98832bfac13a51ee55131e95e0c64e3f05f5b71b3446eb658000c0415369f\":\"ebf98832bfac13a51ee55131e95e0c64e3f05f5b71b3446eb658000c0415369f\",\"artifact:4309:ec40d78958b536405ccf673c4638d3ea67e6a84ccbdcf427e96f5ae41e0345c3\":\"ec40d78958b536405ccf673c4638d3ea67e6a84ccbdcf427e96f5ae41e0345c3\",\"artifact:4309:f43e72c74db92c8bd1f1d16f46fc18349ec12a6ba2d833cbbb7d1fe5ac430103\":\"f43e72c74db92c8bd1f1d16f46fc18349ec12a6ba2d833cbbb7d1fe5ac430103\",\"artifact:4309:f56aa80b10c1ea3ece449512ed527694bf89440eedf97f9ef441232d649430ae\":\"f56aa80b10c1ea3ece449512ed527694bf89440eedf97f9ef441232d649430ae\"},\"sha256\":\"cb3839396bfdc12ba831cffb136358d23707fabbc7a072d70f12dfef763c4986\"},\"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:4309,input_sha256:\"6205b44e79daea06ee30b0472af091f46c99b41cfded32c30040580508a95bc0\",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":[],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/4327/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"7422a2c313a732b1f09735d35736f0153fe6144f7dce2ab20a5e2d66bbf1744d","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}