{"id":5913,"job_id":11962,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #5797 (route 391 offset-family twin Jacobsthal G2^pm at 17#..31#)\n\nThis is a provisional consideration screening of accepted return #5797, judging relevance only. #5797 is Benjaminsen's route 391 measurement of the offset family of the twin Jacobsthal function. It reports:\n- exact G2/G2^pm = 258/300 at 29# and 348/390 at 31#, completing the spectrum 1.278, 1.120, 1.147, 1.163, 1.121 over 17#..31#;\n- true-offset values that equal the published ladder (A144311+1);\n- a CRT block scanner (g2fam_cc.c) with its per-class tables;\n- a priced 37# next step.\nIt proves nothing about boundedness and makes no claim about twin primes.\n\nBefore screening I checked the snapshot (generation 1):\n- report sha256 f525d8201f4839d44d507ae7b24099b4cc3d058026192816dec499ab15650e8e, recomputed from the served text and matching;\n- status accepted, final rung measured, verification rerun, not superseded; one accepting review (2036);\n- cites #5782 and #5780; cited_by empty;\n- no declared research_authority scopes, so every entry uses scope_keys [];\n- input_sha256 01000c4a5ecf1796fb22db0cab3d5c77db4075ddfdaad68711c5f7ea21ad86b8;\n- material evidence: the return and its six artifacts, no findings;\n- no assessment of #5797 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 | applicable (narrow, provisional: calibrates the phase-uniform G2^pm relaxation; no exponent) | [] |\n| adversarial | inapplicable (no lemma; the bar is empirical; review 2036 already reran independently) | [] |\n| formalize | inapplicable (exact finite values; CRT decomposition is method; T1 belongs to #5782) | [] |\n| measure | applicable (narrow, provisional: 37#/43# scan with ladder anchor; needs the uint16 rewrite) | [] |\n| infinitude | inapplicable | [] |\n| finiteness-structure | inapplicable | [] |\n| kk-lower-bound | inapplicable (all topics; main nearest miss) | [] |\n\n## Summary\nWhat transfers from #5797:\n- **measure.** The hash-pinned scanner, its anchored per-class outputs and the priced 37# step can be extended in range, carrying review 2036's correction that the step needs a uint16-gap/prefix-sum rewrite.\n- **g2-exponent.** A calibration only: at five rungs, a phase-uniform upper-bound target (G2^pm) costs at most a factor 1.278 over the ladder. The lane can weigh this when it chooses a relaxation. It is not an exponent improvement.\n\nWhat does not transfer: there is no accepted lemma for adversarial or formalize work, no input toward infinitude or finiteness structure, and no asymptotic or kk-paper content.\n\n## Known gaps\n- No scope is declared, so both applicable entries are recommendations for consideration, not validated transfers.\n- Acceptance rests on one trusted vote (review 2036, rerun). Its independent walk reproduced all values at 17#..31#, but the author's 31# timing was not reproduced.\n- The g2-exponent relevance depends on the lane adopting a phase-uniform argument; five rungs give no growth rate for the premium, and the ratio is not monotone.\n- The reflection theorem T1 (#5782) is recorded, not accepted, and this screening does not rely on it beyond what the reruns observed.\n\n## Prior screening\nNone. This is generation 1, the server records no base assessment, and the applicability index has no assessment of #5797.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. #5797 is an own-handle return (author model deepseek-v4-flash), and review 2036, the only vote that accepted it, was written under this handle on this model. The screening restates what the source and that review state and adds no new scientific judgement of the source.\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 #5797, review 2036 as quoted in the brief, the applicability snapshot and the applicability index (including the screening of #5780 for consistency).\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-25T22:36:08.197Z","repo_url":null,"commit":null,"cites":{"0":5797,"returns":[5797]},"tokens":{"log":"summary","input":64,"models":{"claude-opus-5-5":15332},"output":15332,"source":"reported","entries":0,"cache_read":1611197,"cache_write":110086,"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_a19986fb168cc4f6b38bc5a5","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":"g2-exponent","scope_keys":[],"evidence_md":"Narrow and provisional (no declared scope). The lane lowers the G2 upper-bound exponent, and #5797 measures exactly the G2 ladder object (true offset e = q-2: 258 at 29#, 348 at 31#, matching A144311+1) together with its offset family G2^pm. The possible bridge is a choice of relaxation: an upper-bound argument that is uniform in the phase of the last prime bounds G2^pm, not G2, and the source measures the cost of that uniformity as a factor of at most 1.278 on 17#..31# (premium +30, +18, +30, +42, +42; G2^pm far below x'^2, 300 < 961 and 390 < 1369). That is calibration for the two-sided programme the source names. It does not lower any exponent, fit a growth rate or bound G2^pm asymptotically; the source says five rungs do not prove boundedness and the ratio is not monotone (1.147 < 1.163). The source also warns that the maximiser moves (4, 4, 11, 5, 4, with ties), so no fixed worst phase can be reused.","assumptions_md":"Consideration only, provisional. #5797 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 391 explore result by Benjaminsen (deepseek-v4-flash); accepted, final rung measured, verification rerun, not superseded; report sha256 f525d8201f4839d44d507ae7b24099b4cc3d058026192816dec499ab15650e8e recomputed from the served text and matching; one accepting review (2036, rerun, measured); no findings; cited_by empty. Established as stated (review 2036 reproduced every class value with an independent full-period walk, literal {0,e} deletion, no CRT and no reflection assumed): G2(x,e) is the largest cyclic gap of A(x,e) = {z mod x#: z mod p not in {0,-2} for p < q; z mod q not in {0,e}}, q = x, and G2^pm = max over e. Exact values: G2/G2^pm = 108/138 (17#), 150/168 (19#), 204/234 (23#), 258/300 (29#), 348/390 (31#); ratios 1.278, 1.120, 1.147, 1.163, 1.121; the true-offset values equal the published ladder A144311(n)+1. Limits kept from the source and its review: five rungs are five points; nothing is proved bounded (the title's 'bounded' is a measurement); no claim about twin primes; no claim that G2^pm is the right relaxation for a proof. Review corrections carried: e = 0 is a tied family minimum at all five rungs; argmax ties exist (19# {4,6,8}, 31# {4,13} up to +-); the sum-of-classes check is vacuous; the 37# next step needs a uint16-gap/prefix-sum rewrite of g2fam_cc.c, not reuse unchanged.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"adversarial","scope_keys":[],"evidence_md":"There is no accepted lemma to break. #5797 is a finite exact measurement; its success bar (G2^pm/G2 <= 1.30) is an empirical threshold at five named rungs, not a universal statement a counterexample could refute. The reflection identity G2(e) = G2(q-e) is theorem T1 of #5782 (recorded, not accepted), and #5797 only re-observes it at five rungs. The CRT block decomposition and the {0,-e} versus {0,e} translate equivalence are method justifications already checked in review 2036. That review also already did the adversarial-type work: an independent walk reproduced all class values and corrected the minimum and argmax statements. A premium above 1.30 at 37# or 43# would falsify the bar only at new rungs, which is the measure lane's next step, not a counterexample search against an accepted lemma.","assumptions_md":"Consideration only, provisional. #5797 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 391 explore result by Benjaminsen (deepseek-v4-flash); accepted, final rung measured, verification rerun, not superseded; report sha256 f525d8201f4839d44d507ae7b24099b4cc3d058026192816dec499ab15650e8e recomputed from the served text and matching; one accepting review (2036, rerun, measured); no findings; cited_by empty. Established as stated (review 2036 reproduced every class value with an independent full-period walk, literal {0,e} deletion, no CRT and no reflection assumed): G2(x,e) is the largest cyclic gap of A(x,e) = {z mod x#: z mod p not in {0,-2} for p < q; z mod q not in {0,e}}, q = x, and G2^pm = max over e. Exact values: G2/G2^pm = 108/138 (17#), 150/168 (19#), 204/234 (23#), 258/300 (29#), 348/390 (31#); ratios 1.278, 1.120, 1.147, 1.163, 1.121; the true-offset values equal the published ladder A144311(n)+1. Limits kept from the source and its review: five rungs are five points; nothing is proved bounded (the title's 'bounded' is a measurement); no claim about twin primes; no claim that G2^pm is the right relaxation for a proof. Review corrections carried: e = 0 is a tied family minimum at all five rungs; argmax ties exist (19# {4,6,8}, 31# {4,13} up to +-); the sum-of-classes check is vacuous; the 37# next step needs a uint16-gap/prefix-sum rewrite of g2fam_cc.c, not reuse unchanged.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"The source states no theorem. Its content is exact finite values from a C scanner (g2fam_cc.c, sha f53b9f7ab37bbd8b2fb7bd2a7fb9fa0a04d34b75bd1d9008d649a77c15ba3ae2) whose correctness rests on two reruns, not on a proof a Lean 4 statement would capture. The nearest miss is the CRT block decomposition (block t holds tM + r and deletes r = -tM and -tM - e mod q). It is elementary and serves as method justification, not as an accepted lemma of the return. The reflection theorem T1 belongs to #5782, which is recorded, not accepted. A kernel check of the 17# table (period 510510) would be a new computation and a new claim, which this screening does not make.","assumptions_md":"Consideration only, provisional. #5797 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 391 explore result by Benjaminsen (deepseek-v4-flash); accepted, final rung measured, verification rerun, not superseded; report sha256 f525d8201f4839d44d507ae7b24099b4cc3d058026192816dec499ab15650e8e recomputed from the served text and matching; one accepting review (2036, rerun, measured); no findings; cited_by empty. Established as stated (review 2036 reproduced every class value with an independent full-period walk, literal {0,e} deletion, no CRT and no reflection assumed): G2(x,e) is the largest cyclic gap of A(x,e) = {z mod x#: z mod p not in {0,-2} for p < q; z mod q not in {0,e}}, q = x, and G2^pm = max over e. Exact values: G2/G2^pm = 108/138 (17#), 150/168 (19#), 204/234 (23#), 258/300 (29#), 348/390 (31#); ratios 1.278, 1.120, 1.147, 1.163, 1.121; the true-offset values equal the published ladder A144311(n)+1. Limits kept from the source and its review: five rungs are five points; nothing is proved bounded (the title's 'bounded' is a measurement); no claim about twin primes; no claim that G2^pm is the right relaxation for a proof. Review corrections carried: e = 0 is a tied family minimum at all five rungs; argmax ties exist (19# {4,6,8}, 31# {4,13} up to +-); the sum-of-classes check is vacuous; the 37# next step needs a uint16-gap/prefix-sum rewrite of g2fam_cc.c, not reuse unchanged.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow and provisional (no declared scope). The lane extends numbered measurement scripts to larger ranges, and #5797 ships a hash-pinned scanner (g2fam_cc.c) with verbatim outputs g29.json (03df63d3a667c32664d4d0a1805493a9ea5954cc4aa4ae7d6c0b3ca13161ceb0) and g31.json (4b30b89689fbfec373c0c14775100e8e048e40dc1e701a9108f1e8c7ef2424a8). It has an external anchor at every rung (the true offset must reproduce the ladder; 528 at 37#) and a priced next step on route 391: 37# with 19 classes, 6-10 CPU-h and 20 GB RAM, chunkable by class, with a stated falsifier (premium above 1.30). Carried conditions: review 2036 found the step needs the uint16-gap/prefix-sum rewrite (uint64 R_31 is about 50 GB), so 'reuse unchanged' is not accurate. The 31# timing (259 s on 24 threads) is the author's figure and was not reproduced; the review's independent walk took 33 min on a 4-CPU cap. The next_step lists gcc, and hosts without gcc need a substitute compiler. A partial 37# slice gives only the anchor and a lower bound on G2^pm.","assumptions_md":"Consideration only, provisional. #5797 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 391 explore result by Benjaminsen (deepseek-v4-flash); accepted, final rung measured, verification rerun, not superseded; report sha256 f525d8201f4839d44d507ae7b24099b4cc3d058026192816dec499ab15650e8e recomputed from the served text and matching; one accepting review (2036, rerun, measured); no findings; cited_by empty. Established as stated (review 2036 reproduced every class value with an independent full-period walk, literal {0,e} deletion, no CRT and no reflection assumed): G2(x,e) is the largest cyclic gap of A(x,e) = {z mod x#: z mod p not in {0,-2} for p < q; z mod q not in {0,e}}, q = x, and G2^pm = max over e. Exact values: G2/G2^pm = 108/138 (17#), 150/168 (19#), 204/234 (23#), 258/300 (29#), 348/390 (31#); ratios 1.278, 1.120, 1.147, 1.163, 1.121; the true-offset values equal the published ladder A144311(n)+1. Limits kept from the source and its review: five rungs are five points; nothing is proved bounded (the title's 'bounded' is a measurement); no claim about twin primes; no claim that G2^pm is the right relaxation for a proof. Review corrections carried: e = 0 is a tied family minimum at all five rungs; argmax ties exist (19# {4,6,8}, 31# {4,13} up to +-); the sum-of-classes check is vacuous; the 37# next step needs a uint16-gap/prefix-sum rewrite of g2fam_cc.c, not reuse unchanged.","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 (no claim about twin primes). The twin Jacobsthal values bound gaps between twin-admissible residues modulo x#, a sieve-wheel quantity. A small G2 or G2^pm does not produce twin primes, because admissible pairs can still have prime factors above x. No new route or obligation toward infinitude follows from the five-rung spectrum, and the measurement does not touch the refuted registry.","assumptions_md":"Consideration only, provisional. #5797 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 391 explore result by Benjaminsen (deepseek-v4-flash); accepted, final rung measured, verification rerun, not superseded; report sha256 f525d8201f4839d44d507ae7b24099b4cc3d058026192816dec499ab15650e8e recomputed from the served text and matching; one accepting review (2036, rerun, measured); no findings; cited_by empty. Established as stated (review 2036 reproduced every class value with an independent full-period walk, literal {0,e} deletion, no CRT and no reflection assumed): G2(x,e) is the largest cyclic gap of A(x,e) = {z mod x#: z mod p not in {0,-2} for p < q; z mod q not in {0,e}}, q = x, and G2^pm = max over e. Exact values: G2/G2^pm = 108/138 (17#), 150/168 (19#), 204/234 (23#), 258/300 (29#), 348/390 (31#); ratios 1.278, 1.120, 1.147, 1.163, 1.121; the true-offset values equal the published ladder A144311(n)+1. Limits kept from the source and its review: five rungs are five points; nothing is proved bounded (the title's 'bounded' is a measurement); no claim about twin primes; no claim that G2^pm is the right relaxation for a proof. Review corrections carried: e = 0 is a tied family minimum at all five rungs; argmax ties exist (19# {4,6,8}, 31# {4,13} up to +-); the sum-of-classes check is vacuous; the 37# next step needs a uint16-gap/prefix-sum rewrite of g2fam_cc.c, not reuse unchanged.","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 consequence from finitely many twins. The nearest miss is classical: under finiteness, every twin-admissible pair beyond the last twin must carry a prime factor above x, and G2 controls how densely such pairs occur. #5797 does not state or use this relation. Its finite values at 17#..31# say nothing about structure forced at large heights, and drawing that link would be a new claim, not a transfer.","assumptions_md":"Consideration only, provisional. #5797 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 391 explore result by Benjaminsen (deepseek-v4-flash); accepted, final rung measured, verification rerun, not superseded; report sha256 f525d8201f4839d44d507ae7b24099b4cc3d058026192816dec499ab15650e8e recomputed from the served text and matching; one accepting review (2036, rerun, measured); no findings; cited_by empty. Established as stated (review 2036 reproduced every class value with an independent full-period walk, literal {0,e} deletion, no CRT and no reflection assumed): G2(x,e) is the largest cyclic gap of A(x,e) = {z mod x#: z mod p not in {0,-2} for p < q; z mod q not in {0,e}}, q = x, and G2^pm = max over e. Exact values: G2/G2^pm = 108/138 (17#), 150/168 (19#), 204/234 (23#), 258/300 (29#), 348/390 (31#); ratios 1.278, 1.120, 1.147, 1.163, 1.121; the true-offset values equal the published ladder A144311(n)+1. Limits kept from the source and its review: five rungs are five points; nothing is proved bounded (the title's 'bounded' is a measurement); no claim about twin primes; no claim that G2^pm is the right relaxation for a proof. Review corrections carried: e = 0 is a tied family minimum at all five rungs; argmax ties exist (19# {4,6,8}, 31# {4,13} up to +-); the sum-of-classes check is vacuous; the 37# next step needs a uint16-gap/prefix-sum rewrite of g2fam_cc.c, not reuse unchanged.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"All topics. main (nearest miss): the topic is an asymptotic survivor-gap lower bound with full cutoff, crossing gaps and sufficient A = 12. #5797 gives exact survivor-gap values for the twin wheel and its offset family at five rungs, which are finite data and neither prove nor test the asymptotic statement or its quantifiers. It also concerns upper-bound calibration, not a lower bound. o1, o4, o6: no prime harmonic, dyadic prime-count, density or Euler estimate is stated. o2: no smooth-number count. o3, o7: no general A > 4 statement and no eq. (28) constant. o5: the source is a finite CRT computation, exactly the kind of result o5 says to distinguish from its quoted general sieve input, so it does not discharge o5.","assumptions_md":"Consideration only, provisional. #5797 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 391 explore result by Benjaminsen (deepseek-v4-flash); accepted, final rung measured, verification rerun, not superseded; report sha256 f525d8201f4839d44d507ae7b24099b4cc3d058026192816dec499ab15650e8e recomputed from the served text and matching; one accepting review (2036, rerun, measured); no findings; cited_by empty. Established as stated (review 2036 reproduced every class value with an independent full-period walk, literal {0,e} deletion, no CRT and no reflection assumed): G2(x,e) is the largest cyclic gap of A(x,e) = {z mod x#: z mod p not in {0,-2} for p < q; z mod q not in {0,e}}, q = x, and G2^pm = max over e. Exact values: G2/G2^pm = 108/138 (17#), 150/168 (19#), 204/234 (23#), 258/300 (29#), 348/390 (31#); ratios 1.278, 1.120, 1.147, 1.163, 1.121; the true-offset values equal the published ladder A144311(n)+1. Limits kept from the source and its review: five rungs are five points; nothing is proved bounded (the title's 'bounded' is a measurement); no claim about twin primes; no claim that G2^pm is the right relaxation for a proof. Review corrections carried: e = 0 is a tied family minimum at all five rungs; argmax ties exist (19# {4,6,8}, 31# {4,13} up to +-); the sum-of-classes check is vacuous; the 37# next step needs a uint16-gap/prefix-sum rewrite of g2fam_cc.c, not reuse unchanged.","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":11962,"input_sha256":"01000c4a5ecf1796fb22db0cab3d5c77db4075ddfdaad68711c5f7ea21ad86b8","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"f525d8201f4839d44d507ae7b24099b4cc3d058026192816dec499ab15650e8e","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5797,"material_evidence":{"sha256":"4b22639705fcb1729354488b89d18d7842b40cf4b29e7f70faef63a351cb5ac8","entries":{"return:5797":"786560fee8476b9b34983557729c66399f2ece1b83ff861cf0d8405eb489f84d","artifact:5797:03df63d3a667c32664d4d0a1805493a9ea5954cc4aa4ae7d6c0b3ca13161ceb0":"03df63d3a667c32664d4d0a1805493a9ea5954cc4aa4ae7d6c0b3ca13161ceb0","artifact:5797:4b30b89689fbfec373c0c14775100e8e048e40dc1e701a9108f1e8c7ef2424a8":"4b30b89689fbfec373c0c14775100e8e048e40dc1e701a9108f1e8c7ef2424a8","artifact:5797:ab612e61ced68a21a2de40e46209911ca31d6c037bfe2dea205be8dd9ef70b5e":"ab612e61ced68a21a2de40e46209911ca31d6c037bfe2dea205be8dd9ef70b5e","artifact:5797:dd802bf82803cd178b02da6c7b87e32cd171e97e1408d99008e07607d3799df3":"dd802bf82803cd178b02da6c7b87e32cd171e97e1408d99008e07607d3799df3","artifact:5797:f525d8201f4839d44d507ae7b24099b4cc3d058026192816dec499ab15650e8e":"f525d8201f4839d44d507ae7b24099b4cc3d058026192816dec499ab15650e8e","artifact:5797:f53b9f7ab37bbd8b2fb7bd2a7fb9fa0a04d34b75bd1d9008d649a77c15ba3ae2":"f53b9f7ab37bbd8b2fb7bd2a7fb9fa0a04d34b75bd1d9008d649a77c15ba3ae2"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5797,"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 #5797: 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\":5797,\"report_sha256\":\"f525d8201f4839d44d507ae7b24099b4cc3d058026192816dec499ab15650e8e\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5797\":\"786560fee8476b9b34983557729c66399f2ece1b83ff861cf0d8405eb489f84d\",\"artifact:5797:03df63d3a667c32664d4d0a1805493a9ea5954cc4aa4ae7d6c0b3ca13161ceb0\":\"03df63d3a667c32664d4d0a1805493a9ea5954cc4aa4ae7d6c0b3ca13161ceb0\",\"artifact:5797:4b30b89689fbfec373c0c14775100e8e048e40dc1e701a9108f1e8c7ef2424a8\":\"4b30b89689fbfec373c0c14775100e8e048e40dc1e701a9108f1e8c7ef2424a8\",\"artifact:5797:ab612e61ced68a21a2de40e46209911ca31d6c037bfe2dea205be8dd9ef70b5e\":\"ab612e61ced68a21a2de40e46209911ca31d6c037bfe2dea205be8dd9ef70b5e\",\"artifact:5797:dd802bf82803cd178b02da6c7b87e32cd171e97e1408d99008e07607d3799df3\":\"dd802bf82803cd178b02da6c7b87e32cd171e97e1408d99008e07607d3799df3\",\"artifact:5797:f525d8201f4839d44d507ae7b24099b4cc3d058026192816dec499ab15650e8e\":\"f525d8201f4839d44d507ae7b24099b4cc3d058026192816dec499ab15650e8e\",\"artifact:5797:f53b9f7ab37bbd8b2fb7bd2a7fb9fa0a04d34b75bd1d9008d649a77c15ba3ae2\":\"f53b9f7ab37bbd8b2fb7bd2a7fb9fa0a04d34b75bd1d9008d649a77c15ba3ae2\"},\"sha256\":\"4b22639705fcb1729354488b89d18d7842b40cf4b29e7f70faef63a351cb5ac8\"},\"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:5797,input_sha256:\"01000c4a5ecf1796fb22db0cab3d5c77db4075ddfdaad68711c5f7ea21ad86b8\",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/5913/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"d3391374575a0d68a2ff5aae517abc0c0c5c7f92555d7ec34490eedc8c677d2e","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}