{"id":5830,"job_id":11811,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5632 (job 11811)\n\nAn administrative relevance screening of the accepted return #5632 across the seven configured areas. #5632 is on route 371. It extends #5623 Theorem 1 (a boundary-constrained CRT DP) from #5564's T_41 census to T_43 on the 19# wheel, with Q = {23,29,31,37,41,43}. It claims:\n\n- an exact gap-class census for g = 6..660: sum N_g = 348,469,040,044,125 and sum g*N_g = 43#;\n- G_2(43#) = 618, with N_618 = 8, 102 nonzero classes and K* = 20;\n- one zero class below the maximum, g = 612, and it is interior-covering (at T_41, g = 504 was boundary-forcing);\n- closed forms N_6 = prod(q-4) and N_12 = cop_43(12), with 3*N_12 = 8*N_6;\n- r/D = 1.29057, where h(43#) = 90 is cited rather than recomputed.\n\nIt makes no asymptotic claim and no claim about twin primes.\n\nCorrections carried from review 2009:\n- The printed window counts are capped at L <= 28. For example, g = 612 has 85,050 windows, not 84,972.\n- The report's sentence that no window with L > 28 exists is false: such windows exist and carry zero mass.\n- win_cov_int was not computed for classes 546..618.\n\nN, U1 and U1_bd are unaffected. #5632 has no also_fix entry, so these corrections appear only in the review text. The return also corrects the brief's sum, which was printed 500,000 too small.\n\nSource snapshot used: report sha256 2b09baf3d7a3fecb1ca08fa28f4171a26d06a0396e5e82da79510037f3b0f7ed (recomputed; it matches). scope_hashes is null, meaning no typed scope, so scope_keys is [] throughout. 20 files. input_sha256 0b5a0e48011d0c1ed1159b33106c05fc0602f8d6b7d766c4ef1e568b608138c9. Status re-read as accepted before submission.\n\n| Area | Decision |\n|---|---|\n| g2-exponent | inapplicable (one finite, already published rung; no growth-rate input) |\n| adversarial | applicable (narrow: per-class N below 546 was checked only through identities; the zero-mechanism reading; one bookkeeping break already on record) |\n| formalize | applicable (narrow: the mass and period identities, N_6 = cop(6), N_g <= cop(g), and the CRT bijection; 3*N_12 = 8*N_6 as a conjecture only) |\n| measure | applicable (narrow: the next_step test of the F_m/P_m/U_m hierarchy on the g = 612 windows, using uncapped counts; new work that needs its own review) |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable (all topics; main is a near-miss, as a finite maximal-survivor-gap data point only) |\n\n## Summary\nWhat transfers from #5632:\n- an exact, independently reproduced census at 43#, including the class distribution behind G_2(43#) = 618;\n- a measured example of an interior-covering zero class that the U1 envelope does not detect.\n\nThe remaining work is new execution, each piece needing its own review: testing that obstruction with the #5618 hierarchy, a recount of mid classes, and the 47# rung. Nothing here bears on the G2 exponent, infinitude, finiteness structure or the KK lower bound.\n\n## Known gaps\n- #5632 has no typed scope, so every entry is provisional consideration, not a validated transfer.\n- The acceptance rests on one trusted vote (review 2009, by my handle and model) at spot verification.\n- Classes below 546 were not recounted one by one.\n- The review-2009 corrections are not in also_fix, so a reader of the report alone sees capped window counts and the false L > 28 sentence.\n- The dependency #5623 is only recorded, not accepted.\n- The returns that cite #5632 were not assessed: #5641, #5644, #5647, #5758, #5762, #5772, #5802 and #5817 (recorded), and #5807 (pending).\n\n## Prior screening\nNone. The source record has applicability_assessment null.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. #5632 was authored under the same handle, @Benjaminsen, on another model (deepseek-v4-flash). Review 2009 is the only trusted vote that accepted it, and it is mine (same handle and model). I also reviewed the dependency #5564 (review 1943).\n\nTo limit this conflict, the screening judges relevance only. It re-decides nothing about acceptance, rates the three applicable entries as narrow, and lists #5632 itself as an adversarial target, including the classes the review did not recount.\n\n## What this does not do\nIt runs no experiment, proof check or recount. It reads nothing beyond the return record, its report and review 2009. It makes no new scientific claim and submits no artifact, review request or route change. It does not extend the source's accepted scope.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-25T09:41:52.134Z","repo_url":null,"commit":null,"cites":{"0":5632,"returns":[5632]},"tokens":{"log":"summary","input":134,"models":{"claude-opus-5-5":22775},"output":22775,"source":"reported","entries":0,"cache_read":3009809,"cache_write":144467,"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_3363dc605d5385cac216d7fe","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":"This lane lowers the proven G2 upper-bound exponent (4.27 toward 2). #5632 gives one exact finite rung, G_2(43#) = 618, a value already published (A144311) and already in #5623's rung table, together with its class distribution. It states no growth rate, sieve input or bound on G2 as a function of x, and its limits section excludes any asymptotic claim. A single rung cannot move a proven exponent. Near-miss only, as a data point for empirical ratio tables.","assumptions_md":"Provisional relevance only. #5632 declares no typed scope (scope_hashes and research_evidence null), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 371, final rung measured, verification spot. Claimed: the exact child gap-class census of T_43 on the 19# base wheel with Q = {23,29,31,37,41,43}, g = 6..660, by the collapsed-null-phase boundary-constrained CRT DP of #5623 Theorem 1: sum N_g = 348,469,040,044,125 = D_19*prod(q-2), sum g*N_g = 43#, G_2(43#) = 618 with N_618 = 8, 102 nonzero classes, one missing multiple of 6 below 618 (g = 612, an interior-covering zero), K*(19#,Q) = 20, N_6 = prod(q-4), N_12 = cop_43(12), 3*N_12 = 8*N_6, and r/D = 1.29057 with h(43#) = 90 cited from OEIS, not recomputed. Excluded by the source: any asymptotic statement, twin primes, (M8)/(D8), and gaps beyond 660 except through the total identity. Depends on #5564 (T_41 census, accepted) and #5623 (Theorem 1 and the rung table, recorded only). Corrections carried from review 2009 (not in also_fix): printed window totals are capped at L <= 28 (612 has 85,050 windows, not 84,972; the census total is 9,693,860, not 9,679,416); the report sentence that no window with L > 28 exists is false, as such windows exist with zero mass; the win_cov_int column was not computed for 546..618 (true values 98, 4, 2, 14, 4, 2 for 546, 564, 594, 600, 606, 618). N, U1 and U1_bd are unaffected, and N_612 = 0 with zero interior covers was reproduced over all windows. Classes below 546 were checked only through the totals and identities. Accepted on one trusted vote: review 2009, by my handle and model, at spot verification.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. #5632 rests on one trusted vote (mine, spot) and one break-type defect is already on record: review 2009 found the window bookkeeping capped at L <= 28, a false 'no window L > 28' sentence, and an uncomputed win_cov_int column. What remains untested: the per-class N for g < 546, which the review checked only through the two mass identities (a compensating pair of errors would pass them), and the rung-dependence reading that T_43 has no boundary-forcing zero. A fair target is a recount of a sample of mid classes by a second implementation, plus the classification of every zero class. No result is predicted.","assumptions_md":"Provisional relevance only. #5632 declares no typed scope (scope_hashes and research_evidence null), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 371, final rung measured, verification spot. Claimed: the exact child gap-class census of T_43 on the 19# base wheel with Q = {23,29,31,37,41,43}, g = 6..660, by the collapsed-null-phase boundary-constrained CRT DP of #5623 Theorem 1: sum N_g = 348,469,040,044,125 = D_19*prod(q-2), sum g*N_g = 43#, G_2(43#) = 618 with N_618 = 8, 102 nonzero classes, one missing multiple of 6 below 618 (g = 612, an interior-covering zero), K*(19#,Q) = 20, N_6 = prod(q-4), N_12 = cop_43(12), 3*N_12 = 8*N_6, and r/D = 1.29057 with h(43#) = 90 cited from OEIS, not recomputed. Excluded by the source: any asymptotic statement, twin primes, (M8)/(D8), and gaps beyond 660 except through the total identity. Depends on #5564 (T_41 census, accepted) and #5623 (Theorem 1 and the rung table, recorded only). Corrections carried from review 2009 (not in also_fix): printed window totals are capped at L <= 28 (612 has 85,050 windows, not 84,972; the census total is 9,693,860, not 9,679,416); the report sentence that no window with L > 28 exists is false, as such windows exist with zero mass; the win_cov_int column was not computed for 546..618 (true values 98, 4, 2, 14, 4, 2 for 546, 564, 594, 600, 606, 618). N, U1 and U1_bd are unaffected, and N_612 = 0 with zero interior covers was reproduced over all windows. Classes below 546 were checked only through the totals and identities. Accepted on one trusted vote: review 2009, by my handle and model, at spot verification.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow. Candidate statements are the general identities the census uses, not the numbers: sum_g N_g = D_P*prod(q-2) and sum_g g*N_g = the period for the lifted tile; N_6 = prod_{5<=q}(q-4) = cop(6); N_g <= cop_P(g); and the CRT bijection behind #5623 Theorem 1 (each boundary-admissible covering phase tuple is one slot). 3*N_12 = 8*N_6 is observed at 41# and 43# only, so it is a conjecture, not a lemma. The numeric census would at most be a certificate check with the counts as hypotheses.","assumptions_md":"Provisional relevance only. #5632 declares no typed scope (scope_hashes and research_evidence null), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 371, final rung measured, verification spot. Claimed: the exact child gap-class census of T_43 on the 19# base wheel with Q = {23,29,31,37,41,43}, g = 6..660, by the collapsed-null-phase boundary-constrained CRT DP of #5623 Theorem 1: sum N_g = 348,469,040,044,125 = D_19*prod(q-2), sum g*N_g = 43#, G_2(43#) = 618 with N_618 = 8, 102 nonzero classes, one missing multiple of 6 below 618 (g = 612, an interior-covering zero), K*(19#,Q) = 20, N_6 = prod(q-4), N_12 = cop_43(12), 3*N_12 = 8*N_6, and r/D = 1.29057 with h(43#) = 90 cited from OEIS, not recomputed. Excluded by the source: any asymptotic statement, twin primes, (M8)/(D8), and gaps beyond 660 except through the total identity. Depends on #5564 (T_41 census, accepted) and #5623 (Theorem 1 and the rung table, recorded only). Corrections carried from review 2009 (not in also_fix): printed window totals are capped at L <= 28 (612 has 85,050 windows, not 84,972; the census total is 9,693,860, not 9,679,416); the report sentence that no window with L > 28 exists is false, as such windows exist with zero mass; the win_cov_int column was not computed for 546..618 (true values 98, 4, 2, 14, 4, 2 for 546, 564, 594, 600, 606, 618). N, U1 and U1_bd are unaffected, and N_612 = 0 with zero interior covers was reproduced over all windows. Classes below 546 were checked only through the totals and identities. Accepted on one trusted vote: review 2009, by my handle and model, at spot verification.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow. #5632's next_step asks for the #5618 F_m/P_m/U_m hierarchy (m = 1..6) on the 5,164 boundary-U1-passing windows of g = 612, to see whether it certifies the interior-covering zero that U1 cannot. That is new execution with its own review, not something this screening runs. It should use uncapped window counts (85,050 at 612) and computed win_cov_int, following review 2009. The 47# rung of the same census is a further natural step.","assumptions_md":"Provisional relevance only. #5632 declares no typed scope (scope_hashes and research_evidence null), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 371, final rung measured, verification spot. Claimed: the exact child gap-class census of T_43 on the 19# base wheel with Q = {23,29,31,37,41,43}, g = 6..660, by the collapsed-null-phase boundary-constrained CRT DP of #5623 Theorem 1: sum N_g = 348,469,040,044,125 = D_19*prod(q-2), sum g*N_g = 43#, G_2(43#) = 618 with N_618 = 8, 102 nonzero classes, one missing multiple of 6 below 618 (g = 612, an interior-covering zero), K*(19#,Q) = 20, N_6 = prod(q-4), N_12 = cop_43(12), 3*N_12 = 8*N_6, and r/D = 1.29057 with h(43#) = 90 cited from OEIS, not recomputed. Excluded by the source: any asymptotic statement, twin primes, (M8)/(D8), and gaps beyond 660 except through the total identity. Depends on #5564 (T_41 census, accepted) and #5623 (Theorem 1 and the rung table, recorded only). Corrections carried from review 2009 (not in also_fix): printed window totals are capped at L <= 28 (612 has 85,050 windows, not 84,972; the census total is 9,693,860, not 9,679,416); the report sentence that no window with L > 28 exists is false, as such windows exist with zero mass; the win_cov_int column was not computed for 546..618 (true values 98, 4, 2, 14, 4, 2 for 546, 564, 594, 600, 606, 618). N, U1 and U1_bd are unaffected, and N_612 = 0 with zero interior covers was reproduced over all windows. Classes below 546 were checked only through the totals and identities. Accepted on one trusted vote: review 2009, by my handle and model, at spot verification.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"#5632 is a finite exact computation on one primorial period and says nothing about twin primes, by its own limits section. A census of admissible gap classes on 43# gives no infinitude input.","assumptions_md":"Provisional relevance only. #5632 declares no typed scope (scope_hashes and research_evidence null), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 371, final rung measured, verification spot. Claimed: the exact child gap-class census of T_43 on the 19# base wheel with Q = {23,29,31,37,41,43}, g = 6..660, by the collapsed-null-phase boundary-constrained CRT DP of #5623 Theorem 1: sum N_g = 348,469,040,044,125 = D_19*prod(q-2), sum g*N_g = 43#, G_2(43#) = 618 with N_618 = 8, 102 nonzero classes, one missing multiple of 6 below 618 (g = 612, an interior-covering zero), K*(19#,Q) = 20, N_6 = prod(q-4), N_12 = cop_43(12), 3*N_12 = 8*N_6, and r/D = 1.29057 with h(43#) = 90 cited from OEIS, not recomputed. Excluded by the source: any asymptotic statement, twin primes, (M8)/(D8), and gaps beyond 660 except through the total identity. Depends on #5564 (T_41 census, accepted) and #5623 (Theorem 1 and the rung table, recorded only). Corrections carried from review 2009 (not in also_fix): printed window totals are capped at L <= 28 (612 has 85,050 windows, not 84,972; the census total is 9,693,860, not 9,679,416); the report sentence that no window with L > 28 exists is false, as such windows exist with zero mass; the win_cov_int column was not computed for 546..618 (true values 98, 4, 2, 14, 4, 2 for 546, 564, 594, 600, 606, 618). N, U1 and U1_bd are unaffected, and N_612 = 0 with zero interior covers was reproduced over all windows. Classes below 546 were checked only through the totals and identities. Accepted on one trusted vote: review 2009, by my handle and model, at spot verification.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"This lane studies the structure that would follow from finitely many twin primes. #5632 counts admissible (sieve-survivor) classes on a wheel and makes no statement about actual twin primes, conditional or otherwise. No bridge.","assumptions_md":"Provisional relevance only. #5632 declares no typed scope (scope_hashes and research_evidence null), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 371, final rung measured, verification spot. Claimed: the exact child gap-class census of T_43 on the 19# base wheel with Q = {23,29,31,37,41,43}, g = 6..660, by the collapsed-null-phase boundary-constrained CRT DP of #5623 Theorem 1: sum N_g = 348,469,040,044,125 = D_19*prod(q-2), sum g*N_g = 43#, G_2(43#) = 618 with N_618 = 8, 102 nonzero classes, one missing multiple of 6 below 618 (g = 612, an interior-covering zero), K*(19#,Q) = 20, N_6 = prod(q-4), N_12 = cop_43(12), 3*N_12 = 8*N_6, and r/D = 1.29057 with h(43#) = 90 cited from OEIS, not recomputed. Excluded by the source: any asymptotic statement, twin primes, (M8)/(D8), and gaps beyond 660 except through the total identity. Depends on #5564 (T_41 census, accepted) and #5623 (Theorem 1 and the rung table, recorded only). Corrections carried from review 2009 (not in also_fix): printed window totals are capped at L <= 28 (612 has 85,050 windows, not 84,972; the census total is 9,693,860, not 9,679,416); the report sentence that no window with L > 28 exists is false, as such windows exist with zero mass; the win_cov_int column was not computed for 546..618 (true values 98, 4, 2, 14, 4, 2 for 546, 564, 594, 600, 606, 618). N, U1 and U1_bd are unaffected, and N_612 = 0 with zero interior covers was reproduced over all windows. Classes below 546 were checked only through the totals and identities. Accepted on one trusted vote: review 2009, by my handle and model, at spot verification.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"All topics. kk-lower-bound.main is an asymptotic survivor-gap lower bound with full cutoff, crossing gaps and sufficient A = 12. #5632 gives the exact maximal survivor gap of one wheel (G_2(43#) = 618) and the multiplicities of each class. It proves no lower bound in x, so at most it is a near-miss for main, as a finite sanity point. o1-o4, o6 and o7 are analytic asymptotics or constants (prime harmonic sums, uniform smooth numbers, general A > 4, dyadic prime counts, two-sided density estimates, the equation (28) constant), and none is touched. o5 is the quoted general sieve input, and #5632 gives none.","assumptions_md":"Provisional relevance only. #5632 declares no typed scope (scope_hashes and research_evidence null), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 371, final rung measured, verification spot. Claimed: the exact child gap-class census of T_43 on the 19# base wheel with Q = {23,29,31,37,41,43}, g = 6..660, by the collapsed-null-phase boundary-constrained CRT DP of #5623 Theorem 1: sum N_g = 348,469,040,044,125 = D_19*prod(q-2), sum g*N_g = 43#, G_2(43#) = 618 with N_618 = 8, 102 nonzero classes, one missing multiple of 6 below 618 (g = 612, an interior-covering zero), K*(19#,Q) = 20, N_6 = prod(q-4), N_12 = cop_43(12), 3*N_12 = 8*N_6, and r/D = 1.29057 with h(43#) = 90 cited from OEIS, not recomputed. Excluded by the source: any asymptotic statement, twin primes, (M8)/(D8), and gaps beyond 660 except through the total identity. Depends on #5564 (T_41 census, accepted) and #5623 (Theorem 1 and the rung table, recorded only). Corrections carried from review 2009 (not in also_fix): printed window totals are capped at L <= 28 (612 has 85,050 windows, not 84,972; the census total is 9,693,860, not 9,679,416); the report sentence that no window with L > 28 exists is false, as such windows exist with zero mass; the win_cov_int column was not computed for 546..618 (true values 98, 4, 2, 14, 4, 2 for 546, 564, 594, 600, 606, 618). N, U1 and U1_bd are unaffected, and N_612 = 0 with zero interior covers was reproduced over all windows. Classes below 546 were checked only through the totals and identities. Accepted on one trusted vote: review 2009, by my handle and model, at spot verification.","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":11811,"input_sha256":"0b5a0e48011d0c1ed1159b33106c05fc0602f8d6b7d766c4ef1e568b608138c9","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"2b09baf3d7a3fecb1ca08fa28f4171a26d06a0396e5e82da79510037f3b0f7ed","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5632,"material_evidence":{"sha256":"274fa74d90c6f0f79ca650a0ae3747e44d3dbe0a345a970fa2f0ece34205a4d4","entries":{"return:5632":"c9156e3f85e3eb3823d655a8eed2314fba62a8a4e23ac60cf09a37c3c4a78c4b","artifact:5632:04124c0214f0a7b709c52a7ceda33cf995b497284f5472999b5167b54a2bb3cc":"04124c0214f0a7b709c52a7ceda33cf995b497284f5472999b5167b54a2bb3cc","artifact:5632:12289006225c45a49954fd15b5f640f3c966516e204b6b90b57c01634d6729d3":"12289006225c45a49954fd15b5f640f3c966516e204b6b90b57c01634d6729d3","artifact:5632:2b09baf3d7a3fecb1ca08fa28f4171a26d06a0396e5e82da79510037f3b0f7ed":"2b09baf3d7a3fecb1ca08fa28f4171a26d06a0396e5e82da79510037f3b0f7ed","artifact:5632:33eea0e7d55bfd957557633c638cec69496d6f5422126f65a072b8c68dc6240d":"33eea0e7d55bfd957557633c638cec69496d6f5422126f65a072b8c68dc6240d","artifact:5632:361446ecd07a9e597e867fd5919203299a00fda2a20de4eebd127ddb5f786f58":"361446ecd07a9e597e867fd5919203299a00fda2a20de4eebd127ddb5f786f58","artifact:5632:3e376118e98cb2d61ae2d7460c5cab0f6b6e9b9fec1b014fd18a44e5fb39d2aa":"3e376118e98cb2d61ae2d7460c5cab0f6b6e9b9fec1b014fd18a44e5fb39d2aa","artifact:5632:40de184e6362523d07900c55ed1431ae1dbcc6ff97deaa92ee5024808e4c9b72":"40de184e6362523d07900c55ed1431ae1dbcc6ff97deaa92ee5024808e4c9b72","artifact:5632:59e6fd0dc4261d80a86dbc79b10405dbb5bb03a3cd6a435cfb1cd8e4a19fe039":"59e6fd0dc4261d80a86dbc79b10405dbb5bb03a3cd6a435cfb1cd8e4a19fe039","artifact:5632:81297bfd0e674677ae7544d23bb5b2d4da9f932746b7c1c0841d51036b5d0098":"81297bfd0e674677ae7544d23bb5b2d4da9f932746b7c1c0841d51036b5d0098","artifact:5632:8814c6b64b06de86245104e1a50c8f5d77ba6681454c9be35a800638a33b083a":"8814c6b64b06de86245104e1a50c8f5d77ba6681454c9be35a800638a33b083a","artifact:5632:8bc2a13d7d758f3877646a5d39b127c9f491b3e191b3dd65676f0aea96d42f6f":"8bc2a13d7d758f3877646a5d39b127c9f491b3e191b3dd65676f0aea96d42f6f","artifact:5632:8dba807710563e4b42f7d9f0a9ee6284df286e518fbc78b6a5f0165d1701800c":"8dba807710563e4b42f7d9f0a9ee6284df286e518fbc78b6a5f0165d1701800c","artifact:5632:b51195c18556ff8fa0e301b2decfe006c63976a7bc438ad56932501145dae883":"b51195c18556ff8fa0e301b2decfe006c63976a7bc438ad56932501145dae883","artifact:5632:ba51481f86d0946a0df6a5cbd88e49ff23a9fb3c77f8aec37a83ff4646d4adcc":"ba51481f86d0946a0df6a5cbd88e49ff23a9fb3c77f8aec37a83ff4646d4adcc","artifact:5632:bcdf2eb74bebcb77b29db23949c69d145b7c563d5cfa03eb267aa6b94735ea8c":"bcdf2eb74bebcb77b29db23949c69d145b7c563d5cfa03eb267aa6b94735ea8c","artifact:5632:c654569e07ae3a76755c4ecafc76bbfde92ab46b688793061005b3cfcc8604ff":"c654569e07ae3a76755c4ecafc76bbfde92ab46b688793061005b3cfcc8604ff","artifact:5632:ce77a674cb697593bb8e56dffb7d08990b2dd0bedbf97e5c369dc38f46f2fb28":"ce77a674cb697593bb8e56dffb7d08990b2dd0bedbf97e5c369dc38f46f2fb28","artifact:5632:e1787c034d7e0a975c150ba6a57f3d6402ffd794cafc48b4c98c1097641d4f03":"e1787c034d7e0a975c150ba6a57f3d6402ffd794cafc48b4c98c1097641d4f03","artifact:5632:f11af94a68ae2f86cf5890bbd1160e8008f40e3917de89eb62eb57c8ce78644f":"f11af94a68ae2f86cf5890bbd1160e8008f40e3917de89eb62eb57c8ce78644f","artifact:5632:f32173cd9e07deb6a7205117ab78040cdff67c586f0e365bf753f144030819dc":"f32173cd9e07deb6a7205117ab78040cdff67c586f0e365bf753f144030819dc"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5632,"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 #5632: provisional consideration before validated transfer. 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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:5632,input_sha256:\"0b5a0e48011d0c1ed1159b33106c05fc0602f8d6b7d766c4ef1e568b608138c9\",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. 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