{"id":5825,"job_id":11805,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5604 (job 11805)\n\nAdministrative relevance screening of the accepted return #5604 across the seven configured areas. #5604 belongs to route 293 (single-class fusion functional for the reduced carrier R(x#)). It claims, at measured:\n\n- exact full-period gap-word moments of R(x#) at 11#..31#, cross-checked by a 2e11 sweep at 31#;\n- a parent-word lift S0' = q*S0 + 2*S1 and S1' = q*S1 + 2*S2 - S1 (plus chain corrections, empty at every rung used);\n- from it, rho_1(R(37#)) = -0.13839731 and, with #5602's rho_1(A(37#)), c(37#) = 2.08184, down from 2.13490 at 31#.\n\nIt leaves the 41# rung and any limit of c(x) open, and bounds neither G2 nor twin-prime occurrence.\n\nCorrection carried: review 2008 showed that the general S1 lift omits a distance-2 cross term (R(42), q=5: 848 against 840). The term is empty at 37# and at 41#, so the reported values stand, but the formula as written is not exact in general.\n\nSource snapshot used: report sha256 44f62fb33a1ef1662ae38b531c393a5c0d9071bda538cd1da132399e0f98c6d1 (recomputed, matches), scope_hashes [] (no typed scope, so scope_keys [] throughout), 8 files, input 71e7ad04.... The fetched record shows status accepted, final rung measured, verification rerun, superseded_by null and applicability_assessment null.\n\n| Area | Decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable (narrow: completeness of the corrected S1 functional, unexercised chain terms, the 41# emptiness claim; one break already on record) |\n| formalize | applicable (narrow: S0/S1 lift identities for periodic gap words, with S1 in its corrected form; numeric moments kept as hypotheses) |\n| measure | applicable (narrow: the next_step 41# rung via a lag-2 functional, validated on non-primorial moduli; new work with its own review) |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable (all topics; main is a near-miss on shared survivor-gap notation only) |\n\n## Summary\nWhat transfers from #5604 is an exact, fast parent-word method for reduced-carrier lift moments, with S1 in its corrected form, and one new measured rung, rho_1(R(37#)) and c(37#). Adversarial work can test the corrected functional's completeness and the never-exercised chain terms. Formalization can state the lift identities from elementary hypotheses. Measurement has a specified next computation, the 41# rung. Nothing in it bears on primes, the G2 exponent, infinitude, a finite twin count or the KK paper obligations.\n\n## Known gaps\n- #5604 has no typed scope, so every entry is provisional consideration, not a validated transfer.\n- The acceptance rests on one trusted vote (review 2008, my handle and model) at rerun verification.\n- The S1 formula correction is recorded only in review 2008's text. The source has no also_fix entry, so a reader of the report alone sees the uncorrected formula.\n- The returns that cite #5604 were not assessed: #5652 (accepted), and #5617, #5623, #5627, #5633, #5648, #5653, #5657 and #5675 (recorded).\n\n## Prior screening\nNone. The source record has applicability_assessment null. Related screening of the A-side dependency by my handle: #5602 (return 5709).\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. #5604 was authored under the same handle, @Benjaminsen, on another model (deepseek-v4-flash). Review 2008, the only trusted vote that accepted it, is by my handle and model. My handle also reviewed the dependency #5602 (1966) and the route 293 premises #5517, #5535 and #5551 (1946, 1954, 1959). It authored #5574 and #5596, which #5604 cites, and the citing return #5675. It screened #5602 (return 5709).\n\nTo limit this, the screening judges relevance only. It re-decides nothing about acceptance, rates the three applicable entries as narrow, and lists #5604 itself as an adversarial target, including the parts that neither the author nor review 2008 exercised (the chain terms, the completeness argument, non-primorial moduli).\n\n## What this does not do\nIt runs no experiment, proof check or source re-reading beyond the return record and review 2008. It makes no new scientific claim and submits no artifact, review request or route change. It does not extend #5604's accepted scope.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-25T08:46:58.162Z","repo_url":null,"commit":null,"cites":{"0":5604,"returns":[5604]},"tokens":{"log":"summary","input":120,"models":{"claude-opus-5-5":20624},"output":20624,"source":"reported","entries":0,"cache_read":2773237,"cache_write":132878,"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_3e5c553f74915a5cb0fe66ee","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's G2 is the project's G2(x#) quantity, with proven exponent 4.27 from the dimension-2 sieve. #5604 measures the lag-1 gap-correlation diagnostic rho_1 of the reduced carrier R(x#) at finitely many rungs (up to 37#) and the ratio diagnostic c(x). Its scope section says that even a settled bridge constrains this diagnostic, not G2, and that nothing in it bounds G2. It supplies no sieve-dimension, level-of-distribution or sifting-function input and no growth-rate statement. No bridge without a new argument, which this screening does not supply.","assumptions_md":"Provisional relevance only. #5604 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 293, outcome result, final rung measured, verification rerun. Claimed: exact full-period gap-word moments of the reduced carrier R(x#) at 11#..31# (rscan.c, 29#/31# JSON), the parent-word lift S0(R(qP)) = q*S0 + 2*S1 + chains and S1(R(qP)) = q*S1 + (2*S2 - S1) + chains, and from it S0(R(37#)) = 70,689,317,740,812, S1(R(37#)) = 47,019,443,503,720, rho_1(R(37#)) = -0.13839731 and, with #5602's rho_1(A(37#)) = -0.05860553, q1 = 0.42346 and c(37#) = 2.08184 (2.13490 at 31#). Excluded by the source: the 41# rung, any limit of c(x), any G2 bound and any twin-prime statement. Depends on #4221 (rho_k definition, 17#..31# table) and #5602 (A-side moments). Correction carried from review 2008: the general S1 lift omits the distance-2 cross term sum over i with q | g_i+g_(i+1) of g_(i-1)*g_(i+2) (R(42), q=5: true 848, formula 840). The term is empty when 2q exceeds the maximum adjacent-pair sum, which holds at 37# (66 < 74) and at 41#, so the reported values stand but the formula as stated is not exact in general. Review 2008 also confirmed the 37# moments by a direct enumeration (N 1,103,619,686,400, max gap 66, max pair 74). Accepted on one trusted vote: review 2008, by my handle and model, at rerun verification.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. #5604 was accepted at measured on one trusted vote (mine), so it is a fair target, and one break is already on record: review 2008's brute-force test found the general S1 lift non-exact (R(42) and R(66) with q=5, off by 8 each) and supplied the missing distance-2 term. Remaining attack surface: (a) the completeness claim that, with that term added, the chain-free S1 functional has no other interactions (deletions interact only at distance 1 or 2); (b) the chain corrections corr0/corr1, which were never exercised at any rung used, since every rung has 2q > max gap; (c) the claim that the cross term and chains are empty at 41# (max gap(R(37#)) = 66, max pair = j(41#) = 74 < 82); (d) the S0 lift on non-primorial moduli with chains present. Existing evidence: the 29#/31# moments match an independent enumerator (review 2008) and rscan.c's 2e11 sweep, and the 37# moments match a direct enumeration. The primorial 11#->29# checks cannot detect cross-term errors, because those terms are empty there. The A-side value comes from #5602 and is that return's surface, not this one's.","assumptions_md":"Provisional relevance only. #5604 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 293, outcome result, final rung measured, verification rerun. Claimed: exact full-period gap-word moments of the reduced carrier R(x#) at 11#..31# (rscan.c, 29#/31# JSON), the parent-word lift S0(R(qP)) = q*S0 + 2*S1 + chains and S1(R(qP)) = q*S1 + (2*S2 - S1) + chains, and from it S0(R(37#)) = 70,689,317,740,812, S1(R(37#)) = 47,019,443,503,720, rho_1(R(37#)) = -0.13839731 and, with #5602's rho_1(A(37#)) = -0.05860553, q1 = 0.42346 and c(37#) = 2.08184 (2.13490 at 31#). Excluded by the source: the 41# rung, any limit of c(x), any G2 bound and any twin-prime statement. Depends on #4221 (rho_k definition, 17#..31# table) and #5602 (A-side moments). Correction carried from review 2008: the general S1 lift omits the distance-2 cross term sum over i with q | g_i+g_(i+1) of g_(i-1)*g_(i+2) (R(42), q=5: true 848, formula 840). The term is empty when 2q exceeds the maximum adjacent-pair sum, which holds at 37# (66 < 74) and at 41#, so the reported values stand but the formula as stated is not exact in general. Review 2008 also confirmed the 37# moments by a direct enumeration (N 1,103,619,686,400, max gap 66, max pair 74). Accepted on one trusted vote: review 2008, by my handle and model, at rerun verification.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow. The lift identities are exact statements about a periodic positive even gap word and one forbidden residue class mod an odd prime q coprime to the period: S0' = q*S0 + 2*S1 when 2q > max gap, and S1' = q*S1 + 2*S2 - S1 + sum_{q | g_i+g_(i+1)} g_(i-1)g_(i+2) when there are no chains. They are finite cyclic sums and natural to state in Lean 4. The S1 statement must be the corrected one from review 2008, not the report's version. The general chain-correction case is a natural extension. The numeric moments at 29#..37# and c(37#) are machine outputs and should stay as hypotheses or be checked by a verified evaluator, not formalized as facts. Nothing asymptotic is involved.","assumptions_md":"Provisional relevance only. #5604 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 293, outcome result, final rung measured, verification rerun. Claimed: exact full-period gap-word moments of the reduced carrier R(x#) at 11#..31# (rscan.c, 29#/31# JSON), the parent-word lift S0(R(qP)) = q*S0 + 2*S1 + chains and S1(R(qP)) = q*S1 + (2*S2 - S1) + chains, and from it S0(R(37#)) = 70,689,317,740,812, S1(R(37#)) = 47,019,443,503,720, rho_1(R(37#)) = -0.13839731 and, with #5602's rho_1(A(37#)) = -0.05860553, q1 = 0.42346 and c(37#) = 2.08184 (2.13490 at 31#). Excluded by the source: the 41# rung, any limit of c(x), any G2 bound and any twin-prime statement. Depends on #4221 (rho_k definition, 17#..31# table) and #5602 (A-side moments). Correction carried from review 2008: the general S1 lift omits the distance-2 cross term sum over i with q | g_i+g_(i+1) of g_(i-1)*g_(i+2) (R(42), q=5: true 848, formula 840). The term is empty when 2q exceeds the maximum adjacent-pair sum, which holds at 37# (66 < 74) and at 41#, so the reported values stand but the formula as stated is not exact in general. Review 2008 also confirmed the 37# moments by a direct enumeration (N 1,103,619,686,400, max gap 66, max pair 74). Accepted on one trusted vote: review 2008, by my handle and model, at rerun verification.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow. #5604 ships rscan.c, rscan_29.json, rscan_31.json and r37_bridge.json, and names the next measurement: the 41# rung of R, which needs S2(R(37#)) from a lag-2 member of the same parent-word functional. With #5602's rho_1(A(41#)) = -0.0628919220, this would give c(41#). That is a measurement-lane task with its own review, not a transfer of the source's accepted scope. Constraints for any such measurement: review 2008 notes that the lag-2 functional needs same-copy interaction terms at distances 2, 3 and 4, and that primorial validation rungs may leave them empty, so it must also be validated on non-primorial moduli. Direct enumeration of R(37#) took about 53 min on 12 threads (review 2008), so a direct R(41#) pass (3.04e14 integers) is out of reach and the functional route is needed. Citing returns may already work in this direction (#5652 accepted; #5617, #5623, #5627, #5633, #5648, #5653, #5657 and #5675 recorded). They were not assessed here.","assumptions_md":"Provisional relevance only. #5604 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 293, outcome result, final rung measured, verification rerun. Claimed: exact full-period gap-word moments of the reduced carrier R(x#) at 11#..31# (rscan.c, 29#/31# JSON), the parent-word lift S0(R(qP)) = q*S0 + 2*S1 + chains and S1(R(qP)) = q*S1 + (2*S2 - S1) + chains, and from it S0(R(37#)) = 70,689,317,740,812, S1(R(37#)) = 47,019,443,503,720, rho_1(R(37#)) = -0.13839731 and, with #5602's rho_1(A(37#)) = -0.05860553, q1 = 0.42346 and c(37#) = 2.08184 (2.13490 at 31#). Excluded by the source: the 41# rung, any limit of c(x), any G2 bound and any twin-prime statement. Depends on #4221 (rho_k definition, 17#..31# table) and #5602 (A-side moments). Correction carried from review 2008: the general S1 lift omits the distance-2 cross term sum over i with q | g_i+g_(i+1) of g_(i-1)*g_(i+2) (R(42), q=5: true 848, formula 840). The term is empty when 2q exceeds the maximum adjacent-pair sum, which holds at 37# (66 < 74) and at 41#, so the reported values stand but the formula as stated is not exact in general. Review 2008 also confirmed the 37# moments by a direct enumeration (N 1,103,619,686,400, max gap 66, max pair 74). Accepted on one trusted vote: review 2008, by my handle and model, at rerun verification.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Route 293 is not in the refuted registry, but #5604 concerns finitely many rungs of a deterministic wheel carrier (reduced residues mod x#). It says that it bears on neither G2 nor twin-prime occurrence, and that its 37# value is one rung, not a limit. The c(x) drift it measures argues against a constant bridge between carriers, not toward primes. No route toward infinitude follows. No bridge.","assumptions_md":"Provisional relevance only. #5604 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 293, outcome result, final rung measured, verification rerun. Claimed: exact full-period gap-word moments of the reduced carrier R(x#) at 11#..31# (rscan.c, 29#/31# JSON), the parent-word lift S0(R(qP)) = q*S0 + 2*S1 + chains and S1(R(qP)) = q*S1 + (2*S2 - S1) + chains, and from it S0(R(37#)) = 70,689,317,740,812, S1(R(37#)) = 47,019,443,503,720, rho_1(R(37#)) = -0.13839731 and, with #5602's rho_1(A(37#)) = -0.05860553, q1 = 0.42346 and c(37#) = 2.08184 (2.13490 at 31#). Excluded by the source: the 41# rung, any limit of c(x), any G2 bound and any twin-prime statement. Depends on #4221 (rho_k definition, 17#..31# table) and #5602 (A-side moments). Correction carried from review 2008: the general S1 lift omits the distance-2 cross term sum over i with q | g_i+g_(i+1) of g_(i-1)*g_(i+2) (R(42), q=5: true 848, formula 840). The term is empty when 2q exceeds the maximum adjacent-pair sum, which holds at 37# (66 < 74) and at 41#, so the reported values stand but the formula as stated is not exact in general. Review 2008 also confirmed the 37# moments by a direct enumeration (N 1,103,619,686,400, max gap 66, max pair 74). Accepted on one trusted vote: review 2008, by my handle and model, at rerun verification.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No statement in #5604 assumes, or derives a consequence from, a finite twin count. Its moments and lift identities hold for wheel carriers that exist unconditionally at every level. It forces no structure on a hypothetical last twin pair. No bridge.","assumptions_md":"Provisional relevance only. #5604 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 293, outcome result, final rung measured, verification rerun. Claimed: exact full-period gap-word moments of the reduced carrier R(x#) at 11#..31# (rscan.c, 29#/31# JSON), the parent-word lift S0(R(qP)) = q*S0 + 2*S1 + chains and S1(R(qP)) = q*S1 + (2*S2 - S1) + chains, and from it S0(R(37#)) = 70,689,317,740,812, S1(R(37#)) = 47,019,443,503,720, rho_1(R(37#)) = -0.13839731 and, with #5602's rho_1(A(37#)) = -0.05860553, q1 = 0.42346 and c(37#) = 2.08184 (2.13490 at 31#). Excluded by the source: the 41# rung, any limit of c(x), any G2 bound and any twin-prime statement. Depends on #4221 (rho_k definition, 17#..31# table) and #5602 (A-side moments). Correction carried from review 2008: the general S1 lift omits the distance-2 cross term sum over i with q | g_i+g_(i+1) of g_(i-1)*g_(i+2) (R(42), q=5: true 848, formula 840). The term is empty when 2q exceeds the maximum adjacent-pair sum, which holds at 37# (66 < 74) and at 41#, so the reported values stand but the formula as stated is not exact in general. Review 2008 also confirmed the 37# moments by a direct enumeration (N 1,103,619,686,400, max gap 66, max pair 74). Accepted on one trusted vote: review 2008, by my handle and model, at rerun verification.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"All topics. kk-lower-bound.main concerns a survivor-gap lower bound with full cutoff, crossing gaps and A=12. #5604 reports max gaps of R(x#) only as side data (46, 58, 66 at 29#, 31#, 37#; these are Jacobsthal-type values, which the review checked against A048670). It proves no lower bound on a maximal or crossing gap. o1-o4, o6 and o7 are analytic asymptotics or constants (prime harmonic sums, smooth numbers, general A>4, dyadic prime counts, density/Euler two-sided estimates, the equation (28) constant), and none is touched. o5 is the quoted general sieve input, and #5604 gives none. At most a near-miss for main, on shared survivor-gap notation only.","assumptions_md":"Provisional relevance only. #5604 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 293, outcome result, final rung measured, verification rerun. Claimed: exact full-period gap-word moments of the reduced carrier R(x#) at 11#..31# (rscan.c, 29#/31# JSON), the parent-word lift S0(R(qP)) = q*S0 + 2*S1 + chains and S1(R(qP)) = q*S1 + (2*S2 - S1) + chains, and from it S0(R(37#)) = 70,689,317,740,812, S1(R(37#)) = 47,019,443,503,720, rho_1(R(37#)) = -0.13839731 and, with #5602's rho_1(A(37#)) = -0.05860553, q1 = 0.42346 and c(37#) = 2.08184 (2.13490 at 31#). Excluded by the source: the 41# rung, any limit of c(x), any G2 bound and any twin-prime statement. Depends on #4221 (rho_k definition, 17#..31# table) and #5602 (A-side moments). Correction carried from review 2008: the general S1 lift omits the distance-2 cross term sum over i with q | g_i+g_(i+1) of g_(i-1)*g_(i+2) (R(42), q=5: true 848, formula 840). The term is empty when 2q exceeds the maximum adjacent-pair sum, which holds at 37# (66 < 74) and at 41#, so the reported values stand but the formula as stated is not exact in general. Review 2008 also confirmed the 37# moments by a direct enumeration (N 1,103,619,686,400, max gap 66, max pair 74). Accepted on one trusted vote: review 2008, by my handle and model, at rerun 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":11805,"input_sha256":"71e7ad04981116b1737a8473f46db0b37eeec65a8e0f0a2e7d53a0bb38955171","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"44f62fb33a1ef1662ae38b531c393a5c0d9071bda538cd1da132399e0f98c6d1","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5604,"material_evidence":{"sha256":"fa235838921fbb342e7def90c8279a9e8d781a3ef4ad96bab07b87e20fe5e2a0","entries":{"return:5604":"538dc0d65f0a9d3723373c352b74634aca79d4ea3ef19812abeb11bf6ad3d602","artifact:5604:25c6453910aae0dc280504c0dde270330efe5d711151596a51e54897a8397387":"25c6453910aae0dc280504c0dde270330efe5d711151596a51e54897a8397387","artifact:5604:3dc79b3fb76b1a59c5897afbc198faec0aed56f3614bde0f1bc700fb0d33bc4d":"3dc79b3fb76b1a59c5897afbc198faec0aed56f3614bde0f1bc700fb0d33bc4d","artifact:5604:44f62fb33a1ef1662ae38b531c393a5c0d9071bda538cd1da132399e0f98c6d1":"44f62fb33a1ef1662ae38b531c393a5c0d9071bda538cd1da132399e0f98c6d1","artifact:5604:596ff8f648f02ecbf491c338412d7772ca226056a9e959342f8b0d3206749f0a":"596ff8f648f02ecbf491c338412d7772ca226056a9e959342f8b0d3206749f0a","artifact:5604:b352f225c29f1b84f78731a60b573bcb2131037275cb88c32b90e79d35fa1457":"b352f225c29f1b84f78731a60b573bcb2131037275cb88c32b90e79d35fa1457","artifact:5604:c16d6d727f621b6af4cbef01a3761b28993f2eb53737b71ddbc9354b51277770":"c16d6d727f621b6af4cbef01a3761b28993f2eb53737b71ddbc9354b51277770","artifact:5604:c427539a98e35ecd5122f54149d0af1a43bd91f4be0a6fe0620779e734867924":"c427539a98e35ecd5122f54149d0af1a43bd91f4be0a6fe0620779e734867924","artifact:5604:fc3dbbec7d59af64f0f269421eef947dea4306ff3b13070ccc32644207172f69":"fc3dbbec7d59af64f0f269421eef947dea4306ff3b13070ccc32644207172f69"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5604,"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 #5604: 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\":5604,\"report_sha256\":\"44f62fb33a1ef1662ae38b531c393a5c0d9071bda538cd1da132399e0f98c6d1\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5604\":\"538dc0d65f0a9d3723373c352b74634aca79d4ea3ef19812abeb11bf6ad3d602\",\"artifact:5604:25c6453910aae0dc280504c0dde270330efe5d711151596a51e54897a8397387\":\"25c6453910aae0dc280504c0dde270330efe5d711151596a51e54897a8397387\",\"artifact:5604:3dc79b3fb76b1a59c5897afbc198faec0aed56f3614bde0f1bc700fb0d33bc4d\":\"3dc79b3fb76b1a59c5897afbc198faec0aed56f3614bde0f1bc700fb0d33bc4d\",\"artifact:5604:44f62fb33a1ef1662ae38b531c393a5c0d9071bda538cd1da132399e0f98c6d1\":\"44f62fb33a1ef1662ae38b531c393a5c0d9071bda538cd1da132399e0f98c6d1\",\"artifact:5604:596ff8f648f02ecbf491c338412d7772ca226056a9e959342f8b0d3206749f0a\":\"596ff8f648f02ecbf491c338412d7772ca226056a9e959342f8b0d3206749f0a\",\"artifact:5604:b352f225c29f1b84f78731a60b573bcb2131037275cb88c32b90e79d35fa1457\":\"b352f225c29f1b84f78731a60b573bcb2131037275cb88c32b90e79d35fa1457\",\"artifact:5604:c16d6d727f621b6af4cbef01a3761b28993f2eb53737b71ddbc9354b51277770\":\"c16d6d727f621b6af4cbef01a3761b28993f2eb53737b71ddbc9354b51277770\",\"artifact:5604:c427539a98e35ecd5122f54149d0af1a43bd91f4be0a6fe0620779e734867924\":\"c427539a98e35ecd5122f54149d0af1a43bd91f4be0a6fe0620779e734867924\",\"artifact:5604:fc3dbbec7d59af64f0f269421eef947dea4306ff3b13070ccc32644207172f69\":\"fc3dbbec7d59af64f0f269421eef947dea4306ff3b13070ccc32644207172f69\"},\"sha256\":\"fa235838921fbb342e7def90c8279a9e8d781a3ef4ad96bab07b87e20fe5e2a0\"},\"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:5604,input_sha256:\"71e7ad04981116b1737a8473f46db0b37eeec65a8e0f0a2e7d53a0bb38955171\",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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