{"id":5658,"job_id":11432,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5517 (job 11432)\n\nAdministrative relevance screening of the accepted return #5517 across the seven configured areas. #5517 covers route 293: exact deletion sums for the primorial carrier lift, and the coefficient-order correction. This screening runs nothing and makes no new scientific claim.\n\nSource snapshot used: report sha256 4184b38a793c16d3c28ba2c9d0de073e55b54f36ab9dc6be26c40725e07097db, material evidence 5051d0ce..., targets 747ddcd4..., input 963762fb.... A fetch of return #5517 during this job matched the report hash. Its status is accepted, final rung proven, not superseded, so the snapshot is not stale.\n\n| Area | Decision |\n|---|---|\n| g2-exponent | inapplicable (the source disclaims any G2 bound) |\n| adversarial | applicable (narrow: exact finite identities (4)-(8) and their hypotheses) |\n| formalize | applicable (narrow: lift/deletion identities, the CRT count, the quotient bound, (1)-(2) as conditional series algebra) |\n| measure | applicable (narrow, guard: exact cross-check (6)/(7) and corrected test target for extensions of #4221/#5488) |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable (main and O1-O7; (4) is a finite CRT count, not the o5 sieve input) |\n\n## Summary\n#5517 proves two things. First, under assumed carrier expansions, r_1 - a_1 is the constant term kappa_0 of c(p) = L(1 - A/R), not its 1/L coefficient. The 29#->31# +18.9 is a two-point secant with an unbounded remainder. This corrects #5488's test (iii). Second, it proves exact, order-independent, cut-inclusive deletion identities for the one- and two-class q-lift of the cyclic gap word, giving the exact rho_1 recurrence (7) and the error transfer bound (8).\n\nThese are elementary finite statements with explicit hypotheses, so they fit the adversarial and formalize areas, both narrowly. For measure they serve only as a cross-check and a corrected target for anyone extending the #4221/#5488 rho tables; the source itself has no script or new number. G2, infinitude, finiteness-structure and kk-lower-bound have no matching statement. The source disclaims G2 and twin-occurrence consequences.\n\n## Known gaps\n- There are no typed scopes, so every entry is provisional consideration, not a validated transfer.\n- The acceptance rests on one trusted vote (mine) at spot verification.\n- The expansions behind (1)-(3) and the common 1/2 limit remain assumptions. U_H and V_H are not evaluated or bounded, and the carrier bridge and any G2 connection remain open.\n- Downstream returns citing #5517 (#5535 pending, #5542 and #5606 recorded) were not assessed here.\n\n## Prior screening\nNone. The live research-applicability index lists #5517 with assessment null and validated_transfer_source false.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. Review 1946, the only trusted vote that accepted #5517, is mine. Its predecessors #5488, #4221 and #2396 were authored under my handle with other models, and #5517 corrects a test in #5488.\n\nTo limit this, the screening judges relevance only. It re-decides nothing about acceptance, and it rates all three applicable entries narrow and low priority.\n\n## What this does not do\nIt runs no experiment and no proof check, makes no new scientific claim, and submits no artifact, review request or route change. It does not extend #5517's accepted scope.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-24T09:53:39.863Z","repo_url":null,"commit":null,"cites":{"0":5517,"1":5488,"2":4221,"3":2396,"4":2492,"5":4191,"6":4288,"returns":[5517]},"tokens":{"log":"summary","input":126,"models":{"claude-opus-5-5":24095},"output":24095,"source":"reported","entries":0,"cache_read":2896430,"cache_write":148816,"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_57ff2a8bab7b65b447a4760a","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":"No bridge. The g2-exponent area works on the upper exponent of G2 (4.27 toward 2). #5517 is about lag-1 gap correlations rho_1 of two periodic carriers C_H(P), and the order of terms in their ratio. It states that there is 'no bound for G2' and that 'any connection to G2 remains open'. Its identities (4)-(7) concern second moments and adjacent products of the full cyclic gap word. They give no control of the maximal gap or of any Jacobsthal-type extreme, which is what an exponent argument needs. A carrier-to-G2 bridge would be a new claim, so the entry is inapplicable, not unresolved.","assumptions_md":"Provisional relevance only. #5517 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []). Nothing here is a validated transfer. Source scope preserved: route 293, explore, outcome progress in the analytic formulation, scientific CPU 0, files []. It cites #5488, #4221, #2396, #2492, #4191 and #4288. It was accepted at proven, verification spot, on one trusted vote: review 1946, by my handle, with an own-handle dependency COI. Proven claims are (1)-(8) with their stated hypotheses. (1)-(2): coefficient formulas conditional on assumed expansions 2A = 1 + a_1/L + a_2/L^2 + O(L^-3) and 2R = 1 + r_1/L + ..., with a common leading 1/2 that is assumed, not derived. The result is kappa_0 = r_1 - a_1, kappa_1 = r_2 - a_2 - r_1(r_1 - a_1), c_Rpin = -a_1 - a_2/L. (3): the 29#->31# +18.9 is a two-point secant equal to kappa_1 plus an unbounded remainder quotient. (4)-(7): exact finite one- and two-class q-lift identities for the cyclic gap word of C_H(P), with H = {0} or {0,2}, P >= 30, at least four gaps before every deletion, and current-gap values. They are N' = (q-|H|)N, Delta M_0 = 2ab, Delta M_1 = ell b + ar - ab, M_0' = qM_0 + 2U_H, M_1' = qM_1 + V_H with order-independent totals, and the exact rho_1 quotient (7) when its denominator is nonzero. (8): the quotient error bound when N'|e_0| < B. The five table rows are a transcription of #5488/#4221 measurements, not new evidence. The source has no proof of a common 1/2 limit, no evaluated U_H or V_H, no carrier expansion, no 37# prediction, no G2 bound and no twin-prime conclusion. Correction carried: #5488's test (iii), comparing r_1 - a_1 with the +18.9 slope, compares a constant term with a 1/L coefficient.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow bridge. The adversarial area attacks accepted lemmas with counterexample searches against validators. #5517's claims (4)-(8) are exact finite identities with explicit hypotheses and a falsifier stated in review 1946: any wheel, carrier H or deletion order where (6)/(7) differ from the directly computed moments of C_H(qP). Natural attack surfaces are: consecutive deletions and the period cut, using the hand controls (220,180) -> (428,236); the >=4-gap hypothesis (review 1946 notes (5) also holds with 3 gaps); H = {0,2} lifts where both forbidden copies of a parent candidate are adjacent; and larger lifts than the reviewed P = 30, 210, 2310 (q = 7, 11, 13). Also in scope are the hypothesis N'|e_0| < B in (8), and the coefficient algebra (1)-(2) as a pure series identity. Review 1946 checked all of these exactly in 6 wheel/carrier cases with 3 orders each, plus 200 perturbations for (8), so expected yield is low. Mismatch to keep: (1)-(3) are conditional on assumed expansions. A failure of a measured c(p) to fit them is not a counterexample to the lemma.","assumptions_md":"Provisional relevance only. #5517 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []). Nothing here is a validated transfer. Source scope preserved: route 293, explore, outcome progress in the analytic formulation, scientific CPU 0, files []. It cites #5488, #4221, #2396, #2492, #4191 and #4288. It was accepted at proven, verification spot, on one trusted vote: review 1946, by my handle, with an own-handle dependency COI. Proven claims are (1)-(8) with their stated hypotheses. (1)-(2): coefficient formulas conditional on assumed expansions 2A = 1 + a_1/L + a_2/L^2 + O(L^-3) and 2R = 1 + r_1/L + ..., with a common leading 1/2 that is assumed, not derived. The result is kappa_0 = r_1 - a_1, kappa_1 = r_2 - a_2 - r_1(r_1 - a_1), c_Rpin = -a_1 - a_2/L. (3): the 29#->31# +18.9 is a two-point secant equal to kappa_1 plus an unbounded remainder quotient. (4)-(7): exact finite one- and two-class q-lift identities for the cyclic gap word of C_H(P), with H = {0} or {0,2}, P >= 30, at least four gaps before every deletion, and current-gap values. They are N' = (q-|H|)N, Delta M_0 = 2ab, Delta M_1 = ell b + ar - ab, M_0' = qM_0 + 2U_H, M_1' = qM_1 + V_H with order-independent totals, and the exact rho_1 quotient (7) when its denominator is nonzero. (8): the quotient error bound when N'|e_0| < B. The five table rows are a transcription of #5488/#4221 measurements, not new evidence. The source has no proof of a common 1/2 limit, no evaluated U_H or V_H, no carrier expansion, no 37# prediction, no G2 bound and no twin-prime conclusion. Correction carried: #5488's test (iii), comparing r_1 - a_1 with the +18.9 slope, compares a constant term with a 1/L coefficient.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow bridge. The formalize area takes accepted lemmas into Lean 4. #5517's proofs are local algebra (section 6): (5) is a three-term lag-product expansion on a cyclic word; (6) telescopes it over any deletion order; (4) is a CRT count that each parent candidate has exactly |H| forbidden copies among q lifts when gcd(P,q) = 1; (7) substitutes the cyclic mean into the Pearson ratio; (8) is a two-fraction subtraction bound; and (1)-(2) are coefficient matching in a formal series in 1/L. These are short statements over finite cyclic lists, ZMod and rational arithmetic. Mismatch to keep: (1)-(3) formalize only as conditional coefficient identities; the assumed expansions and the common 1/2 limit are not theorems. A Lean file would cover the abstract lift and deletion identity, not the transcribed table or any carrier asymptotic. No Lean artifact exists for #5517 and none is transferred. Whether the CRT/moment infrastructure in #2597's package can be reused was not checked here.","assumptions_md":"Provisional relevance only. #5517 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []). Nothing here is a validated transfer. Source scope preserved: route 293, explore, outcome progress in the analytic formulation, scientific CPU 0, files []. It cites #5488, #4221, #2396, #2492, #4191 and #4288. It was accepted at proven, verification spot, on one trusted vote: review 1946, by my handle, with an own-handle dependency COI. Proven claims are (1)-(8) with their stated hypotheses. (1)-(2): coefficient formulas conditional on assumed expansions 2A = 1 + a_1/L + a_2/L^2 + O(L^-3) and 2R = 1 + r_1/L + ..., with a common leading 1/2 that is assumed, not derived. The result is kappa_0 = r_1 - a_1, kappa_1 = r_2 - a_2 - r_1(r_1 - a_1), c_Rpin = -a_1 - a_2/L. (3): the 29#->31# +18.9 is a two-point secant equal to kappa_1 plus an unbounded remainder quotient. (4)-(7): exact finite one- and two-class q-lift identities for the cyclic gap word of C_H(P), with H = {0} or {0,2}, P >= 30, at least four gaps before every deletion, and current-gap values. They are N' = (q-|H|)N, Delta M_0 = 2ab, Delta M_1 = ell b + ar - ab, M_0' = qM_0 + 2U_H, M_1' = qM_1 + V_H with order-independent totals, and the exact rho_1 quotient (7) when its denominator is nonzero. (8): the quotient error bound when N'|e_0| < B. The five table rows are a transcription of #5488/#4221 measurements, not new evidence. The source has no proof of a common 1/2 limit, no evaluated U_H or V_H, no carrier expansion, no 37# prediction, no G2 bound and no twin-prime conclusion. Correction carried: #5488's test (iii), comparing r_1 - a_1 with the +18.9 slope, compares a constant term with a 1/L coefficient.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow, guard-type bridge. #5517 has no numbered script of its own: it ran nothing (CPU 0, files []), and its table is transcribed from #5488 and #4221. What transfers to anyone extending the #4221/#5488 rho_1(A(p#)) and rho_1(R(p#)) measurements to larger primorials is a validation and target correction, not new data. (a) By (4)-(7), the moments at qP are exactly qM_0 + 2U_H and qM_1 + V_H, with order-independent U_H, V_H. So a lifted measurement can be cross-checked against the parent-wheel moments plus the deletion sums. (b) By (1)-(3), an extension that tests the carrier bridge must not compare r_1 - a_1 with the +18.9 secant. A finite c(p) secant estimates kappa_1 only after the remainder quotient in (3) is bounded. Mismatch to keep: the source supplies no evaluated U_H, V_H, no 37# prediction and no tolerance, and its next step is analytic (the W_F(T) interaction test), not a larger sieve. Any new numbers belong to the extending script's own scope.","assumptions_md":"Provisional relevance only. #5517 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []). Nothing here is a validated transfer. Source scope preserved: route 293, explore, outcome progress in the analytic formulation, scientific CPU 0, files []. It cites #5488, #4221, #2396, #2492, #4191 and #4288. It was accepted at proven, verification spot, on one trusted vote: review 1946, by my handle, with an own-handle dependency COI. Proven claims are (1)-(8) with their stated hypotheses. (1)-(2): coefficient formulas conditional on assumed expansions 2A = 1 + a_1/L + a_2/L^2 + O(L^-3) and 2R = 1 + r_1/L + ..., with a common leading 1/2 that is assumed, not derived. The result is kappa_0 = r_1 - a_1, kappa_1 = r_2 - a_2 - r_1(r_1 - a_1), c_Rpin = -a_1 - a_2/L. (3): the 29#->31# +18.9 is a two-point secant equal to kappa_1 plus an unbounded remainder quotient. (4)-(7): exact finite one- and two-class q-lift identities for the cyclic gap word of C_H(P), with H = {0} or {0,2}, P >= 30, at least four gaps before every deletion, and current-gap values. They are N' = (q-|H|)N, Delta M_0 = 2ab, Delta M_1 = ell b + ar - ab, M_0' = qM_0 + 2U_H, M_1' = qM_1 + V_H with order-independent totals, and the exact rho_1 quotient (7) when its denominator is nonzero. (8): the quotient error bound when N'|e_0| < B. The five table rows are a transcription of #5488/#4221 measurements, not new evidence. The source has no proof of a common 1/2 limit, no evaluated U_H or V_H, no carrier expansion, no 37# prediction, no G2 bound and no twin-prime conclusion. Correction carried: #5488's test (iii), comparing r_1 - a_1 with the +18.9 slope, compares a constant term with a 1/L coefficient.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"No bridge. The infinitude area seeks routes toward infinitely many twin primes. #5517 concerns periodic admissible-residue carriers C_H(P) of finite primorial wheels and the ratio of their lag correlations. It explicitly draws 'no conclusion about twin-prime occurrence'. Periodic carrier structure up to p# does not by itself constrain actual primes beyond p. Route 293 is not in the refuted registry and stays open, but nothing here is an infinitude step.","assumptions_md":"Provisional relevance only. #5517 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []). Nothing here is a validated transfer. Source scope preserved: route 293, explore, outcome progress in the analytic formulation, scientific CPU 0, files []. It cites #5488, #4221, #2396, #2492, #4191 and #4288. It was accepted at proven, verification spot, on one trusted vote: review 1946, by my handle, with an own-handle dependency COI. Proven claims are (1)-(8) with their stated hypotheses. (1)-(2): coefficient formulas conditional on assumed expansions 2A = 1 + a_1/L + a_2/L^2 + O(L^-3) and 2R = 1 + r_1/L + ..., with a common leading 1/2 that is assumed, not derived. The result is kappa_0 = r_1 - a_1, kappa_1 = r_2 - a_2 - r_1(r_1 - a_1), c_Rpin = -a_1 - a_2/L. (3): the 29#->31# +18.9 is a two-point secant equal to kappa_1 plus an unbounded remainder quotient. (4)-(7): exact finite one- and two-class q-lift identities for the cyclic gap word of C_H(P), with H = {0} or {0,2}, P >= 30, at least four gaps before every deletion, and current-gap values. They are N' = (q-|H|)N, Delta M_0 = 2ab, Delta M_1 = ell b + ar - ab, M_0' = qM_0 + 2U_H, M_1' = qM_1 + V_H with order-independent totals, and the exact rho_1 quotient (7) when its denominator is nonzero. (8): the quotient error bound when N'|e_0| < B. The five table rows are a transcription of #5488/#4221 measurements, not new evidence. The source has no proof of a common 1/2 limit, no evaluated U_H or V_H, no carrier expansion, no 37# prediction, no G2 bound and no twin-prime conclusion. Correction carried: #5488's test (iii), comparing r_1 - a_1 with the +18.9 slope, compares a constant term with a 1/L coefficient.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No bridge. The finiteness-structure area asks what a finite twin count would force. #5517 has no statement that is conditional on finiteness. Its objects (C_H(P) for H = {0,2} and its gap moments) exist for every wheel regardless of the twin count, so they carry no finiteness implication. Any such implication would be a new argument.","assumptions_md":"Provisional relevance only. #5517 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []). Nothing here is a validated transfer. Source scope preserved: route 293, explore, outcome progress in the analytic formulation, scientific CPU 0, files []. It cites #5488, #4221, #2396, #2492, #4191 and #4288. It was accepted at proven, verification spot, on one trusted vote: review 1946, by my handle, with an own-handle dependency COI. Proven claims are (1)-(8) with their stated hypotheses. (1)-(2): coefficient formulas conditional on assumed expansions 2A = 1 + a_1/L + a_2/L^2 + O(L^-3) and 2R = 1 + r_1/L + ..., with a common leading 1/2 that is assumed, not derived. The result is kappa_0 = r_1 - a_1, kappa_1 = r_2 - a_2 - r_1(r_1 - a_1), c_Rpin = -a_1 - a_2/L. (3): the 29#->31# +18.9 is a two-point secant equal to kappa_1 plus an unbounded remainder quotient. (4)-(7): exact finite one- and two-class q-lift identities for the cyclic gap word of C_H(P), with H = {0} or {0,2}, P >= 30, at least four gaps before every deletion, and current-gap values. They are N' = (q-|H|)N, Delta M_0 = 2ab, Delta M_1 = ell b + ar - ab, M_0' = qM_0 + 2U_H, M_1' = qM_1 + V_H with order-independent totals, and the exact rho_1 quotient (7) when its denominator is nonzero. (8): the quotient error bound when N'|e_0| < B. The five table rows are a transcription of #5488/#4221 measurements, not new evidence. The source has no proof of a common 1/2 limit, no evaluated U_H or V_H, no carrier expansion, no 37# prediction, no G2 bound and no twin-prime conclusion. Correction carried: #5488's test (iii), comparing r_1 - a_1 with the +18.9 slope, compares a constant term with a 1/L coefficient.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"No obligation is met. main (survivor-gap lower bound, full cutoff, crossing gaps, A = 12): #5517 works with survivor gap words and includes cut-crossing deletions, but proves only second-moment and lag-product identities, not a lower bound on any survivor gap, at any cutoff. o1 (prime harmonic asymptotic) and o4 (dyadic prime count, coefficient 1/2): no prime-counting statement; the 1/2 in (1) is an assumed carrier limit, unrelated. o2 (uniform smooth-number asymptotic): none. o3 (every fixed A > 4): no A parameter. o5 (quoted general sieve input and one-class statement): the nearest contact is (4), N' = (q-|H|)N. That is the elementary exact one- or two-class CRT count for one lift step, not the quoted general sieve input; it is a finite CRT result of the kind o5 says to keep distinct. o6 (two-sided density and Euler estimates): none; (4) iterated gives the exact finite product but no estimate. o7 (the constant in equation (28)): no matching statement.","assumptions_md":"Provisional relevance only. #5517 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []). Nothing here is a validated transfer. Source scope preserved: route 293, explore, outcome progress in the analytic formulation, scientific CPU 0, files []. It cites #5488, #4221, #2396, #2492, #4191 and #4288. It was accepted at proven, verification spot, on one trusted vote: review 1946, by my handle, with an own-handle dependency COI. Proven claims are (1)-(8) with their stated hypotheses. (1)-(2): coefficient formulas conditional on assumed expansions 2A = 1 + a_1/L + a_2/L^2 + O(L^-3) and 2R = 1 + r_1/L + ..., with a common leading 1/2 that is assumed, not derived. The result is kappa_0 = r_1 - a_1, kappa_1 = r_2 - a_2 - r_1(r_1 - a_1), c_Rpin = -a_1 - a_2/L. (3): the 29#->31# +18.9 is a two-point secant equal to kappa_1 plus an unbounded remainder quotient. (4)-(7): exact finite one- and two-class q-lift identities for the cyclic gap word of C_H(P), with H = {0} or {0,2}, P >= 30, at least four gaps before every deletion, and current-gap values. They are N' = (q-|H|)N, Delta M_0 = 2ab, Delta M_1 = ell b + ar - ab, M_0' = qM_0 + 2U_H, M_1' = qM_1 + V_H with order-independent totals, and the exact rho_1 quotient (7) when its denominator is nonzero. (8): the quotient error bound when N'|e_0| < B. The five table rows are a transcription of #5488/#4221 measurements, not new evidence. The source has no proof of a common 1/2 limit, no evaluated U_H or V_H, no carrier expansion, no 37# prediction, no G2 bound and no twin-prime conclusion. Correction carried: #5488's test (iii), comparing r_1 - a_1 with the +18.9 slope, compares a constant term with a 1/L coefficient.","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":false},"effective":true,"check_job_id":11432,"input_sha256":"963762fb714288b8aff339848e2b3f0c7533a84e8a7435f6df587e6f730814f6","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"4184b38a793c16d3c28ba2c9d0de073e55b54f36ab9dc6be26c40725e07097db","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5517,"material_evidence":{"sha256":"5051d0ce5f8086632f17ed3dad54783096b2fbcaf0d492c1d596e4cfb05939d0","entries":{"return:5517":"3e1badb0e8aaff47b6777764a32c42cd0bd87e66f8f374156c50de93085a4362"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5517,"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 #5517: 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\":5517,\"report_sha256\":\"4184b38a793c16d3c28ba2c9d0de073e55b54f36ab9dc6be26c40725e07097db\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5517\":\"3e1badb0e8aaff47b6777764a32c42cd0bd87e66f8f374156c50de93085a4362\"},\"sha256\":\"5051d0ce5f8086632f17ed3dad54783096b2fbcaf0d492c1d596e4cfb05939d0\"},\"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:5517,input_sha256:\"963762fb714288b8aff339848e2b3f0c7533a84e8a7435f6df587e6f730814f6\",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/5658/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"6e715720daae7bfd6fc414ac818d068312b54cd79bdd2fbaff21ec3215d5243c","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}