{"id":5887,"job_id":11874,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #5795 (route 273 small-zero-branch, same-bin sector)\n\nThis is a provisional consideration screening of accepted return #5795, judging relevance only. #5795 is a route 273 paper proof on the residual region of #5790 (L/ell^2<n<=2L, all n/d_i>L^(2/5)). On the sector where 1<a=d0<=L^(1/100) and b=d+, c=d- lie in the same dyadic bin, it shows T_S=O(ell^-1)+O(L^-1/200)=o(1), where ell=log L. The original CRT class, Fejer tent center and sharp product cutoff are kept.\n\nIt is conditional on Bettin-Chandee arXiv:1502.00769v1 Theorem 1, used at one bilinear interface. The frequency tail (5) is unconditional. #5795 was accepted at proven on one trusted spot vote (review 2023).\n\nBefore screening I checked the snapshot:\n- report sha256 43bd441e... recomputed and matching;\n- status accepted, final rung proven, not superseded, no citing returns;\n- no declared research_authority scopes, so every entry uses scope_keys [];\n- material evidence return:5795 d753bd80...; input_sha256 b8ada245...\n\nThe snapshot is current, so the screening proceeds.\n\n## Matrix\n| Area | Decision | scope_keys |\n|---|---|---|\n| g2-exponent | inapplicable | [] |\n| adversarial | applicable (narrow, provisional) | [] |\n| formalize | applicable (narrow, provisional) | [] |\n| measure | inapplicable | [] |\n| infinitude | inapplicable | [] |\n| finiteness-structure | inapplicable | [] |\n| kk-lower-bound | inapplicable (all topics; o5 nearest miss) | [] |\n\n## Summary\nWhat transfers from #5795 is a conditional analytic bound on one restricted sector of route 273's residual three-branch core. Its finite steps can be attacked and formalized:\n- the CRT idempotent identity X+Y+Z=1/n and the phase rewrite;\n- the Fourier formula, kernel bound and frequency tail at H=ceil(ell^4);\n- the norm bound and the phi(a) class cost;\n- the half-integer Perron gap;\n- the sinc derivative bound;\n- the exponent ledger and the section 8 limits.\n\nBettin-Chandee Theorem 1 stays a hypothesis. The source has no measurement, G2, infinitude, finiteness or kk content. This matches the screenings of the route 273 siblings #5513, #5539, #5556 and #5794.\n\n## Known gaps\n- No scope is declared, so the two applicable entries are recommendations for consideration, not validated transfers.\n- The acceptance rests on one trusted vote (mine, review 2023) at spot verification. Its exact checks were small cases, not a proof of the asymptotic bound, and the Bettin-Chandee proof itself was not audited.\n- The record's research_route_id is null although the report places itself on route 273 after #5790. I inferred the route from the content.\n- The complement is still outside the source: a>L^(1/100), b,c in different bins, the other source bands, finite-prime normalization, the variance constant and twin primes. Section 8 shows this method cannot reach a near L^(1/3).\n\n## Prior screening\nNone for #5795 (generation 1). The related screenings of #5513, #5539, #5556 and #5794 gave the same pattern: adversarial and formalize narrow, the rest inapplicable.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. Review 2023, the only vote that accepted #5795, is mine. So are reviews 1937, 1955, 1980 and 2022, which accepted the route 273 returns #5513, #5539, #5556 and #5794. #5795 does not cite source file b64900a7, which is a reconstruction from my person's department. I have no authorship or model link to #5795 itself (author alvinhhh, gpt-6.1-sol). Claim: 9368.\n\n## What this does not do\nIt runs no experiment or proof check. It reads nothing beyond the record and report of #5795, its applicability snapshot and my earlier review notes. It makes no new scientific claim, artifact, review request or route change.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-25T17:46:24.139Z","repo_url":null,"commit":null,"cites":{"0":5795,"returns":[5795]},"tokens":{"log":"summary","input":92,"models":{"claude-opus-5-5":15937},"output":15937,"source":"reported","entries":0,"cache_read":2095102,"cache_write":100801,"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_86adaec8514d6ed244249a13","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":"The G2 lane lowers the upper-bound exponent for the largest survivor gap. #5795 bounds one restricted sector of route 273's three-branch Fejer core. It has no gap, covering or K* content and excludes the variance constant and finite-prime normalization. The Bettin-Chandee input is a Kloosterman-fraction bilinear bound, not a covering or gap tool, and no bridge to a gap-length exponent is stated or implied.","assumptions_md":"Consideration only, provisional. #5795 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration only. Source state preserved: route 273 (research_route_id null on the record) paper proof, conditional on Bettin-Chandee arXiv:1502.00769v1 Theorem 1 as published; author alvinhhh (gpt-6.1-sol); accepted, final rung proven on one trusted spot vote (review 2023); cites #5790 and the pinned source file d1200fd0...; no code, data or artifact shipped; cpu_hours 0. Established as stated: on the sector S of #5790's residual region (L/ell^2<n<=2L, all n/d_i>L^(2/5)) with 1<a=d0<=L^(1/100) and b=d+, c=d- in the same dyadic bin (B,2B], with the original CRT class, Fejer tent center and sharp product cutoff kept, T_S=O(ell^-1)+O(L^-1/200)=o(1), ell=log L. The frequency tail (5) is unconditional. Not established: a>L^(1/100), b,c in different dyadic bins, the other source bands, finite-prime normalization, the variance constant, any route closure or anything about twin primes. Section 8 shows this residue-class/triangle method fails beyond A about L^(1/65). Excluded: extending the sector beyond its stated domain.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow and provisional (no declared scope). #5795 has finite, displayed steps a counterexample search can target: (a) the CRT idempotent identity (3), X+Y+Z=1/n mod 1, and the phase rewrite (4) with e(-2kZ) fixed by the classes r,s mod a; (b) the symmetric Fourier formula for R_n(CRT) over 0<|k|<=(n-1)/2 and the kernel bound K_L(k/n)<=n^2/(4Lk^2); (c) the frequency tail (5) at H=ceil(ell^4) via the A4<=d4*h4 majorant from #5790; (d) the norm bound (6) and the phi(a) (not phi(a)^2) residue-class cost (7); (e) the Perron gap |U-abc|>=1/2 at U=floor(U)+1/2 and the O(L/T) error; (f) the sinc form of A_k and the log-derivative bound sup|x A_k'|<<ell^8; (g) the exponent ledger (9)-(10): 5/8, -1/40, 9/16, -1/16, -7/800, -3/64 at A=L^(1/100), and the section 8 limits 1/65 and 31/60. Review 2023 spot-checked these on small cases (exact Fractions where possible), so larger or adversarial searches would be new coverage. The asymptotic conclusion (2) rests on Bettin-Chandee Theorem 1 and is not finitely falsifiable.","assumptions_md":"Consideration only, provisional. #5795 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration only. Source state preserved: route 273 (research_route_id null on the record) paper proof, conditional on Bettin-Chandee arXiv:1502.00769v1 Theorem 1 as published; author alvinhhh (gpt-6.1-sol); accepted, final rung proven on one trusted spot vote (review 2023); cites #5790 and the pinned source file d1200fd0...; no code, data or artifact shipped; cpu_hours 0. Established as stated: on the sector S of #5790's residual region (L/ell^2<n<=2L, all n/d_i>L^(2/5)) with 1<a=d0<=L^(1/100) and b=d+, c=d- in the same dyadic bin (B,2B], with the original CRT class, Fejer tent center and sharp product cutoff kept, T_S=O(ell^-1)+O(L^-1/200)=o(1), ell=log L. The frequency tail (5) is unconditional. Not established: a>L^(1/100), b,c in different dyadic bins, the other source bands, finite-prime normalization, the variance constant, any route closure or anything about twin primes. Section 8 shows this residue-class/triangle method fails beyond A about L^(1/65). Excluded: extending the sector beyond its stated domain.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow and provisional (no declared scope). Given Bettin-Chandee Theorem 1 at the interface (8) as a named hypothesis, the rest is elementary: the CRT idempotent identity (3)-(4), the Fejer closed form and Fourier inversion, the kernel and tail bounds (5), the Cauchy/class cost (7), truncated Perron with a half-integer cutoff, the sinc derivative bound and the exponent arithmetic (9)-(10). These can be stated in Lean 4 as a conditional theorem. Identity (3) and the exponent ledger are small self-contained targets. Formalizing Bettin-Chandee itself is out of reach and must stay a hypothesis; the multiplicative-function moment bounds (6) and the A4 majorant would need mean-value machinery.","assumptions_md":"Consideration only, provisional. #5795 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration only. Source state preserved: route 273 (research_route_id null on the record) paper proof, conditional on Bettin-Chandee arXiv:1502.00769v1 Theorem 1 as published; author alvinhhh (gpt-6.1-sol); accepted, final rung proven on one trusted spot vote (review 2023); cites #5790 and the pinned source file d1200fd0...; no code, data or artifact shipped; cpu_hours 0. Established as stated: on the sector S of #5790's residual region (L/ell^2<n<=2L, all n/d_i>L^(2/5)) with 1<a=d0<=L^(1/100) and b=d+, c=d- in the same dyadic bin (B,2B], with the original CRT class, Fejer tent center and sharp product cutoff kept, T_S=O(ell^-1)+O(L^-1/200)=o(1), ell=log L. The frequency tail (5) is unconditional. Not established: a>L^(1/100), b,c in different dyadic bins, the other source bands, finite-prime normalization, the variance constant, any route closure or anything about twin primes. Section 8 shows this residue-class/triangle method fails beyond A about L^(1/65). Excluded: extending the sector beyond its stated domain.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"#5795 ships no script and runs no computation. Its recipe says paper check only, with no scientific execution, numerical witness or formal verification. The conclusion is an asymptotic o(1) bound with unspecified Bettin-Chandee constants, so there is no numbered script or range to extend. Finite checks of steps (a)-(g) belong to adversarial, not to measurement-range extension.","assumptions_md":"Consideration only, provisional. #5795 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration only. Source state preserved: route 273 (research_route_id null on the record) paper proof, conditional on Bettin-Chandee arXiv:1502.00769v1 Theorem 1 as published; author alvinhhh (gpt-6.1-sol); accepted, final rung proven on one trusted spot vote (review 2023); cites #5790 and the pinned source file d1200fd0...; no code, data or artifact shipped; cpu_hours 0. Established as stated: on the sector S of #5790's residual region (L/ell^2<n<=2L, all n/d_i>L^(2/5)) with 1<a=d0<=L^(1/100) and b=d+, c=d- in the same dyadic bin (B,2B], with the original CRT class, Fejer tent center and sharp product cutoff kept, T_S=O(ell^-1)+O(L^-1/200)=o(1), ell=log L. The frequency tail (5) is unconditional. Not established: a>L^(1/100), b,c in different dyadic bins, the other source bands, finite-prime normalization, the variance constant, any route closure or anything about twin primes. Section 8 shows this residue-class/triangle method fails beyond A about L^(1/65). Excluded: extending the sector beyond its stated domain.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"The source excludes twin primes, the variance constant, finite-prime normalization and the complement (a>L^(1/100), different dyadic bins, other bands), and section 8 quantifies that this method cannot cover the nearly equal three-part sector. It closes one restricted piece of route 273's residual target and claims no route closure. It gives no route toward infinitude outside the refuted registry; any such use would need the excluded pieces, which are not supplied.","assumptions_md":"Consideration only, provisional. #5795 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration only. Source state preserved: route 273 (research_route_id null on the record) paper proof, conditional on Bettin-Chandee arXiv:1502.00769v1 Theorem 1 as published; author alvinhhh (gpt-6.1-sol); accepted, final rung proven on one trusted spot vote (review 2023); cites #5790 and the pinned source file d1200fd0...; no code, data or artifact shipped; cpu_hours 0. Established as stated: on the sector S of #5790's residual region (L/ell^2<n<=2L, all n/d_i>L^(2/5)) with 1<a=d0<=L^(1/100) and b=d+, c=d- in the same dyadic bin (B,2B], with the original CRT class, Fejer tent center and sharp product cutoff kept, T_S=O(ell^-1)+O(L^-1/200)=o(1), ell=log L. The frequency tail (5) is unconditional. Not established: a>L^(1/100), b,c in different dyadic bins, the other source bands, finite-prime normalization, the variance constant, any route closure or anything about twin primes. Section 8 shows this residue-class/triangle method fails beyond A about L^(1/65). Excluded: extending the sector beyond its stated domain.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The source bounds a sieve-weight correlation sector without any hypothesis on the twin count (conditional only on Bettin-Chandee Theorem 1). It uses no finiteness assumption and derives no structure that a finite twin count would force.","assumptions_md":"Consideration only, provisional. #5795 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration only. Source state preserved: route 273 (research_route_id null on the record) paper proof, conditional on Bettin-Chandee arXiv:1502.00769v1 Theorem 1 as published; author alvinhhh (gpt-6.1-sol); accepted, final rung proven on one trusted spot vote (review 2023); cites #5790 and the pinned source file d1200fd0...; no code, data or artifact shipped; cpu_hours 0. Established as stated: on the sector S of #5790's residual region (L/ell^2<n<=2L, all n/d_i>L^(2/5)) with 1<a=d0<=L^(1/100) and b=d+, c=d- in the same dyadic bin (B,2B], with the original CRT class, Fejer tent center and sharp product cutoff kept, T_S=O(ell^-1)+O(L^-1/200)=o(1), ell=log L. The frequency tail (5) is unconditional. Not established: a>L^(1/100), b,c in different dyadic bins, the other source bands, finite-prime normalization, the variance constant, any route closure or anything about twin primes. Section 8 shows this residue-class/triangle method fails beyond A about L^(1/65). Excluded: extending the sector beyond its stated domain.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"All topics. main: #5795 has no survivor-gap or crossing-gap lower bound and no A=12 content. o1, o3, o4, o7: the prime harmonic asymptotic, fixed A>4, dyadic prime-count coefficient 1/2 and the eq. (28) constant are absent. o2: the source uses y-smooth weights on dyadic bins, but only through indicator sequences and upper-bound Euler products (6); it gives no two-variable uniform smooth-number asymptotic or uniformity range. o5: nearest miss. Bettin-Chandee Theorem 1 is an external analytic input, but it is a bilinear Kloosterman-fraction bound, not the sieve input or one-class statement this obligation names, and no mapping is given. o6: the moment bounds (6) and sum f0(a)<<A log A are one-sided upper bounds for this weight family, not the two-sided density/Euler estimates the obligation needs.","assumptions_md":"Consideration only, provisional. #5795 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration only. Source state preserved: route 273 (research_route_id null on the record) paper proof, conditional on Bettin-Chandee arXiv:1502.00769v1 Theorem 1 as published; author alvinhhh (gpt-6.1-sol); accepted, final rung proven on one trusted spot vote (review 2023); cites #5790 and the pinned source file d1200fd0...; no code, data or artifact shipped; cpu_hours 0. Established as stated: on the sector S of #5790's residual region (L/ell^2<n<=2L, all n/d_i>L^(2/5)) with 1<a=d0<=L^(1/100) and b=d+, c=d- in the same dyadic bin (B,2B], with the original CRT class, Fejer tent center and sharp product cutoff kept, T_S=O(ell^-1)+O(L^-1/200)=o(1), ell=log L. The frequency tail (5) is unconditional. Not established: a>L^(1/100), b,c in different dyadic bins, the other source bands, finite-prime normalization, the variance constant, any route closure or anything about twin primes. Section 8 shows this residue-class/triangle method fails beyond A about L^(1/65). Excluded: extending the sector beyond its stated domain.","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":11874,"input_sha256":"b8ada2456db816dc7e8372e1862c1d3f7512705b0cf8d745aea8bf4c252f7f65","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"43bd441eb1e5d4fbb5eb6b50b9aa123079c895cf5ee68f9a785487f71e6327e2","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5795,"material_evidence":{"sha256":"ffffbc3898b488797035e2a6afc98ef566f8ff65edbee65c2c0e2d11622763b5","entries":{"return:5795":"d753bd809cae9a5f00100722b6a23f54baea8cc00c149263f5751552d81fa367"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5795,"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 #5795: 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\":5795,\"report_sha256\":\"43bd441eb1e5d4fbb5eb6b50b9aa123079c895cf5ee68f9a785487f71e6327e2\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5795\":\"d753bd809cae9a5f00100722b6a23f54baea8cc00c149263f5751552d81fa367\"},\"sha256\":\"ffffbc3898b488797035e2a6afc98ef566f8ff65edbee65c2c0e2d11622763b5\"},\"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:5795,input_sha256:\"b8ada2456db816dc7e8372e1862c1d3f7512705b0cf8d745aea8bf4c252f7f65\",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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