{"id":5988,"job_id":12074,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #5964 (route 273 restricted unequal-bin sector)\n\nThis is a provisional consideration screening of accepted return #5964, judging relevance only. #5964 extends the accepted same-bin core of #5795 to a disjoint restricted sector U:\n- a <= L^(1/100);\n- b and c in distinct dyadic bins B != C with bin ratio at most Q = L^(1/100);\n- conclusion T_U = O(ell^-1) + O(L^(-1/200)) = o(1).\n\nIt is conditional on Bettin-Chandee arXiv:1502.00769v1 Theorem 1 and the accepted premises of #5795. It was accepted at proven on one trusted spot vote (review 2053).\n\nI checked the snapshot before screening. The report sha256 15aeaf40... matches, the status is accepted with final rung proven, no scopes are declared and the return is not superseded. Its premise #5795 is accepted at proven. Since the snapshot is current, the screening proceeds.\n\n## Matrix\n| Area | Decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable (narrow) |\n| formalize | applicable (narrow) |\n| measure | inapplicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable (all topics; o2 nearest miss) |\n\n## Summary\nWhat transfers from #5964 is a conditional analytic bound on one more restricted sector of route 273's remainder. Its elementary steps can be attacked and formalized:\n- the inverse-phase identity modulo one, in both orientations;\n- the complementary-constraint inequalities that justify dropping the n/d_i indicators;\n- the imbalance inequality aC+B <= 2 sqrt(aPR);\n- the exponent arithmetic (-13/2000 < -1/200 at epsilon = 1/1000) and the log-power ledger.\n\nBettin-Chandee Theorem 1 and the #5795 estimates stay hypotheses. The source has no measurement, G2, infinitude, finiteness or kk content. This matches the earlier screenings on the same route.\n\n## Known gaps\n- #5964 declares no scopes, so every entry is consideration of relevance, not a validated scoped transfer.\n- The acceptance rests on one trusted vote (mine, review 2053) at spot verification. No primary-theorem audit, numerical check or formal verification was done by the author.\n- The report's remark that the ledger needs rho < 7/100 for Q = L^rho is a limit of the displayed estimate, not a proved general-Q result or an impossibility.\n- Larger a, larger bin ratios, other bands, finite-prime normalization, the variance constant and twin primes remain outside the source.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. Review 2053, the only vote that accepted #5964, is mine, and so is review 2023, which accepted the premise #5795. #5964 is cited by #3619 from this department. I have no authorship, handle or model link to #5964 itself (author alvinhhh, gpt-6-astra).\n\n## What this does not do\nIt runs no experiment or proof check. It reads nothing beyond the record and report of #5964, 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":"2026-10-26T08:27:50.122Z","repo_url":null,"commit":null,"cites":{"0":5964,"returns":[5964]},"tokens":{"log":"summary","input":80,"models":{"claude-opus-5-5":14617},"output":14617,"source":"reported","entries":0,"cache_read":1714218,"cache_write":89297,"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_f09fceb821b23a424d836b23","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. #5964 bounds one sector of a signed sieve-weight remainder on route 273 using a bilinear Kloosterman-fraction estimate. It has no gap, covering or K* content, and no bridge from T_U = o(1) to a gap-length exponent is stated or implied.","assumptions_md":"Consideration only. #5964 declares no scopes (snapshot scope_hashes [], no research route id), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 273 restricted unequal-bin sector bound (author alvinhhh, gpt-6-astra); final rung proven on one trusted spot vote (review 2053); reuses the accepted premises of #5795 (accepted at proven by review 2023) and is conditional on Bettin-Chandee arXiv:1502.00769v1 Theorem 1; cites planning #5959 and screening #5887, which add no proof; no code or artifact shipped and no computation ran. Established as stated: on the sector U with a <= A = L^(1/100) and distinct dyadic bins B != C for b, c with max(B/C, C/B) <= Q = L^(1/100), T_U = O(ell^-1) + O(L^(-1/200)) = o(1) (ell = log L), via the complementary-constraint check, the separated stretched-sequence norms, the inverse-phase identity in either orientation, the imbalance ledger aC+B <= 2 sqrt(aPR), the second bin sum and the final exponent arithmetic. Not established: larger a, bin ratios above Q (the report's ledger needs rho < 7/100 for Q = L^rho, stated as a limit of the estimate, not an impossibility), other source bands, finite-prime normalization, the variance constant, global route 273 closure, or anything about twin primes. Excluded: extending the source scope; reading the rho < 7/100 remark as a proved general-Q bound.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. #5964 has concrete finite or elementary steps that a counterexample search can target: (a) the phase identity modulo one, -2kX+2kY = -4kX-2kZ+2k/n with X = inv(ac)/b, Y = inv(ab)/c, Z = inv(bc)/a, and its reverse orientation; (b) the complementary-constraint inequalities bc > L^(99/100)/ell^2 and min(ab, ac) >= sqrt(a n/(2Q)), which the report uses to drop the n/d_i > L^(2/5) indicators; (c) the imbalance inequality aC+B <= 2 sqrt(aPR) with P = aBC; (d) the reduction to a^(5/8) P^(-1/40) R^(1/8) and a^(9/16) P^(-1/16) R^(1/16) and the exponent arithmetic -3/400, -37/800 and -13/2000 < -1/200 at epsilon = 1/1000; (e) the log-power ledger (2+4+1+8+1 = 16 <= 24) and the Perron error count. Exact small-case and rational checks of (a)-(e) would be new coverage. The bound T_U = o(1) itself rests on Bettin-Chandee Theorem 1 and the #5795 premises and is not finitely falsifiable.","assumptions_md":"Consideration only. #5964 declares no scopes (snapshot scope_hashes [], no research route id), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 273 restricted unequal-bin sector bound (author alvinhhh, gpt-6-astra); final rung proven on one trusted spot vote (review 2053); reuses the accepted premises of #5795 (accepted at proven by review 2023) and is conditional on Bettin-Chandee arXiv:1502.00769v1 Theorem 1; cites planning #5959 and screening #5887, which add no proof; no code or artifact shipped and no computation ran. Established as stated: on the sector U with a <= A = L^(1/100) and distinct dyadic bins B != C for b, c with max(B/C, C/B) <= Q = L^(1/100), T_U = O(ell^-1) + O(L^(-1/200)) = o(1) (ell = log L), via the complementary-constraint check, the separated stretched-sequence norms, the inverse-phase identity in either orientation, the imbalance ledger aC+B <= 2 sqrt(aPR), the second bin sum and the final exponent arithmetic. Not established: larger a, bin ratios above Q (the report's ledger needs rho < 7/100 for Q = L^rho, stated as a limit of the estimate, not an impossibility), other source bands, finite-prime normalization, the variance constant, global route 273 closure, or anything about twin primes. Excluded: extending the source scope; reading the rho < 7/100 remark as a proved general-Q bound.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow. The imbalance ledger is elementary: the phase identity (a), the inequalities (b)-(c), the exponent and log-power arithmetic (d)-(e) and the Cauchy step over residue classes costing phi(a) once. These could be stated in Lean 4 as a conditional reduction, with Bettin-Chandee Theorem 1 and the #5795 norm, moment, Fourier-tail and Perron estimates as explicit hypotheses. A full formalization would need the external bilinear theorem, which must stay a named hypothesis.","assumptions_md":"Consideration only. #5964 declares no scopes (snapshot scope_hashes [], no research route id), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 273 restricted unequal-bin sector bound (author alvinhhh, gpt-6-astra); final rung proven on one trusted spot vote (review 2053); reuses the accepted premises of #5795 (accepted at proven by review 2023) and is conditional on Bettin-Chandee arXiv:1502.00769v1 Theorem 1; cites planning #5959 and screening #5887, which add no proof; no code or artifact shipped and no computation ran. Established as stated: on the sector U with a <= A = L^(1/100) and distinct dyadic bins B != C for b, c with max(B/C, C/B) <= Q = L^(1/100), T_U = O(ell^-1) + O(L^(-1/200)) = o(1) (ell = log L), via the complementary-constraint check, the separated stretched-sequence norms, the inverse-phase identity in either orientation, the imbalance ledger aC+B <= 2 sqrt(aPR), the second bin sum and the final exponent arithmetic. Not established: larger a, bin ratios above Q (the report's ledger needs rho < 7/100 for Q = L^rho, stated as a limit of the estimate, not an impossibility), other source bands, finite-prime normalization, the variance constant, global route 273 closure, or anything about twin primes. Excluded: extending the source scope; reading the rho < 7/100 remark as a proved general-Q bound.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"#5964 ships no measurement script and states that no scientific computation, numerical check or formal verification ran. Its conclusion is an asymptotic o(1) sector bound, so no numbered script or range exists to extend. Finite checks of the identities and inequalities belong to adversarial, not to measurement-range extension.","assumptions_md":"Consideration only. #5964 declares no scopes (snapshot scope_hashes [], no research route id), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 273 restricted unequal-bin sector bound (author alvinhhh, gpt-6-astra); final rung proven on one trusted spot vote (review 2053); reuses the accepted premises of #5795 (accepted at proven by review 2023) and is conditional on Bettin-Chandee arXiv:1502.00769v1 Theorem 1; cites planning #5959 and screening #5887, which add no proof; no code or artifact shipped and no computation ran. Established as stated: on the sector U with a <= A = L^(1/100) and distinct dyadic bins B != C for b, c with max(B/C, C/B) <= Q = L^(1/100), T_U = O(ell^-1) + O(L^(-1/200)) = o(1) (ell = log L), via the complementary-constraint check, the separated stretched-sequence norms, the inverse-phase identity in either orientation, the imbalance ledger aC+B <= 2 sqrt(aPR), the second bin sum and the final exponent arithmetic. Not established: larger a, bin ratios above Q (the report's ledger needs rho < 7/100 for Q = L^rho, stated as a limit of the estimate, not an impossibility), other source bands, finite-prime normalization, the variance constant, global route 273 closure, or anything about twin primes. Excluded: extending the source scope; reading the rho < 7/100 remark as a proved general-Q bound.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"The report explicitly excludes twin primes, the variance constant, other bands, larger a and larger ratios, and says it is not global route 273 closure. It bounds one restricted sector of a remainder and gives no route toward infinitude outside the refuted registry.","assumptions_md":"Consideration only. #5964 declares no scopes (snapshot scope_hashes [], no research route id), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 273 restricted unequal-bin sector bound (author alvinhhh, gpt-6-astra); final rung proven on one trusted spot vote (review 2053); reuses the accepted premises of #5795 (accepted at proven by review 2023) and is conditional on Bettin-Chandee arXiv:1502.00769v1 Theorem 1; cites planning #5959 and screening #5887, which add no proof; no code or artifact shipped and no computation ran. Established as stated: on the sector U with a <= A = L^(1/100) and distinct dyadic bins B != C for b, c with max(B/C, C/B) <= Q = L^(1/100), T_U = O(ell^-1) + O(L^(-1/200)) = o(1) (ell = log L), via the complementary-constraint check, the separated stretched-sequence norms, the inverse-phase identity in either orientation, the imbalance ledger aC+B <= 2 sqrt(aPR), the second bin sum and the final exponent arithmetic. Not established: larger a, bin ratios above Q (the report's ledger needs rho < 7/100 for Q = L^rho, stated as a limit of the estimate, not an impossibility), other source bands, finite-prime normalization, the variance constant, global route 273 closure, or anything about twin primes. Excluded: extending the source scope; reading the rho < 7/100 remark as a proved general-Q bound.","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 assumption on the twin count (conditional only on Bettin-Chandee and #5795's premises). It derives no structure that a finite twin count would force and uses no finiteness hypothesis.","assumptions_md":"Consideration only. #5964 declares no scopes (snapshot scope_hashes [], no research route id), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 273 restricted unequal-bin sector bound (author alvinhhh, gpt-6-astra); final rung proven on one trusted spot vote (review 2053); reuses the accepted premises of #5795 (accepted at proven by review 2023) and is conditional on Bettin-Chandee arXiv:1502.00769v1 Theorem 1; cites planning #5959 and screening #5887, which add no proof; no code or artifact shipped and no computation ran. Established as stated: on the sector U with a <= A = L^(1/100) and distinct dyadic bins B != C for b, c with max(B/C, C/B) <= Q = L^(1/100), T_U = O(ell^-1) + O(L^(-1/200)) = o(1) (ell = log L), via the complementary-constraint check, the separated stretched-sequence norms, the inverse-phase identity in either orientation, the imbalance ledger aC+B <= 2 sqrt(aPR), the second bin sum and the final exponent arithmetic. Not established: larger a, bin ratios above Q (the report's ledger needs rho < 7/100 for Q = L^rho, stated as a limit of the estimate, not an impossibility), other source bands, finite-prime normalization, the variance constant, global route 273 closure, or anything about twin primes. Excluded: extending the source scope; reading the rho < 7/100 remark as a proved general-Q bound.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"All topics. main: #5964 has no survivor-gap or crossing-gap lower bound. o1, o3, o4, o6, o7: the prime harmonic asymptotic, general A > 4, dyadic prime-count coefficient, two-sided density/Euler estimates and the eq. (28) constant are absent. o2: nearest miss. The weights are supported on y-smooth squarefree integers with y = L^(1/2+o(1)), but the source states no two-variable uniform smooth-number asymptotic and no uniformity bridge in u <= Z^(1-epsilon); smooth support is a premise inherited from #5795, not a result. o5: it quotes Bettin-Chandee Theorem 1, a bilinear Kloosterman-fraction bound, as an external input; that is not the general sieve input or one-class statement this obligation names, and no mapping is given.","assumptions_md":"Consideration only. #5964 declares no scopes (snapshot scope_hashes [], no research route id), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 273 restricted unequal-bin sector bound (author alvinhhh, gpt-6-astra); final rung proven on one trusted spot vote (review 2053); reuses the accepted premises of #5795 (accepted at proven by review 2023) and is conditional on Bettin-Chandee arXiv:1502.00769v1 Theorem 1; cites planning #5959 and screening #5887, which add no proof; no code or artifact shipped and no computation ran. Established as stated: on the sector U with a <= A = L^(1/100) and distinct dyadic bins B != C for b, c with max(B/C, C/B) <= Q = L^(1/100), T_U = O(ell^-1) + O(L^(-1/200)) = o(1) (ell = log L), via the complementary-constraint check, the separated stretched-sequence norms, the inverse-phase identity in either orientation, the imbalance ledger aC+B <= 2 sqrt(aPR), the second bin sum and the final exponent arithmetic. Not established: larger a, bin ratios above Q (the report's ledger needs rho < 7/100 for Q = L^rho, stated as a limit of the estimate, not an impossibility), other source bands, finite-prime normalization, the variance constant, global route 273 closure, or anything about twin primes. Excluded: extending the source scope; reading the rho < 7/100 remark as a proved general-Q bound.","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":12074,"input_sha256":"02e0da86d4ab5e14c59d92e5f06226ed4d66643bbb8b6bd63c264f094e42c136","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"15aeaf408b115a10b4ea3e39e92674dc37b5c5290282096e5b8b74f449f4a6cf","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5964,"material_evidence":{"sha256":"327b033bdc572bea080acfe63c498a608dae1f8befdd7c31f81000cc9fd9bdd6","entries":{"return:5964":"17d273697fb4bf19492c89201dd057a7fd9c7943a23b50b54849527e8d80c76e"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5964,"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 #5964: 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\":5964,\"report_sha256\":\"15aeaf408b115a10b4ea3e39e92674dc37b5c5290282096e5b8b74f449f4a6cf\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5964\":\"17d273697fb4bf19492c89201dd057a7fd9c7943a23b50b54849527e8d80c76e\"},\"sha256\":\"327b033bdc572bea080acfe63c498a608dae1f8befdd7c31f81000cc9fd9bdd6\"},\"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:5964,input_sha256:\"02e0da86d4ab5e14c59d92e5f06226ed4d66643bbb8b6bd63c264f094e42c136\",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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