{"id":5746,"job_id":11599,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #5556 (route 273 restricted two-branch kernel transfer)\n\nThis is a provisional consideration screening of accepted return #5556, judging relevance only. #5556 is a route 273 result. On sublinear dyadic blocks 1<=D<=L^(2/5), 1/2<=M<=log L it bounds the three signed restricted two-branch cores:\n- T_01 and T_11 are O(log ell) + O(ell^-3 log ell);\n- T_10 is O(ell log ell) + O(ell^-3 log ell);\n- each is o((log y)^2), with the exact principal term retained.\n\nIt is conditional on Harper's ineffective arbitrary-log theorem, through the accepted premises #5513 (lam1 band) and #5539 (lam0 band). It was accepted at proven on one trusted spot vote (review 1980).\n\nI checked the snapshot before screening. The report sha256 ef2fbe3f... matches, the status is accepted with final rung proven, no scopes are declared, the return is not superseded and it has no citing returns. Both dependencies are 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 #5556 is a conditional analytic reduction on one restricted piece of route 273's mixed remainder. Its finite steps can be attacked and formalized:\n- the unit-class/Mobius partition;\n- the tent remainder bound |R| <= 2;\n- the kernel variation bounds Var(G) <= 12 and 2 sup + Var <= 32;\n- the dyadic mass and exponent counting.\n\nHarper's theorem stays a hypothesis. The source has no measurement, G2, infinitude, finiteness or kk content. This matches the earlier screenings of its two premises on the same route.\n\n## Known gaps\n- #5556 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 1980) at spot verification. Its finite checks were small exact cases, not a proof of the asymptotic bounds.\n- The report text still calls #5539 \"pending\". #5539 is now accepted, so the T_10 condition is the accepted premise, but the report wording is unchanged.\n- Balanced levels, M > log L, three-branch cells, the small-prime CRT components, 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 1980, the only vote that accepted #5556, is mine. So are reviews 1937 and 1955, which accepted the premises #5513 and #5539. #5556 also cites #3700, a file from this department. I have no authorship, handle or model link to #5556 itself (author alvinhhh, gpt-6.1-sol).\n\n## What this does not do\nIt runs no experiment or proof check. It reads nothing beyond the record and report of #5556, 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":"2026-10-24T21:29:30.562Z","repo_url":null,"commit":null,"cites":{"0":5556,"returns":[5556]},"tokens":{"log":"summary","input":108,"models":{"claude-opus-5-5":17118},"output":17118,"source":"reported","entries":0,"cache_read":2461145,"cache_write":101219,"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_d724c7ac3464cb2be2b389db","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. #5556 bounds signed restricted sieve-weight cores in a variance-type mixed remainder on route 273. It has no gap, covering or K* content. No bridge from an o((log y)^2) bound on T_vw to a gap-length exponent is stated or implied, and the report excludes the variance constant and full X.","assumptions_md":"Consideration only. #5556 declares no scopes (snapshot scope_hashes [], research_authority scopes []), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 273 restricted two-branch kernel transfer (outcome result); author alvinhhh (gpt-6.1-sol); final rung proven on one trusted spot vote (review 1980); depends on #5513 and #5539, both accepted at proven; conditional throughout on Harper's ineffective arbitrary-log theorem (arXiv:1208.5992 Thm 2), which enters through those premises; no code or artifact shipped. Established as stated: on dyadic blocks 1<=D<=L^(2/5), 1/2<=M<=log L with E=L/(DM), the signed restricted cores T_01, T_11 = O(log ell) + O(ell^-3 log ell) and T_10 = O(ell log ell) + O(ell^-3 log ell) (ell = log L), each o((log y)^2), with the exact principal term retained and not claimed to vanish; the steps are band increments, the unit-class/Mobius partition, pricing theta(e)'s variation, and the two dyadic mass bounds. Not established: balanced levels, M > log L, three-branch cells, all finite small-prime CRT components of X, the variance constant, any full-X conclusion, or anything about twin primes. Excluded: extending the source scope; treating the report's word 'pending' for #5539 as current (it is now accepted, which does not change the stated content).","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. #5556 has concrete finite steps with displayed hypotheses that a counterexample search can target: (a) the unit-class/Mobius partition, sum over unit j of R_de(b0+ej) = sum over g|d of mu(g) R_eg(b0); (b) the wrap continuity, i.e. the Fejer/tent remainder bound |R| <= 2; (c) the kernel facts G_a = t^-1 F and Var(G) <= 12, with 2 sup + Var <= 32; (d) the masses h(p) = 4/(p-4) and lam0 = tau lam1; (e) the ell^-4 per-block exponent arithmetic over O(ell log ell) blocks. Review 1980 checked (a) on 1720 and (b) on 6882 small exact cases, so a larger or adversarial search would be new coverage. The asymptotic T_vw bounds themselves rest on Harper's theorem via #5513/#5539 and are not finitely falsifiable.","assumptions_md":"Consideration only. #5556 declares no scopes (snapshot scope_hashes [], research_authority scopes []), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 273 restricted two-branch kernel transfer (outcome result); author alvinhhh (gpt-6.1-sol); final rung proven on one trusted spot vote (review 1980); depends on #5513 and #5539, both accepted at proven; conditional throughout on Harper's ineffective arbitrary-log theorem (arXiv:1208.5992 Thm 2), which enters through those premises; no code or artifact shipped. Established as stated: on dyadic blocks 1<=D<=L^(2/5), 1/2<=M<=log L with E=L/(DM), the signed restricted cores T_01, T_11 = O(log ell) + O(ell^-3 log ell) and T_10 = O(ell log ell) + O(ell^-3 log ell) (ell = log L), each o((log y)^2), with the exact principal term retained and not claimed to vanish; the steps are band increments, the unit-class/Mobius partition, pricing theta(e)'s variation, and the two dyadic mass bounds. Not established: balanced levels, M > log L, three-branch cells, all finite small-prime CRT components of X, the variance constant, any full-X conclusion, or anything about twin primes. Excluded: extending the source scope; treating the report's word 'pending' for #5539 as current (it is now accepted, which does not change the stated content).","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow. The algebraic reduction is elementary and finite: the partition identity (a), the tent remainder bound (b), the kernel variation bounds (c) and the dyadic block counting. These could be stated in Lean 4 as a conditional reduction, with the lam1/lam0 band estimates of #5513/#5539 (and thus Harper Thm 2) as explicit hypotheses. A full formalization would need Harper's theorem, which is outside reach and must stay a named hypothesis.","assumptions_md":"Consideration only. #5556 declares no scopes (snapshot scope_hashes [], research_authority scopes []), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 273 restricted two-branch kernel transfer (outcome result); author alvinhhh (gpt-6.1-sol); final rung proven on one trusted spot vote (review 1980); depends on #5513 and #5539, both accepted at proven; conditional throughout on Harper's ineffective arbitrary-log theorem (arXiv:1208.5992 Thm 2), which enters through those premises; no code or artifact shipped. Established as stated: on dyadic blocks 1<=D<=L^(2/5), 1/2<=M<=log L with E=L/(DM), the signed restricted cores T_01, T_11 = O(log ell) + O(ell^-3 log ell) and T_10 = O(ell log ell) + O(ell^-3 log ell) (ell = log L), each o((log y)^2), with the exact principal term retained and not claimed to vanish; the steps are band increments, the unit-class/Mobius partition, pricing theta(e)'s variation, and the two dyadic mass bounds. Not established: balanced levels, M > log L, three-branch cells, all finite small-prime CRT components of X, the variance constant, any full-X conclusion, or anything about twin primes. Excluded: extending the source scope; treating the report's word 'pending' for #5539 as current (it is now accepted, which does not change the stated content).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"#5556 ships no measurement script and runs no computation (the report states no producer execution, scientific computation or numerical experiment). Its conclusions are asymptotic o((log y)^2) bounds conditional on an ineffective theorem, so no numbered script or range exists to extend. Finite checks of identities (a)-(c) belong to adversarial, not to measurement-range extension.","assumptions_md":"Consideration only. #5556 declares no scopes (snapshot scope_hashes [], research_authority scopes []), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 273 restricted two-branch kernel transfer (outcome result); author alvinhhh (gpt-6.1-sol); final rung proven on one trusted spot vote (review 1980); depends on #5513 and #5539, both accepted at proven; conditional throughout on Harper's ineffective arbitrary-log theorem (arXiv:1208.5992 Thm 2), which enters through those premises; no code or artifact shipped. Established as stated: on dyadic blocks 1<=D<=L^(2/5), 1/2<=M<=log L with E=L/(DM), the signed restricted cores T_01, T_11 = O(log ell) + O(ell^-3 log ell) and T_10 = O(ell log ell) + O(ell^-3 log ell) (ell = log L), each o((log y)^2), with the exact principal term retained and not claimed to vanish; the steps are band increments, the unit-class/Mobius partition, pricing theta(e)'s variation, and the two dyadic mass bounds. Not established: balanced levels, M > log L, three-branch cells, all finite small-prime CRT components of X, the variance constant, any full-X conclusion, or anything about twin primes. Excluded: extending the source scope; treating the report's word 'pending' for #5539 as current (it is now accepted, which does not change the stated content).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"The report explicitly makes no claim for twin primes, the variance constant, balanced levels, M > log L or three-branch cells. It closes one restricted piece of a mixed remainder on route 273 and gives no route toward infinitude outside the refuted registry. Any use toward infinitude would need the excluded pieces and is not supplied.","assumptions_md":"Consideration only. #5556 declares no scopes (snapshot scope_hashes [], research_authority scopes []), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 273 restricted two-branch kernel transfer (outcome result); author alvinhhh (gpt-6.1-sol); final rung proven on one trusted spot vote (review 1980); depends on #5513 and #5539, both accepted at proven; conditional throughout on Harper's ineffective arbitrary-log theorem (arXiv:1208.5992 Thm 2), which enters through those premises; no code or artifact shipped. Established as stated: on dyadic blocks 1<=D<=L^(2/5), 1/2<=M<=log L with E=L/(DM), the signed restricted cores T_01, T_11 = O(log ell) + O(ell^-3 log ell) and T_10 = O(ell log ell) + O(ell^-3 log ell) (ell = log L), each o((log y)^2), with the exact principal term retained and not claimed to vanish; the steps are band increments, the unit-class/Mobius partition, pricing theta(e)'s variation, and the two dyadic mass bounds. Not established: balanced levels, M > log L, three-branch cells, all finite small-prime CRT components of X, the variance constant, any full-X conclusion, or anything about twin primes. Excluded: extending the source scope; treating the report's word 'pending' for #5539 as current (it is now accepted, which does not change the stated content).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The source bounds sieve-weight correlation cores unconditionally in the twin count (conditional only on Harper's theorem). It derives no structure that a finite twin count would force and uses no finiteness hypothesis.","assumptions_md":"Consideration only. #5556 declares no scopes (snapshot scope_hashes [], research_authority scopes []), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 273 restricted two-branch kernel transfer (outcome result); author alvinhhh (gpt-6.1-sol); final rung proven on one trusted spot vote (review 1980); depends on #5513 and #5539, both accepted at proven; conditional throughout on Harper's ineffective arbitrary-log theorem (arXiv:1208.5992 Thm 2), which enters through those premises; no code or artifact shipped. Established as stated: on dyadic blocks 1<=D<=L^(2/5), 1/2<=M<=log L with E=L/(DM), the signed restricted cores T_01, T_11 = O(log ell) + O(ell^-3 log ell) and T_10 = O(ell log ell) + O(ell^-3 log ell) (ell = log L), each o((log y)^2), with the exact principal term retained and not claimed to vanish; the steps are band increments, the unit-class/Mobius partition, pricing theta(e)'s variation, and the two dyadic mass bounds. Not established: balanced levels, M > log L, three-branch cells, all finite small-prime CRT components of X, the variance constant, any full-X conclusion, or anything about twin primes. Excluded: extending the source scope; treating the report's word 'pending' for #5539 as current (it is now accepted, which does not change the stated content).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"All topics. main: #5556 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 source works with smooth weights and dyadic sublinear blocks, but it states no two-variable uniform smooth-number asymptotic. It also gives no uniformity bridge in u <= Z^(1-epsilon), and its inputs are an ineffective arbitrary-log theorem. o5: it quotes Harper's theorem as an external input, but that is not the general sieve input or one-class statement this obligation names, and no mapping is given.","assumptions_md":"Consideration only. #5556 declares no scopes (snapshot scope_hashes [], research_authority scopes []), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 273 restricted two-branch kernel transfer (outcome result); author alvinhhh (gpt-6.1-sol); final rung proven on one trusted spot vote (review 1980); depends on #5513 and #5539, both accepted at proven; conditional throughout on Harper's ineffective arbitrary-log theorem (arXiv:1208.5992 Thm 2), which enters through those premises; no code or artifact shipped. Established as stated: on dyadic blocks 1<=D<=L^(2/5), 1/2<=M<=log L with E=L/(DM), the signed restricted cores T_01, T_11 = O(log ell) + O(ell^-3 log ell) and T_10 = O(ell log ell) + O(ell^-3 log ell) (ell = log L), each o((log y)^2), with the exact principal term retained and not claimed to vanish; the steps are band increments, the unit-class/Mobius partition, pricing theta(e)'s variation, and the two dyadic mass bounds. Not established: balanced levels, M > log L, three-branch cells, all finite small-prime CRT components of X, the variance constant, any full-X conclusion, or anything about twin primes. Excluded: extending the source scope; treating the report's word 'pending' for #5539 as current (it is now accepted, which does not change the stated content).","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":11599,"input_sha256":"cacfb3a1e8795995f0e53523dbdd2298ed335f6c0994b7d597501f8282a4b3c6","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"ef2fbe3f420746180b9b791927392d2474ee1a69b907494f3b8a0e2700f6216a","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5556,"material_evidence":{"sha256":"44298de0b980f99e08108cff799f70452272315a4f220d5d54757781e833b135","entries":{"return:5556":"d5fc721c940eb8f73898b82c48ae2580e0d66e953d2493b20dbf67f0fc1637bf"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5556,"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 #5556: 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\":5556,\"report_sha256\":\"ef2fbe3f420746180b9b791927392d2474ee1a69b907494f3b8a0e2700f6216a\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5556\":\"d5fc721c940eb8f73898b82c48ae2580e0d66e953d2493b20dbf67f0fc1637bf\"},\"sha256\":\"44298de0b980f99e08108cff799f70452272315a4f220d5d54757781e833b135\"},\"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:5556,input_sha256:\"cacfb3a1e8795995f0e53523dbdd2298ed335f6c0994b7d597501f8282a4b3c6\",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/5746/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"e6595d8a00093a078d05e7dcc7217a7a99537a40acb822b56964acf83b2af3bb","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}