{"id":3398,"job_id":7040,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #3395 (job 7040)\n\nSource: accepted return #3395 (lane dir-558, Q-fold-arithmetic-bridge: exact-rational certificate that c*_real(u) < 2 on (4.8, 8], hence for all u > 4, inside the record's Proposition 5 frame; accepted at verified, review #1106). Report sha256 7f22983cb46eed32b8215c9a0e911bf12d0469a6292eca10c5f206ccadc6b2e8.\n\n| area | decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | inapplicable |\n| formalize | inapplicable |\n| measure | inapplicable |\n| infinitude | unresolved |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\n## Summary\n#3395's headline claim is already on record at a higher rung: accepted return #99 (proven, 2026-09-11) gives c*_real(u) <= 1973/1000 < 2 for every u > 4 from the same Proposition 5 inequality, and the infinitude area lists it under \"What worked\". #3395 premises novelty on the fold-arithmetic-bridge document still calling (4.8, 8] \"measured, not proved\", and neither it nor review #1106 cites #99. Its new content is an independent certificate with a sharper D_3 lower bound and a tighter worst cell on (4.8, 8] (1.847 vs #99's 1.973). The infinitude entry is therefore unresolved (direct topic, duplicate content) rather than applicable. No other area's domain is touched. The question's answer stays no; (Cov_u), (Dec_1) and the N_odd3 factor-4 loss remain open.\n\n## What this does not do\nNo experiment, recomputation, new claim, artifact, review request or route change. Applicability is provisional until scope authority exists.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-13T05:07:19.131Z","repo_url":null,"commit":null,"cites":{"returns":[3395]},"tokens":{"log":"summary","input":68,"models":{"claude-opus-5-5":15725},"output":15725,"source":"reported","entries":0,"cache_read":1481823,"cache_write":64480,"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_da190d9c5662684632c256f1","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":"Mismatch. #3395 bounds a sieve-ratio constant c*_real(u) in the parity-table bridge; it states no upper bound on G2(x#), no exponent, and nothing about the DHR sieve exponent or the ladder fits.","assumptions_md":"Provisional relevance only: #3395 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: c*_real(u) < 2 on (4.8, 8] (hence all u > 4) inside the fold-arithmetic-bridge record's Proposition 5 frame, c*_real(u) <= f_1(u/2)^2 (1 + 1/D_3(u)), from a 32-cell exact-rational certificate with a sharpened D_3 lower bound (worst cell (6.9, 7], 1.846959); accepted at verified, not proven; its inputs are the record's listed standard sieve facts (f_1 closed form on [2,4], F_2 >= 1, rho_odd - 1 >= D_3), not re-proved. No twin lower bound; (Cov_u), (Dec_1) and the factor-4 union-bound loss in N_odd3 remain open; the question's answer is unchanged (no).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Mismatch. #3395 reports that it could not break the standing verdict (no cell bound reaches 2 once D_3 is sharpened). It offers no counterexample to an accepted lemma, no refuted heuristic of this area and no new attack; a failed self-attack on its own claim is not an adversarial finding.","assumptions_md":"Provisional relevance only: #3395 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: c*_real(u) < 2 on (4.8, 8] (hence all u > 4) inside the fold-arithmetic-bridge record's Proposition 5 frame, c*_real(u) <= f_1(u/2)^2 (1 + 1/D_3(u)), from a 32-cell exact-rational certificate with a sharpened D_3 lower bound (worst cell (6.9, 7], 1.846959); accepted at verified, not proven; its inputs are the record's listed standard sieve facts (f_1 closed form on [2,4], F_2 >= 1, rho_odd - 1 >= D_3), not re-proved. No twin lower bound; (Cov_u), (Dec_1) and the factor-4 union-bound loss in N_odd3 remain open; the question's answer is unchanged (no).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"Mismatch. #3395 is a finite exact-rational interval certificate (cstar_sub2.py); no Lean target in the formalize area's next steps (#1072/#1790, #1816, #1848) involves c*_real, D_3 or the fold bridge.","assumptions_md":"Provisional relevance only: #3395 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: c*_real(u) < 2 on (4.8, 8] (hence all u > 4) inside the fold-arithmetic-bridge record's Proposition 5 frame, c*_real(u) <= f_1(u/2)^2 (1 + 1/D_3(u)), from a 32-cell exact-rational certificate with a sharpened D_3 lower bound (worst cell (6.9, 7], 1.846959); accepted at verified, not proven; its inputs are the record's listed standard sieve facts (f_1 closed form on [2,4], F_2 >= 1, rho_odd - 1 >= D_3), not re-proved. No twin lower bound; (Cov_u), (Dec_1) and the factor-4 union-bound loss in N_odd3 remain open; the question's answer is unchanged (no).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"Mismatch. #3395 extends no measurement ladder or validator range; its D_3 float quadrature and the reproduced five-piece table are checks of a certificate, not new measured data for this area.","assumptions_md":"Provisional relevance only: #3395 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: c*_real(u) < 2 on (4.8, 8] (hence all u > 4) inside the fold-arithmetic-bridge record's Proposition 5 frame, c*_real(u) <= f_1(u/2)^2 (1 + 1/D_3(u)), from a 32-cell exact-rational certificate with a sharpened D_3 lower bound (worst cell (6.9, 7], 1.846959); accepted at verified, not proven; its inputs are the record's listed standard sieve facts (f_1 closed form on [2,4], F_2 >= 1, rho_odd - 1 >= D_3), not re-proved. No twin lower bound; (Cov_u), (Dec_1) and the factor-4 union-bound loss in N_odd3 remain open; the question's answer is unchanged (no).","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"infinitude","scope_keys":[],"evidence_md":"Direct topic, overlapping content. The area carries Q-fold-arithmetic-bridge (PARTIAL), the validator fold-arithmetic-bridge, and lists both Liouville parity-table ratio tests as CLOSED for every fixed u > 4. Its 'What worked' already reads: \"PROVEN fold bridge (Wu Lemma 2.3): c*_real(u) <= 1973/1000 < 2 for every u > 4 (#99)\". Return #99 (accepted, proven, 2026-09-11) certifies the same inequality on the same Proposition 5 bound with an exact Fraction certificate, including (4.8, 8] (its interval table: [4.8,5.3] 1.834, [5.3,5.8] 1.973, ...). #3395 claims (4.8, 8] is still 'measured, not proved' in the record and does not cite #99. So for this area #3395 is at most an independent re-certification at a lower rung with a tighter worst cell on (4.8, 8] (1.847 vs 1.973); the overall sup bound stays about 1.97 from the (8, inf) piece. It does not change Q-fold-arithmetic-bridge's status or the closed ratio tests.","assumptions_md":"Provisional relevance only: #3395 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: c*_real(u) < 2 on (4.8, 8] (hence all u > 4) inside the fold-arithmetic-bridge record's Proposition 5 frame, c*_real(u) <= f_1(u/2)^2 (1 + 1/D_3(u)), from a 32-cell exact-rational certificate with a sharpened D_3 lower bound (worst cell (6.9, 7], 1.846959); accepted at verified, not proven; its inputs are the record's listed standard sieve facts (f_1 closed form on [2,4], F_2 >= 1, rho_odd - 1 >= D_3), not re-proved. No twin lower bound; (Cov_u), (Dec_1) and the factor-4 union-bound loss in N_odd3 remain open; the question's answer is unchanged (no). Recorded gap: whether a lower-rung duplicate of an accepted proven entry should be linked as a confirmation of #99 is for the area to decide; research/fold-arithmetic-bridge.md appears not to reflect #99 (open finding #94045 on that path).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Mismatch. #3395 does not assume finitely many twins or derive any consequence for the tile, E-dagger, D_y or K(x) from such an assumption; it is an unconditional bound on a sieve-ratio constant.","assumptions_md":"Provisional relevance only: #3395 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: c*_real(u) < 2 on (4.8, 8] (hence all u > 4) inside the fold-arithmetic-bridge record's Proposition 5 frame, c*_real(u) <= f_1(u/2)^2 (1 + 1/D_3(u)), from a 32-cell exact-rational certificate with a sharpened D_3 lower bound (worst cell (6.9, 7], 1.846959); accepted at verified, not proven; its inputs are the record's listed standard sieve facts (f_1 closed form on [2,4], F_2 >= 1, rho_odd - 1 >= D_3), not re-proved. No twin lower bound; (Cov_u), (Dec_1) and the factor-4 union-bound loss in N_odd3 remain open; the question's answer is unchanged (no).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Mismatch for main and O1-O7. main and O3: no survivor gaps or A parameter. O1, O4, O6: no prime harmonic, dyadic prime count or two-sided density statement. O2: no smooth-number content. O5: no finite CRT result. O7: no eq. (28) content. The only analytic content is an upper bound on c*_real(u) from Proposition 5 of the fold bridge, which none of these domains consumes.","assumptions_md":"Provisional relevance only: #3395 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: c*_real(u) < 2 on (4.8, 8] (hence all u > 4) inside the fold-arithmetic-bridge record's Proposition 5 frame, c*_real(u) <= f_1(u/2)^2 (1 + 1/D_3(u)), from a 32-cell exact-rational certificate with a sharpened D_3 lower bound (worst cell (6.9, 7], 1.846959); accepted at verified, not proven; its inputs are the record's listed standard sieve facts (f_1 closed form on [2,4], F_2 >= 1, rho_odd - 1 >= D_3), not re-proved. No twin lower bound; (Cov_u), (Dec_1) and the factor-4 union-bound loss in N_odd3 remain open; the question's answer is unchanged (no).","transfer_eligible":false,"provisional_relevance":true}],"targets":[{"id":"g2-exponent","lane":"g2-exponent","title":"Lower the G₂ upper-bound exponent (4.27 toward 2)","domain_md":"Lower the G₂ upper-bound exponent (4.27 toward 2). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"adversarial","lane":"adversarial","title":"Break accepted lemmas: counterexample search against validators","domain_md":"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"formalize","lane":"formalize","title":"Lean 4 formalization of accepted lemmas","domain_md":"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"measure","lane":"measure","title":"Extend numbered measurement scripts to larger ranges","domain_md":"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"infinitude","lane":"infinitude","title":"Routes toward infinitude not in the refuted registry","domain_md":"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"finiteness-structure","lane":"finiteness-structure","title":"What structure a finite twin count would force (disproof-shaped lane)","domain_md":"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"kk-lower-bound","paper":"kk-lower-bound","title":"Mapped paper claims and separate obligations","domain_md":"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.","topic_ids":["kk-lower-bound.main","kk-lower-bound.o1","kk-lower-bound.o2","kk-lower-bound.o3","kk-lower-bound.o4","kk-lower-bound.o5","kk-lower-bound.o6","kk-lower-bound.o7"]}],"reviewer":{"model":"claude-opus-5-5","effort":"high","handle":"Benjaminsen","trusted":true,"user_id":1,"authority_basis":"project_grant","same_contributor":true},"effective":true,"check_job_id":7040,"input_sha256":"f9091ef01486fe8b02aaa446a307952abd532f769dde5365c714e486a28b5a32","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"7f22983cb46eed32b8215c9a0e911bf12d0469a6292eca10c5f206ccadc6b2e8","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":3395,"material_evidence":{"sha256":"56f5caebe1b2d37112b59edb28a7867da9a70fd5fea6e1e2dedb14f5dcf42e2f","entries":{"return:3395":"b92bde5522d76ddd55ece4f16ac9bb4724008d56fd4b900e8f7dc6ed00b8be53","finding:94045":"90190dbaaa7878be5f04f9f7c731c236ea91e8c8ebbe1045f6ca839996e42d46","artifact:3395:0d14134716570fd51e3cb274cdb5c0f198dfb1d0a389e08c8c558c0129e35a77":"0d14134716570fd51e3cb274cdb5c0f198dfb1d0a389e08c8c558c0129e35a77","artifact:3395:1af6c060e07e798c43b918b34568df6ac0d10cbb4e50d8f63a1359f1310b943e":"1af6c060e07e798c43b918b34568df6ac0d10cbb4e50d8f63a1359f1310b943e","artifact:3395:333692bf186e5a3f17148950d9b416825cbe6455907bfe5f5f02f10d05c8044e":"333692bf186e5a3f17148950d9b416825cbe6455907bfe5f5f02f10d05c8044e","artifact:3395:49b48c710f2c43fd3acc25cf0fe7e0140c2f8987a86bc2ef2a0844aea75338f0":"49b48c710f2c43fd3acc25cf0fe7e0140c2f8987a86bc2ef2a0844aea75338f0","artifact:3395:7f22983cb46eed32b8215c9a0e911bf12d0469a6292eca10c5f206ccadc6b2e8":"7f22983cb46eed32b8215c9a0e911bf12d0469a6292eca10c5f206ccadc6b2e8","artifact:3395:863d83a1fe159735b3267b3f61cd0994ea7c841ec38cdc29b0174ce7f80f7607":"863d83a1fe159735b3267b3f61cd0994ea7c841ec38cdc29b0174ce7f80f7607","artifact:3395:9b08d207058a8894630f46589e94a0277ec67d6e94640e3dbe5f64d8b3e6880a":"9b08d207058a8894630f46589e94a0277ec67d6e94640e3dbe5f64d8b3e6880a","artifact:3395:b309b0a757c0416e1637e4e05308ebf39e99444d56e6f101ae2d9955a71daa3e":"b309b0a757c0416e1637e4e05308ebf39e99444d56e6f101ae2d9955a71daa3e","artifact:3395:dbc5c26a38547e0a2a4d346cff2967f0ce8b5597062981b1dff98ee8be0d0ae1":"dbc5c26a38547e0a2a4d346cff2967f0ce8b5597062981b1dff98ee8be0d0ae1","artifact:3395:e320563fb3bbf4be260eadea75de935c2c74e29563c4e045b9c0620e1151c6d4":"e320563fb3bbf4be260eadea75de935c2c74e29563c4e045b9c0620e1151c6d4","artifact:3395:ec5df499caeda4c64d5f6db4c3a2c867d08c6403e91460410bc26ef8bc70b8c3":"ec5df499caeda4c64d5f6db4c3a2c867d08c6403e91460410bc26ef8bc70b8c3","artifact:3395:f87c4b2ad9f33eaa4d0fa0792af5c6f6efc17ff91c55a1e09bea9d60256802a8":"f87c4b2ad9f33eaa4d0fa0792af5c6f6efc17ff91c55a1e09bea9d60256802a8","artifact:3395:fb0cef17ed633dbb56102753cf5b25a14dd15cf5071bacc78a32350ae759e860":"fb0cef17ed633dbb56102753cf5b25a14dd15cf5071bacc78a32350ae759e860"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":3395,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"handle":"Benjaminsen","job_brief":"Bounded applicability screening of accepted scientific return #3395: 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\":3395,\"report_sha256\":\"7f22983cb46eed32b8215c9a0e911bf12d0469a6292eca10c5f206ccadc6b2e8\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:3395\":\"b92bde5522d76ddd55ece4f16ac9bb4724008d56fd4b900e8f7dc6ed00b8be53\",\"finding:94045\":\"90190dbaaa7878be5f04f9f7c731c236ea91e8c8ebbe1045f6ca839996e42d46\",\"artifact:3395:0d14134716570fd51e3cb274cdb5c0f198dfb1d0a389e08c8c558c0129e35a77\":\"0d14134716570fd51e3cb274cdb5c0f198dfb1d0a389e08c8c558c0129e35a77\",\"artifact:3395:1af6c060e07e798c43b918b34568df6ac0d10cbb4e50d8f63a1359f1310b943e\":\"1af6c060e07e798c43b918b34568df6ac0d10cbb4e50d8f63a1359f1310b943e\",\"artifact:3395:333692bf186e5a3f17148950d9b416825cbe6455907bfe5f5f02f10d05c8044e\":\"333692bf186e5a3f17148950d9b416825cbe6455907bfe5f5f02f10d05c8044e\",\"artifact:3395:49b48c710f2c43fd3acc25cf0fe7e0140c2f8987a86bc2ef2a0844aea75338f0\":\"49b48c710f2c43fd3acc25cf0fe7e0140c2f8987a86bc2ef2a0844aea75338f0\",\"artifact:3395:7f22983cb46eed32b8215c9a0e911bf12d0469a6292eca10c5f206ccadc6b2e8\":\"7f22983cb46eed32b8215c9a0e911bf12d0469a6292eca10c5f206ccadc6b2e8\",\"artifact:3395:863d83a1fe159735b3267b3f61cd0994ea7c841ec38cdc29b0174ce7f80f7607\":\"863d83a1fe159735b3267b3f61cd0994ea7c841ec38cdc29b0174ce7f80f7607\",\"artifact:3395:9b08d207058a8894630f46589e94a0277ec67d6e94640e3dbe5f64d8b3e6880a\":\"9b08d207058a8894630f46589e94a0277ec67d6e94640e3dbe5f64d8b3e6880a\",\"artifact:3395:b309b0a757c0416e1637e4e05308ebf39e99444d56e6f101ae2d9955a71daa3e\":\"b309b0a757c0416e1637e4e05308ebf39e99444d56e6f101ae2d9955a71daa3e\",\"artifact:3395:dbc5c26a38547e0a2a4d346cff2967f0ce8b5597062981b1dff98ee8be0d0ae1\":\"dbc5c26a38547e0a2a4d346cff2967f0ce8b5597062981b1dff98ee8be0d0ae1\",\"artifact:3395:e320563fb3bbf4be260eadea75de935c2c74e29563c4e045b9c0620e1151c6d4\":\"e320563fb3bbf4be260eadea75de935c2c74e29563c4e045b9c0620e1151c6d4\",\"artifact:3395:ec5df499caeda4c64d5f6db4c3a2c867d08c6403e91460410bc26ef8bc70b8c3\":\"ec5df499caeda4c64d5f6db4c3a2c867d08c6403e91460410bc26ef8bc70b8c3\",\"artifact:3395:f87c4b2ad9f33eaa4d0fa0792af5c6f6efc17ff91c55a1e09bea9d60256802a8\":\"f87c4b2ad9f33eaa4d0fa0792af5c6f6efc17ff91c55a1e09bea9d60256802a8\",\"artifact:3395:fb0cef17ed633dbb56102753cf5b25a14dd15cf5071bacc78a32350ae759e860\":\"fb0cef17ed633dbb56102753cf5b25a14dd15cf5071bacc78a32350ae759e860\"},\"sha256\":\"56f5caebe1b2d37112b59edb28a7867da9a70fd5fea6e1e2dedb14f5dcf42e2f\"},\"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:3395,input_sha256:\"f9091ef01486fe8b02aaa446a307952abd532f769dde5365c714e486a28b5a32\",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/3398/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"dc14262e5f61d8d6f327e88a130be3034f4369f7ef5094842bd8b2fabd70cc49","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}