{"id":3441,"job_id":7086,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #3439 (job 7086)\n\nSource: #3439 (route 233, job 5402; accepted at proven, review #1107; report sha256 0d42e573...). The snapshot is current: sha256 matches, status accepted, final_rung proven, not superseded, decided 2026-10-13T06:46:41Z. Disclosure: review #1107, which accepted the source, came from this department (prior run, job 7084).\n\n| area | decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | unresolved |\n| formalize | unresolved |\n| measure | inapplicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\n## Summary\n#3439 pins finite set-covering multiplicities for route 233 at x <= 17 (tau = 12, tau_set = 72, kappa = 4860/1547, 31-row table, G_2(17#) = 108, product assembly 14 > 12). No area asks for these values. Two entries are unresolved: adversarial, because kappa(17) > 3 contradicts a corpus 'below 3' line that is not a listed lemma; and formalize, because the claims are finite and decidable but are not a named Lean target and depend on BJR Lemma 3.6. The other five areas are mismatches.\n\n## What this does not do\nNo experiment, recomputation, new claim, artifact, review request or route change. Every entry is provisional (scope_keys []) and none is a validated transfer.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-13T06:51:42.771Z","repo_url":null,"commit":null,"cites":{"returns":[3439]},"tokens":{"log":"summary","input":58,"models":{"claude-opus-5-5":15866},"output":15866,"source":"reported","entries":0,"cache_read":1260670,"cache_write":64140,"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_d2bc56c1898adea7eceb2ac7","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. The area asks for an unconditional two-class exponent below 4.2665, the doubling cap C2 or a K* bound. #3439 gives a finite set-covering ladder; its only G2 item is G_2(17#) = 108 (ladder 12, 30, 42, 66, 108), a small-x value that reproduces G_2(11#) = 42 and gives no upper bound in x and no exponent. tau_set(17) = 72 < 108 shows only that the set relaxation is strictly cheaper at x = 17.","assumptions_md":"Provisional relevance only: #3439 declares no typed research_evidence scopes (research_authority.scopes = []), so scope_keys is [] and nothing here is a validated transfer. Source scope preserved: finite statements only, x <= 17: tau_{5..17}(D, Z/85085) = 12 (ceilinged projection LB == explicit 12-cover), tau_set(17) = 72, kappa(17) = 4860/1547, the full 31-row subset table pinned by LB == cover, G_2(17#) = 108, cheapest CRT product assembly 14 > 12. LBs inherit BJR 2011 Lemma 3.6 (re-derived); no asymptotic or kappa-limit claim.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"adversarial","scope_keys":[],"evidence_md":"Possible bridge, not an attack. #3439's Limits section states that the corpus line \"kappa stays below 3\" is no longer literally true at x = 17 (kappa(17) = 3.141564), which #2592's reviewer had already flagged as unsupported. That is an exact finite counterexample to a corpus statement, but the line is not an accepted lemma in this area's list, and #3439 used the validator's own enumeration path (check_ao.py) rather than an independent method. Which corpus file and line carry the 'below 3' wording, and whether it is a held lemma, is undecided here.","assumptions_md":"Provisional relevance only: #3439 declares no typed research_evidence scopes (research_authority.scopes = []), so scope_keys is [] and nothing here is a validated transfer. Source scope preserved: finite statements only, x <= 17: tau_{5..17}(D, Z/85085) = 12 (ceilinged projection LB == explicit 12-cover), tau_set(17) = 72, kappa(17) = 4860/1547, the full 31-row subset table pinned by LB == cover, G_2(17#) = 108, cheapest CRT product assembly 14 > 12. LBs inherit BJR 2011 Lemma 3.6 (re-derived); no asymptotic or kappa-limit claim.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"Possible Lean target, not named in the area. #3439 is accepted at proven, and its claims are finite and decidable: the bottom-up ceilinged projection chain {13,17} >= 3 -> {7,13,17} >= 5 -> {7,11,13,17} >= 7 -> {5,7,11,13,17} >= 12 in exact rationals, plus explicit covers checkable by enumeration (moduli up to 510510). It fits the area's 'accepted PROVEN lemmas with no Lean file' class, but the general step rests on BJR 2011 Lemma 3.6 (re-derived on paper, not in Mathlib), and the area's next step names #1072/#1790 rather than this route. Whether it is queued as a target is undecided.","assumptions_md":"Provisional relevance only: #3439 declares no typed research_evidence scopes (research_authority.scopes = []), so scope_keys is [] and nothing here is a validated transfer. Source scope preserved: finite statements only, x <= 17: tau_{5..17}(D, Z/85085) = 12 (ceilinged projection LB == explicit 12-cover), tau_set(17) = 72, kappa(17) = 4860/1547, the full 31-row subset table pinned by LB == cover, G_2(17#) = 108, cheapest CRT product assembly 14 > 12. LBs inherit BJR 2011 Lemma 3.6 (re-derived); no asymptotic or kappa-limit claim.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"Mismatch. The area's frontier is exact G2 beyond x = 79, the T37 L-ladder tile and a(25). #3439's G_2(17#) = 108 is far below that frontier and reproduces recorded small values. tau_set is route 233's object, not a numbered measurement script.","assumptions_md":"Provisional relevance only: #3439 declares no typed research_evidence scopes (research_authority.scopes = []), so scope_keys is [] and nothing here is a validated transfer. Source scope preserved: finite statements only, x <= 17: tau_{5..17}(D, Z/85085) = 12 (ceilinged projection LB == explicit 12-cover), tau_set(17) = 72, kappa(17) = 4860/1547, the full 31-row subset table pinned by LB == cover, G_2(17#) = 108, cheapest CRT product assembly 14 > 12. LBs inherit BJR 2011 Lemma 3.6 (re-derived); no asymptotic or kappa-limit claim.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Mismatch. #3439 makes no claim about routes 42, 7, 27, 35 or 24, or obligations D and A2. Its covering numbers are finite at x <= 17, with no moment saving or signed estimate for B.","assumptions_md":"Provisional relevance only: #3439 declares no typed research_evidence scopes (research_authority.scopes = []), so scope_keys is [] and nothing here is a validated transfer. Source scope preserved: finite statements only, x <= 17: tau_{5..17}(D, Z/85085) = 12 (ceilinged projection LB == explicit 12-cover), tau_set(17) = 72, kappa(17) = 4860/1547, the full 31-row subset table pinned by LB == cover, G_2(17#) = 108, cheapest CRT product assembly 14 > 12. LBs inherit BJR 2011 Lemma 3.6 (re-derived); no asymptotic or kappa-limit claim.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Mismatch. The area asks for a quantified consequence of finiteness, such as window/G2 unbounded or a third mechanism. Finite exact covering multiplicities at x <= 17, and kappa rising to 3.1416, carry no consequence of the finiteness hypothesis; #3439 says explicitly that the rise does not tell a limit from growth.","assumptions_md":"Provisional relevance only: #3439 declares no typed research_evidence scopes (research_authority.scopes = []), so scope_keys is [] and nothing here is a validated transfer. Source scope preserved: finite statements only, x <= 17: tau_{5..17}(D, Z/85085) = 12 (ceilinged projection LB == explicit 12-cover), tau_set(17) = 72, kappa(17) = 4860/1547, the full 31-row subset table pinned by LB == cover, G_2(17#) = 108, cheapest CRT product assembly 14 > 12. LBs inherit BJR 2011 Lemma 3.6 (re-derived); no asymptotic or kappa-limit claim.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Mismatch. The main topic's 'A = 12' (survivor-gap LB) is unrelated to tau_{5..17} = 12. O5 lists accepted finite CRT and covering results as things to distinguish from the needed bound; #3439 is such a finite CRT covering result, so it belongs on O5's 'not this' side and supplies no O1-O7 constant, hypothesis or range.","assumptions_md":"Provisional relevance only: #3439 declares no typed research_evidence scopes (research_authority.scopes = []), so scope_keys is [] and nothing here is a validated transfer. Source scope preserved: finite statements only, x <= 17: tau_{5..17}(D, Z/85085) = 12 (ceilinged projection LB == explicit 12-cover), tau_set(17) = 72, kappa(17) = 4860/1547, the full 31-row subset table pinned by LB == cover, G_2(17#) = 108, cheapest CRT product assembly 14 > 12. LBs inherit BJR 2011 Lemma 3.6 (re-derived); no asymptotic or kappa-limit claim.","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":7086,"input_sha256":"89cdc94ca9ffe866e23e6bc9f2a70b15655bbc403809580be2c093e1d6c5d0dd","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"0d42e57378d0b7c013633652c7bfe1664337e0a560623cab1d60eebd8873eddd","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":3439,"material_evidence":{"sha256":"64e20ac1760acdf495284f91454591a0b794b1003a147fe5d747132e00608248","entries":{"return:3439":"4dd5471d6b37433479375eb0a034017e215324aee50c67c6ab52320c905e84f6","artifact:3439:04d5c136527f48b5c19ba872b4155b8b00a2572c8f7476f4ee8d0476f83e28f0":"04d5c136527f48b5c19ba872b4155b8b00a2572c8f7476f4ee8d0476f83e28f0","artifact:3439:065717c9b1c1dc98452e1b19d2ea4242cbd21f7827527473a35af9e2e815561e":"065717c9b1c1dc98452e1b19d2ea4242cbd21f7827527473a35af9e2e815561e","artifact:3439:0d42e57378d0b7c013633652c7bfe1664337e0a560623cab1d60eebd8873eddd":"0d42e57378d0b7c013633652c7bfe1664337e0a560623cab1d60eebd8873eddd","artifact:3439:0edcc9e70d246d0fe0c6a4b69e21c309e20064d8d12118ebcd76c7ad995b1a62":"0edcc9e70d246d0fe0c6a4b69e21c309e20064d8d12118ebcd76c7ad995b1a62","artifact:3439:18cead5daf73903c72593c36ad5bc38694eb5e377dad72d624b70acee703bf49":"18cead5daf73903c72593c36ad5bc38694eb5e377dad72d624b70acee703bf49","artifact:3439:22bc7861830abd0aabe675812c3fbae3bed17caad74cf0438ab306d168c89832":"22bc7861830abd0aabe675812c3fbae3bed17caad74cf0438ab306d168c89832","artifact:3439:25121b8ceb1311636ef17ab4d5c15942ea39c5e1a86ca0ebaf5fd04e4fd643c9":"25121b8ceb1311636ef17ab4d5c15942ea39c5e1a86ca0ebaf5fd04e4fd643c9","artifact:3439:2bcfb6d80fa5509ab09622cd23655fff2281cbc6f0a54daf72dc63aad983f4ae":"2bcfb6d80fa5509ab09622cd23655fff2281cbc6f0a54daf72dc63aad983f4ae","artifact:3439:36ebe481d2de1d235de44eab80962c6fa253409b14acd27cadb795c424d536c9":"36ebe481d2de1d235de44eab80962c6fa253409b14acd27cadb795c424d536c9","artifact:3439:4208a2c2eece70dac09ef680c09e7fae515ba53ebc096f0989ee9ac87719db85":"4208a2c2eece70dac09ef680c09e7fae515ba53ebc096f0989ee9ac87719db85","artifact:3439:4fbdf47977c119514517f287053ca1778d9a81989658144489316c72ab1a84d7":"4fbdf47977c119514517f287053ca1778d9a81989658144489316c72ab1a84d7","artifact:3439:795a19835bb5184444de4ba4dc455178ad4437868af58050bff79599530567ab":"795a19835bb5184444de4ba4dc455178ad4437868af58050bff79599530567ab","artifact:3439:839f290856c2beaa85d6038faf6ed6036bca4fb7963dc5a53b825e9be3c79b85":"839f290856c2beaa85d6038faf6ed6036bca4fb7963dc5a53b825e9be3c79b85","artifact:3439:868da061f215cf0ddc8a73893003473da81de4b1eb1568d132306c4a9be33d10":"868da061f215cf0ddc8a73893003473da81de4b1eb1568d132306c4a9be33d10","artifact:3439:8add1975fb6971b9e433ad8896bf3b4f666d815d37ebc783a44044a8ca675b39":"8add1975fb6971b9e433ad8896bf3b4f666d815d37ebc783a44044a8ca675b39","artifact:3439:8cbe6e846d02e3ee801d78a3413e45824516ca1f84450535ac88322b99026a10":"8cbe6e846d02e3ee801d78a3413e45824516ca1f84450535ac88322b99026a10","artifact:3439:a17a3d2fdbed36d10832e065a3bb25650516800c2b594da780b3c99aa08d460f":"a17a3d2fdbed36d10832e065a3bb25650516800c2b594da780b3c99aa08d460f","artifact:3439:dda0e05f63849d1fe4cadf0c4f87654d43b26782caf45c67134d5ba2bf101c79":"dda0e05f63849d1fe4cadf0c4f87654d43b26782caf45c67134d5ba2bf101c79","artifact:3439:fa55ff974db97c6fb87b849bc8ab973044b7e0195f3bb1ddd6da6065d3412b82":"fa55ff974db97c6fb87b849bc8ab973044b7e0195f3bb1ddd6da6065d3412b82","artifact:3439:fe44d179d3c0e30ab4d649caad3dd1280ae46b8e46e001544b0baf805440ed20":"fe44d179d3c0e30ab4d649caad3dd1280ae46b8e46e001544b0baf805440ed20"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":3439,"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 #3439: 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\":3439,\"report_sha256\":\"0d42e57378d0b7c013633652c7bfe1664337e0a560623cab1d60eebd8873eddd\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:3439\":\"4dd5471d6b37433479375eb0a034017e215324aee50c67c6ab52320c905e84f6\",\"artifact:3439:04d5c136527f48b5c19ba872b4155b8b00a2572c8f7476f4ee8d0476f83e28f0\":\"04d5c136527f48b5c19ba872b4155b8b00a2572c8f7476f4ee8d0476f83e28f0\",\"artifact:3439:065717c9b1c1dc98452e1b19d2ea4242cbd21f7827527473a35af9e2e815561e\":\"065717c9b1c1dc98452e1b19d2ea4242cbd21f7827527473a35af9e2e815561e\",\"artifact:3439:0d42e57378d0b7c013633652c7bfe1664337e0a560623cab1d60eebd8873eddd\":\"0d42e57378d0b7c013633652c7bfe1664337e0a560623cab1d60eebd8873eddd\",\"artifact:3439:0edcc9e70d246d0fe0c6a4b69e21c309e20064d8d12118ebcd76c7ad995b1a62\":\"0edcc9e70d246d0fe0c6a4b69e21c309e20064d8d12118ebcd76c7ad995b1a62\",\"artifact:3439:18cead5daf73903c72593c36ad5bc38694eb5e377dad72d624b70acee703bf49\":\"18cead5daf73903c72593c36ad5bc38694eb5e377dad72d624b70acee703bf49\",\"artifact:3439:22bc7861830abd0aabe675812c3fbae3bed17caad74cf0438ab306d168c89832\":\"22bc7861830abd0aabe675812c3fbae3bed17caad74cf0438ab306d168c89832\",\"artifact:3439:25121b8ceb1311636ef17ab4d5c15942ea39c5e1a86ca0ebaf5fd04e4fd643c9\":\"25121b8ceb1311636ef17ab4d5c15942ea39c5e1a86ca0ebaf5fd04e4fd643c9\",\"artifact:3439:2bcfb6d80fa5509ab09622cd23655fff2281cbc6f0a54daf72dc63aad983f4ae\":\"2bcfb6d80fa5509ab09622cd23655fff2281cbc6f0a54daf72dc63aad983f4ae\",\"artifact:3439:36ebe481d2de1d235de44eab80962c6fa253409b14acd27cadb795c424d536c9\":\"36ebe481d2de1d235de44eab80962c6fa253409b14acd27cadb795c424d536c9\",\"artifact:3439:4208a2c2eece70dac09ef680c09e7fae515ba53ebc096f0989ee9ac87719db85\":\"4208a2c2eece70dac09ef680c09e7fae515ba53ebc096f0989ee9ac87719db85\",\"artifact:3439:4fbdf47977c119514517f287053ca1778d9a81989658144489316c72ab1a84d7\":\"4fbdf47977c119514517f287053ca1778d9a81989658144489316c72ab1a84d7\",\"artifact:3439:795a19835bb5184444de4ba4dc455178ad4437868af58050bff79599530567ab\":\"795a19835bb5184444de4ba4dc455178ad4437868af58050bff79599530567ab\",\"artifact:3439:839f290856c2beaa85d6038faf6ed6036bca4fb7963dc5a53b825e9be3c79b85\":\"839f290856c2beaa85d6038faf6ed6036bca4fb7963dc5a53b825e9be3c79b85\",\"artifact:3439:868da061f215cf0ddc8a73893003473da81de4b1eb1568d132306c4a9be33d10\":\"868da061f215cf0ddc8a73893003473da81de4b1eb1568d132306c4a9be33d10\",\"artifact:3439:8add1975fb6971b9e433ad8896bf3b4f666d815d37ebc783a44044a8ca675b39\":\"8add1975fb6971b9e433ad8896bf3b4f666d815d37ebc783a44044a8ca675b39\",\"artifact:3439:8cbe6e846d02e3ee801d78a3413e45824516ca1f84450535ac88322b99026a10\":\"8cbe6e846d02e3ee801d78a3413e45824516ca1f84450535ac88322b99026a10\",\"artifact:3439:a17a3d2fdbed36d10832e065a3bb25650516800c2b594da780b3c99aa08d460f\":\"a17a3d2fdbed36d10832e065a3bb25650516800c2b594da780b3c99aa08d460f\",\"artifact:3439:dda0e05f63849d1fe4cadf0c4f87654d43b26782caf45c67134d5ba2bf101c79\":\"dda0e05f63849d1fe4cadf0c4f87654d43b26782caf45c67134d5ba2bf101c79\",\"artifact:3439:fa55ff974db97c6fb87b849bc8ab973044b7e0195f3bb1ddd6da6065d3412b82\":\"fa55ff974db97c6fb87b849bc8ab973044b7e0195f3bb1ddd6da6065d3412b82\",\"artifact:3439:fe44d179d3c0e30ab4d649caad3dd1280ae46b8e46e001544b0baf805440ed20\":\"fe44d179d3c0e30ab4d649caad3dd1280ae46b8e46e001544b0baf805440ed20\"},\"sha256\":\"64e20ac1760acdf495284f91454591a0b794b1003a147fe5d747132e00608248\"},\"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:3439,input_sha256:\"89cdc94ca9ffe866e23e6bc9f2a70b15655bbc403809580be2c093e1d6c5d0dd\",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/3441/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"9f568b94fa69f52d56f276a954b423bec8325202caa018a37e1dcf2584e2d79f","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}