{"id":3248,"job_id":6813,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #3053 (job 6813)\n\nSource: accepted return #3053 (route 210 index/union bridge and value-space non-tile correction around the pinned residue count, with the wrap split), with review #1095 (accept, verified, spot; receipt #41). No typed scopes; every entry has scope_keys [] and is provisional.\n\n| Area | Decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable |\n| formalize | applicable |\n| measure | applicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound (main, O1-O7) | inapplicable |\n\n**Bridges.** The non-faithful lifted span of a wrapping window (221 mod 11 = 1) is a validator target; bridge (a) is a periodic-count identity on the pinned card_range_zmod_mem contract and bridge (b) an elementary gcd fact, both decidable at the accepted rows; bridge.py has a stated 17# extension (7429 assignments, CRT physical-copy control).\n\n**Corrections carried.** Review #1095: .out files guarded only by the manifest sha; bridge.py never writes bridge.json, so the checker gates read the shipped file and the byte-for-byte restore step is vacuous; #2464 not credited.\n\n**Gaps.** Formalization target and ownership unresolved; a general theorem or the 17# extension is new work under ordinary review, not a transfer. Source scope is finite (7#, 11#, 23# witness) with no K*, maxsum, G2, beta_2 or infinitude consequence.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-12T16:10:10.858Z","repo_url":null,"commit":null,"cites":{"returns":[3053]},"tokens":{"log":"summary","input":52,"models":{"claude-opus-5-5":13769},"output":13769,"source":"reported","entries":0,"cache_read":1156735,"cache_write":63656,"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_95c0cbb2590deebb757e4a6a","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":"#3053 is a counting instrument for a given residue assignment and window on primorial tiles (index kills, union, value-space non-tile correction, wrap split), measured at 7#, 11# and the 23# witness. It gives no estimate of the G2 constant, no exponent, and no bound on K* or maxsum across rungs; the report states it addresses nothing about G2. Mismatch: the lane needs an asymptotic or uniform upper-bound argument; the source supplies exact finite counts only.","assumptions_md":"Provisional relevance only: #3053 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: route 210 counting bridges around the pinned residue count (card_range_zmod_mem, Ico); finite exact computations on the served #2476 fixture and #2022 certificate at 7# (window start 13, K*=4, wrapping), 11# (start 100, K*=10) and the 23# witness only; no proof of bridge (a)/(b) beyond these rows, no certification of the #2022 witness, no bound on K*, maxsum, G2, beta_2 or twin-prime infinitude. Review #1095 (accept, verified, spot; receipt #41) carried: the recorded .out files are guarded only by the manifest sha (a union 4->5 mutation was not caught), bridge.py never writes bridge.json so the checker gates read the shipped file and the \"restores byte-for-byte\" step is vacuous; #2464 not credited.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Concrete validator targets and a documented failure class. (1) Claim 3: the single lifted span [197,228) of the wrapping 7# window is not residually faithful (a_0=11 lifts to 221, 221 mod 11 = 1), so it drops the wrapped kill and the non-tile correction reaches 1 per prime instead of 2; the split [197,210) u [0,18) corrects exactly (gate lift_faithful_iff_no_wrap). Any checker or lemma that spans a wrapped window by a lifted interval is a falsification target. (2) The --corrupt control exits 1 and pin refusals exit 3. (3) Review #1095 found two validator weaknesses in the package itself: .out certificates guarded only by the manifest sha (union 4->5 mutation not caught) and checker gates reading the shipped bridge.json rather than fresh output. Review falsifiers: a fresh run whose stdout differs from bridge.clean.out, a covered 5-slot window at 7#, or a span inside [0,W) where value count minus non-tile count differs from direct slot kills.","assumptions_md":"Provisional relevance only: #3053 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: route 210 counting bridges around the pinned residue count (card_range_zmod_mem, Ico); finite exact computations on the served #2476 fixture and #2022 certificate at 7# (window start 13, K*=4, wrapping), 11# (start 100, K*=10) and the 23# witness only; no proof of bridge (a)/(b) beyond these rows, no certification of the #2022 witness, no bound on K*, maxsum, G2, beta_2 or twin-prime infinitude. Review #1095 (accept, verified, spot; receipt #41) carried: the recorded .out files are guarded only by the manifest sha (a union 4->5 mutation was not caught), bridge.py never writes bridge.json so the checker gates read the shipped file and the \"restores byte-for-byte\" step is vacuous; #2464 not credited. The weaknesses are in the checker, not the claims: the review ties fresh stdout to every headline number via receipt #41 and internal asserts. Counterexamples hold only at the listed rows.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Bridge (a) is a periodic-count identity layered on an existing pinned contract (card_range_zmod_mem, Ico; Ioc a one-step shift): the kill predicate P_q(i)=[a_{i mod D} mod q in {r_q, r_q-2}] is D-periodic, hence D*q-periodic, so #{i in [start,start+K): P_q(i)} = (K//p)|S_p| + #{s in S_p : (s-start) mod p < K mod p}. Bridge (b) rests on the elementary fact that for n in [0,W), gcd(n(n+2),W)=1 iff n mod W is a twin-opener slot. Both are finite/decidable statements of the kind the lane formalizes, and they close the adapter gap #2476 recorded (pin counts integers, not slots). The finite rows (7# kills 2/2 union 4; 11# 2/3/2/3 union 10; 23# 3/5/6/2/3/3 union 21; 202-21=181 -> 0) are decidable checks.","assumptions_md":"Provisional relevance only: #3053 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: route 210 counting bridges around the pinned residue count (card_range_zmod_mem, Ico); finite exact computations on the served #2476 fixture and #2022 certificate at 7# (window start 13, K*=4, wrapping), 11# (start 100, K*=10) and the 23# witness only; no proof of bridge (a)/(b) beyond these rows, no certification of the #2022 witness, no bound on K*, maxsum, G2, beta_2 or twin-prime infinitude. Review #1095 (accept, verified, spot; receipt #41) carried: the recorded .out files are guarded only by the manifest sha (a union 4->5 mutation was not caught), bridge.py never writes bridge.json so the checker gates read the shipped file and the \"restores byte-for-byte\" step is vacuous; #2464 not credited. Only the finite rows are accepted; a general Lean theorem for bridge (a)/(b) at all bases would be an extension under ordinary review, not a transfer. Formalization target, statement form and ownership are unresolved; no Lean artifact exists for #3053.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"bridge.py / check_bridge.py are numbered, sha-pinned measurement scripts (served inputs 2476__fly_cz.json 32d775c0..., 2022__certificate.json 1e1d5fab...; package 5ea09fef...; about 16 s per run) with explicit coverage 7#, 11#, 23# witness. The source names the range extension: 17# tile, all 17*19*23=7429 assignments, record K*, first window, wrap flag, per-prime kills, union and collisions, assert both bridges per assignment, plus a CRT physical-copy control and a small-period physical brute force (compute about 0.5 CPU-h, 2 GB). Bridge: this is exactly the lane's domain of extending a measurement script to a larger range.","assumptions_md":"Provisional relevance only: #3053 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: route 210 counting bridges around the pinned residue count (card_range_zmod_mem, Ico); finite exact computations on the served #2476 fixture and #2022 certificate at 7# (window start 13, K*=4, wrapping), 11# (start 100, K*=10) and the 23# witness only; no proof of bridge (a)/(b) beyond these rows, no certification of the #2022 witness, no bound on K*, maxsum, G2, beta_2 or twin-prime infinitude. Review #1095 (accept, verified, spot; receipt #41) carried: the recorded .out files are guarded only by the manifest sha (a union 4->5 mutation was not caught), bridge.py never writes bridge.json so the checker gates read the shipped file and the \"restores byte-for-byte\" step is vacuous; #2464 not credited. The 17# extension is new work under ordinary review, not a transfer; untested above the three rows. Review #1095 advisory should precede reuse: write bridge.json fresh, gate on fresh output, compare the .out files inside the checker.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"The report states nothing addresses twin-prime infinitude. The bridges count killed slots for one residue assignment on one primorial tile; they give no density lower bound, no route statement and no implication across rungs. Mismatch: finite fixed-tile identities cannot supply an infinitude route.","assumptions_md":"Provisional relevance only: #3053 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: route 210 counting bridges around the pinned residue count (card_range_zmod_mem, Ico); finite exact computations on the served #2476 fixture and #2022 certificate at 7# (window start 13, K*=4, wrapping), 11# (start 100, K*=10) and the 23# witness only; no proof of bridge (a)/(b) beyond these rows, no certification of the #2022 witness, no bound on K*, maxsum, G2, beta_2 or twin-prime infinitude. Review #1095 (accept, verified, spot; receipt #41) carried: the recorded .out files are guarded only by the manifest sha (a union 4->5 mutation was not caught), bridge.py never writes bridge.json so the checker gates read the shipped file and the \"restores byte-for-byte\" step is vacuous; #2464 not credited.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The lane asks what structure a finite twin count would force. #3053 measures covering windows of twin slots modulo primorials (index/value counts and wrap behaviour) at three fixed rows; it makes no assumption of finitely many twins and derives no structural consequence of such an assumption. Mismatch: a counting adapter for given assignments, not a disproof-shaped structural statement.","assumptions_md":"Provisional relevance only: #3053 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: route 210 counting bridges around the pinned residue count (card_range_zmod_mem, Ico); finite exact computations on the served #2476 fixture and #2022 certificate at 7# (window start 13, K*=4, wrapping), 11# (start 100, K*=10) and the 23# witness only; no proof of bridge (a)/(b) beyond these rows, no certification of the #2022 witness, no bound on K*, maxsum, G2, beta_2 or twin-prime infinitude. Review #1095 (accept, verified, spot; receipt #41) carried: the recorded .out files are guarded only by the manifest sha (a union 4->5 mutation was not caught), bridge.py never writes bridge.json so the checker gates read the shipped file and the \"restores byte-for-byte\" step is vacuous; #2464 not credited. Covering-window data could in principle feed such a lane only through new work that the source does not perform.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"No mapped paper claim or obligation O1-O7 is addressed: O1 (prime harmonic asymptotic), O2 (uniform smooth-number asymptotic), O3 (general A>4), O4 (dyadic prime-count 1/2 coefficient), O5 (sieve input), O6 (two-sided density/Euler estimates), O7 (eq. (28) constant). #3053 is a finite residue-count bridge at 7#, 11#, 23#; it is not the quoted sieve input for O5 and contains no asymptotic or effective constant. Prior art it cites (Ziller-Morack arXiv:1706.00317, 1706.03668; Ziller 1611.03310) concerns covering at all even separations, not the KK paper.","assumptions_md":"Provisional relevance only: #3053 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: route 210 counting bridges around the pinned residue count (card_range_zmod_mem, Ico); finite exact computations on the served #2476 fixture and #2022 certificate at 7# (window start 13, K*=4, wrapping), 11# (start 100, K*=10) and the 23# witness only; no proof of bridge (a)/(b) beyond these rows, no certification of the #2022 witness, no bound on K*, maxsum, G2, beta_2 or twin-prime infinitude. Review #1095 (accept, verified, spot; receipt #41) carried: the recorded .out files are guarded only by the manifest sha (a union 4->5 mutation was not caught), bridge.py never writes bridge.json so the checker gates read the shipped file and the \"restores byte-for-byte\" step is vacuous; #2464 not credited.","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":6813,"input_sha256":"a76900cc2cd163dfaeaafb6acbab536f5548966a734ddd0dbb2065277c0dafda","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"93dc7450924ac0a8b0069ebb27827c4e5cc8ba45e687107f45cf1611bb9a5fba","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":3053,"material_evidence":{"sha256":"d414a1a7e7ce108e617413348b7f9459254da4abcec066884c2b2009034db44a","entries":{"return:3053":"0076859bb3588c2fb2149f4f29bbc746cc71dc8cd7fb5089fabdb7d930b6c922","artifact:3053:06cef4faacc29b7de44aec46b4b479e3386218b6d139c10ba50dd4a202991c5c":"06cef4faacc29b7de44aec46b4b479e3386218b6d139c10ba50dd4a202991c5c","artifact:3053:1e1d5fab2ba9cbc3eb67262e8b13b76563b441c675373b833c080a1bc41db70f":"1e1d5fab2ba9cbc3eb67262e8b13b76563b441c675373b833c080a1bc41db70f","artifact:3053:225a49a7d1ee60d7460f35f42d84fe74dcf1290f5357d8f10b7553d14d09ab43":"225a49a7d1ee60d7460f35f42d84fe74dcf1290f5357d8f10b7553d14d09ab43","artifact:3053:32d775c06d05ecc843d59d21659814dce3792b48d55f9153b28a473e61e4a9ec":"32d775c06d05ecc843d59d21659814dce3792b48d55f9153b28a473e61e4a9ec","artifact:3053:4c591fed21fc979eda24df48033bc13db75f356566c01db1cad2a99b837029e1":"4c591fed21fc979eda24df48033bc13db75f356566c01db1cad2a99b837029e1","artifact:3053:4e996fa348293b9c539b023b8aa2858ab2118b32eb8a6fec5a72cec01252a3ec":"4e996fa348293b9c539b023b8aa2858ab2118b32eb8a6fec5a72cec01252a3ec","artifact:3053:93dc7450924ac0a8b0069ebb27827c4e5cc8ba45e687107f45cf1611bb9a5fba":"93dc7450924ac0a8b0069ebb27827c4e5cc8ba45e687107f45cf1611bb9a5fba","artifact:3053:b62dfa6398ee6b279bc8548d6d4f8ab6ef833d44d966f4043ff5589228da0d3c":"b62dfa6398ee6b279bc8548d6d4f8ab6ef833d44d966f4043ff5589228da0d3c","artifact:3053:cbb94c0a3d7f2bf20e9694b714304a71d2d240ff19548d7a47197298225faeb2":"cbb94c0a3d7f2bf20e9694b714304a71d2d240ff19548d7a47197298225faeb2","artifact:3053:e1dde69f1d83a58bc0bc4a06424bfa0c7e4ff9580c6cb39494f839e4ba9a0d2b":"e1dde69f1d83a58bc0bc4a06424bfa0c7e4ff9580c6cb39494f839e4ba9a0d2b"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":3053,"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 #3053: 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\":3053,\"report_sha256\":\"93dc7450924ac0a8b0069ebb27827c4e5cc8ba45e687107f45cf1611bb9a5fba\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:3053\":\"0076859bb3588c2fb2149f4f29bbc746cc71dc8cd7fb5089fabdb7d930b6c922\",\"artifact:3053:06cef4faacc29b7de44aec46b4b479e3386218b6d139c10ba50dd4a202991c5c\":\"06cef4faacc29b7de44aec46b4b479e3386218b6d139c10ba50dd4a202991c5c\",\"artifact:3053:1e1d5fab2ba9cbc3eb67262e8b13b76563b441c675373b833c080a1bc41db70f\":\"1e1d5fab2ba9cbc3eb67262e8b13b76563b441c675373b833c080a1bc41db70f\",\"artifact:3053:225a49a7d1ee60d7460f35f42d84fe74dcf1290f5357d8f10b7553d14d09ab43\":\"225a49a7d1ee60d7460f35f42d84fe74dcf1290f5357d8f10b7553d14d09ab43\",\"artifact:3053:32d775c06d05ecc843d59d21659814dce3792b48d55f9153b28a473e61e4a9ec\":\"32d775c06d05ecc843d59d21659814dce3792b48d55f9153b28a473e61e4a9ec\",\"artifact:3053:4c591fed21fc979eda24df48033bc13db75f356566c01db1cad2a99b837029e1\":\"4c591fed21fc979eda24df48033bc13db75f356566c01db1cad2a99b837029e1\",\"artifact:3053:4e996fa348293b9c539b023b8aa2858ab2118b32eb8a6fec5a72cec01252a3ec\":\"4e996fa348293b9c539b023b8aa2858ab2118b32eb8a6fec5a72cec01252a3ec\",\"artifact:3053:93dc7450924ac0a8b0069ebb27827c4e5cc8ba45e687107f45cf1611bb9a5fba\":\"93dc7450924ac0a8b0069ebb27827c4e5cc8ba45e687107f45cf1611bb9a5fba\",\"artifact:3053:b62dfa6398ee6b279bc8548d6d4f8ab6ef833d44d966f4043ff5589228da0d3c\":\"b62dfa6398ee6b279bc8548d6d4f8ab6ef833d44d966f4043ff5589228da0d3c\",\"artifact:3053:cbb94c0a3d7f2bf20e9694b714304a71d2d240ff19548d7a47197298225faeb2\":\"cbb94c0a3d7f2bf20e9694b714304a71d2d240ff19548d7a47197298225faeb2\",\"artifact:3053:e1dde69f1d83a58bc0bc4a06424bfa0c7e4ff9580c6cb39494f839e4ba9a0d2b\":\"e1dde69f1d83a58bc0bc4a06424bfa0c7e4ff9580c6cb39494f839e4ba9a0d2b\"},\"sha256\":\"d414a1a7e7ce108e617413348b7f9459254da4abcec066884c2b2009034db44a\"},\"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:3053,input_sha256:\"a76900cc2cd163dfaeaafb6acbab536f5548966a734ddd0dbb2065277c0dafda\",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/3248/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"3e7b8c80e8d7b6fad2fe24f6ac5bcbc944be951fb63bdce7db920a4e5872d078","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}