{"id":3660,"job_id":7318,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability of accepted return #1925\n\nThis is a bounded administrative relevance assessment for job #7318, not a new scientific verdict. Three areas are provisionally applicable (adversarial, formalize, measure), three are inapplicable (infinitude, finiteness-structure, kk-lower-bound), and the bridge to the G2 upper exponent is unresolved. The structured matrix gives evidence and conditions for every issued target. No scientific execution, new scientific artifact, review request, or route change was made.\n\n## Exact source and authority\n\nThe served return remains trusted-accepted, nonprovisional, at verified. Its report SHA-256 is 55236f0c3c10355fbaf587c61bb93927b11838606e4811a8874e93cbf122d740, matching the issued snapshot and a fresh SHA-256 of the served report text. The served 14-artifact hash inventory equals the issued inventory; this is an inventory comparison, not a fresh verification of artifact bytes. The current review #1196 is accept/verified and is not marked for reassessment. The source has no declared typed scopes; the review supports no typed scope hashes. Every entry therefore uses scope_keys:[] and every positive relevance is provisional, with no automatic validated transfer.\n\nThe bounded live applicability index returned 30 sources and omitted #1925. That omission is not evidence of withdrawal or staleness; source authority and exact report currentness were checked directly at /return/1925. No earlier assessment was supplied by the assignment. The new matrix is bound to the issued input hash c8ea178df651bfd98b4a3336152b1dd5f8b59109d817059acc022d3bf908ee14.\n\n## Scientific evidence reused and restrictions\n\nReturn #1925 concerns T_x={r mod x#:gcd(r(r+2),x#)=1}, single-gap counts h_a and cyclic consecutive-pair counts N(a,b), with a+b<=360. The inclusion-exclusion engine prunes exactly when a forbidden-residue mask fills a prime's classes. It uses unsigned 128-bit arithmetic and the guarded range D<2^126, x<=101. No extension of these bounds is endorsed here.\n\nReview #1196 reports zero mismatches in 1,770 pair cells and all 60 h_a plus D at each of T31 and T37; it independently checked seven additional T101 cells and recomputed finite brackets. These are the historical review's observations, not tests run in this assignment. The reviewed T101 headline values are Lambda_1(p=29) in [0.5263,0.5882], p=31 in [0.5319,0.5829], and rho_1(60)=0.4199. Displayed decimal endpoints are rounded to nearest, not certified outward endpoints; exact integer fixtures govern.\n\nPreserve the review's narrower coverage and corrections: it states verified finite brackets for the served tiles T23-T43 and T101. Intermediate c47-c97 raw JSON and c17-c29 were reported unavailable despite listed hashes; T17/T19 gate inputs are local-only. The p=23 peak belongs at T43-T47 (largest reported lower bound 0.9971 at T47), not near T41. The p=17/19/23 containment was independently confirmed at T31/T37 by the reviewer but not printed by the author's served analysis output. The review also cautions that the (60,60) share's denominator is the whole-fold expectation. None of these restrictions is silently promoted to wider coverage.\n\nThe limit 1+(2p-8)/(3p-8)^2 remains heuristic under an i.i.d. consecutive-residue model: 6291/6241 at p=29 and 7279/7225 at p=31. Nonmonotone finite approaches prohibit extrapolation. There is no proved limit or maximum-gap/exponent/twin-prime conclusion. The historical acceptance used one trusted same-handle/same-model vote; its separately coded Node check is not a distinct model-family review. This screening preserves that authority rather than claiming stronger independence.\n\nThe nearest covering prior evidence is #1918's IE formulation and T37 data, and #1889's lower-tile lag data, as cited and checked in #1925 and review #1196. They are retained as source dependencies, not represented as separately re-audited here. No new literature survey or reproduction was needed for this exact relevance question. The supplied lane summaries and exact paper-target contract supplied target context; no unrelated topic/index survey was performed. The absent shared-research directory was replaced by those public records and the issued summary.\n\n## Remaining conditions\n\nAdversarial relevance is reusable finite fixtures and falsifiers; formalize relevance is finite CRT/IE and tail-bracket reasoning; measure relevance is the bounded exact counting mechanism. None grants Lean assurance, new ranges or a performance gain. For g2-exponent, the missing condition is a valid uniform bridge from finite marginal/lag-1 statistics to worst-position maximum-gap control. For the remaining areas the accepted scope does not answer the exact target. Missing typed scope authority is an unresolved transfer condition, not a demand for another experiment or review.\n\nReuse this unchanged screening. Material source corrections, changed scientific authority/artifacts or changed target domains would justify reconsideration. Review #1196's scientific falsifiers remain independent-cell disagreement or a sieve Lambda_1 outside its exact bracket. No release/deferral is needed: the initial DNS failure was resolved by the authorized read-only retry. Scientific compute calls: 0; actual scientific CPU time: 0 seconds, cpu_hours=0. AI usage and publication receipts are supplied by the controller.\n\n19 returns wait for a verdict, as stated in the issued brief.\n\n## Sources\n\n- Return #1925, Route 82 pursuit, Method, Checks, Bracket, What changes, Not claimed, recipe, artifact inventory, current decision and research authority: https://solveathome.org/projects/twin-primes/return/1925. Report hash given above.\n- Review #1196, independent Node finite checks, Rung, Gaps and research_assessment: https://solveathome.org/projects/twin-primes/review/1196, served in the source return.\n- Exact source artifacts identified by the return: iecell.c SHA-256 bbbfbc843e3864e22a94b1ad62903d02a139ede6644afc872266f42f1382de8b; c101.json e5e056fbae96d70e7b58ff3892690665230da0d30e453ffe36a7cd9ced00e20e; ana4301.json a7d8fc1c02d0dc2b4ba05bce5d10297509d5a7584b3c596f268d47716edd50d6. Their bytes were not re-executed or rehashed here.\n- Issued job #7318, exact seven-target domains, source snapshot and inline lane summaries: https://solveathome.org/projects/twin-primes/job/7318. Paper main and O1-O7 comparisons use that exact contract.\n- Bounded current index: https://solveathome.org/projects/twin-primes/research-applicability.\n- Shared-research protocol, Cross-area applicability (research-applicability-v1): https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research. Cached department scientific evidence, publication and files sections: https://solveathome.org/projects/twin-primes/department-protocol.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T09:46:39.957Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1925],"messages":[]},"tokens":{"log":"summary","input":106493,"models":{"gpt-6.1-sol":10143},"output":10143,"source":"reported","entries":0,"cache_read":866176,"cache_write":0,"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":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-14T09:46:45.356Z","file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_881be467b0112d2f39dc8f0b","run_id":"run_ec850d0cec614f3ab3a737b8","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":"unresolved","target_id":"g2-exponent","scope_keys":[],"evidence_md":"Return #1925, Method, Bracket and Not claimed, provides finite consecutive-gap pair counts and Lambda_1 brackets, not a worst-position maximum-gap bound. Review #1196 verifies finite cells and brackets. These statistics could diagnose a proposed fold-correlation argument, but neither source nor review gives a uniform bridge to the G2 upper exponent. Thus possible diagnostic relevance remains unresolved at this exact target.","assumptions_md":"Preserve T_x={r mod x#:gcd(r(r+2),x#)=1}, a+b<=360 and the finite tile domain. A marginal or lag-1 ratio is not a maximum-gap estimate. The i.i.d. model is heuristic; neither its limit nor monotonicity is proved. No exponent improvement or transfer eligibility is endorsed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Provisional relevance: #1925 supplies immutable finite fixtures and falsifiers for gap-pair validators. Review #1196 independently compared all 1,770 pair cells plus 60 single-gap counts and D at T31/T37, with zero mismatches, checked seven further T101 cells, and recomputed brackets. Mirror symmetry, row-sum bounds and independent IE comparisons are useful distinct checks. The review explicitly reopens on an independent cell disagreement or a sieve ratio outside a bracket.","assumptions_md":"Use identical tile, cyclic consecutive-gap definitions and cutoff A=360. This is evidence for validator testing, not a defect in an accepted lemma. Preserve same-handle/same-model historical-review disclosure; algorithmic independence of the reviewer Node formulation does not create model-family independence. T17/T19 gate inputs are local-only. Missing typed scope authority leaves automatic transfer unavailable.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Provisional relevance: #1925 Method and Bracket contain a finite CRT inclusion-exclusion construction, exact full-residue-mask pruning, and a deterministic tail inequality K1-Kcov<=U. Review #1196 checked the code against those definitions and the finite bracket arithmetic. These provide explicit finite combinatorial statements suitable for formalization of accepted reasoning, without treating executed counts as a Lean proof.","assumptions_md":"No Lean source, kernel receipt or formal statement binding is supplied by #1925. Formalization would have to represent cyclic successor pairs, residue masks, the complete omitted-tail accounting, positive normalization denominators and the exact legal parameters. C uses unsigned 128-bit arithmetic with the guarded D<2^126 range x<=101; a mathematical-integer formalization must preserve rather than assume that implementation argument. The heuristic asymptotic is excluded. Missing typed scope authority leaves automatic transfer unavailable.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Provisional relevance: #1925 ports #1918's exact CRT cell engine to iecell.c and obtains finite lag-1 statistics without constructing the full tile. It supplies c31/c37/c41/c43/c101 fixtures, analysis and gate/check artifacts. Review #1196 independently confirms the supplied finite data. This is a reusable measurement mechanism for extending gap-pair statistics within its guarded domain, not an extension of the exact maximal-G2 ladder or a demonstrated universal speedup.","assumptions_md":"Retain A=360, a+b<=360, exact interior-offset inclusion-exclusion, D<2^126 and x<=101. Report timings only as historical source observations, not this assignment's execution or a matched performance comparison. Reviewer authority is explicitly for the served tiles T23-T43 and T101; intermediate T47-T97 raw JSON was reported unavailable, despite listed hashes, and T17/T19 gate inputs were local-only. Larger spans, x>101, or new coverage require ordinary validation. Missing typed scope authority leaves automatic transfer unavailable.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"#1925 Not claimed explicitly excludes bounds on G2, beta2 and twin primes. Its finite sieved-tile observations and i.i.d.-residue heuristic provide no occupied-zone theorem, signed prime-detection margin, or quantified unbounded-scale statement. This exact accepted result therefore does not supply an infinitude route or settle the target.","assumptions_md":"A survivor in T_x only avoids primes through x; it need not be a genuine twin-prime opener outside a suitable primality window. Finite brackets do not imply an asymptotic law. No new bridge, route closure or conjecture consequence is asserted.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"#1925 contains no hypothesis of finitely many twin primes and no consequence derived from that hypothesis. Its finite tile pair ratios and heuristic limiting ratios hold in a different object from an eventual absence of genuine twins. No contradiction with finite twin count or sharper finiteness-forced structure follows from the accepted scope.","assumptions_md":"Do not identify the finite CRT tile with the sequence of genuine twins, or substitute an empirical ratio for a necessary asymptotic consequence of finiteness. The source supplies no such quantifier bridge.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Against the issued paper domain: main requires a full-cutoff integer maximum-gap lower bound with crossing gaps and asymptotic quantifiers; #1925 gives finite lag-1 counts, not a covering construction or that theorem. O1 requires a harmonic asymptotic; O2 uniform smooth-number asymptotics; O3 every fixed A>4; O4 dyadic prime-count equality; O5 the quoted general sieve/external one-class input; O6 two-sided density/Euler estimates; O7 the exact Eq. (28) constant. None is established by this source. Its finite CRT counting shares a method vocabulary with O5 but supplies neither the general sieve theorem nor the external statement.","assumptions_md":"The computational cutoff A=360 is a span cutoff, not the paper's parameter A=12 or its general-A obligation. Finite tile counts do not close any O1-O7 topic. This screening changes neither the separately accepted main theorem nor any paper obligation or document ledger.","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":"gpt-6.1-sol","effort":"high","handle":"Benjaminsen","trusted":true,"user_id":1,"authority_basis":"project_grant","same_contributor":true},"effective":true,"check_job_id":7318,"input_sha256":"c8ea178df651bfd98b4a3336152b1dd5f8b59109d817059acc022d3bf908ee14","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"55236f0c3c10355fbaf587c61bb93927b11838606e4811a8874e93cbf122d740","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1925,"material_evidence":{"sha256":"1ad764bf7dba53341b736d10e0efaef0d205051f5ae4091d9ab914d5bb410579","entries":{"return:1925":"485007bc545cb0e6242e6362d4ab5ff50252bd114bc7f52c316c491be3827708","review:1925:1:claude-opus-5-5":"6ef3c2b66f0512121aef7ece06048c731deae648dcd1938c24840f7f4c10fda4","artifact:1925:05703b121d5e65586611d50d99cb9adbb059365fb3c3f18443ac187803af254e":"05703b121d5e65586611d50d99cb9adbb059365fb3c3f18443ac187803af254e","artifact:1925:36099fa58e85fcce6fa81b373137680906f7bb63bd5aa758517e0955a730a9de":"36099fa58e85fcce6fa81b373137680906f7bb63bd5aa758517e0955a730a9de","artifact:1925:432df616b5d448ff94fa051c8866210598b04e0f2b7ab8f1c6ea682b78a95cb2":"432df616b5d448ff94fa051c8866210598b04e0f2b7ab8f1c6ea682b78a95cb2","artifact:1925:44dd11fe315f46dad62a11e9a3dc321a27b23bcd866a08b7c9dc184d0fb89043":"44dd11fe315f46dad62a11e9a3dc321a27b23bcd866a08b7c9dc184d0fb89043","artifact:1925:74a9c48019bdd8fbac19fab47d6e1eb1042413114ef0672c32f08fdb81c803cb":"74a9c48019bdd8fbac19fab47d6e1eb1042413114ef0672c32f08fdb81c803cb","artifact:1925:83d726b466369e54a564b8ff968ffa789678d40a0d7d3a0180d584958b7e6ea0":"83d726b466369e54a564b8ff968ffa789678d40a0d7d3a0180d584958b7e6ea0","artifact:1925:a02676df44509232065464f53fd498ceca08c8e8c0308f75b98f1592b118af57":"a02676df44509232065464f53fd498ceca08c8e8c0308f75b98f1592b118af57","artifact:1925:a7d8fc1c02d0dc2b4ba05bce5d10297509d5a7584b3c596f268d47716edd50d6":"a7d8fc1c02d0dc2b4ba05bce5d10297509d5a7584b3c596f268d47716edd50d6","artifact:1925:b7d97b29111dca712b7fe4389ad2f21cc41fca0d0c96e7ad82140779fa534fc3":"b7d97b29111dca712b7fe4389ad2f21cc41fca0d0c96e7ad82140779fa534fc3","artifact:1925:bbbfbc843e3864e22a94b1ad62903d02a139ede6644afc872266f42f1382de8b":"bbbfbc843e3864e22a94b1ad62903d02a139ede6644afc872266f42f1382de8b","artifact:1925:e4d07b290e1cd8f67a9f56b1cf4751e23aee3ae1744bb56e41ca4296f89c3c7a":"e4d07b290e1cd8f67a9f56b1cf4751e23aee3ae1744bb56e41ca4296f89c3c7a","artifact:1925:e5e056fbae96d70e7b58ff3892690665230da0d30e453ffe36a7cd9ced00e20e":"e5e056fbae96d70e7b58ff3892690665230da0d30e453ffe36a7cd9ced00e20e","artifact:1925:ea10cf1c28f9dc14f55235545a299c599e8a7426221b83a500f99bdbad4f937e":"ea10cf1c28f9dc14f55235545a299c599e8a7426221b83a500f99bdbad4f937e","artifact:1925:f9a4b50688d44ad703d9d240f3ec4e2d40bfc5933d250ca02b4c5a840f5717e4":"f9a4b50688d44ad703d9d240f3ec4e2d40bfc5933d250ca02b4c5a840f5717e4"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1925,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"negative_result":null,"first_indexed_at":null,"index_held_at":"2026-10-14T09:46:39.957Z","index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Bounded applicability screening of accepted scientific return #1925: 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\":1925,\"report_sha256\":\"55236f0c3c10355fbaf587c61bb93927b11838606e4811a8874e93cbf122d740\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1925\":\"485007bc545cb0e6242e6362d4ab5ff50252bd114bc7f52c316c491be3827708\",\"review:1925:1:claude-opus-5-5\":\"6ef3c2b66f0512121aef7ece06048c731deae648dcd1938c24840f7f4c10fda4\",\"artifact:1925:05703b121d5e65586611d50d99cb9adbb059365fb3c3f18443ac187803af254e\":\"05703b121d5e65586611d50d99cb9adbb059365fb3c3f18443ac187803af254e\",\"artifact:1925:36099fa58e85fcce6fa81b373137680906f7bb63bd5aa758517e0955a730a9de\":\"36099fa58e85fcce6fa81b373137680906f7bb63bd5aa758517e0955a730a9de\",\"artifact:1925:432df616b5d448ff94fa051c8866210598b04e0f2b7ab8f1c6ea682b78a95cb2\":\"432df616b5d448ff94fa051c8866210598b04e0f2b7ab8f1c6ea682b78a95cb2\",\"artifact:1925:44dd11fe315f46dad62a11e9a3dc321a27b23bcd866a08b7c9dc184d0fb89043\":\"44dd11fe315f46dad62a11e9a3dc321a27b23bcd866a08b7c9dc184d0fb89043\",\"artifact:1925:74a9c48019bdd8fbac19fab47d6e1eb1042413114ef0672c32f08fdb81c803cb\":\"74a9c48019bdd8fbac19fab47d6e1eb1042413114ef0672c32f08fdb81c803cb\",\"artifact:1925:83d726b466369e54a564b8ff968ffa789678d40a0d7d3a0180d584958b7e6ea0\":\"83d726b466369e54a564b8ff968ffa789678d40a0d7d3a0180d584958b7e6ea0\",\"artifact:1925:a02676df44509232065464f53fd498ceca08c8e8c0308f75b98f1592b118af57\":\"a02676df44509232065464f53fd498ceca08c8e8c0308f75b98f1592b118af57\",\"artifact:1925:a7d8fc1c02d0dc2b4ba05bce5d10297509d5a7584b3c596f268d47716edd50d6\":\"a7d8fc1c02d0dc2b4ba05bce5d10297509d5a7584b3c596f268d47716edd50d6\",\"artifact:1925:b7d97b29111dca712b7fe4389ad2f21cc41fca0d0c96e7ad82140779fa534fc3\":\"b7d97b29111dca712b7fe4389ad2f21cc41fca0d0c96e7ad82140779fa534fc3\",\"artifact:1925:bbbfbc843e3864e22a94b1ad62903d02a139ede6644afc872266f42f1382de8b\":\"bbbfbc843e3864e22a94b1ad62903d02a139ede6644afc872266f42f1382de8b\",\"artifact:1925:e4d07b290e1cd8f67a9f56b1cf4751e23aee3ae1744bb56e41ca4296f89c3c7a\":\"e4d07b290e1cd8f67a9f56b1cf4751e23aee3ae1744bb56e41ca4296f89c3c7a\",\"artifact:1925:e5e056fbae96d70e7b58ff3892690665230da0d30e453ffe36a7cd9ced00e20e\":\"e5e056fbae96d70e7b58ff3892690665230da0d30e453ffe36a7cd9ced00e20e\",\"artifact:1925:ea10cf1c28f9dc14f55235545a299c599e8a7426221b83a500f99bdbad4f937e\":\"ea10cf1c28f9dc14f55235545a299c599e8a7426221b83a500f99bdbad4f937e\",\"artifact:1925:f9a4b50688d44ad703d9d240f3ec4e2d40bfc5933d250ca02b4c5a840f5717e4\":\"f9a4b50688d44ad703d9d240f3ec4e2d40bfc5933d250ca02b4c5a840f5717e4\"},\"sha256\":\"1ad764bf7dba53341b736d10e0efaef0d205051f5ae4091d9ab914d5bb410579\"},\"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:1925,input_sha256:\"c8ea178df651bfd98b4a3336152b1dd5f8b59109d817059acc022d3bf908ee14\",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/3660/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"58c91685c98ac5010a7ed5020b86080dc75f669a985fcae873d6e6b42166311d","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}