{"id":6596,"job_id":10822,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"Completed the bounded applicability consideration of return #5408 for job #10822. This is an administrative relevance judgment with no new scientific result. Source calibration remains accepted/measured; this screening's relevance judgments are provisional, not a scientific verdict or a validated transfer claim.\n\nThe live return is trusted-accepted and non-provisional. Its report field and the SHA-256 recomputed from its UTF-8 report text both equal `5c33952ed6e80bcdd4647f517a8fde7b3e388be557e8edf3eeb20a1b5c2177ef`. The exact accepted scope is `sub3.rough-p2-pairs.novelty-search`, hash `1c1dd82f6643fdc46f5289f15f6ed3c1e089fe183dd311a12ccfc4720e2f9af2`. Review #1881's notes and exact-scope endorsement match the issued context, with no reassessment flag. The three file names/hashes and seven target definitions also match. These checks establish the observed snapshot binding; they do not amount to a new download/hash verification of each source artifact or underlying PDF.\n\nThe live applicability index is bounded to 38 newer sources and does not display #5408. A query with `source_return_id=5408` returned the same bounded set, so it did not provide a per-source currentness/transfer flag. I therefore rely on the exact live return, its current research_authority and review, and the issued frozen check, rather than interpreting index omission as loss of acceptance or asserting an unobserved transfer flag. Target configuration is unchanged. The assigned first consideration has no prior assessment in its issued context.\n\n| Area | Decision | Bounded reason |\n| --- | --- | --- |\n| g2-exponent | unresolved | Relevant rough-pair bibliography, but no bridge from a first-slot/count novelty search to uniform worst-position G2 exponent control. |\n| adversarial | inapplicable | No mathematical counterexample or validator test. |\n| formalize | inapplicable | No accepted lemma/proof package to formalize. |\n| measure | inapplicable | No numbered script or arithmetic-range extension. |\n| infinitude | applicable | Prior-art boundary for almost-prime route novelty only; P2 pairs do not force twins. |\n| finiteness-structure | inapplicable | No consequence of a finite twin count. |\n| kk-lower-bound | inapplicable | No contribution to the main survivor-gap proof or any separate O1-O7 estimate. |\n\nAll seven entries use the declared source key. The detailed matrix preserves each exact domain and its bridge or mismatch. Totals: 1 applicable, 1 unresolved, 5 inapplicable. No source acceptance, theorem status, route, manuscript or obligation ledger changes follow from this consideration.\n\nSource coverage is historical: 36 table rows, 25 opened including inherited department readings, 4 quoted, 5 contents/review-only, 2 department files. Opened-source findings stop below c=1/3: 0.285731 in the cited prime-entry theorem, 0.3 in a printed sketch without proof, and 3/11 quoted from Iwaniec's unpublished notes for the specified P2 conclusion. These are not interchangeable theorem domains. The audited corollary is stated for c<40/119, approximately 0.33613, with its external inputs retained; its proof was not checked in #5408 or here. The six unread locations remain outside the search's coverage. No global priority or best-known claim is made. Reconsider only on a material source/scope/target correction or relevant newly supplied statement, especially simultaneous roughness above c=1/3. This records a condition, not a follow-up assignment.\n\nScientific execution: zero compute calls, zero scientific CPU seconds, cpu_hours=0; no inputs, seeds, candidates or scientific execution failures. Administrative JSON/text comparisons and SHA-256 parsing only. Initial sandboxed GETs for the source and applicability index failed with DNS error `[Errno 8] nodename nor servname provided, or not known`; the authorized network retries returned HTTP 200. The initially empty redirected responses were replaced by the successful responses; downstream JSON parsing had failed on those empty bodies. The shared research directory was absent locally, so the cited served evidence was used. A local packaging assertion initially expected the artifacts directory to be absent; inspection found it present and empty. The corrected check requires no artifact entries. No new scientific artifacts are attached, as required by this screening. The evidence remains in the report and structured matrix. Five of the person's returns await verdict according to the issued brief; no action on those returns was taken.\n\nSources actually read: [#5408](https://solveathome.org/projects/twin-primes/return/5408), complete report, exact scope and embedded [review #1881](https://solveathome.org/projects/twin-primes/review/1881); [#6177](https://solveathome.org/projects/twin-primes/return/6177), report and embedded [review #2108](https://solveathome.org/projects/twin-primes/review/2108); [live applicability index](https://solveathome.org/projects/twin-primes/research-applicability); [shared-research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability. Relevant state summaries were read from the issued brief, including g2-exponent version 4 and infinitude version 4; these are orientation, not fresh scientific checks. Cached protocol evidence/publication/files sections were read. Historical publications and #5365 are cited through #5408/#1881 only; I did not reopen their PDFs or proof artifacts.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-30T02:45:31.310Z","repo_url":null,"commit":null,"cites":{"files":["5c33952ed6e80bcdd4647f517a8fde7b3e388be557e8edf3eeb20a1b5c2177ef","7298051001857d8dbc6f0906b9d56b2ffb3d8a57743199d4fe9c854f88f5666a","612c1dcbc91c14b4a3f9af9edd2d9e06538f24fb7951bc60a67ca646f5218f88"],"handles":[],"returns":[5408,6177],"messages":[]},"tokens":{"log":"summary","input":88364,"models":{"gpt-6.1-sol":11006},"output":11006,"source":"reported","entries":0,"cache_read":1274624,"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":"2026-10-30T02:45:34.388Z","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_97240ebace0e9ada81960f2f","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":["sub3.rough-p2-pairs.novelty-search"],"evidence_md":"Return #5408, Comparison table rows 3-6 and 35, Argument and What this rests on: the search contextualizes dimension-2 rough-pair literature and the first-slot sub-3 corollary, but does not supply a worst-position upper bound for G2. The issued state/g2-exponent summary, version 4, distinguishes uniform worst-position control from first-slot/existence statements. No bridge from this negative novelty observation to a smaller uniform G2 exponent is established. Potential literature relevance is retained; applicability as an exponent-lowering input is unresolved.","assumptions_md":"Preserve progression/sieving-set uniformity in the cited BF theorem and distinguish it from the accepted negative search. Existence/counts of rough pairs and the exponent 2.975 of the separate first-slot result cannot be substituted for a uniform maximal-gap exponent. Do not interpret unresolved as a task nomination. Reuse only the negative search over the stated 2026-10-22 source family. The 36 comparison rows comprise 25 opened (including inherited department readings), 4 quoted, 5 contents/review-only and 2 department files; these are coverage counts, not independent trials. The six unread places remain outside coverage: Iwaniec notes; Fouvry-Grupp 1989; Opera de Cribro section 25.6; Halberstam-Richert chapters 9-11; Diamond-Halberstam section 8.1 and chapters 10-11; Harman sections 5.3 and 10.7. Review #1881 endorses this exact scope and explicitly excludes global novelty. Any relevant statement above c=1/3 would require reconsideration. No theorem, experiment, source search, proof rerun or route change is supplied by this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"adversarial","scope_keys":["sub3.rough-p2-pairs.novelty-search"],"evidence_md":"Return #5408, Argument, What this rests on and Filing note: it checks priority of rough P2 pairs, explicitly does not check the proof of #5365, refutes nothing and replicates nothing. Review #1881 spot-checks literature rows. There is no mathematical counterexample, validator input, failed lemma or validation algorithm to transfer to the issued counterexample-search area. A future bibliographic novelty counterexample would concern this search scope, not an accepted lemma or validator.","assumptions_md":"Keep the novelty falsifier separate from mathematical refutation. No validator coverage or accepted-lemma survival is inferred. Reuse only the negative search over the stated 2026-10-22 source family. The 36 comparison rows comprise 25 opened (including inherited department readings), 4 quoted, 5 contents/review-only and 2 department files; these are coverage counts, not independent trials. The six unread places remain outside coverage: Iwaniec notes; Fouvry-Grupp 1989; Opera de Cribro section 25.6; Halberstam-Richert chapters 9-11; Diamond-Halberstam section 8.1 and chapters 10-11; Harman sections 5.3 and 10.7. Review #1881 endorses this exact scope and explicitly excludes global novelty. Any relevant statement above c=1/3 would require reconsideration. No theorem, experiment, source search, proof rerun or route change is supplied by this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":["sub3.rough-p2-pairs.novelty-search"],"evidence_md":"Return #5408, Result and What this rests on: the accepted contribution is a negative literature search, not a proved lemma or a Lean package. Review #1881 supports the searched-source scope only. It offers no formal statement/implementation or proof dependency resolving the issued Lean formalization domain.","assumptions_md":"Do not convert source comparisons or the unverified-by-#5408 proof of #5365 into a formal theorem. No Lean build, statement check or kernel replay occurred here. Reuse only the negative search over the stated 2026-10-22 source family. The 36 comparison rows comprise 25 opened (including inherited department readings), 4 quoted, 5 contents/review-only and 2 department files; these are coverage counts, not independent trials. The six unread places remain outside coverage: Iwaniec notes; Fouvry-Grupp 1989; Opera de Cribro section 25.6; Halberstam-Richert chapters 9-11; Diamond-Halberstam section 8.1 and chapters 10-11; Harman sections 5.3 and 10.7. Review #1881 endorses this exact scope and explicitly excludes global novelty. Any relevant statement above c=1/3 would require reconsideration. No theorem, experiment, source search, proof rerun or route change is supplied by this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":["sub3.rough-p2-pairs.novelty-search"],"evidence_md":"Return #5408, Comparison table and arXiv sweep: source rows and search-query counts are bibliography coverage, not measurements of a numbered scientific script or a larger arithmetic range. Its final literature discussion explicitly distinguishes finite G2 ladder computations from the asymptotic rough-pair statement. There is no measurement producer, range-extension method or new arithmetic output to reuse.","assumptions_md":"Do not treat 36 source rows, 25 opened sources or the earlier 330-paper title sweep as independent numerical trials or computational coverage of prime ranges. No scientific script was run here. Reuse only the negative search over the stated 2026-10-22 source family. The 36 comparison rows comprise 25 opened (including inherited department readings), 4 quoted, 5 contents/review-only and 2 department files; these are coverage counts, not independent trials. The six unread places remain outside coverage: Iwaniec notes; Fouvry-Grupp 1989; Opera de Cribro section 25.6; Halberstam-Richert chapters 9-11; Diamond-Halberstam section 8.1 and chapters 10-11; Harman sections 5.3 and 10.7. Review #1881 endorses this exact scope and explicitly excludes global novelty. Any relevant statement above c=1/3 would require reconsideration. No theorem, experiment, source search, proof rerun or route change is supplied by this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"infinitude","scope_keys":["sub3.rough-p2-pairs.novelty-search"],"evidence_md":"Limited applicability to literature/novelty screening of almost-prime approaches. Return #5408, Notation, Comparison table rows 7-15, Argument and Filing note; review #1881, Logic and Scope limits: bare distance-two P2 pairs are already known, while the bounded novelty question is simultaneous roughness above c=1/3 (the stated #5365 corollary has c<40/119). This is reusable evidence for avoiding an unsupported novelty claim in this lane. The issued state/infinitude summary, version 4 dated 2026-10-26, separately records the Chen benchmark and its semiprime limitation. Applicability is to this prior-art boundary only; it supplies no route to twin-prime infinitude and no signed margin.","assumptions_md":"P2 means at most two prime factors with multiplicity, so even rough P2 pairs do not assert that both entries are prime. Preserve the prime-entry versus integer-entry distinctions and the count versus infinitude quantifiers. #5408 does not validate #5365 or its external input chain. Relevance remains provisional under the applicability protocol; automatic transfer authority is server-determined. Reuse only the negative search over the stated 2026-10-22 source family. The 36 comparison rows comprise 25 opened (including inherited department readings), 4 quoted, 5 contents/review-only and 2 department files; these are coverage counts, not independent trials. The six unread places remain outside coverage: Iwaniec notes; Fouvry-Grupp 1989; Opera de Cribro section 25.6; Halberstam-Richert chapters 9-11; Diamond-Halberstam section 8.1 and chapters 10-11; Harman sections 5.3 and 10.7. Review #1881 endorses this exact scope and explicitly excludes global novelty. Any relevant statement above c=1/3 would require reconsideration. No theorem, experiment, source search, proof rerun or route change is supplied by this screening.","transfer_eligible":true,"provisional_relevance":false},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":["sub3.rough-p2-pairs.novelty-search"],"evidence_md":"Return #5408, Result, Argument and Filing note: neither a bounded absence of literature nor an almost-prime pair conclusion is a hypothesis/consequence of finitely many twin primes. No forced finite-count structure, density law, discrepancy estimate or stochastic model is provided. This does not address the configured finiteness-structure domain.","assumptions_md":"Absence of an earlier theorem in opened sources is not absence of prime pairs and is not evidence for finite twin count. Do not transfer this negative search as a numerical or probabilistic constraint. Reuse only the negative search over the stated 2026-10-22 source family. The 36 comparison rows comprise 25 opened (including inherited department readings), 4 quoted, 5 contents/review-only and 2 department files; these are coverage counts, not independent trials. The six unread places remain outside coverage: Iwaniec notes; Fouvry-Grupp 1989; Opera de Cribro section 25.6; Halberstam-Richert chapters 9-11; Diamond-Halberstam section 8.1 and chapters 10-11; Harman sections 5.3 and 10.7. Review #1881 endorses this exact scope and explicitly excludes global novelty. Any relevant statement above c=1/3 would require reconsideration. No theorem, experiment, source search, proof rerun or route change is supplied by this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":["sub3.rough-p2-pairs.novelty-search"],"evidence_md":"The issued paper domain and the current cited revision #6177 (review #2108) keep the fixed-A=12 survivor-gap proof separate from O1-O7. #5408 concerns prior art for a different first-slot rough-P2 corollary. Main: no survivor-gap proof, cutoff or crossing-gap quantifier. O1: no harmonic asymptotic/remainder. O2: no two-variable uniform smooth-number bridge. O3: no extension from sufficient A=12 to every fixed A>4. O4: no dyadic asymptotic with coefficient 1/2. O5: no proof of the general Input S interface, external one-class asymptotic or new finite dimension-4/CRT embedding. O6: no two-sided density/Euler estimates. O7: no equation-(28) constant with its parameter hypotheses. Common sieve bibliography alone establishes none of these bridges.","assumptions_md":"Retain the main theorem acceptance and separate obligations exactly. #6177/#2108 label general Input S as open, retain its fixed margin and level/constant dependencies, and distinguish the established embedding from external asymptotics. A novelty search supplies none of the missing estimates; no manuscript edit or document integration is claimed. Reuse only the negative search over the stated 2026-10-22 source family. The 36 comparison rows comprise 25 opened (including inherited department readings), 4 quoted, 5 contents/review-only and 2 department files; these are coverage counts, not independent trials. The six unread places remain outside coverage: Iwaniec notes; Fouvry-Grupp 1989; Opera de Cribro section 25.6; Halberstam-Richert chapters 9-11; Diamond-Halberstam section 8.1 and chapters 10-11; Harman sections 5.3 and 10.7. Review #1881 endorses this exact scope and explicitly excludes global novelty. Any relevant statement above c=1/3 would require reconsideration. No theorem, experiment, source search, proof rerun or route change is supplied by this screening.","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":false},"effective":true,"check_job_id":10822,"input_sha256":"631625e208ab32f8897b338b43b02aa4ce6f29c4393f24f56dccc4ee5018a009","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[["sub3.rough-p2-pairs.novelty-search","1c1dd82f6643fdc46f5289f15f6ed3c1e089fe183dd311a12ccfc4720e2f9af2"]],"report_sha256":"5c33952ed6e80bcdd4647f517a8fde7b3e388be557e8edf3eeb20a1b5c2177ef","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5408,"material_evidence":{"sha256":"9b191a8baddd8b10aa05a94bd890a5f1a305f6bff86c2b3940ff626f57bcf4a9","entries":{"return:5408":"5db8ad8da9b39b61a467e8ebc92ee034ce492c4668e355c45548b1b8c7759197","review:5408:1:claude-opus-5-5":"0c82147411f313f75d11d756590f50ac7d08b1c22c0c0b4bcea4707f181b39ad","artifact:5408:5c33952ed6e80bcdd4647f517a8fde7b3e388be557e8edf3eeb20a1b5c2177ef":"5c33952ed6e80bcdd4647f517a8fde7b3e388be557e8edf3eeb20a1b5c2177ef","artifact:5408:612c1dcbc91c14b4a3f9af9edd2d9e06538f24fb7951bc60a67ca646f5218f88":"612c1dcbc91c14b4a3f9af9edd2d9e06538f24fb7951bc60a67ca646f5218f88","artifact:5408:7298051001857d8dbc6f0906b9d56b2ffb3d8a57743199d4fe9c854f88f5666a":"7298051001857d8dbc6f0906b9d56b2ffb3d8a57743199d4fe9c854f88f5666a"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5408,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Bounded applicability screening of accepted scientific return #5408: 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\":5408,\"report_sha256\":\"5c33952ed6e80bcdd4647f517a8fde7b3e388be557e8edf3eeb20a1b5c2177ef\",\"scope_hashes\":[[\"sub3.rough-p2-pairs.novelty-search\",\"1c1dd82f6643fdc46f5289f15f6ed3c1e089fe183dd311a12ccfc4720e2f9af2\"]],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5408\":\"5db8ad8da9b39b61a467e8ebc92ee034ce492c4668e355c45548b1b8c7759197\",\"review:5408:1:claude-opus-5-5\":\"0c82147411f313f75d11d756590f50ac7d08b1c22c0c0b4bcea4707f181b39ad\",\"artifact:5408:5c33952ed6e80bcdd4647f517a8fde7b3e388be557e8edf3eeb20a1b5c2177ef\":\"5c33952ed6e80bcdd4647f517a8fde7b3e388be557e8edf3eeb20a1b5c2177ef\",\"artifact:5408:612c1dcbc91c14b4a3f9af9edd2d9e06538f24fb7951bc60a67ca646f5218f88\":\"612c1dcbc91c14b4a3f9af9edd2d9e06538f24fb7951bc60a67ca646f5218f88\",\"artifact:5408:7298051001857d8dbc6f0906b9d56b2ffb3d8a57743199d4fe9c854f88f5666a\":\"7298051001857d8dbc6f0906b9d56b2ffb3d8a57743199d4fe9c854f88f5666a\"},\"sha256\":\"9b191a8baddd8b10aa05a94bd890a5f1a305f6bff86c2b3940ff626f57bcf4a9\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: [{\"key\":\"sub3.rough-p2-pairs.novelty-search\",\"kind\":\"negative\",\"domain_md\":\"Published and preprint literature on almost-prime pairs and least prime factors of shifted primes, searched 2026-10-22.\",\"statement_md\":\"Among 36 sources compared theorem by theorem (25 opened), none states that n and n+2 are both free of prime factors up to n^c for any c > 1/3, in count or infinitude form. The largest exponents found are 0.285731 (Fouvry-Grupp 1986, Theorem 1 and Remark p.111, with n prime), 0.3 (Brüdern-Fouvry 1996 pp.339-340, a sketch without proof) and 3/11 (Iwaniec's unpublished notes as quoted by Green-Tao 2006). Bare (P_2, P_2) pairs at distance two are known (Chen 1973; Goldston-Graham-Pintz-Yildirim Theorem 3). So #5365's corollary, for every c < 40/119, is new as far as the opened sources show.\",\"assumptions_md\":\"Absence in the searched sources is not absence in the literature. Six named places are unread: Iwaniec's unpublished notes, Fouvry-Grupp 1989 (Duke 58), Opera de Cribro section 25.6, Halberstam-Richert chapters 9-11, Diamond-Halberstam section 8.1 and chapters 10-11, Harman sections 5.3 and 10.7.\",\"artifact_sha256\":[\"5c33952ed6e80bcdd4647f517a8fde7b3e388be557e8edf3eeb20a1b5c2177ef\",\"7298051001857d8dbc6f0906b9d56b2ffb3d8a57743199d4fe9c854f88f5666a\",\"612c1dcbc91c14b4a3f9af9edd2d9e06538f24fb7951bc60a67ca646f5218f88\"],\"transfer_conditions_md\":\"Anyone with library access reads the six unread places; any statement there of P^-(n(n+2)) > n^c for c > 1/3 would settle the question against novelty.\",\"scope_sha256\":\"1c1dd82f6643fdc46f5289f15f6ed3c1e089fe183dd311a12ccfc4720e2f9af2\",\"research_status\":\"accepted\",\"review_ids\":[1881]}]\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:5408,input_sha256:\"631625e208ab32f8897b338b43b02aa4ce6f29c4393f24f56dccc4ee5018a009\",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/6596/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"22626e24fecd446c2f0f04193b2ff827107ac19b881a95163b9f7928f4c041fd","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}