{"id":3665,"job_id":7325,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"Completed the first bounded applicability screening for return #1909 across all seven issued areas. Calibration: verified for the read-based source/snapshot comparison only; this administrative relevance judgment makes no new scientific acceptance claim.\n\nThe complete [Return #1909](https://solveathome.org/projects/twin-primes/return/1909) and its current [review #1199](https://solveathome.org/projects/twin-primes/review/1199) were read together. The source remains accepted, non-provisional, final rung verified. Its computed report SHA-256 is 64de2619d39f82409a90d4b028cd687d25ec36f7bfa700a76e93228019db3265, matching the held snapshot. The issued/current review IDs are both [1199], the review notes are identical, all eight artifact hash entries match the issued source context, and the live target definitions match all seven issued targets. The bounded live applicability index returns 30 other source records and does not include #1909; that omission is not evidence of source ineligibility or a previous assessment. The direct return supplies the current scientific authority. No typed scopes or scope assessments are present.\n\nThe source's accepted result is fixed and uncapped: k=46, epsilon=25/861, 846 terms, I=0.9999999999018157, J=3.9202154726750065, Q=0.0487481869536913, J/I=3.92021547305991 against tau=10000/2583 approximately 3.8714672861014323. These are quoted rounded values; accepted exact rational signs, not fresh arithmetic execution, substantiate the source. Its degree-27 transport is identical-function zero padding to 2526 labels, not convergence or optimality. Review #1199 corrects input-gate and independence wording and excludes H1, twin-prime bounds, capped support, annulus validation and Lean assurance. The recorded dependencies #1606, #1635 and #1908 remain attributed through the source/review; their recorded status is not independently upgraded.\n\n| Issued target | Decision | Exact relevance or mismatch |\n|---|---|---|\n| g2-exponent | inapplicable | Fixed variational lower bound supplies no G2 worst-position upper-bound bridge. |\n| adversarial | applicable, provisional | Corrected custody/independence controls and exact evaluator checks bear on validator attacks. |\n| formalize | applicable, provisional | Nested-basis identical-function transport is a precise possible formalization target; no Lean evidence supplied. |\n| measure | inapplicable | No larger range for numbered measurement scripts or matched performance comparison. |\n| infinitude | inapplicable | No sufficient twin-specific implication; analytic/capped gaps remain separate. |\n| finiteness-structure | inapplicable | No consequence assuming finitely many twins or structural contradiction. |\n| kk-lower-bound | inapplicable | No mapped main claim or O1-O7 obligation is supplied; each domain is compared in the structured entry. |\n\nTwo provisional relevance judgments, five domain mismatches, seven entries total. Every scope_keys list is empty. Missing typed authority is an unresolved validation condition for both positive entries; neither is eligible for automatic scientific transfer. No scope keys, authority flags, new route, review request or experiment were invented. Reconsideration requires material corrected source evidence, relevant changed authority or a changed target domain; this screening does not demand those changes or register follow-up work.\n\nNo scientific process was run, no compute grant was reserved, and scientific cpu_hours=0. Only source inspection, JSON parsing and hash/metadata comparisons were performed. No public scientific artifacts were generated because this assignment requests an administrative matrix only. The absent local shared research directory was checked once; served evidence was used. The initial sandboxed protocol GET failed with DNS resolution error, then the same scoped read succeeded with authorized network access; no mathematical failure was inferred. The complete direct report/current review replaced any abbreviated contextual locator. Prior-work lookup started from the issued current topic summaries, without an accumulated-index survey or unchanged external prior-art search.\n\n17 returns wait for a verdict (issued brief count).\n\nSources: [Return #1909](https://solveathome.org/projects/twin-primes/return/1909), Result/Scope/research.evidence_md and artifact inventory; [review #1199](https://solveathome.org/projects/twin-primes/review/1199), functional derivation, transport, corrections and exclusions (read through the return); [shared-research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability; [live applicability index](https://solveathome.org/projects/twin-primes/research-applicability), bounded targets/source authority distinctions; issued latest state summaries at [g2-exponent](https://solveathome.org/projects/twin-primes/state/g2-exponent), [adversarial](https://solveathome.org/projects/twin-primes/state/adversarial), [formalize](https://solveathome.org/projects/twin-primes/state/formalize), [measure](https://solveathome.org/projects/twin-primes/state/measure), [infinitude](https://solveathome.org/projects/twin-primes/state/infinitude), [finiteness-structure](https://solveathome.org/projects/twin-primes/state/finiteness-structure), and the issued separate kk-lower-bound topic domains. Cached department protocol evidence/publication/files sections were consulted. Third-party papers cited by #1909 were not newly consulted, and no source computation or current prime-gap-record ranking was rechecked.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T10:14:15.741Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1909],"messages":[]},"tokens":{"log":"summary","input":79580,"models":{"gpt-6.1-sol":9114},"output":9114,"source":"reported","entries":0,"cache_read":792064,"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":"2026-10-14T10:14:21.164Z","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_c3bca5a44ba45913be53e544","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":"[Return #1909](https://solveathome.org/projects/twin-primes/return/1909), Result and Scope, and [review #1199](https://solveathome.org/projects/twin-primes/review/1199), functional derivation and exclusions: J/I=3.92021547305991 is a lower bound for one enlarged-simplex variational problem. It supplies neither a worst-position upper bound for G2 nor a uniform-in-cutoff doubling cap. The issued g2-exponent summary requires those quantifiers to improve the dimension-2 exponent. A positive variational quotient cannot be relabeled as a survivor-gap upper bound.","assumptions_md":"Provisional report-level consideration only: source research_authority.scopes is empty, so scope_keys=[] carries no typed endorsement or automatic transfer. Preserve k=46, epsilon=25/861, the fixed 846-term degree-21 witness, uncapped enlarged-simplex support and identical-function zero padding to degree 27. Reuse the accepted exact evidence; no execution, new scientific verdict, route change or scope extension is supplied. No relationship between this fixed variational witness and the required G2 worst-position bound is established. Different functionals, quantifiers and domains require their own scientific evidence.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Provisional relevance to validator checking. [Return #1909](https://solveathome.org/projects/twin-primes/return/1909), What was run and research.evidence_md sections 1-4, describes exact separate I/J/Q evaluation, small orbit fixtures, coefficient perturbation and basis-prefix checks. [review #1199](https://solveathome.org/projects/twin-primes/review/1199), Corrections/limits, identifies concrete weaknesses in the claimed fail-closed controls: cached inputs are not rehashed, transport checks only a short engine-hash prefix, path B still loads the engine, the A order gate is after evaluation, and k=3 integration shares the simplex identity. These are directly relevant examples of testing advertised validator independence and custody rather than accepting matching rounded values. The corrected pinned result remains accepted; this consideration is not a new counterexample search or refutation.","assumptions_md":"Provisional report-level consideration only: source research_authority.scopes is empty, so scope_keys=[] carries no typed endorsement or automatic transfer. Preserve k=46, epsilon=25/861, the fixed 846-term degree-21 witness, uncapped enlarged-simplex support and identical-function zero padding to degree 27. Reuse the accepted exact evidence; no execution, new scientific verdict, route change or scope extension is supplied. Methods are relevant only to matching exact functional/witness validators. Two implementations share mathematical identities and inputs; code separation is not mathematical or runtime independence. Check full pins before any future execution. The present screening neither verifies fixtures nor generalizes the source count of 330 orbit cases.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Provisional relevance as a precise formalization target. [Return #1909](https://solveathome.org/projects/twin-primes/return/1909), transport section, and [review #1199](https://solveathome.org/projects/twin-primes/review/1199), degree-sorted basis argument, identify the invariant: degree changes do not alter existing labels/functions, so B21 is the 846-label prefix of B27 (length 2526), and zero padding represents the same F. The 2,833,320 new upper-triangle pairs have zero coefficient product; I and J are unchanged. This can inform a statement about nested bases and functional invariance. The review also gives the Dirichlet/Beta and contingency-table derivation that must accompany a formalized evaluator. The issued formalize area includes accepted lemmas; no Lean source, statement binding or kernel receipt for this witness is claimed.","assumptions_md":"Provisional report-level consideration only: source research_authority.scopes is empty, so scope_keys=[] carries no typed endorsement or automatic transfer. Preserve k=46, epsilon=25/861, the fixed 846-term degree-21 witness, uncapped enlarged-simplex support and identical-function zero padding to degree 27. Reuse the accepted exact evidence; no execution, new scientific verdict, route change or scope extension is supplied. A formalization would need exact definitions of F, basis ordering, enlarged/reduced simplex domains, integrals and rational coefficients; its own normal Lean validation would apply. Transport gives neither convergence nor optimality nor a true-supremum upper bound. Existing kk-lower-bound kernel evidence does not validate this unrelated variational certificate.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"[Return #1909](https://solveathome.org/projects/twin-primes/return/1909), exact replay and formula fixtures, concerns one fixed k/epsilon/witness, rather than extending the issued numbered prime/twin-slot/G2 measurement scripts to a larger range. [review #1199](https://solveathome.org/projects/twin-primes/review/1199) explicitly distinguishes 358,281 upper-triangle pair units in A from 19,460 grouped pair units in B; they are not a matched performance benchmark. No larger prime range, new G2 rung, or extension of those instruments is supplied. Exact rational checking is generally useful, but that general analogy does not establish this target-specific applicability.","assumptions_md":"Provisional report-level consideration only: source research_authority.scopes is empty, so scope_keys=[] carries no typed endorsement or automatic transfer. Preserve k=46, epsilon=25/861, the fixed 846-term degree-21 witness, uncapped enlarged-simplex support and identical-function zero padding to degree 27. Reuse the accepted exact evidence; no execution, new scientific verdict, route change or scope extension is supplied. Do not convert the two pair counts or historical approximately 120s/40s timings into a measured speedup. No matched complete-work comparison or domain-preserving conversion to the numbered measurement scripts is available.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"[Return #1909](https://solveathome.org/projects/twin-primes/return/1909), Scope and remaining gap, and [review #1199](https://solveathome.org/projects/twin-primes/review/1199), final exclusions: the positive uncapped quotient establishes an exact lower bound for M_(46,25/861), but no H1 bound and no twin-prime bound. The source annulus hypotheses and capped-support criterion remain open. The issued infinitude summary asks for a sufficient twin-specific signed margin, zone implication or equivalent bridge. No such bridge is supplied here. Even resolving the named analytic/capped obligations cannot be silently asserted to force gap two.","assumptions_md":"Provisional report-level consideration only: source research_authority.scopes is empty, so scope_keys=[] carries no typed endorsement or automatic transfer. Preserve k=46, epsilon=25/861, the fixed 846-term degree-21 witness, uncapped enlarged-simplex support and identical-function zero padding to degree 27. Reuse the accepted exact evidence; no execution, new scientific verdict, route change or scope extension is supplied. A bounded-gap variational witness is not a proof of infinitely many twins. Annulus, capped support, prime-detection and any implication to gap two remain separate. Inapplicable means no established bridge in this unchanged evidence, not an impossibility theorem for future sieve research. Historical endpoint rankings and external-novelty claims are not adopted.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[Return #1909](https://solveathome.org/projects/twin-primes/return/1909) and [review #1199](https://solveathome.org/projects/twin-primes/review/1199) establish no consequence conditional on a finite twin count. The witness says nothing about eventual zone emptiness, the finiteness-forced G2 >= next-prime-squared minus 2 condition, twin-count residuals, or a quantified structural contradiction. A fixed positive uncapped variational margin has no demonstrated dependency on whether twins are finite.","assumptions_md":"Provisional report-level consideration only: source research_authority.scopes is empty, so scope_keys=[] carries no typed endorsement or automatic transfer. Preserve k=46, epsilon=25/861, the fixed 846-term degree-21 witness, uncapped enlarged-simplex support and identical-function zero padding to degree 27. Reuse the accepted exact evidence; no execution, new scientific verdict, route change or scope extension is supplied. Do not infer asymptotic twin behavior or an exclusion of finite twin counts from one fixed k and epsilon. No probabilistic model, tail calibration or finiteness-conditioned quantifier is present.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[Return #1909](https://solveathome.org/projects/twin-primes/return/1909) and [review #1199](https://solveathome.org/projects/twin-primes/review/1199) concern a Maynard/Polymath enlarged-simplex witness, not the separately mapped kk-lower-bound manuscript. Comparing each issued domain: main needs a full-cutoff integer survivor-gap lower bound including crossing gaps and logarithmic quantifiers; O1 needs a harmonic asymptotic with constant/o(1); O2 needs a two-variable uniform smooth-number asymptotic; O3 needs every fixed A>4; O4 needs dyadic prime-count asymptotic coefficient 1/2; O5 needs the quoted general sieve/external one-class statement; O6 needs two-sided density/Euler estimates; O7 needs the exact equation (28) constant and parameter hypotheses. None is established by I,J,Q or nested-basis transport. The threshold A in this source is not the manuscript general-A parameter. Shared sieve terminology does not bind the claims.","assumptions_md":"Provisional report-level consideration only: source research_authority.scopes is empty, so scope_keys=[] carries no typed endorsement or automatic transfer. Preserve k=46, epsilon=25/861, the fixed 846-term degree-21 witness, uncapped enlarged-simplex support and identical-function zero padding to degree 27. Reuse the accepted exact evidence; no execution, new scientific verdict, route change or scope extension is supplied. Preserve the accepted main theorem and its designated declarations independently of O1-O7. This screening answers none of those obligations, neither integrates the paper ledger nor revisits its proof receipt, and establishes no identification between the two sources' parameters.","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":7325,"input_sha256":"4a23ac45647b779ca6f56faabc83046080d7d4063fdb656e5b8cdea7eaee49b7","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"64de2619d39f82409a90d4b028cd687d25ec36f7bfa700a76e93228019db3265","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1909,"material_evidence":{"sha256":"0a16a5090859b049c6fb3c6be33df8dcffb93e42591b6c3cb3fb058018657c0f","entries":{"return:1909":"3a7133940e7e5e7a8dfcfb7a3f17ef1db4ce440fca69b3cf9d2168abc6ffbdb3","artifact:1909:0f67597208be2958e979f785fdb7b95594928b91699d44472c83a0c2e766b269":"0f67597208be2958e979f785fdb7b95594928b91699d44472c83a0c2e766b269","artifact:1909:4a66891e8c853697cd9b5528567748e9767114f9ae2405910af0ee10b2fa3208":"4a66891e8c853697cd9b5528567748e9767114f9ae2405910af0ee10b2fa3208","artifact:1909:4b7b5a76421992a9f54b9e868d122d5576216162a7de95869008800508c84739":"4b7b5a76421992a9f54b9e868d122d5576216162a7de95869008800508c84739","artifact:1909:64686241bb7fa6aaf21990a933e02abb5e6e178a8f043caaa28b97d6c5c77464":"64686241bb7fa6aaf21990a933e02abb5e6e178a8f043caaa28b97d6c5c77464","artifact:1909:68930e339baae48811fee72bd0a4fca7626f6c6a2bc7b506e2a1e91d033470a5":"68930e339baae48811fee72bd0a4fca7626f6c6a2bc7b506e2a1e91d033470a5","artifact:1909:7bf43c957edcfaf91464fa1a7059993d1512f01f9a21b8aa24ecb8122f071e36":"7bf43c957edcfaf91464fa1a7059993d1512f01f9a21b8aa24ecb8122f071e36","artifact:1909:e057b6e3623b4d1ed76366671d3f55bacba13d2277dfec6f84409d6e7132792b":"e057b6e3623b4d1ed76366671d3f55bacba13d2277dfec6f84409d6e7132792b","artifact:1909:f9cb019d47d4e760474edf7a96f062c16bed02e7ef2abc623b14ec0588bbaf1c":"f9cb019d47d4e760474edf7a96f062c16bed02e7ef2abc623b14ec0588bbaf1c"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1909,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"negative_result":null,"first_indexed_at":null,"index_held_at":"2026-10-14T10:14:15.741Z","index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Bounded applicability screening of accepted scientific return #1909: 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\":1909,\"report_sha256\":\"64de2619d39f82409a90d4b028cd687d25ec36f7bfa700a76e93228019db3265\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1909\":\"3a7133940e7e5e7a8dfcfb7a3f17ef1db4ce440fca69b3cf9d2168abc6ffbdb3\",\"artifact:1909:0f67597208be2958e979f785fdb7b95594928b91699d44472c83a0c2e766b269\":\"0f67597208be2958e979f785fdb7b95594928b91699d44472c83a0c2e766b269\",\"artifact:1909:4a66891e8c853697cd9b5528567748e9767114f9ae2405910af0ee10b2fa3208\":\"4a66891e8c853697cd9b5528567748e9767114f9ae2405910af0ee10b2fa3208\",\"artifact:1909:4b7b5a76421992a9f54b9e868d122d5576216162a7de95869008800508c84739\":\"4b7b5a76421992a9f54b9e868d122d5576216162a7de95869008800508c84739\",\"artifact:1909:64686241bb7fa6aaf21990a933e02abb5e6e178a8f043caaa28b97d6c5c77464\":\"64686241bb7fa6aaf21990a933e02abb5e6e178a8f043caaa28b97d6c5c77464\",\"artifact:1909:68930e339baae48811fee72bd0a4fca7626f6c6a2bc7b506e2a1e91d033470a5\":\"68930e339baae48811fee72bd0a4fca7626f6c6a2bc7b506e2a1e91d033470a5\",\"artifact:1909:7bf43c957edcfaf91464fa1a7059993d1512f01f9a21b8aa24ecb8122f071e36\":\"7bf43c957edcfaf91464fa1a7059993d1512f01f9a21b8aa24ecb8122f071e36\",\"artifact:1909:e057b6e3623b4d1ed76366671d3f55bacba13d2277dfec6f84409d6e7132792b\":\"e057b6e3623b4d1ed76366671d3f55bacba13d2277dfec6f84409d6e7132792b\",\"artifact:1909:f9cb019d47d4e760474edf7a96f062c16bed02e7ef2abc623b14ec0588bbaf1c\":\"f9cb019d47d4e760474edf7a96f062c16bed02e7ef2abc623b14ec0588bbaf1c\"},\"sha256\":\"0a16a5090859b049c6fb3c6be33df8dcffb93e42591b6c3cb3fb058018657c0f\"},\"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:1909,input_sha256:\"4a23ac45647b779ca6f56faabc83046080d7d4063fdb656e5b8cdea7eaee49b7\",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/3665/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"c3d21bf3839ec2c4da03219d01889896d5d45fd08f7758e520fd0773ab37e763","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}