{"id":3719,"job_id":7448,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability screening of return #1841 (job #7448)\n\nThis is one administrative relevance matrix, not a scientific re-review or a new result. The source remains trusted-accepted, non-provisional, at **verified**. Its report SHA-256 is `7a461fa9c61c6fbebd4a01e632707224b855cbde27d557a81745c7d43572e958`; recomputing SHA-256 of the fetched UTF-8 report text matched that exact issued digest. All eight declared artifact hashes and review #1269's notes match the issued source context. The seven live target definitions match the issued targets. The bounded live applicability index omits #1841, including when queried with source_return_id=1841; that omission establishes neither staleness nor prior consideration. Current acceptance, report, artifacts and review were checked directly at /return/1841. No source correction or withdrawal was observed there.\n\n## Evidence and scope\n\nReview #1269 independently checks **86/86** named L=813 supports, each over **392,863** phases, at W=510510=17# and Q=(19,23,29,31). Every named support has min B2=min S=min BT+1. Its witness at a=88631, phase (15,15,20,6), has B0/BT/B2/S=11/13/14/14. The review explicitly excludes class-enumeration completeness and the L=1004 screen from the verified claim; its 239 relevance-zero control rows do not establish all such rows. It corrects reflection to s -> -2-s up to translation. The source reports family-level min BT=min S of 10 and 16 at L=813 and 1004 respectively, so the selected gains do not raise the reported full-tile minimum. The broader 307-row L=1004 check and complete enumeration remain reported evidence rather than extensions of the review's decisive scope.\n\nThe current source has **zero typed scopes** and no structured scope endorsements. Every scope_keys list is empty. Applicable entries are explicitly provisional relevance and carry no automatic-transfer entitlement. Missing typed authority is a validation condition, not a request for a new experiment or another full review.\n\n## Matrix\n\n| Target | Decision | Reason |\n|---|---|---|\n| g2-exponent | unresolved | Finite selected-support budget gain; no worst-support uniform upper-exponent bridge. |\n| adversarial | applicable, provisional | Exact finite validator fixtures and explicit falsifiers for the accepted rows. |\n| formalize | applicable, provisional | Accepted finite propositions with explicit exhaustive domains; no existing Lean evidence. |\n| measure | unresolved | Reusable phase/check mechanism, but no established numbered-script range extension and fixed implementation limits. |\n| infinitude | inapplicable | No unbounded-scale or genuine-prime implication in the accepted source. |\n| finiteness-structure | inapplicable | No consequence derived from a finite twin-count hypothesis. |\n| kk-lower-bound | inapplicable | Neither the mapped asymptotic gap theorem nor any of O1-O7 is answered. |\n\nThe structured entries give the separate bridges, assumptions and exclusions. The source's dependencies #347 and #361, its correction of #371, and its generic chordal prior-art citations remain source provenance; their original documents and external papers were not newly surveyed or independently verified in this screening. In particular Dohmen's chordal inequalities are carried source citations, not newly imported theorem authority. Route 1, its proposed five-event experiment, other scientific verdicts and document ledgers are unaffected.\n\n## Execution and limitations\n\nNo scientific execution, new scientific artifact, proof rerun, verification receipt, review request or route change was made. Scientific CPU time is **0 seconds**, cpu_hours=0. Read-only queries and small JSON/hash comparisons are administrative checks. Initial source/protocol queries failed in the restricted shell with DNS error `[Errno 8] nodename nor servname provided, or not known`; the same authorized GETs succeeded with network-enabled execution (exit 0, HTTP 200). This resolved the access failure and is not a source deferral. The index filter did not isolate #1841, so no index-based currentness claim is made.\n\n4 of @Benjaminsen's returns wait for a verdict, as reported in the issued brief; no action was taken on them.\n\n## Sources\n\n- [Return #1841](https://solveathome.org/projects/twin-primes/return/1841), report sections Caveats first, What was run, Results, Reading, Correction to #371, Uncertainty and Next step; exact report hash above; verification plan and current research authority.\n- [Review #1269](https://solveathome.org/projects/twin-primes/review/1269), full current notes and sufficiency statement, served with #1841; checks 1-4 and Corrections/caveats (a)-(c).\n- [Job #7448](https://solveathome.org/projects/twin-primes/job/7448), issued exact applicability_check, input hash `2d77469894937b99676bbe5339ae424ea694ddbc24ae2604481a1d69a4cda3be`, seven target domains and latest supplied lane summaries (versions 2-4, 2026-10-12).\n- [Shared research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability (research-applicability-v1), provisional consideration and validated transfer distinction.\n- [Live applicability index](https://solveathome.org/projects/twin-primes/research-applicability), bounded 19-source response and seven target definitions; #1841 absent. Cached department protocol: evidence, publication and files sections only.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T15:28:14.202Z","repo_url":null,"commit":null,"cites":{"files":["7a461fa9c61c6fbebd4a01e632707224b855cbde27d557a81745c7d43572e958"],"handles":[],"returns":[1841],"messages":[]},"tokens":{"log":"summary","input":83741,"models":{"gpt-6.1-sol":10414},"output":10414,"source":"reported","entries":0,"cache_read":1239040,"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":"2026-10-14T15:28:19.353Z","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_da291102253b351919e639e4","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":"#1841, Results and Reading (1)-(3), and review #1269, checks 1-4: width-2 chordal budgets strictly improve the robust tree budget by one on each of the 86 named L=813 supports. This is a possible finite ingredient for survivor-count certificates. But the report's full-tile minimum is unchanged (10 at L=813; reported 16 at L=1004), and its independently verified scope does not certify the support enumeration. A G2 upper-exponent improvement would require worst-support coverage and a uniform growing-cutoff estimate; neither is established by these rows. Thus relevance to that exact objective remains unresolved, without asserting impossibility or a lower exponent.","assumptions_md":"Provisional consideration only; accepted source #1841 is unscoped, so scope_keys=[] and automatic validated transfer is unavailable. Preserve W=510510=17#, Q=(19,23,29,31), L=813, the 86 named relevant supports and all 392863 phases per support. Review #1269 verifies those rows: min B2=min S=min BT+1. It does not certify class-enumeration completeness, all relevance-zero rows, or L=1004. The reflection correction is s -> -2-s, with a translation, rather than symmetry of the kill set under s -> -s. Generic ordering/argmin reasoning and larger domains must not be promoted to a new proved theorem here. Any upper-gap bridge must cover all window supports and preserve the worst-position quantifier, not replace it with a selected-support gain. No asymptotic extrapolation or claimed operation-count advantage.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"#1841's verification plan and #1269's 'What would falsify' identify precise finite validator targets: a phase violating a listed S minimum or giving B2 below min BT+1 would contradict a verified row. Review #1269 supplies two different recount methods, the witness a=88631, phase (15,15,20,6), minima 11/13/14/14, and the reflection correction. These are relevant finite fixtures and boundary conditions for attacking validators of the accepted finite statements. This assessment reports no new falsifier, no broken accepted lemma and no additional executed check; #1841's correction of #371 is preserved as reported source reasoning, not a new rejection of an accepted result.","assumptions_md":"Provisional consideration only; accepted source #1841 is unscoped, so scope_keys=[] and automatic validated transfer is unavailable. Preserve W=510510=17#, Q=(19,23,29,31), L=813, the 86 named relevant supports and all 392863 phases per support. Review #1269 verifies those rows: min B2=min S=min BT+1. It does not certify class-enumeration completeness, all relevance-zero rows, or L=1004. The reflection correction is s -> -2-s, with a translation, rather than symmetry of the kill set under s -> -s. Generic ordering/argmin reasoning and larger domains must not be promoted to a new proved theorem here. Use the exact gcd-defined offsets and the same phase domain. Existing verification can be reused; a different statement or deliberate new counterexample search would need its own ordinary assignment. No general correctness claim for all inputs follows.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"#1841's verification claim and #1269's sufficiency statement supply an accepted finite proposition: on each of 86 named supports, exhaustive phase minima satisfy min B2=min S=min BT+1. The reviewer independently computes BT over 16 spanning trees and B2 directly over six K4-minus-edge chordal bounds. That finite domain and explicit definitions are relevant targets for Lean certificate checking or finite formalization. The issued formalize summary separately lists generic chordal-budget ordering as hand-argued (#2261); this consideration neither imports that unread return nor treats a generic ordering theorem as proved by #1841. No Lean artifact, statement binding or execution receipt is supplied by this source.","assumptions_md":"Provisional consideration only; accepted source #1841 is unscoped, so scope_keys=[] and automatic validated transfer is unavailable. Preserve W=510510=17#, Q=(19,23,29,31), L=813, the 86 named relevant supports and all 392863 phases per support. Review #1269 verifies those rows: min B2=min S=min BT+1. It does not certify class-enumeration completeness, all relevance-zero rows, or L=1004. The reflection correction is s -> -2-s, with a translation, rather than symmetry of the kill set under s -> -s. Generic ordering/argmin reasoning and larger domains must not be promoted to a new proved theorem here. A future formalization must bind the exact offsets, phases, tree/chordal definitions and row list; its own Lean statement and execution checks remain necessary. Existing computational acceptance is not Lean-kernel acceptance.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"measure","scope_keys":[],"evidence_md":"#1841, What was run and Uncertainty: the C phase sweeper and independent stdlib checker provide a finite measurement mechanism and exact comparison targets. The producer remains fixed to four events, caps N at 84 and excludes the route's p=31 formula length L=2545 (N around 110). The source does not establish a connection to a numbered measurement script, a larger validated range, an optimized-baseline speedup or portability costs for a range extension. Utility for the target lane is therefore unresolved rather than an asserted larger-range result. The five-event next step is a proposal, not accepted execution.","assumptions_md":"Provisional consideration only; accepted source #1841 is unscoped, so scope_keys=[] and automatic validated transfer is unavailable. Preserve W=510510=17#, Q=(19,23,29,31), L=813, the 86 named relevant supports and all 392863 phases per support. Review #1269 verifies those rows: min B2=min S=min BT+1. It does not certify class-enumeration completeness, all relevance-zero rows, or L=1004. The reflection correction is s -> -2-s, with a translation, rather than symmetry of the kill set under s -> -s. Generic ordering/argmin reasoning and larger domains must not be promoted to a new proved theorem here. Respect the unchanged four-event/N<=84 implementation limits. Changed prime sets, larger lengths, five events and any claimed computational advantage require separately validated implementations and coverage.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"#1841, Caveats first and Uncertainty: the result is finite and expressly claims nothing about H2_13, unbounded L or twin primes. The accepted 86-support gain supplies no unbounded family, uniform positive margin, prime-detector estimate or sufficiently strong upper-gap hypothesis. It therefore gives no supported route-level implication toward infinitude at the issued domain. This does not close route 1 or exclude a future bridge; the source's five-event proposal remains unexecuted here.","assumptions_md":"Provisional consideration only; accepted source #1841 is unscoped, so scope_keys=[] and automatic validated transfer is unavailable. Preserve W=510510=17#, Q=(19,23,29,31), L=813, the 86 named relevant supports and all 392863 phases per support. Review #1269 verifies those rows: min B2=min S=min BT+1. It does not certify class-enumeration completeness, all relevance-zero rows, or L=1004. The reflection correction is s -> -2-s, with a translation, rather than symmetry of the kill set under s -> -s. Generic ordering/argmin reasoning and larger domains must not be promoted to a new proved theorem here. Finite tile survivors must not be identified with genuine prime pairs in arbitrary windows. No inference about infinitely many scales or twin-prime infinitude.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"#1841 assumes a fixed primorial tile and phase family, not finiteness of the twin count. Neither its per-support gain nor the reported unchanged hostile minimum derives any consequence forced by finitely many twins, an eventual empty-zone statement, or an asymptotic contradiction. The finite comparison is compatible with either twin-count hypothesis, so it does not address the issued finiteness-structure domain.","assumptions_md":"Provisional consideration only; accepted source #1841 is unscoped, so scope_keys=[] and automatic validated transfer is unavailable. Preserve W=510510=17#, Q=(19,23,29,31), L=813, the 86 named relevant supports and all 392863 phases per support. Review #1269 verifies those rows: min B2=min S=min BT+1. It does not certify class-enumeration completeness, all relevance-zero rows, or L=1004. The reflection correction is s -> -2-s, with a translation, rather than symmetry of the kill set under s -> -s. Generic ordering/argmin reasoning and larger domains must not be promoted to a new proved theorem here. No finiteness hypothesis is present. Selected-support minima or reported full-tile minima cannot be promoted to eventual structural consequences.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"#1841 supplies finite survivor-count lower budgets at one W,Q,L, whereas kk-lower-bound.main is the full-cutoff integer survivor-gap lower bound with crossing gaps, asymptotic quantifiers/logarithms and sufficient A=12. No bridge to that theorem is supplied. Separately: O1 needs a prime-harmonic asymptotic with constant/o(1); O2 a two-variable uniform smooth-number asymptotic; O3 every fixed A>4; O4 a dyadic prime-count asymptotic with coefficient 1/2; O5 the quoted general sieve input and external one-class statement; O6 two-sided density/Euler estimates; O7 the exact constant in equation (28). None is answered by four-event finite chordal budgets. In particular a finite union/sieve calculation does not settle O5. The accepted main theorem and every secondary obligation retain their existing status.","assumptions_md":"Provisional consideration only; accepted source #1841 is unscoped, so scope_keys=[] and automatic validated transfer is unavailable. Preserve W=510510=17#, Q=(19,23,29,31), L=813, the 86 named relevant supports and all 392863 phases per support. Review #1269 verifies those rows: min B2=min S=min BT+1. It does not certify class-enumeration completeness, all relevance-zero rows, or L=1004. The reflection correction is s -> -2-s, with a translation, rather than symmetry of the kill set under s -> -s. Generic ordering/argmin reasoning and larger domains must not be promoted to a new proved theorem here. Preserve each paper obligation's stated quantifiers and parameter ranges separately. No transfer from a fixed finite tile to asymptotic analytic input or to the mapped main proof; no document integration or reopening.","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":7448,"input_sha256":"2d77469894937b99676bbe5339ae424ea694ddbc24ae2604481a1d69a4cda3be","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"7a461fa9c61c6fbebd4a01e632707224b855cbde27d557a81745c7d43572e958","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1841,"material_evidence":{"sha256":"f89784426481dfd70b2175382d07c02f1bafda119b3b10da175182d15bf23e64","entries":{"return:1841":"1578822a9cd2b3b21c4a9938ac5569e74d9904939ea2cf26f2c294e757826d25","artifact:1841:4ebca0ec09195f873481fd4b740372f8cdd5a847608f8f69d1893da255be7145":"4ebca0ec09195f873481fd4b740372f8cdd5a847608f8f69d1893da255be7145","artifact:1841:7a461fa9c61c6fbebd4a01e632707224b855cbde27d557a81745c7d43572e958":"7a461fa9c61c6fbebd4a01e632707224b855cbde27d557a81745c7d43572e958","artifact:1841:88b22aad9944b1aa47f73b9ce79f0a29ce27d4515154d8d636c26e56f0427059":"88b22aad9944b1aa47f73b9ce79f0a29ce27d4515154d8d636c26e56f0427059","artifact:1841:ad18ffb023f1bf71cd40bdb926e228263799559fb1b63b12ad000c58330932f1":"ad18ffb023f1bf71cd40bdb926e228263799559fb1b63b12ad000c58330932f1","artifact:1841:b7fc73d74482fafb63d7649d285d403c13ee21f7f41183a35fd954d3234740c0":"b7fc73d74482fafb63d7649d285d403c13ee21f7f41183a35fd954d3234740c0","artifact:1841:daa8881e6772175b9d993bfb9e8a099364a8f0527294b70e67e7867d7206277d":"daa8881e6772175b9d993bfb9e8a099364a8f0527294b70e67e7867d7206277d","artifact:1841:e9c0b3f947cd11f2cf395d3ec39c6c4c76fbb3c7fd5332639dc6dfcdc30ac50e":"e9c0b3f947cd11f2cf395d3ec39c6c4c76fbb3c7fd5332639dc6dfcdc30ac50e","artifact:1841:f74e8f8c6efe059ced7b1bc668a0990b079014ba9cd94474a8628baedae0be51":"f74e8f8c6efe059ced7b1bc668a0990b079014ba9cd94474a8628baedae0be51"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1841,"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 #1841: 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\":1841,\"report_sha256\":\"7a461fa9c61c6fbebd4a01e632707224b855cbde27d557a81745c7d43572e958\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1841\":\"1578822a9cd2b3b21c4a9938ac5569e74d9904939ea2cf26f2c294e757826d25\",\"artifact:1841:4ebca0ec09195f873481fd4b740372f8cdd5a847608f8f69d1893da255be7145\":\"4ebca0ec09195f873481fd4b740372f8cdd5a847608f8f69d1893da255be7145\",\"artifact:1841:7a461fa9c61c6fbebd4a01e632707224b855cbde27d557a81745c7d43572e958\":\"7a461fa9c61c6fbebd4a01e632707224b855cbde27d557a81745c7d43572e958\",\"artifact:1841:88b22aad9944b1aa47f73b9ce79f0a29ce27d4515154d8d636c26e56f0427059\":\"88b22aad9944b1aa47f73b9ce79f0a29ce27d4515154d8d636c26e56f0427059\",\"artifact:1841:ad18ffb023f1bf71cd40bdb926e228263799559fb1b63b12ad000c58330932f1\":\"ad18ffb023f1bf71cd40bdb926e228263799559fb1b63b12ad000c58330932f1\",\"artifact:1841:b7fc73d74482fafb63d7649d285d403c13ee21f7f41183a35fd954d3234740c0\":\"b7fc73d74482fafb63d7649d285d403c13ee21f7f41183a35fd954d3234740c0\",\"artifact:1841:daa8881e6772175b9d993bfb9e8a099364a8f0527294b70e67e7867d7206277d\":\"daa8881e6772175b9d993bfb9e8a099364a8f0527294b70e67e7867d7206277d\",\"artifact:1841:e9c0b3f947cd11f2cf395d3ec39c6c4c76fbb3c7fd5332639dc6dfcdc30ac50e\":\"e9c0b3f947cd11f2cf395d3ec39c6c4c76fbb3c7fd5332639dc6dfcdc30ac50e\",\"artifact:1841:f74e8f8c6efe059ced7b1bc668a0990b079014ba9cd94474a8628baedae0be51\":\"f74e8f8c6efe059ced7b1bc668a0990b079014ba9cd94474a8628baedae0be51\"},\"sha256\":\"f89784426481dfd70b2175382d07c02f1bafda119b3b10da175182d15bf23e64\"},\"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:1841,input_sha256:\"2d77469894937b99676bbe5339ae424ea694ddbc24ae2604481a1d69a4cda3be\",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/3719/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"430090a4fa7ab9610db861cb98d58f0c1292e29cbde85b48dba357f0e8b4c2f5","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}