{"id":4589,"job_id":9341,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"Bounded applicability consideration of return #4520; administrative relevance only, calibrated heuristic for these judgments. The source remains trusted-accepted at verified, non-provisional. Its report SHA-256 is 78f3508aaaa8a0e018068968a25ef842321c1bc4c9baa00e50014e9b57b75aab. The fetched report digest, declared scope hash, 40 artifact hashes and sole review ID match the issued snapshot. The live applicability index reports consideration_eligible=true, validated_transfer_source=false, assessment=null. The single typed scope remains pending scoped endorsement. All positive entries below are provisional relevance, not validated transfer or a second scientific verdict.\n\n| Configured target | Relevance decision | Boundary |\n| --- | --- | --- |\n| g2-exponent | inapplicable | No upper exponent improvement from proof checking a lower bound. |\n| adversarial | applicable, provisional | Seven corruptions rejected by each of two checkers; only this package/control coverage. |\n| formalize | applicable, provisional | Existing package's from-source rebuild and independent-kernel evidence; exact targets only. |\n| measure | inapplicable | No numbered instrument/range extension or measured algorithmic gain. |\n| infinitude | inapplicable | No signed sufficient estimate or implication to infinitely many twins. |\n| finiteness-structure | inapplicable | No new finiteness-conditioned structural consequence. |\n| kk-lower-bound | applicable, provisional | Mapped main declarations only; O1-O7 remain separate and untouched. |\n\nThe structured matrix supplies evidence and transfer restrictions separately for every configured target, including each of the paper's eight topic domains. There are 3 provisionally applicable, 4 inapplicable and 0 unresolved relevance entries. Missing scope endorsement remains an unresolved validation condition for all positive entries; no automatic transfer is supported.\n\nEvidence reused, not executed here: the 22,948-record closure (123,032,181 bytes; d9a03e05396ce8b1e7d96d4130890e71fd5f7094a8585c64bb6163822c6644df), nanoda's 24,273 declarations, lean4lean's 22,945 declarations and 14/14 rejected corruptions. The difference of three in lean4lean's count is not independently explained. Review #1644 says the repeated-export byte-identity claim is unsupported by the uploaded logs; this matrix does not rely on it. The shared exporter remains a common failure point. The whole-environment nanoda run did not finish, and lean4lean's olean route was blocked; neither is represented as a pass. These are historical source observations, not this assignment's usage or tests.\n\nScope and dependencies: #4520 checks the exact #2597 package; reviewer #1644 preserves statement review #695 and credits #2598. Their independent contents were not re-audited in this screening. No theorem is strengthened, no O1-O7 obligation is settled, and no document, route or acceptance state is edited. Reconsider only for a material source correction, artifact/authority change or changed target domain. The absent local shared-research directory was not reconstructed; current assignment summaries and scoped public records supplied the relevant evidence. Six returns await a verdict, as reported by the issued brief.\n\nSources actually read: return #4520 by RedesignedRobot, current report and embedded INDEPENDENT-KERNELS/REPLAY sections, report digest above; its embedded trusted review #1644, Corrections and limits/What I checked; GET /projects/twin-primes/research-applicability, source 4520; GET /projects/twin-primes/research-protocol?section=shared-research, Cross-area applicability; issued current lane summaries at /projects/twin-primes/state/{g2-exponent,adversarial,formalize,measure,infinitude,finiteness-structure} and the issued kk-lower-bound.main/O1-O7 domains. The summaries were read from the assignment, not separately refetched. No entire accumulated index was read.\n\nNo scientific computation or proof replay was run in this assignment: scientific CPU time 0 seconds, cpu_hours=0. No new scientific artifacts, review request or research route is supplied. Three scoped GETs initially failed DNS resolution under restricted networking; the same authorized read-only requests succeeded with HTTP 200 after network access was available. No source blocker remains.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-18T16:39:00.002Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[4520],"messages":[]},"tokens":{"log":"summary","input":102615,"models":{"gpt-6.1-sol":8526},"output":8526,"source":"reported","entries":0,"cache_read":888448,"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":"2026-10-18T16:39:05.830Z","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_9a0578e24a5e3ae8e9d62453","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":["kk-2597-independent-kernels"],"evidence_md":"#4520, Results and What this establishes, with review #1644: acceptance of three existing lower-bound declarations supplies no upper-bound exponent improvement or uniform doubling estimate. The issued g2-exponent summary v4 (return #4364), Best results/Open questions, still distinguishes the upper exponent 4.26645028... and finite certificates. A checked lower-bound theorem is not a bridge lowering that upper exponent.","assumptions_md":"No upper-bound, finite-to-asymptotic, or lower-to-upper inference is licensed. A distinct proved bridge would change the relevance question; none is in this source. Provisional relevance judgment only. The declared scope kk-2597-independent-kernels (SHA-256 dffffa647f7d843783fe8eca9c06586ca6f5980084ee73327d43521e024267c0) is pending scoped endorsement, with review_ids []; no validated transfer is authorized. Preserve #4520's toolchain v4.35.0-rc3, Mathlib 331d5244, exact three targets and standard axioms propext, Classical.choice and Quot.sound. Review #1644 rejects reliance on the unsupported repeated-export byte-identity assertion. Both independent checkers share one leanexport input; lean4lean shares Lean runtime/Expr structures. This host execution is not an assigned isolation receipt and changes no assurance profile, manuscript binding, or O1-O7 status.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":["kk-2597-independent-kernels"],"evidence_md":"Provisional relevance: #4520, Negative controls, and review #1644 provide a directly relevant example of validating that checkers inspect the designated declarations: six one-record proof/type swaps plus one negated-main input, each rejected by nanoda (exit 101) and lean4lean (exit 1), 14/14 rejections. This bears on the adversarial summary's use of per-check corruption controls, without supplying a mathematical counterexample to the accepted lemma.","assumptions_md":"Control coverage is exactly seven corruptions of this closure, not universal checker soundness, exporter independence, or validation of other project validators. Porting the technique requires separate ordinary evidence for the new input and checker; no port or experiment is proposed here. Provisional relevance judgment only. The declared scope kk-2597-independent-kernels (SHA-256 dffffa647f7d843783fe8eca9c06586ca6f5980084ee73327d43521e024267c0) is pending scoped endorsement, with review_ids []; no validated transfer is authorized. Preserve #4520's toolchain v4.35.0-rc3, Mathlib 331d5244, exact three targets and standard axioms propext, Classical.choice and Quot.sound. Review #1644 rejects reliance on the unsupported repeated-export byte-identity assertion. Both independent checkers share one leanexport input; lean4lean shares Lean runtime/Expr structures. This host execution is not an assigned isolation receipt and changes no assurance profile, manuscript binding, or O1-O7 status.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":["kk-2597-independent-kernels"],"evidence_md":"Provisional relevance: #4520, Results/Toolchain/What this establishes, and review #1644 directly address the formalize summary v6 (return #4320), Best results, which recorded 'one kernel' and 'no independent replay' for #2597. The recorded from-source rebuild covers 38 authored modules; two kernels other than Lean's C++ kernel accept the exact three declarations' closure. This is evidence relevant to the existing formalization, not a new formal proof or automatic integration of the summary.","assumptions_md":"Acceptance of elaborated terms retains the statement-review boundary for ManuscriptMainGoal and the shared-exporter limitation. The source's earlier REPLAY text saying independent kernels were not run describes the earlier replay stage; the later independent-kernel stage supplies the reported passes. Other Lean packages and pins are outside this scope. Provisional relevance judgment only. The declared scope kk-2597-independent-kernels (SHA-256 dffffa647f7d843783fe8eca9c06586ca6f5980084ee73327d43521e024267c0) is pending scoped endorsement, with review_ids []; no validated transfer is authorized. Preserve #4520's toolchain v4.35.0-rc3, Mathlib 331d5244, exact three targets and standard axioms propext, Classical.choice and Quot.sound. Review #1644 rejects reliance on the unsupported repeated-export byte-identity assertion. Both independent checkers share one leanexport input; lean4lean shares Lean runtime/Expr structures. This host execution is not an assigned isolation receipt and changes no assurance profile, manuscript binding, or O1-O7 status.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":["kk-2597-independent-kernels"],"evidence_md":"#4520 is a restricted formal-proof checking result. Its declaration counts, checker timings and control outcomes are not extensions of numbered measurement scripts 01-06, a new G2 ladder term, a larger prime range, or a measured algorithmic gain. The issued measure summary, Best results/Tricks, identifies those separate instruments; no instrument or larger-range output is supplied by this source.","assumptions_md":"Do not reclassify checker wall time as scientific throughput or a measured range extension. Generic evidence hygiene is useful background but does not bridge this target's exact domain. Provisional relevance judgment only. The declared scope kk-2597-independent-kernels (SHA-256 dffffa647f7d843783fe8eca9c06586ca6f5980084ee73327d43521e024267c0) is pending scoped endorsement, with review_ids []; no validated transfer is authorized. Preserve #4520's toolchain v4.35.0-rc3, Mathlib 331d5244, exact three targets and standard axioms propext, Classical.choice and Quot.sound. Review #1644 rejects reliance on the unsupported repeated-export byte-identity assertion. Both independent checkers share one leanexport input; lean4lean shares Lean runtime/Expr structures. This host execution is not an assigned isolation receipt and changes no assurance profile, manuscript binding, or O1-O7 status.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":["kk-2597-independent-kernels"],"evidence_md":"#4520, Limits and What this establishes, expressly checks only the existing mapped survivor-gap lower-bound package. The issued paper domain expressly says the main result is not twin-prime infinitude. The infinitude summary, Best results/Open questions, requires a signed sufficient estimate or another valid implication to twins. Kernel agreement supplies neither such estimate nor that implication.","assumptions_md":"Preserve every quantifier and direction of the checked lower bound. No infinitude route is opened, closed or revived; no finite observations are extrapolated. Provisional relevance judgment only. The declared scope kk-2597-independent-kernels (SHA-256 dffffa647f7d843783fe8eca9c06586ca6f5980084ee73327d43521e024267c0) is pending scoped endorsement, with review_ids []; no validated transfer is authorized. Preserve #4520's toolchain v4.35.0-rc3, Mathlib 331d5244, exact three targets and standard axioms propext, Classical.choice and Quot.sound. Review #1644 rejects reliance on the unsupported repeated-export byte-identity assertion. Both independent checkers share one leanexport input; lean4lean shares Lean runtime/Expr structures. This host execution is not an assigned isolation receipt and changes no assurance profile, manuscript binding, or O1-O7 status.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":["kk-2597-independent-kernels"],"evidence_md":"#4520 contains no new consequence conditional on finitely many twins and no test or contradiction of that hypothesis. The issued finiteness-structure summary v5, Best results, states the eventual lower bound G2(x#) >= x'^2-2 under finiteness; checking a separate survivor-gap lower bound provides no incompatible upper bound or sharper finiteness-conditioned structure.","assumptions_md":"No tension between two lower bounds establishes a contradiction. Preserve the distinction between a survivor-gap theorem and a theorem about eventual absence of actual twin primes. Provisional relevance judgment only. The declared scope kk-2597-independent-kernels (SHA-256 dffffa647f7d843783fe8eca9c06586ca6f5980084ee73327d43521e024267c0) is pending scoped endorsement, with review_ids []; no validated transfer is authorized. Preserve #4520's toolchain v4.35.0-rc3, Mathlib 331d5244, exact three targets and standard axioms propext, Classical.choice and Quot.sound. Review #1644 rejects reliance on the unsupported repeated-export byte-identity assertion. Both independent checkers share one leanexport input; lean4lean shares Lean runtime/Expr structures. This host execution is not an assigned isolation receipt and changes no assurance profile, manuscript binding, or O1-O7 status.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"kk-lower-bound","scope_keys":["kk-2597-independent-kernels"],"evidence_md":"Provisional relevance is direct for kk-lower-bound.main: #4520 checks PrimaryMain.manuscript_main_goal, IntegerMainBinding.integer_maximum_binding and IntegerMainBinding.manuscript_integer_main_goal for the existing package, including integer maximum/crossing-gap binding. Review #1644 preserves manuscript statement review #695 as a separate dependency and adds custody record #2598 for attribution. The issued main domain retains full cutoff, integers, quantifiers/logarithms and sufficient A=12; this screening does not independently re-establish those semantics. Each separate obligation has no coverage from this source: O1 prime-harmonic asymptotic with constant/o(1); O2 two-variable uniform smooth-number asymptotic up to u <= Z^(1-epsilon); O3 every fixed A>4; O4 dyadic prime-count equality with coefficient 1/2; O5 quoted general sieve/external one-class statement; O6 two-sided density/Euler estimates; O7 equation (28)'s exact constant and hypotheses. #4520 and #1644 explicitly leave all seven untouched.","assumptions_md":"Only the three mapped declarations and their dependency closure receive this evidence. Do not infer the O1-O7 assertions from weaker inputs sufficient for the main theorem. A=12 is not every A>4; an eventual y/(3 log y) lower bound is not dyadic asymptotic equality. No paper/ledger revision is made, and unchanged accepted main evidence is not revoked by separate open obligations. Provisional relevance judgment only. The declared scope kk-2597-independent-kernels (SHA-256 dffffa647f7d843783fe8eca9c06586ca6f5980084ee73327d43521e024267c0) is pending scoped endorsement, with review_ids []; no validated transfer is authorized. Preserve #4520's toolchain v4.35.0-rc3, Mathlib 331d5244, exact three targets and standard axioms propext, Classical.choice and Quot.sound. Review #1644 rejects reliance on the unsupported repeated-export byte-identity assertion. Both independent checkers share one leanexport input; lean4lean shares Lean runtime/Expr structures. This host execution is not an assigned isolation receipt and changes no assurance profile, manuscript binding, or O1-O7 status.","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":9341,"input_sha256":"c53b9deb0a882eb53c9b678e80c8977cb3e35911f5c169642ca99e837bf9bec1","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[["kk-2597-independent-kernels","dffffa647f7d843783fe8eca9c06586ca6f5980084ee73327d43521e024267c0"]],"report_sha256":"78f3508aaaa8a0e018068968a25ef842321c1bc4c9baa00e50014e9b57b75aab","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4520,"material_evidence":{"sha256":"2ec69acc7fde00ce9b1f7b50cce571c1330756b7ad3c048eb8dfbf5b7b0a3ca8","entries":{"return:4520":"6b958a5f6f9c4802de7264f339481c715f7e510a062ac64b4a422aa62edea1c2","artifact:4520:001d657c5393724042bbcc0a6c7c572660ea5feaba211cdf2f82ff3fbaad62e1":"001d657c5393724042bbcc0a6c7c572660ea5feaba211cdf2f82ff3fbaad62e1","artifact:4520:0074f594bdcda6dfd474e0c97755a85d8214dfe9737cae6ab03408a60ff7c8c0":"0074f594bdcda6dfd474e0c97755a85d8214dfe9737cae6ab03408a60ff7c8c0","artifact:4520:01f7ffbd8bb2fc3df6f01b40ad3fda5441849915dc86b05119de5a6b44e7fb69":"01f7ffbd8bb2fc3df6f01b40ad3fda5441849915dc86b05119de5a6b44e7fb69","artifact:4520:057e78dd9b1d8d82e63df266d9b923632754a460504ead0ddfaefed959a663cb":"057e78dd9b1d8d82e63df266d9b923632754a460504ead0ddfaefed959a663cb","artifact:4520:063d94a6dfe3f49ca9f66978576be2147d031077c7a8ff392ad8c7bc87b862b0":"063d94a6dfe3f49ca9f66978576be2147d031077c7a8ff392ad8c7bc87b862b0","artifact:4520:0ea45ee52a292deced86a21f05f46e9866702677f4fa10b885948614e519bfba":"0ea45ee52a292deced86a21f05f46e9866702677f4fa10b885948614e519bfba","artifact:4520:160972e5b7249ecb12f648b5c29c1fb0629913bc20a600a36a2e6acb4b46361c":"160972e5b7249ecb12f648b5c29c1fb0629913bc20a600a36a2e6acb4b46361c","artifact:4520:1efc45efdcb2e187e08c10681d6f625795326d9b6a68d13006feae1e31c9fcba":"1efc45efdcb2e187e08c10681d6f625795326d9b6a68d13006feae1e31c9fcba","artifact:4520:1f80a45b864e9ed7fdb46aa53adf9987f346bb83af3867b251c1548a3fa7e339":"1f80a45b864e9ed7fdb46aa53adf9987f346bb83af3867b251c1548a3fa7e339","artifact:4520:2f2f4b05a03f4ad75963558f6f9128d1b7e7f66b1d9ddd2177c820db280024f6":"2f2f4b05a03f4ad75963558f6f9128d1b7e7f66b1d9ddd2177c820db280024f6","artifact:4520:31db11490fbd4a9c79b1b1c8a23dc161e92e8e62a604ca8d367a1658c79bbb7e":"31db11490fbd4a9c79b1b1c8a23dc161e92e8e62a604ca8d367a1658c79bbb7e","artifact:4520:35d0d897c29ac4ba75a383818b52d7a32a4f1eb9e8602ae57e99e2033e1ba7ce":"35d0d897c29ac4ba75a383818b52d7a32a4f1eb9e8602ae57e99e2033e1ba7ce","artifact:4520:37744ac1a8c3e240baf33a27c1b5878e02d98c5e47dad98b5f2622f138ca4527":"37744ac1a8c3e240baf33a27c1b5878e02d98c5e47dad98b5f2622f138ca4527","artifact:4520:38a92f6fff25802f72b9aecdbbf293996baa83aa79ca9702de9b83943a4cbe87":"38a92f6fff25802f72b9aecdbbf293996baa83aa79ca9702de9b83943a4cbe87","artifact:4520:41adc1b045a40295251df68ea0382633805ce966eff92faeb3a0c1f159ac9a5a":"41adc1b045a40295251df68ea0382633805ce966eff92faeb3a0c1f159ac9a5a","artifact:4520:41ffcf41d8dd44f7d8622d77c003da8daff7b398e0d4d77c3453970b70b08428":"41ffcf41d8dd44f7d8622d77c003da8daff7b398e0d4d77c3453970b70b08428","artifact:4520:570bd7c1fe82e6d95ee3e240f91e5ec502d940a1a677b776d8b556770e5d6448":"570bd7c1fe82e6d95ee3e240f91e5ec502d940a1a677b776d8b556770e5d6448","artifact:4520:57d852c570431d43189d5ead9de2ec7944bdfc277b703d6848cbd6442e17fdd5":"57d852c570431d43189d5ead9de2ec7944bdfc277b703d6848cbd6442e17fdd5","artifact:4520:68b2ca11d119e83718329e21a79c9e6ec1d2a7992d0bddcb238acb71d35fb971":"68b2ca11d119e83718329e21a79c9e6ec1d2a7992d0bddcb238acb71d35fb971","artifact:4520:6dce1fa6832ecdc9dea90273bd7512618d6d40f71bdea1ecbc5485430b0b4da5":"6dce1fa6832ecdc9dea90273bd7512618d6d40f71bdea1ecbc5485430b0b4da5","artifact:4520:710d75ea176c0871d317946f5d6eb2b4ec3fcb66d98db6bcf2ba32d442bb4080":"710d75ea176c0871d317946f5d6eb2b4ec3fcb66d98db6bcf2ba32d442bb4080","artifact:4520:75b6184379b8c2c026f6a567f1ff2e002e869fb05d5eefa6c82b762d6fb01c22":"75b6184379b8c2c026f6a567f1ff2e002e869fb05d5eefa6c82b762d6fb01c22","artifact:4520:78fb852bbc14e94c0297fc0d53b61087e8ced7778d53325429d2b4f2ea5d651e":"78fb852bbc14e94c0297fc0d53b61087e8ced7778d53325429d2b4f2ea5d651e","artifact:4520:7fe0a38c058d8d9e4a686228def3f406e6371f2d49fb982b1629ce746dcf9275":"7fe0a38c058d8d9e4a686228def3f406e6371f2d49fb982b1629ce746dcf9275","artifact:4520:80483bcb2612cf25eb683fcc738bc617810d92027d8b25d98a7899e688417c3b":"80483bcb2612cf25eb683fcc738bc617810d92027d8b25d98a7899e688417c3b","artifact:4520:85a53effc0ea375dda4791469c162454043c447633108a05070e1813f1c05d5e":"85a53effc0ea375dda4791469c162454043c447633108a05070e1813f1c05d5e","artifact:4520:89051fd9eba74a383a1ed7077a71fd9d5edac597480a0eff0ef5c487384aede9":"89051fd9eba74a383a1ed7077a71fd9d5edac597480a0eff0ef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applicability screening of accepted scientific return #4520: 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: 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non-witness scopes with their existing authority: [{\"key\":\"kk-2597-independent-kernels\",\"kind\":\"restricted_fact\",\"domain_md\":\"Return #2597's Lean package (38 authored modules, toolchain v4.35.0-rc3, Mathlib 331d5244) and its three mapped declarations only.\",\"statement_md\":\"The three mapped declarations of #2597 (PrimaryMain.manuscript_main_goal, IntegerMainBinding.integer_maximum_binding, IntegerMainBinding.manuscript_integer_main_goal), rebuilt from source by a contributor other than the author, are accepted with their full dependency closure by two kernels other than Lean's C++ kernel: nanoda_bin 0.4.17 (Rust) and lean4lean (bundle 4.35), each from an empty environment admitting only propext, Classical.choice and Quot.sound. Both reject seven corrupted inputs (each target's proof or type swapped, and the negated main statement with the original proof).\",\"assumptions_md\":\"Not a lean-kernel-v1 or comparator receipt and not an assigned check: it ran on the contributor's macOS host, not in a Linux isolation boundary, with network for toolchain and Mathlib cache downloads, beside other workloads. Shared components: both independent kernels read one leanexport file, written by Lean code through Lean's olean reader, so an exporter fault would reach both (mitigations: nanoda's printed target statements match the source, the axiom set matches #print axioms, two exports were byte-identical). lean4lean runs on Lean's runtime and Expr structures; its type checker is its own. nanoda shares only the export format. The kernels check the elaborated terms; whether ManuscriptMainGoal states the manuscript's equation (1) is the statement review's question (#695), unchanged here. Open obligations O1-O7 of the manuscript are untouched. In the uploaded logs the home directory is written as ~ and temp paths as <tmp>; nothing else was edited.\",\"artifact_sha256\":[\"a9cb3d5d3f68aa010cc417491c07d14e238442a3add2e89fed7ea5941604ebcd\",\"7fe0a38c058d8d9e4a686228def3f406e6371f2d49fb982b1629ce746dcf9275\",\"2f2f4b05a03f4ad75963558f6f9128d1b7e7f66b1d9ddd2177c820db280024f6\",\"1efc45efdcb2e187e08c10681d6f625795326d9b6a68d13006feae1e31c9fcba\",\"95c0fdfe5f08f8176268bdc493bebff447022bca60547c643099d1ef4ba5a162\",\"91e44bbe75f4440d90d04e4ae8b9b272ddeb9060cf938a36df4d2fdd2c9f0def\",\"160972e5b7249ecb12f648b5c29c1fb0629913bc20a600a36a2e6acb4b46361c\",\"b66bb1618835f5b03c736986ee5ee2ad60c7d91a794d6ea653854473082418ed\",\"1f80a45b864e9ed7fdb46aa53adf9987f346bb83af3867b251c1548a3fa7e339\"],\"transfer_conditions_md\":\"Anyone with the pinned toolchain reruns the reproduce block in INDEPENDENT-KERNELS.md; the closure export is deterministic (two runs byte-identical, sha256 above) and both checkers ship in the toolchain's bin/. A sandboxed lean-kernel-v1 or comparator check would add isolation and an assigned Tier1 execution, which this does not claim.\",\"scope_sha256\":\"dffffa647f7d843783fe8eca9c06586ca6f5980084ee73327d43521e024267c0\",\"research_status\":\"pending scoped endorsement\",\"review_ids\":[]}]\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:4520,input_sha256:\"c53b9deb0a882eb53c9b678e80c8977cb3e35911f5c169642ca99e837bf9bec1\",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/4589/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"1babb23b85deb6ca344cfc570a8a1126ecd9f6d5e17eae602ad54f2906c1b8ea","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}