{"id":6464,"job_id":10487,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability screening of return #5265\n\nAdministrative source comparison, calibrated verified for the checks below only. The mathematical source retains its existing **proven** rung; this screen makes no new scientific claim or acceptance decision.\n\nThe previously unscreened obligation is one relevance matrix for all seven issued areas. The exact source theorem is g(P) <= G2(P) for every natural P >= 1, with both largest gaps over Z and the original coprimality definitions. Equation (5) stays external. The original assumptions, quantifiers, artifacts, and standard Lean axioms remain unchanged.\n\n| Target | Decision | Exact relevance boundary |\n|---|---|---|\n| g2-exponent | inapplicable | Lower floor does not reduce an upper exponent. |\n| adversarial | applicable | Exact invariant and definition boundary for validator comparisons only. |\n| formalize | applicable | Reuse the accepted equation-(4) core-Lean statement under matching definitions. |\n| measure | inapplicable | No extension method for the configured numbered measurement scripts. |\n| infinitude | inapplicable | No prime-zone occupancy, upper-gap estimate or signed margin. |\n| finiteness-structure | inapplicable | Unconditional comparison adds no consequence specific to finitely many twins. |\n| kk-lower-bound | applicable | O5 embedding component only; main and O1-O7 obligations retain their separate scopes. |\n\nThe structured entries supply the evidence and assumptions for each row. These are provisional relevance judgments. The existing exact scope endorsement is preserved; current automatic transfer eligibility is determined by the server. No source acceptance, route change, document integration, finding resolution or additional experiment is requested.\n\n## Source identity and preservation checks\n\nRead the full current return #5265 and its complete review #1828, including research_assessment. Recomputed the UTF-8 report hash: 0f6398183ead17f59591a13c0bd82c6053a40c30c47d90663aab9457d22a7275, equal to the issued snapshot and the served report_sha256. The full current research_authority.scopes value equals the issued scopes, including accepted status, review 1828 and scope hash 3e0adb3db5291c0bc72fa72078415765cc54054a677ee28243b8c6b1ad63afab. Review notes and exact scope assessment equal the issued records; needs_reassessment is false. All 16 artifact hashes in the current source inventory equal the 16 issued material-evidence artifact entries. This compares the inventory metadata; it does not claim that the 16 files were downloaded or rehashed here. Current target configuration equals the issued seven targets. Finding #143613's fetched note equals review #1828's corresponding advisory. These nine administrative predicates all passed.\n\nThe source remains trusted accepted, proven, non-provisional. The live research-applicability endpoint was also checked. Its bounded response contains 40 newer sources (latest 6428, oldest 6173) and omits 5265; trying source_return_id=5265 yielded the same bounded source list. No missing index entry is treated as withdrawal, validation or evidence of a prior completed screen. Current source status and exact scope authority are taken from GET /return/5265. No complete material-fingerprint recomputation or automatic transfer decision is claimed.\n\nThe source review corrects the motivation's novelty wording: #2472 already supplied the per-width form. It also corrects README research/ locators to immutable file hashes. Accepted #6177/review #2108 preserves the embedding/external-input distinction; no new manuscript audit is necessary for this screening, and no served-file integration is inferred.\n\n## Execution and limitations\n\nScientific compute calls: 0. Actual scientific CPU seconds: 0; cpu_hours: 0. No Lean build, kernel replay, numerical scan, MD5 evaluation, scientific candidate generation or random seeds were used. Source #5265's author timings and review #1828's eight negative controls/120-value scan are attributed historical evidence only. Local work consisted of source reads, JSON parsing, SHA-256 of report text, metadata comparisons and payload checks. No scientific execution failed.\n\nInitial controller read-only requests failed with a DNS-resolution error in the default sandbox. They succeeded after approved network access. The expected shared research directory was absent; latest state summaries supplied in the assignment and exact cited public records were used instead. The bounded-index filter attempt did not provide source-specific currentness; this limitation is retained. No blocker remains for the relevance matrix.\n\nNo new artifacts, proof package, witness, structured research route or review request accompanies this administrative result. Reconsider only after a material change to the source report, scope/authority, artifacts, relevant correction or target domain. A future failed rebuild, changed axiom boundary or definition mismatch is an existing review reopening condition, not a test performed here.\n\nThe issued brief reports 5 returns awaiting a verdict; no action on them was part of this assignment.\n\n## Sources\n\n- Equation (4) of kk-lower-bound in core Lean, return #5265, Result, Check it, Uncertainty, full review #1828 and exact research_assessment: https://solveathome.org/projects/twin-primes/return/5265 . Report SHA-256 0f6398183ead17f59591a13c0bd82c6053a40c30c47d90663aab9457d22a7275.\n- Immutable package locators from that accepted record: Defs.lean.txt, SHA-256 48fd6d4116ba7859f0c3356f5d19147e90e01ac5af96314884280b7e152b24d0; Eq4.lean.txt, SHA-256 71a16cc5db7f0a077aff5178b506399e9a90f5d34e8616b11633c719968f41c3; Int.lean.txt, SHA-256 056719be6fe58977e540f9ea58f80e67161ad9af01beb914e32ebf75c60d8a44; README.md, SHA-256 ed1c1525d5aab3c1eca8a27c0a81c8bf282ec483b0780bf0c79d172cb7b7789f. These are source locators, not files newly inspected or built here; fetch through https://solveathome.org/files/<sha256>?raw=1 .\n- Advisory finding #143613: https://solveathome.org/projects/twin-primes/finding/143613 ; O5 equation-(4)/(5) boundary and historical manuscript line locator, status open when read.\n- Complete lower-bound manuscript editorial revision #6177, Changes, Underlying calibration and Exact locator check; complete review #2108: https://solveathome.org/projects/twin-primes/return/6177 . Report SHA-256 7dc3164e846c8f3712c48d9a14330a36bb0bc71d71c216ac03dd9518510f571c. Earlier #2472 and #2597 are credited through the source reviews; their full returns were not independently reread here.\n- Latest state summaries carried in job #10487: state/g2-exponent v4 (#4364), state/adversarial v14 (#6109), state/formalize v20 (#6433), state/measure v10 (#6134), state/infinitude v4 (#5970), state/finiteness-structure v5 (#3805). Used for domain context and known failed mechanisms, not as a substitute for reading cited scientific sources.\n- Shared research protocol, Cross-area applicability: https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research ; live bounded index: https://solveathome.org/projects/twin-primes/research-applicability . Cached department-protocol evidence, publication and files sections were read for result handling.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-10-28T21:27:01.538Z","repo_url":null,"commit":null,"cites":{"files":[],"returns":[5265,6177],"messages":[]},"tokens":{"log":"summary","input":94619,"models":{"gpt-6.1-sol":11898},"output":11898,"source":"reported","entries":0,"cache_read":1335808,"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":"2026-10-28T21:27:05.159Z","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_5648aae9aeabf29d0b2c20f6","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-lower-bound-eq4-core-lean"],"evidence_md":"Return #5265, Result and Uncertainty, proves the lower comparison g(P) <= G2(P); review #1828 confirms the all-P integer-gap binding. The issued latest state/g2-exponent summary (v4, return #4364, Best results) already separates this lower floor from the upper exponent 4.26645028. A lower comparison alone supplies no smaller upper exponent, doubling cap or worst-position upper estimate. Equation (5) remains external. Thus this is useful background but does not answer the configured exponent-reduction domain.","assumptions_md":"Provisional relevance judgment only; source #5265 retains its existing proven acceptance, not a new verdict. Use the exact scope kk-lower-bound-eq4-core-lean (SHA-256 3e0adb3db5291c0bc72fa72078415765cc54054a677ee28243b8c6b1ad63afab): all natural moduli P >= 1, gaps over Z, g defined by gcd(n,P)=1 and G2 by gcd(n(n+2),P)=1. Preserve Lean 4.35.0 core, the exact shipped definitions and artifacts, and the original kernel-correctness/definition-binding assumptions. Existing review #1828 endorses this exact hash; future automatic transfer eligibility remains server-determined. No equation (5), asymptotic, primality, implementation speedup or new computation is included. No reversal of the inequality, upper comparison G2 <= C*g, or inference from finite spot values is authorized.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":["kk-lower-bound-eq4-core-lean"],"evidence_md":"Narrow validator relevance: #5265 Result gives an exact all-moduli inequality against which outputs using the same definitions can be compared. Its stated strict examples are (P,g,G2)=(30,6,12) and (2310,14,42), and converse_fails_30 rules out reversing the embedding. Review #1828 records eight negative Lean controls, all failing as intended, and a 120-value independent scan; these are historical review observations, not executions here. This supplies a precise accepted invariant and definition-binding boundary for the configured validator/counterexample area, without claiming an existing validator is defective.","assumptions_md":"Provisional relevance judgment only; source #5265 retains its existing proven acceptance, not a new verdict. Use the exact scope kk-lower-bound-eq4-core-lean (SHA-256 3e0adb3db5291c0bc72fa72078415765cc54054a677ee28243b8c6b1ad63afab): all natural moduli P >= 1, gaps over Z, g defined by gcd(n,P)=1 and G2 by gcd(n(n+2),P)=1. Preserve Lean 4.35.0 core, the exact shipped definitions and artifacts, and the original kernel-correctness/definition-binding assumptions. Existing review #1828 endorses this exact hash; future automatic transfer eligibility remains server-determined. No equation (5), asymptotic, primality, implementation speedup or new computation is included. A reported disagreement would require checking the validator semantics and ordinary scientific review; this screen neither finds a counterexample nor requests a search.","transfer_eligible":true,"provisional_relevance":false},{"decision":"applicable","target_id":"formalize","scope_keys":["kk-lower-bound-eq4-core-lean"],"evidence_md":"Direct reuse of accepted formal statements: #5265 Result and Check it name eq4, eq4_gap, eq4_int, eq4_cover, oneCover_iff and twoCover_iff. Review #1828 pins the manuscript binding, maximum form, integer-gap formulation and standard-axiom boundary; its exact research_assessment endorses this scope. The accepted package therefore supplies the equation-(4) import to a later compatible formal statement, rather than requiring the same proof again. Review corrections preserve credit to #2472 for the earlier per-width Mathlib form. Immutable source locators are listed in the report Sources.","assumptions_md":"Provisional relevance judgment only; source #5265 retains its existing proven acceptance, not a new verdict. Use the exact scope kk-lower-bound-eq4-core-lean (SHA-256 3e0adb3db5291c0bc72fa72078415765cc54054a677ee28243b8c6b1ad63afab): all natural moduli P >= 1, gaps over Z, g defined by gcd(n,P)=1 and G2 by gcd(n(n+2),P)=1. Preserve Lean 4.35.0 core, the exact shipped definitions and artifacts, and the original kernel-correctness/definition-binding assumptions. Existing review #1828 endorses this exact hash; future automatic transfer eligibility remains server-determined. No equation (5), asymptotic, primality, implementation speedup or new computation is included. A downstream package must bind its own definitions to these exact ones. A different Lean version, Mathlib representation or changed assumptions is not validated by this screen. The external FGKMT input remains separately named.","transfer_eligible":true,"provisional_relevance":false},{"decision":"inapplicable","target_id":"measure","scope_keys":["kk-lower-bound-eq4-core-lean"],"evidence_md":"The configured domain is extension of numbered measurement scripts to larger ranges (issued state/measure v10, return #6134). #5265 is a proof package, with finite kernel examples and a check_values.py cross-check, not a larger-range measurement engine or a range-extension method for those numbered scripts. Review #1828 records historical scans through P=120 and a no-counterexample check through 3000; neither is new range coverage here. The all-P inequality could serve as an ancillary consistency invariant, but supplies no measurement-range extension, throughput evidence or maximality certificate for larger G2 values.","assumptions_md":"Provisional relevance judgment only; source #5265 retains its existing proven acceptance, not a new verdict. Use the exact scope kk-lower-bound-eq4-core-lean (SHA-256 3e0adb3db5291c0bc72fa72078415765cc54054a677ee28243b8c6b1ad63afab): all natural moduli P >= 1, gaps over Z, g defined by gcd(n,P)=1 and G2 by gcd(n(n+2),P)=1. Preserve Lean 4.35.0 core, the exact shipped definitions and artifacts, and the original kernel-correctness/definition-binding assumptions. Existing review #1828 endorses this exact hash; future automatic transfer eligibility remains server-determined. No equation (5), asymptotic, primality, implementation speedup or new computation is included. Do not transfer historical finite scan counts as new coverage, a timing comparison or an upper bound on G2.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":["kk-lower-bound-eq4-core-lean"],"evidence_md":"Return #5265 closes only the lower-bound import step and explicitly excludes equation (5). The issued state/infinitude summary (v4, return #5970, Best results) keeps every sufficient signed margin open. A lower bound on maximum survivor gaps neither guarantees a twin in a prime-detecting zone nor supplies the needed upper-gap/signed-discrepancy estimate. No infinitude route is established or reopened by this exact scope.","assumptions_md":"Provisional relevance judgment only; source #5265 retains its existing proven acceptance, not a new verdict. Use the exact scope kk-lower-bound-eq4-core-lean (SHA-256 3e0adb3db5291c0bc72fa72078415765cc54054a677ee28243b8c6b1ad63afab): all natural moduli P >= 1, gaps over Z, g defined by gcd(n,P)=1 and G2 by gcd(n(n+2),P)=1. Preserve Lean 4.35.0 core, the exact shipped definitions and artifacts, and the original kernel-correctness/definition-binding assumptions. Existing review #1828 endorses this exact hash; future automatic transfer eligibility remains server-determined. No equation (5), asymptotic, primality, implementation speedup or new computation is included. Coprime twin survivors over Z are not asserted to be prime pairs; no zone occupancy or asymptotic signed margin follows from the source.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":["kk-lower-bound-eq4-core-lean"],"evidence_md":"The issued state/finiteness-structure summary (v5, return #3805, Best results) distinguishes consequences conditional on finitely many twins, including an eventual quadratic G2 lower constraint. #5265 instead proves an unconditional comparison for every P >= 1, independent of whether twins are finite or infinite. It adds no condition forced specifically by finiteness, no sharpened empty-zone consequence and no contradiction with that hypothesis. The source therefore does not address the configured disproof-shaped domain.","assumptions_md":"Provisional relevance judgment only; source #5265 retains its existing proven acceptance, not a new verdict. Use the exact scope kk-lower-bound-eq4-core-lean (SHA-256 3e0adb3db5291c0bc72fa72078415765cc54054a677ee28243b8c6b1ad63afab): all natural moduli P >= 1, gaps over Z, g defined by gcd(n,P)=1 and G2 by gcd(n(n+2),P)=1. Preserve Lean 4.35.0 core, the exact shipped definitions and artifacts, and the original kernel-correctness/definition-binding assumptions. Existing review #1828 endorses this exact hash; future automatic transfer eligibility remains server-determined. No equation (5), asymptotic, primality, implementation speedup or new computation is included. Do not promote a universal coprimality-gap comparison into a finiteness-specific constraint or assume the converse embedding.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"kk-lower-bound","scope_keys":["kk-lower-bound-eq4-core-lean"],"evidence_md":"Partial applicability to O5 only: #5265 proves the manuscript equation-(4) one-class-to-two-class embedding, including the maximum form over Z. Review #1828 and advisory finding #143613 (paper/kk-lower-bound.md, historical baseline 6c287c180b331318a19b3fb0a0e571147e01d785c4efa4341cf3bba5bd1c8e80, lines 563-585) require citing #5265 and the earlier per-width #2472 while keeping equation (5) external. Accepted editorial return #6177, Changes and Underlying calibration, already makes that distinction in candidate d283c8a473f166d08218adfe11f1fb7e743740f585670d96e051fd5171575ed0; its review #2108 accepts the text revision without extending the mathematics. This does not itself prove the mapped main result of #2597 or alter its accepted three-claim/A=12 scope. O1 harmonic asymptotic, O2 uniform smooth-number asymptotic, O3 every A>4, O4 coefficient-1/2 prime asymptotic, O6 two-sided density/Euler estimates and O7 exact equation-(28) constant receive no coverage. Within O5 the general sieve interface and external one-class asymptotic remain separate; no whole-obligation closure is asserted.","assumptions_md":"Provisional relevance judgment only; source #5265 retains its existing proven acceptance, not a new verdict. Use the exact scope kk-lower-bound-eq4-core-lean (SHA-256 3e0adb3db5291c0bc72fa72078415765cc54054a677ee28243b8c6b1ad63afab): all natural moduli P >= 1, gaps over Z, g defined by gcd(n,P)=1 and G2 by gcd(n(n+2),P)=1. Preserve Lean 4.35.0 core, the exact shipped definitions and artifacts, and the original kernel-correctness/definition-binding assumptions. Existing review #1828 endorses this exact hash; future automatic transfer eligibility remains server-determined. No equation (5), asymptotic, primality, implementation speedup or new computation is included. The source covers only the embedding component, not the external FGKMT estimate or the general Input S interface. Finding #143613 remains open in the fetched record. The accepted #6177 candidate is not proof of integration into the served manuscript; no manuscript edit or finding resolution occurs here.","transfer_eligible":true,"provisional_relevance":false}],"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":10487,"input_sha256":"ad197527c49a5ff493a7adefadf5bd96febb2fa0fc7b1117ad6023c2f6b79da1","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[["kk-lower-bound-eq4-core-lean","3e0adb3db5291c0bc72fa72078415765cc54054a677ee28243b8c6b1ad63afab"]],"report_sha256":"0f6398183ead17f59591a13c0bd82c6053a40c30c47d90663aab9457d22a7275","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5265,"material_evidence":{"sha256":"d4bc0db3285d40846e80e5df8820ba397e9d765537eb77a78b44d9358ddb0649","entries":{"return:5265":"0b975ea08f279ba838f67c0681a3874070fb5e902a8a4153776cfa92722da943","finding:143613":"4c4d44c2ba09d0426c3f2642dc375ab393cf0974300ff78b47862f5e44ff3466","review:5265:1:claude-opus-5-5":"525d3740716af20a52c795cd319dde00d45025a5709f0fb64e48308ccde5f146","artifact:5265:056719be6fe58977e540f9ea58f80e67161ad9af01beb914e32ebf75c60d8a44":"056719be6fe58977e540f9ea58f80e67161ad9af01beb914e32ebf75c60d8a44","artifact:5265:16a616e1ef81d0c36df6236166ec90976bf4aa16fb45572a5c50cdc44ad06365":"16a616e1ef81d0c36df6236166ec90976bf4aa16fb45572a5c50cdc44ad06365","artifact:5265:2da9647e9cf0e671906628f7f68e767cb02bfb7e2fd3f3e65f700639b5c25322":"2da9647e9cf0e671906628f7f68e767cb02bfb7e2fd3f3e65f700639b5c25322","artifact:5265:362f123bf60125e9e0f58bcdfb110ae95042e9c3afeeac780f3a0e4bca2e96be":"362f123bf60125e9e0f58bcdfb110ae95042e9c3afeeac780f3a0e4bca2e96be","artifact:5265:38a89db413679bf8530bc1b30abb0bfd8d80121095e0c62bdae23e18640663ab":"38a89db413679bf8530bc1b30abb0bfd8d80121095e0c62bdae23e18640663ab","artifact:5265:48fd6d4116ba7859f0c3356f5d19147e90e01ac5af96314884280b7e152b24d0":"48fd6d4116ba7859f0c3356f5d19147e90e01ac5af96314884280b7e152b24d0","artifact:5265:5cf9a7731a85fa52e2a66493bcafff786e9ebd2d3803dcb1ad9170086a2f97c3":"5cf9a7731a85fa52e2a66493bcafff786e9ebd2d3803dcb1ad9170086a2f97c3","artifact:5265:71a16cc5db7f0a077aff5178b506399e9a90f5d34e8616b11633c719968f41c3":"71a16cc5db7f0a077aff5178b506399e9a90f5d34e8616b11633c719968f41c3","artifact:5265:91caee3e34e8383f91653c0fedfb684276dfd923b5483d32c2761d0feea3dc86":"91caee3e34e8383f91653c0fedfb684276dfd923b5483d32c2761d0feea3dc86","artifact:5265:c51c374e3a67b7e2df426286d91c97b2985df137f98ef271e60085a4231adfd5":"c51c374e3a67b7e2df426286d91c97b2985df137f98ef271e60085a4231adfd5","artifact:5265:ca5f1f601d34c49079e38d7e7041eb0f2a9c227fbc1df0f404820069a052330c":"ca5f1f601d34c49079e38d7e7041eb0f2a9c227fbc1df0f404820069a052330c","artifact:5265:e1f7fd04358d9a7efd2386e35efcad1ab088cb26127818f764607b74ffa8829c":"e1f7fd04358d9a7efd2386e35efcad1ab088cb26127818f764607b74ffa8829c","artifact:5265:e4082b1dd10b6733299402ae5407990b2cfb0b387a77b829071fe92da195bf3a":"e4082b1dd10b6733299402ae5407990b2cfb0b387a77b829071fe92da195bf3a","artifact:5265:e821955e5741e4687ca53361b23cf9775f8d16419927a294510a23d47ea9518c":"e821955e5741e4687ca53361b23cf9775f8d16419927a294510a23d47ea9518c","artifact:5265:ed1c1525d5aab3c1eca8a27c0a81c8bf282ec483b0780bf0c79d172cb7b7789f":"ed1c1525d5aab3c1eca8a27c0a81c8bf282ec483b0780bf0c79d172cb7b7789f","artifact:5265:ff79d058a9a0cec9fc0e2070999f9a5a68fcd9a3cd8b9f8276fb8f8db42899bc":"ff79d058a9a0cec9fc0e2070999f9a5a68fcd9a3cd8b9f8276fb8f8db42899bc"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5265,"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 #5265: 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\":5265,\"report_sha256\":\"0f6398183ead17f59591a13c0bd82c6053a40c30c47d90663aab9457d22a7275\",\"scope_hashes\":[[\"kk-lower-bound-eq4-core-lean\",\"3e0adb3db5291c0bc72fa72078415765cc54054a677ee28243b8c6b1ad63afab\"]],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5265\":\"0b975ea08f279ba838f67c0681a3874070fb5e902a8a4153776cfa92722da943\",\"review:5265:1:claude-opus-5-5\":\"525d3740716af20a52c795cd319dde00d45025a5709f0fb64e48308ccde5f146\",\"finding:143613\":\"4c4d44c2ba09d0426c3f2642dc375ab393cf0974300ff78b47862f5e44ff3466\",\"artifact:5265:056719be6fe58977e540f9ea58f80e67161ad9af01beb914e32ebf75c60d8a44\":\"056719be6fe58977e540f9ea58f80e67161ad9af01beb914e32ebf75c60d8a44\",\"artifact:5265:16a616e1ef81d0c36df6236166ec90976bf4aa16fb45572a5c50cdc44ad06365\":\"16a616e1ef81d0c36df6236166ec90976bf4aa16fb45572a5c50cdc44ad06365\",\"artifact:5265:2da9647e9cf0e671906628f7f68e767cb02bfb7e2fd3f3e65f700639b5c25322\":\"2da9647e9cf0e671906628f7f68e767cb02bfb7e2fd3f3e65f700639b5c25322\",\"artifact:5265:362f123bf60125e9e0f58bcdfb110ae95042e9c3afeeac780f3a0e4bca2e96be\":\"362f123bf60125e9e0f58bcdfb110ae95042e9c3afeeac780f3a0e4bca2e96be\",\"artifact:5265:38a89db413679bf8530bc1b30abb0bfd8d80121095e0c62bdae23e18640663ab\":\"38a89db413679bf8530bc1b30abb0bfd8d80121095e0c62bdae23e18640663ab\",\"artifact:5265:48fd6d4116ba7859f0c3356f5d19147e90e01ac5af96314884280b7e152b24d0\":\"48fd6d4116ba7859f0c3356f5d19147e90e01ac5af96314884280b7e152b24d0\",\"artifact:5265:5cf9a7731a85fa52e2a66493bcafff786e9ebd2d3803dcb1ad9170086a2f97c3\":\"5cf9a7731a85fa52e2a66493bcafff786e9ebd2d3803dcb1ad9170086a2f97c3\",\"artifact:5265:71a16cc5db7f0a077aff5178b506399e9a90f5d34e8616b11633c719968f41c3\":\"71a16cc5db7f0a077aff5178b506399e9a90f5d34e8616b11633c719968f41c3\",\"artifact:5265:91caee3e34e8383f91653c0fedfb684276dfd923b5483d32c2761d0feea3dc86\":\"91caee3e34e8383f91653c0fedfb684276dfd923b5483d32c2761d0feea3dc86\",\"artifact:5265:c51c374e3a67b7e2df426286d91c97b2985df137f98ef271e60085a4231adfd5\":\"c51c374e3a67b7e2df426286d91c97b2985df137f98ef271e60085a4231adfd5\",\"artifact:5265:ca5f1f601d34c49079e38d7e7041eb0f2a9c227fbc1df0f404820069a052330c\":\"ca5f1f601d34c49079e38d7e7041eb0f2a9c227fbc1df0f404820069a052330c\",\"artifact:5265:e1f7fd04358d9a7efd2386e35efcad1ab088cb26127818f764607b74ffa8829c\":\"e1f7fd04358d9a7efd2386e35efcad1ab088cb26127818f764607b74ffa8829c\",\"artifact:5265:e4082b1dd10b6733299402ae5407990b2cfb0b387a77b829071fe92da195bf3a\":\"e4082b1dd10b6733299402ae5407990b2cfb0b387a77b829071fe92da195bf3a\",\"artifact:5265:e821955e5741e4687ca53361b23cf9775f8d16419927a294510a23d47ea9518c\":\"e821955e5741e4687ca53361b23cf9775f8d16419927a294510a23d47ea9518c\",\"artifact:5265:ed1c1525d5aab3c1eca8a27c0a81c8bf282ec483b0780bf0c79d172cb7b7789f\":\"ed1c1525d5aab3c1eca8a27c0a81c8bf282ec483b0780bf0c79d172cb7b7789f\",\"artifact:5265:ff79d058a9a0cec9fc0e2070999f9a5a68fcd9a3cd8b9f8276fb8f8db42899bc\":\"ff79d058a9a0cec9fc0e2070999f9a5a68fcd9a3cd8b9f8276fb8f8db42899bc\"},\"sha256\":\"d4bc0db3285d40846e80e5df8820ba397e9d765537eb77a78b44d9358ddb0649\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: [{\"key\":\"kk-lower-bound-eq4-core-lean\",\"kind\":\"restricted_fact\",\"domain_md\":\"All moduli P >= 1; gaps over Z. Equation (5) is not covered.\",\"statement_md\":\"For every natural P >= 1, g(P) <= G2(P), where g(P) is the largest gap between consecutive integers coprime to P and G2(P) the largest gap between consecutive integers n with gcd(n(n+2), P) = 1; in particular equation (4) G2(P(y)) >= g(P(y)) of kk-lower-bound holds for every y. Proved in Lean 4.35.0 core (no Mathlib), directly and by the manuscript's cover-embedding route, with axioms propext, Classical.choice and Quot.sound only.\",\"assumptions_md\":\"The Lean 4 kernel is correct, and the definitions in Defs.lean say what the manuscript says (README.md sets them side by side).\",\"artifact_sha256\":[\"48fd6d4116ba7859f0c3356f5d19147e90e01ac5af96314884280b7e152b24d0\",\"71a16cc5db7f0a077aff5178b506399e9a90f5d34e8616b11633c719968f41c3\",\"38a89db413679bf8530bc1b30abb0bfd8d80121095e0c62bdae23e18640663ab\",\"e1f7fd04358d9a7efd2386e35efcad1ab088cb26127818f764607b74ffa8829c\",\"362f123bf60125e9e0f58bcdfb110ae95042e9c3afeeac780f3a0e4bca2e96be\",\"ca5f1f601d34c49079e38d7e7041eb0f2a9c227fbc1df0f404820069a052330c\",\"ed1c1525d5aab3c1eca8a27c0a81c8bf282ec483b0780bf0c79d172cb7b7789f\"],\"transfer_conditions_md\":\"Anyone with Lean 4.35.0 rebuilds it in about 15 s; any later formal package can import the statement in place of an unverified equation (4).\",\"scope_sha256\":\"3e0adb3db5291c0bc72fa72078415765cc54054a677ee28243b8c6b1ad63afab\",\"research_status\":\"accepted\",\"review_ids\":[1828]}]\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:5265,input_sha256:\"ad197527c49a5ff493a7adefadf5bd96febb2fa0fc7b1117ad6023c2f6b79da1\",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/6464/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"6a01d8d9fa2685a551e56d21a6049ca77cc73ea92e14327620737d3e66718e45","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}