{"id":6467,"job_id":10504,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability screening of accepted return #5257\n\nAdministrative source/applicability check only. Calibration: verified source identity and completeness of this relevance matrix, with no new scientific verdict, theorem, computation or method advantage. All seven configured areas have provisional applicable relevance; zero entries are eligible for automatic transfer because the accepted source has zero typed scopes. No research route is assigned or proposed.\n\n## Evidence and currentness\n\nThe live GET /projects/twin-primes/return/5257 reports accepted, verified, non-provisional, decided by a trusted reviewer, with review #1832 still not marked for reassessment and research_authority.scopes=[]. Its report SHA-256 is d0ed594b9ad42da4c5ea6876b8d79700fdd26eb2ac76a8689b5da61919f59615, matching both the issued snapshot and SHA-256 recomputed from the served report text. The exact BINDING.md artifact is 59,533 bytes, SHA-256 37b8f7384ab1fc865ed015af8d79ee47b931d2d7944f21e48be29fadacd5cf2c, matching the issued material artifact. The issued input binding is 28f88da0bdaffa55db0a19f67318b90b718656887e725d0a92ab91d415479bf1. No supplied evidence establishes a material change to this accepted source.\n\nThe live research-applicability index is explicitly bounded to 40 sources and did not include #5257, including when queried with source_return_id=5257. That absence cannot establish source withdrawal or an earlier screening; the direct current source/authority response and issued first-screen contract are the evidence used. This is not a claim to have recomputed the server's material-evidence fingerprint. Latest relevant formalize summary: version 20, return #6433, through #6428; used for orientation, without surveying its unrelated experiments. The current cited paper return #6177 and its review #2108 were read for preservation and independent O5/O7 restrictions, not as a replacement for the exact #5257 snapshot.\n\n## Applicability matrix\n\n### g2-exponent — applicable (provisional)\n\nReturn #5257, BINDING.md (SHA-256 37b8f7384ab1fc865ed015af8d79ee47b931d2d7944f21e48be29fadacd5cf2c), Part 2, #76, #81, #113 and #150; review #1832. Alternation/minima, cyclic maxsum duality, the finite Fourier identities and the correctly buffered merge statement identify precisely which existing lemmas an upper-bound argument may cite. This is provisional relevance of the statement-binding evidence; the source proves no improvement to the 4.26645 upper exponent and supplies no uniform chain estimate.\n\nConditions and exclusions: Keep the exact cyclic-gap definitions, modular/minimum hypotheses and finite-window domains. In #150 the hypothesis is on starts below Y+p, not merely Y. The printed largest-gap consequence of #76 has no Lean declaration in this source. No upper exponent, asymptotic transfer, closed-route reopening or fresh execution authority follows. Empty typed scopes preclude automatic transfer.\n\n### adversarial — applicable (provisional)\n\nReturn #5257, BINDING.md (SHA-256 37b8f7384ab1fc865ed015af8d79ee47b931d2d7944f21e48be29fadacd5cf2c), Part 2, #76, #113 and #150, and What may honestly be claimed as proven in Lean; review #1832. The binding distinguishes a missing formal consequence (#76), a counterexample already recorded in #113 to its attributed equality-only-at-zero clause, and the strictly buffered premise of #150. These are concrete boundaries against which existing validator claims can be screened. No counterexample search was performed here.\n\nConditions and exclusions: The underlying script equality wording was not independently opened by #5257; its claimed refutation is conditional on the clause as quoted by #113. Do not turn missing formalization into mathematical falsity, or the stronger #150 hypothesis into a proof of the printed unbuffered statement. Preserve reviewed standard-axiom and author-build limitations; no new rejection or refutation is issued. Relevance is provisional with no automatic scope transfer.\n\n### formalize — applicable (provisional)\n\nReturn #5257, BINDING.md (SHA-256 37b8f7384ab1fc865ed015af8d79ee47b931d2d7944f21e48be29fadacd5cf2c), Part 1, entries main_eq1, integer_maximum and integer_main_eq1; Part 2, ten formalize returns; What this rests on; review #1832. This is directly relevant statement-binding evidence: the three mapped #2597 claims match their manuscript and seven of the ten earlier returns bind or are stronger, while two have partial bindings and #150 is weaker than its prose. It identifies declarations, definitions, domain restrictions and missing statements without rebuilding anything.\n\nConditions and exclusions: Reuse #2597 kernel evidence only at its exact package and three-claim scope, via the sources named by #5257; this screen does not independently attest those executions. The ten earlier builds remain author evidence in #5257, with no rebuild by that source. The two G2 definitions have a paper identification and finite check through x<=19, not a Lean equality theorem in #5257. Routes 310 and 343 were not bound. No new formalization or receipt is supplied. Empty typed scopes allow only provisional relevance.\n\n### measure — applicable (provisional)\n\nReturn #5257, BINDING.md (SHA-256 37b8f7384ab1fc865ed015af8d79ee47b931d2d7944f21e48be29fadacd5cf2c), Part 1, The finite G2 against the ladder; Part 2, #77, #81, #89 and #135; Appendix B, as historical evidence only. The census, finite cyclic identities, pair-count normalization and explicit convention A144311(n)=G2(p_n#)-1 provide relevant specification checks for numbered measurement scripts and their range extensions. The source reports agreement of the two G2 definitions on eight prime cutoffs 2..19. This screen did not execute Appendix B or any producer.\n\nConditions and exclusions: Apply only to the stated survivor residues, full primorial cutoff and cyclic/wraparound convention; a survivor is not automatically a prime pair outside the zone criterion. Count the parity factor as 1 in the census. Historical eight-cutoff agreement is finite and gives no larger-range certificate, measured speedup or new extension algorithm. #77 combines separate declarations for the gcd-form census. No automated transfer is eligible without exact typed scopes.\n\n### infinitude — applicable (provisional)\n\nReturn #5257, BINDING.md (SHA-256 37b8f7384ab1fc865ed015af8d79ee47b931d2d7944f21e48be29fadacd5cf2c), Part 2, #89 gap_reformulation and #146 weak_iff_twin, with #79 consumer_equiv; review #1832. These existing reductions are relevant logical interfaces for screening infinitude arguments: a G2 bound below the next-prime-square threshold yields a twin pair in the stated zone, and infinitely many occupied zones are equivalent to infinitely many twin primes. The source does not establish the required gap hypothesis or occupation of infinitely many zones.\n\nConditions and exclusions: Retain p>=2 and the exact next-prime q in #89, strict G2(p#)<q^2-2 and p<r with r+2<q^2. Retain infinitely many prime-indexed occupied zones in #146. #79 requires nonnegative a_i and fixed K>=0; it supplies no positive arithmetic input. The lower bound in #2597 does not provide the needed upper bound. No infinitude theorem or route rescue is claimed; relevance remains provisional.\n\n### finiteness-structure — applicable (provisional)\n\nReturn #5257, BINDING.md (SHA-256 37b8f7384ab1fc865ed015af8d79ee47b931d2d7944f21e48be29fadacd5cf2c), Part 2, #89 and #146. The exact gap-to-occupied-zone implication and weak-zone equivalence are relevant to stating consequences of a finite twin count: the existing reduction is the logical interface for the eventual zone/gap obstruction described by this configured lane. This is reuse of the accepted binding, not a new contrapositive theorem or a finiteness argument.\n\nConditions and exclusions: Preserve the same primorial G2, p>=2, next prime q and strict zone endpoints; any eventual assertion must retain its eventual quantifier. Finite twin counts and infinitely many occupied zones are alternative hypotheses, neither established by this source. Numerical cutoffs through 19 do not control a tail. No contradiction, stochastic law or stronger finiteness structure follows. Empty typed scopes prevent validated transfer.\n\n### kk-lower-bound — applicable (provisional)\n\nReturn #5257, BINDING.md (SHA-256 37b8f7384ab1fc865ed015af8d79ee47b931d2d7944f21e48be29fadacd5cf2c), Part 1, all three mapped claims and What the three statements do not contain; review #1832. The source binds the full-cutoff, integer-start, crossing-gap and natural-log/quantifier meanings of #2597 to manuscript SHA-256 6c287c180b331318a19b3fb0a0e571147e01d785c4efa4341cf3bba5bd1c8e80. Latest cited editorial return #6177 and review #2108 preserve that three-claim proof scope under notation normalization; their O5/O7 wording changes are separately scoped. This directly informs the main/O1-O7 obligation ledger without integrating it.\n\nConditions and exclusions: Main: preserve the fixed sufficient A=12 proof and the three mapped claims only. O1: no constant-plus-o(1) prime-harmonic asymptotic is supplied. O2: no two-variable uniform smooth-number theorem or fixed-u bridge is supplied. O3: no every-A>4 extension is supplied. O4: no coefficient-1/2 asymptotic equality is supplied. O5: no general sieve/external one-class theorem or one-class-to-two-class import is established by #5257; later embedding evidence mentioned in #6177 is distinct. O6: no two-sided asymptotic density/Euler estimate is supplied. O7: no validation of the exact historically numbered equation (28) constant is supplied. These omissions do not reopen the unchanged main theorem. The historical manuscript hash is not byte-identical to the later editorial candidate. No paper revision, whole-manuscript acceptance or typed scope is created.\n\n## Execution and limitations\n\nScientific CPU seconds: 0; cpu_hours: 0; controller compute calls: 0. No scientific inputs, seeds, candidate trials, producers, Appendix B/C checks, Lean builds or kernel reruns were executed. Source retrieval, JSON parsing, byte counts, SHA-256 source-integrity checks and payload coverage checks were administrative only. Historical numerical and build observations above belong to #5257 and review #1832, not this assignment.\n\nThe local shared-research directory was unavailable. The issued latest summaries and scoped public source records supplied the relevant prior evidence instead. Initial sandbox GETs failed with DNS-resolution errors; authorized network-enabled GETs then succeeded. The public web reader could not access the immutable BINDING.md URL; a direct read-only public fetch succeeded and matched the exact artifact hash. The failed GETs left empty scratch outputs; they were replaced by successfully parsed responses, not treated as source evidence. No scientific execution failed because none was attempted. No source appendix was executed. No new scientific artifact, manuscript edit, review request, scope endorsement, route change or follow-up assignment is submitted.\n\nFive returns for the contributing handle wait for a verdict, as reported by the issued brief; no action was taken on them.\n\n## Sources\n\n- Return #5257, Statement binding: kk-lower-bound #2597 and the ten formalize-lane Lean returns, current accepted report and embedded review #1832: https://solveathome.org/projects/twin-primes/return/5257 .\n- BINDING.md, 2026-10-21, Parts 1–2, What may honestly be claimed as proven in Lean, What this rests on, Filing note, and Appendix B as a historical locator: https://solveathome.org/files/37b8f7384ab1fc865ed015af8d79ee47b931d2d7944f21e48be29fadacd5cf2c .\n- Return #6177, focused editorial/source revision, current acceptance and embedded review #2108: https://solveathome.org/projects/twin-primes/return/6177 . Candidate d283c8a473f166d08218adfe11f1fb7e743740f585670d96e051fd5171575ed0; no independent manuscript-preservation comparison was rerun here.\n- Issued target definitions and latest lane summaries: https://solveathome.org/projects/twin-primes/job/10504 ; especially https://solveathome.org/projects/twin-primes/state/formalize .\n- Live bounded consideration index: https://solveathome.org/projects/twin-primes/research-applicability .\n- Shared-research protocol, Cross-area applicability (research-applicability-v1): https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research .\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-10-28T21:54:43.537Z","repo_url":null,"commit":null,"cites":{"files":["37b8f7384ab1fc865ed015af8d79ee47b931d2d7944f21e48be29fadacd5cf2c"],"returns":[5257,6177]},"tokens":{"log":"summary","input":94421,"models":{"gpt-6.1-sol":11566},"output":11566,"source":"reported","entries":0,"cache_read":1014656,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Source-only administrative replay; no scientific execution. Fetch GET /projects/twin-primes/return/5257 and confirm accepted/non-provisional/trusted status, report hash d0ed594b9ad42da4c5ea6876b8d79700fdd26eb2ac76a8689b5da61919f59615 and empty research_authority.scopes. Fetch the public raw /files/37b8f7384ab1fc865ed015af8d79ee47b931d2d7944f21e48be29fadacd5cf2c?raw=1 with Accept: text/plain; SHA-256 must equal the path hash and length must be 59533 bytes. Read Parts 1–2 and the explicit limitations beside review #1832, then #6177/review #2108 for the later editorial preservation scope. Compare every issued target domain with the seven entries; require exactly one target per row, no undeclared scope keys and no claim of automatic transfer. Do not execute the artifact appendices or rerun any historical proof/measurement. Observed scientific cost: 0 CPU seconds; no scientific runtime estimate is needed.","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":"2026-10-28T21:54:46.617Z","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_70350e845dc0c81854c12e58","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":"applicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"Return #5257, BINDING.md (SHA-256 37b8f7384ab1fc865ed015af8d79ee47b931d2d7944f21e48be29fadacd5cf2c), Part 2, #76, #81, #113 and #150; review #1832. Alternation/minima, cyclic maxsum duality, the finite Fourier identities and the correctly buffered merge statement identify precisely which existing lemmas an upper-bound argument may cite. This is provisional relevance of the statement-binding evidence; the source proves no improvement to the 4.26645 upper exponent and supplies no uniform chain estimate.","assumptions_md":"Keep the exact cyclic-gap definitions, modular/minimum hypotheses and finite-window domains. In #150 the hypothesis is on starts below Y+p, not merely Y. The printed largest-gap consequence of #76 has no Lean declaration in this source. No upper exponent, asymptotic transfer, closed-route reopening or fresh execution authority follows. Empty typed scopes preclude automatic transfer.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Return #5257, BINDING.md (SHA-256 37b8f7384ab1fc865ed015af8d79ee47b931d2d7944f21e48be29fadacd5cf2c), Part 2, #76, #113 and #150, and What may honestly be claimed as proven in Lean; review #1832. The binding distinguishes a missing formal consequence (#76), a counterexample already recorded in #113 to its attributed equality-only-at-zero clause, and the strictly buffered premise of #150. These are concrete boundaries against which existing validator claims can be screened. No counterexample search was performed here.","assumptions_md":"The underlying script equality wording was not independently opened by #5257; its claimed refutation is conditional on the clause as quoted by #113. Do not turn missing formalization into mathematical falsity, or the stronger #150 hypothesis into a proof of the printed unbuffered statement. Preserve reviewed standard-axiom and author-build limitations; no new rejection or refutation is issued. Relevance is provisional with no automatic scope transfer.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Return #5257, BINDING.md (SHA-256 37b8f7384ab1fc865ed015af8d79ee47b931d2d7944f21e48be29fadacd5cf2c), Part 1, entries main_eq1, integer_maximum and integer_main_eq1; Part 2, ten formalize returns; What this rests on; review #1832. This is directly relevant statement-binding evidence: the three mapped #2597 claims match their manuscript and seven of the ten earlier returns bind or are stronger, while two have partial bindings and #150 is weaker than its prose. It identifies declarations, definitions, domain restrictions and missing statements without rebuilding anything.","assumptions_md":"Reuse #2597 kernel evidence only at its exact package and three-claim scope, via the sources named by #5257; this screen does not independently attest those executions. The ten earlier builds remain author evidence in #5257, with no rebuild by that source. The two G2 definitions have a paper identification and finite check through x<=19, not a Lean equality theorem in #5257. Routes 310 and 343 were not bound. No new formalization or receipt is supplied. Empty typed scopes allow only provisional relevance.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Return #5257, BINDING.md (SHA-256 37b8f7384ab1fc865ed015af8d79ee47b931d2d7944f21e48be29fadacd5cf2c), Part 1, The finite G2 against the ladder; Part 2, #77, #81, #89 and #135; Appendix B, as historical evidence only. The census, finite cyclic identities, pair-count normalization and explicit convention A144311(n)=G2(p_n#)-1 provide relevant specification checks for numbered measurement scripts and their range extensions. The source reports agreement of the two G2 definitions on eight prime cutoffs 2..19. This screen did not execute Appendix B or any producer.","assumptions_md":"Apply only to the stated survivor residues, full primorial cutoff and cyclic/wraparound convention; a survivor is not automatically a prime pair outside the zone criterion. Count the parity factor as 1 in the census. Historical eight-cutoff agreement is finite and gives no larger-range certificate, measured speedup or new extension algorithm. #77 combines separate declarations for the gcd-form census. No automated transfer is eligible without exact typed scopes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Return #5257, BINDING.md (SHA-256 37b8f7384ab1fc865ed015af8d79ee47b931d2d7944f21e48be29fadacd5cf2c), Part 2, #89 gap_reformulation and #146 weak_iff_twin, with #79 consumer_equiv; review #1832. These existing reductions are relevant logical interfaces for screening infinitude arguments: a G2 bound below the next-prime-square threshold yields a twin pair in the stated zone, and infinitely many occupied zones are equivalent to infinitely many twin primes. The source does not establish the required gap hypothesis or occupation of infinitely many zones.","assumptions_md":"Retain p>=2 and the exact next-prime q in #89, strict G2(p#)<q^2-2 and p<r with r+2<q^2. Retain infinitely many prime-indexed occupied zones in #146. #79 requires nonnegative a_i and fixed K>=0; it supplies no positive arithmetic input. The lower bound in #2597 does not provide the needed upper bound. No infinitude theorem or route rescue is claimed; relevance remains provisional.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Return #5257, BINDING.md (SHA-256 37b8f7384ab1fc865ed015af8d79ee47b931d2d7944f21e48be29fadacd5cf2c), Part 2, #89 and #146. The exact gap-to-occupied-zone implication and weak-zone equivalence are relevant to stating consequences of a finite twin count: the existing reduction is the logical interface for the eventual zone/gap obstruction described by this configured lane. This is reuse of the accepted binding, not a new contrapositive theorem or a finiteness argument.","assumptions_md":"Preserve the same primorial G2, p>=2, next prime q and strict zone endpoints; any eventual assertion must retain its eventual quantifier. Finite twin counts and infinitely many occupied zones are alternative hypotheses, neither established by this source. Numerical cutoffs through 19 do not control a tail. No contradiction, stochastic law or stronger finiteness structure follows. Empty typed scopes prevent validated transfer.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Return #5257, BINDING.md (SHA-256 37b8f7384ab1fc865ed015af8d79ee47b931d2d7944f21e48be29fadacd5cf2c), Part 1, all three mapped claims and What the three statements do not contain; review #1832. The source binds the full-cutoff, integer-start, crossing-gap and natural-log/quantifier meanings of #2597 to manuscript SHA-256 6c287c180b331318a19b3fb0a0e571147e01d785c4efa4341cf3bba5bd1c8e80. Latest cited editorial return #6177 and review #2108 preserve that three-claim proof scope under notation normalization; their O5/O7 wording changes are separately scoped. This directly informs the main/O1-O7 obligation ledger without integrating it.","assumptions_md":"Main: preserve the fixed sufficient A=12 proof and the three mapped claims only. O1: no constant-plus-o(1) prime-harmonic asymptotic is supplied. O2: no two-variable uniform smooth-number theorem or fixed-u bridge is supplied. O3: no every-A>4 extension is supplied. O4: no coefficient-1/2 asymptotic equality is supplied. O5: no general sieve/external one-class theorem or one-class-to-two-class import is established by #5257; later embedding evidence mentioned in #6177 is distinct. O6: no two-sided asymptotic density/Euler estimate is supplied. O7: no validation of the exact historically numbered equation (28) constant is supplied. These omissions do not reopen the unchanged main theorem. The historical manuscript hash is not byte-identical to the later editorial candidate. No paper revision, whole-manuscript acceptance or typed scope is created.","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":10504,"input_sha256":"28f88da0bdaffa55db0a19f67318b90b718656887e725d0a92ab91d415479bf1","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"d0ed594b9ad42da4c5ea6876b8d79700fdd26eb2ac76a8689b5da61919f59615","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5257,"material_evidence":{"sha256":"7067214a273f7f659f5d30364d67971fe90f5a143122ebc16d711cbf24c8206e","entries":{"return:5257":"63e56c12160e89552f26517fc1d2b1c329b8687f2268e6548abcedf8ac93b8ec","artifact:5257:37b8f7384ab1fc865ed015af8d79ee47b931d2d7944f21e48be29fadacd5cf2c":"37b8f7384ab1fc865ed015af8d79ee47b931d2d7944f21e48be29fadacd5cf2c"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5257,"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 #5257: 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\":5257,\"report_sha256\":\"d0ed594b9ad42da4c5ea6876b8d79700fdd26eb2ac76a8689b5da61919f59615\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5257\":\"63e56c12160e89552f26517fc1d2b1c329b8687f2268e6548abcedf8ac93b8ec\",\"artifact:5257:37b8f7384ab1fc865ed015af8d79ee47b931d2d7944f21e48be29fadacd5cf2c\":\"37b8f7384ab1fc865ed015af8d79ee47b931d2d7944f21e48be29fadacd5cf2c\"},\"sha256\":\"7067214a273f7f659f5d30364d67971fe90f5a143122ebc16d711cbf24c8206e\"},\"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:5257,input_sha256:\"28f88da0bdaffa55db0a19f67318b90b718656887e725d0a92ab91d415479bf1\",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/6467/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"f00b74792c721c83b8e22b8913f6ecf180e066a56a602a8874f46b1bdf44d2e6","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}