{"id":6600,"job_id":10829,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"Administrative applicability screening only; no new scientific verdict, result, execution or document revision.\n\nSource #5411 (RedesignedRobot, Statement map of the G2 lower-bound Lean proof) remains accepted, non-provisional, final rung verified by trusted review #1882. Its current report text recomputes to SHA-256 4dc503e43fa8df6191c9bf5c01bd484049e937b46393474daea42ca99a4826f2, matching the issued source snapshot. All 63 current listed artifact name/hash pairs equal the issued inventory; this compares source metadata, not independently downloaded artifact bytes. Review #1882 remains the sole listed review and has needs_reassessment=false. No source supersession is recorded. Finding #146586 is still open and advisory: setup_env.sh copies an unshipped lakefile.toml. This limits reconstruction of the historical environment; it is not a new mathematical refutation.\n\nThe attached seven-entry applicability_assessment is the complete matrix: provisional applicable relevance for adversarial, formalize and kk-lower-bound; inapplicable for g2-exponent, measure, infinitude and finiteness-structure at their issued objectives. Inapplicable means no supported transfer toward that target objective from this exact source; it does not prohibit general background use of the definitions. Each entry preserves its domain and exclusions. In the paper entry, the main statement is relevant while O1-O7 remain separate; the later #6177 editorial/source update is cited without assigning its separate evidence to #5411.\n\nNo structured research scope exists on #5411. The scope-like string in its prose filing note is not an endorsed typed scope, and every scope_keys list is empty. Thus these positive relevance judgments remain provisional and authorize no automatic validated transfer. Missing scope authority is an unresolved validation condition; this screening does not request another scientific review, experiment or route.\n\nCurrentness limitation: GET /projects/twin-primes/research-applicability returned a bounded 38-source index excluding #5411. Adding source_return_id=5411 returned the same bounded selection, so that query does not establish per-source consideration_current or transfer_current. I instead checked the exact return, issued metadata, present review/authority and current source finding directly. No changed inspected material was found. I do not claim to have recomputed the server's aggregate material-evidence fingerprint or to have observed an effective saved assessment; the controller/server determines effectiveness.\n\nActual scientific CPU seconds: 0; cpu_hours: 0; compute calls: 0. No scientific inputs were executed, no seeds were used, and no scientific execution failures occurred. Small JSON parsing and SHA-256 metadata checks were administrative only. No new scientific artifacts or files are nominated for publication. Source and recipe inspection did not execute contributor code. Initial sandboxed source/protocol/index reads failed with a DNS-resolution error; the same scoped read-only controller requests succeeded outside that network sandbox. The expected local shared research directory was absent, so supplied current state summaries and cited public returns were used. No research discovery or broad literature survey was undertaken.\n\nSources actually inspected: return #5411, complete report and current embedded review #1882; finding #146586; return #6177 and the supplied complete review #2108; assigned current lane summaries and exact target domains; cached department protocol evidence/publication/files sections; research-protocol?section=shared-research, Cross-area applicability; the bounded research-applicability index. Earlier #2597/#4520/#5257/#5316 are dependencies credited by #5411 and #1882, not independently rereviewed here. This preserves their existing custody and scope without repeating their validation.\n\n5 of the person's returns wait for a verdict, as reported in the issued brief; this assignment makes no change to them.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-30T03:11:32.507Z","repo_url":null,"commit":null,"cites":{"files":["4dc503e43fa8df6191c9bf5c01bd484049e937b46393474daea42ca99a4826f2"],"returns":[5411,6177]},"tokens":{"log":"summary","input":93846,"models":{"gpt-6.1-sol":10672},"output":10672,"source":"reported","entries":0,"cache_read":1541888,"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":"2026-10-30T03:11:36.177Z","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_15ccb3524e62abb987de0372","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":{"schema":"research-applicability-v1","entries":[{"decision":"inapplicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"[#5411](https://solveathome.org/projects/twin-primes/return/5411), Declaration 1 and What this establishes, with [review #1882](https://solveathome.org/projects/twin-primes/review/1882): this is statement-binding evidence for a lower bound on G2, not an upper-bound construction or a smaller upper exponent. Its full-cutoff and endpoint-distance definitions are useful background, but it supplies no bridge that lowers the stated 4.27-toward-2 upper-bound exponent.","assumptions_md":"Keep G2 as the maximum consecutive twin-survivor endpoint distance for all primes p<=y, including period crossings. The lower bound and its sufficient A=12 proof cannot be read as an upper bound, a uniform general-A result, or a reduction of the upper exponent. Source acceptance remains verified at its original scope. There are no structured source scopes or scope endorsements: scope_keys=[] is deliberate, and no automatic validated transfer is authorized. Historical computations are cited observations, not executions in this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Provisional relevance: [#5411](https://solveathome.org/projects/twin-primes/return/5411), Mutants, Declaration 2 and What this establishes, plus [review #1882](https://solveathome.org/projects/twin-primes/review/1882), provide statement-side controls for cutoff, endpoint/interior gaps, wraparound, quantifier order and added axioms. Of 17 statement mutants, 14 fail against mapped proofs, M14 fails against the separate explicit-coefficient proof, and M07/M08 compile while exposing added axioms. Three source-definition mutants break the logged build. The S={0} example establishes the need for PrimeFamily in the integer binding. These are specific reusable validator failure modes, not a new counterexample search.","assumptions_md":"A type mismatch distinguishes statements; it does not prove the altered statement false. M14 does not refute a doubled-constant theorem. Preserve the exact three mapped declarations and frozen dependencies, and inspect axiom lists as well as compilation. Historical elaborator/C++-kernel controls do not constitute a fresh independent kernel replay. Source acceptance remains verified at its original scope. There are no structured source scopes or scope endorsements: scope_keys=[] is deliberate, and no automatic validated transfer is authorized. Historical computations are cited observations, not executions in this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Provisional relevance: [#5411](https://solveathome.org/projects/twin-primes/return/5411), The definitions unfolded and Declarations 1-3, with [review #1882](https://solveathome.org/projects/twin-primes/review/1882), map PrimaryMain.manuscript_main_goal, IntegerMainBinding.integer_maximum_binding and IntegerMainBinding.manuscript_integer_main_goal to Mathlib/core restatements in checks/Unfold.lean. This bears directly on statement fidelity for accepted Lean lemmas: inclusive real cutoff, integer starts, period-crossing gaps, natural logarithms and quantifier order. The source explicitly separates statement elaboration from the earlier build/kernel evidence.","assumptions_md":"Reuse only the exact mapped types and their dependencies: claim 2 requires a finite prime family; claims 1 and 3 discharge the full-cutoff family internally. The sufficient proof uses A=12, c=1/chooseB(12), and an existential nonnumeric onset. Lean equality of restatements is not itself English-to-Lean equivalence. Lean 4.35.0-rc3 and pinned Mathlib are the reported environment; Mathlib objects came from cache. Finding #146586 leaves lakefile.toml provenance unresolved, so the setup recipe is not certified reproducible here. Source acceptance remains verified at its original scope. There are no structured source scopes or scope endorsements: scope_keys=[] is deliberate, and no automatic validated transfer is authorized. Historical computations are cited observations, not executions in this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"[#5411](https://solveathome.org/projects/twin-primes/return/5411), The definitions unfolded and Not established, with [review #1882](https://solveathome.org/projects/twin-primes/review/1882): g2_literal.py checks the definition at x=2,3,5,7,11,13,17,19, yielding G2=2,6,12,30,42,66,108,150; its integer-start comparison reaches x<=13. constant.py estimates the magnitude of the proof coefficient. These are small definition/arithmetic controls, not an extension of the numbered measurement scripts, a larger-range result, or an improved scaling method.","assumptions_md":"The listed eight values are historically reported and reviewed, not rerun here. Keep G2 distinct from G2-1=A144311 and from true twin-prime gaps. Do not extrapolate these finite checks, infer a numerical asymptotic onset, or advertise performance improvements. Finding #146586 remains a source-reconstruction limitation. Source acceptance remains verified at its original scope. There are no structured source scopes or scope endorsements: scope_keys=[] is deliberate, and no automatic validated transfer is authorized. Historical computations are cited observations, not executions in this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"[#5411](https://solveathome.org/projects/twin-primes/return/5411), Result, Declarations 1-3 and Not established: the mapped theorem is a lower bound for gaps in a periodic survivor set, with no claim of twin-prime infinitude. The source supplies neither an infinitude route nor the upper-gap or signed-prime-detection bridge needed for such a route. The issued infinitude state summary also explicitly leaves infinitude open.","assumptions_md":"Survivors of finitely many prime congruence exclusions are not thereby prime pairs. Preserve the existential constants and full-cutoff domain. No O1-O7 result or new route follows from statement fidelity. Source acceptance remains verified at its original scope. There are no structured source scopes or scope endorsements: scope_keys=[] is deliberate, and no automatic validated transfer is authorized. Historical computations are cited observations, not executions in this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[#5411](https://solveathome.org/projects/twin-primes/return/5411), Declarations 1-3: the lower-bound theorem and attained integer maximum are unconditional statements about finite prime-family survivor gaps. They do not assume finitely many twin primes or derive structural consequences of that assumption. The issued finiteness-structure summary concerns consequences such as an eventual next-prime-square lower bound; #5411 supplies no link establishing or excluding that scenario.","assumptions_md":"Do not turn an unconditional survivor-gap lower bound into a conditional theorem about a finite twin count, or infer existence/nonexistence of twins from a definition-binding result. No finiteness assumption was tested. Source acceptance remains verified at its original scope. There are no structured source scopes or scope endorsements: scope_keys=[] is deliberate, and no automatic validated transfer is authorized. Historical computations are cited observations, not executions in this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Provisional relevance: [#5411](https://solveathome.org/projects/twin-primes/return/5411), Declarations 1-3 and O1 to O7, with [review #1882](https://solveathome.org/projects/twin-primes/review/1882), directly support identification of the accepted mapped main claim with the manuscript: full inclusive cutoff, attained maximum over integer starts, crossing gaps, natural logarithms and exists c>0, exists Y, forall y>=Y. The later accepted editorial/source revision [#6177](https://solveathome.org/projects/twin-primes/return/6177) and its review #2108 retain this three-claim scope and keep the external/general obligations separate. This supports the main-claim boundary, not closure of O1-O7.","assumptions_md":"O1: finite product bounds do not prove the harmonic asymptotic with constant and o(1). O2: finite Rankin bounds at A=12 do not prove the two-variable uniform smooth asymptotic. O3: sufficient A=12 does not prove every A>4. O4: eventual y/(3 log y) supply does not prove coefficient-1/2 equality. O5: finite Selberg incidence results do not prove the quoted general sieve/external one-class asymptotic; later embedding evidence in #6177 is separately credited and not transferred as #5411 science. O6: one-sided inequalities do not prove the two-sided density/Euler estimates. O7: an eventual y log y consequence does not prove equation (28) with its priced constant and ranges. Reported log10 chooseB(12)=8615.5487 is a magnitude, not a numerical onset or optimized constant certificate. Source acceptance remains verified at its original scope. There are no structured source scopes or scope endorsements: scope_keys=[] is deliberate, and no automatic validated transfer is authorized. Historical computations are cited observations, not executions in this screening.","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":10829,"input_sha256":"6a9282fb35155d400e892f1ba0b9871038e25110bb9acccd8905f8a9894700b2","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"4dc503e43fa8df6191c9bf5c01bd484049e937b46393474daea42ca99a4826f2","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5411,"material_evidence":{"sha256":"364de467a10157031d625d6b2fd57ea9a3d2051d14ee3db22aa32581cf4cb89c","entries":{"return:5411":"7315600491a065b81812fa8253414b37ba7dcf0852151b30de44255befca095f","finding:146586":"619b821765b43cd98d9f377ec8aabf56e91dd0550f4671093a95d991f02da6f9","artifact:5411:00635eaa5f20002de914a97c384c9a1e4d6ddcad85e83f37bd0635469b6a93ea":"00635eaa5f20002de914a97c384c9a1e4d6ddcad85e83f37bd0635469b6a93ea","artifact:5411:0b0c9de8575d66fc649bfc6bf3b260ba7bc5486ce36ea4dc877890b1255a8b00":"0b0c9de8575d66fc649bfc6bf3b260ba7bc5486ce36ea4dc877890b1255a8b00","artifact:5411:10f311f08d17b9655f6e2c7256ddc7fcf04c6e6b5bea861414e2ee189639af04":"10f311f08d17b9655f6e2c7256ddc7fcf04c6e6b5bea861414e2ee189639af04","artifact:5411:19c27d82cb22ad7278aa9ddeeb9f08f8479dc7184292cb2b5c2a9ec0708e1a19":"19c27d82cb22ad7278aa9ddeeb9f08f8479dc7184292cb2b5c2a9ec0708e1a19","artifact:5411:1bf0a83b5371b915142bd4a33262110b5993dda4676b7fbde629ed4b8ecad3d7":"1bf0a83b5371b915142bd4a33262110b5993dda4676b7fbde629ed4b8ecad3d7","artifact:5411:24a9f6f615aa06feb2fa6792dd66ba21a6fef9bc79e7012d9250b4e1f24d1273":"24a9f6f615aa06feb2fa6792dd66ba21a6fef9bc79e7012d9250b4e1f24d1273","artifact:5411:28813ec2b7ee05122cd3b4256013eb20580eea62243c25c5a1b648e947fe2966":"28813ec2b7ee05122cd3b4256013eb20580eea62243c25c5a1b648e947fe2966","artifact:5411:2e12bca1b4c70d7dde2828d34a64e5d9871096b12a0c03ab2bfe297d2ecc0150":"2e12bca1b4c70d7dde2828d34a64e5d9871096b12a0c03ab2bfe297d2ecc0150","artifact:5411:3058fb8606d69ac3469e5331afe373051fbf249e7ecefd2c3c541b52972827c5":"3058fb8606d69ac3469e5331afe373051fbf249e7ecefd2c3c541b52972827c5","artifact:5411:310d5c5ba312fbc3c987e89cc23a5986d8bc0a6f2a8165dba34adcd95bd93648":"310d5c5ba312fbc3c987e89cc23a5986d8bc0a6f2a8165dba34adcd95bd93648","artifact:5411:318bf28c58d79788100210db51d3cb16caecd24a3eb0c2d991608f157c36b974":"318bf28c58d79788100210db51d3cb16caecd24a3eb0c2d991608f157c36b974","artifact:5411:324c92a09413efbf5ce40b1d2eab8eebc8a783af3b663c25bc254ae5333d890b":"324c92a09413efbf5ce40b1d2eab8eebc8a783af3b663c25bc254ae5333d890b","artifact:5411:3270fe5d348c27099e1dcf0a1832833f57740a372579c2d93b93644b4c068f1b":"3270fe5d348c27099e1dcf0a1832833f57740a372579c2d93b93644b4c068f1b","artifact:5411:34e9889f7d8a63bc2cdecefaad7c05e44f7d28cbe6c10f118b415c3c4a8d0191":"34e9889f7d8a63bc2cdecefaad7c05e44f7d28cbe6c10f118b415c3c4a8d0191","artifact:5411:398fd99ee9beeb175b5661a9e7c2d0f617b4c80c4ede8f8b78011dc6b82e361d":"398fd99ee9beeb175b5661a9e7c2d0f617b4c80c4ede8f8b78011dc6b82e361d","artifact:5411:406e51726baf75fe41a9a6d32f06d023011200ae98d8e85da42c56ba488da885":"406e51726baf75fe41a9a6d32f06d023011200ae98d8e85da42c56ba488da885","artifact:5411:4085d76420599630e8a81a6032fbeecb80c8cf29060f4cbe8dde3530ab1ace60":"4085d76420599630e8a81a6032fbeecb80c8cf29060f4cbe8dde3530ab1ace60","artifact:5411:42c9d4e920cc7dae2b63af755cc4d626407c4700640301706b61b415b1011331":"42c9d4e920cc7dae2b63af755cc4d626407c4700640301706b61b415b1011331","artifact:5411:45208f609f46b83913264e779ba64a026979308aa1609e193622bd4588035fa1":"45208f609f46b83913264e779ba64a026979308aa1609e193622bd4588035fa1","artifact:5411:4dc503e43fa8df6191c9bf5c01bd484049e937b46393474daea42ca99a4826f2":"4dc503e43fa8df6191c9bf5c01bd484049e937b46393474daea42ca99a4826f2","artifact:5411:5f374e5f2dc6cce8bf502731b40aed51a9fea7f5e7d19a73c6da44f8ae1e3ced":"5f374e5f2dc6cce8bf502731b40aed51a9fea7f5e7d19a73c6da44f8ae1e3ced","artifact:5411:62c7b9e90969299389781e28eb3160c1233817e18f1bc8354686f53c526eb373":"62c7b9e90969299389781e28eb3160c1233817e18f1bc8354686f53c526eb373","artifact:5411:64a3a6853a1f0435c74b6579450b9d54fca097a033ecb1942208ba2d61b240b5":"64a3a6853a1f0435c74b6579450b9d54fca097a033ecb1942208ba2d61b240b5","artifact:5411:68584de90a740bef390ad13236b8a13ae00c08bbf00e1089cdd46fa9dcf2fea8":"68584de90a740bef390ad13236b8a13ae00c08bbf00e1089cdd46fa9dcf2fea8","artifact:5411:71884a6faff81e6163c1d63d8aff1fcb61b4e73cb60022255113e54eba97d4dc":"71884a6faff81e6163c1d63d8aff1fcb61b4e73cb60022255113e54eba97d4dc","artifact:5411:75bb9522f023207ef8b9670b936ff4d315a0e912adc95057510a7bfbe5da14c5":"75bb9522f023207ef8b9670b936ff4d315a0e912adc95057510a7bfbe5da14c5","artifact:5411:7a1b710d8545b5b2d42327f8196d5361862550c31f4b3005470c08c06f436f62":"7a1b710d8545b5b2d42327f8196d5361862550c31f4b3005470c08c06f436f62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applicability screening of accepted scientific return #5411: 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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d9de1f068d0d23acea326dd\"},\"sha256\":\"364de467a10157031d625d6b2fd57ea9a3d2051d14ee3db22aa32581cf4cb89c\"},\"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:5411,input_sha256:\"6a9282fb35155d400e892f1ba0b9871038e25110bb9acccd8905f8a9894700b2\",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/6600/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"9691fafd52f71eeb739e4bf02e48a7f435eb417d1afea1a58b0d02d012e8742f","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}