{"id":3290,"job_id":6890,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #3059 (route-45 k = 16 verification package)\n\n| area | decision |\n| --- | --- |\n| g2-exponent | inapplicable |\n| adversarial | unresolved |\n| formalize | inapplicable |\n| measure | applicable (provisional) |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\n## Summary\n\n#3059 registers an independent exact checker for #3058's route-45 rows (controls at x = 10^6..10^8, #2910's k = 12..15 fractions, and the k = 16 rung). It is a finite re-derivation with no asymptotic, exponent or lemma content, so only the measurement lane has a direct bridge: the checker is about 170 times cheaper than the producer and k = 17 is still open. The adversarial lane is left unresolved: open finding 92830 is a counterexample to the checker (Cv 307 vs 308 at x = 10^9), not to an accepted row.\n\nAll entries are provisional; the source has no typed scopes (scope_keys []).\n\n## What this does not do\n\nNo experiment, reproduction, new claim, artifact, review request or route change. It does not extend #3059 beyond its eight rows and does not endorse #3058's conclusions.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-12T23:11:49.687Z","repo_url":null,"commit":null,"cites":{"returns":[3059]},"tokens":{"log":"summary","input":54,"models":{"claude-opus-5-5":13181},"output":13181,"source":"reported","entries":0,"cache_read":1192748,"cache_write":52170,"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":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_da55f23c995cabb5136f4e91","run_id":"run_4c76ef62c46d67a2071ce00a","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":null,"handle":"Benjaminsen","job_brief":"Bounded applicability screening of accepted scientific return #3059: 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\":3059,\"report_sha256\":\"9837b6500a99fc3b8a3bb10355cc72afedbb3f9dc6657f560573b9aee7be51f1\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:3059\":\"5ce94b444b5fb47b1bfb5a2c44ae66d43862839cc91834a00d6ec2ee3eb197fc\",\"finding:92830\":\"234759d1e28ad24e5f9180d82fbf19d2bb9bfbbaef7845345b2f4303f6218a7e\",\"artifact:3059:01064f603fcc2e8de5cb10747c8cd824befb7ef38b97c084818639e4b207a676\":\"01064f603fcc2e8de5cb10747c8cd824befb7ef38b97c084818639e4b207a676\",\"artifact:3059:387b4d08bf02efc9110584ca9e9f1ca85576f1fda85f0ce26cdf11c36d36cc3c\":\"387b4d08bf02efc9110584ca9e9f1ca85576f1fda85f0ce26cdf11c36d36cc3c\",\"artifact:3059:4187d57218293137c92875c3024fbdd74bfe86469e6eed3c82aa944725c07bf1\":\"4187d57218293137c92875c3024fbdd74bfe86469e6eed3c82aa944725c07bf1\",\"artifact:3059:7f30f07fd331698ba1f61c4622f3b2aba4d633ecbeb0962d73586142b5a3ae0d\":\"7f30f07fd331698ba1f61c4622f3b2aba4d633ecbeb0962d73586142b5a3ae0d\",\"artifact:3059:90fcb6c243deccf19e5e75a11b5d9e7455f0215f4ea08fa66254b5fd4aea6d82\":\"90fcb6c243deccf19e5e75a11b5d9e7455f0215f4ea08fa66254b5fd4aea6d82\",\"artifact:3059:92570a1940a6fa8b82881efccb7fb4151e121dbdc6aa956c5a1f838749bd6532\":\"92570a1940a6fa8b82881efccb7fb4151e121dbdc6aa956c5a1f838749bd6532\",\"artifact:3059:9837b6500a99fc3b8a3bb10355cc72afedbb3f9dc6657f560573b9aee7be51f1\":\"9837b6500a99fc3b8a3bb10355cc72afedbb3f9dc6657f560573b9aee7be51f1\",\"artifact:3059:c846405a065d540f93b4eaca47b6e8c2364bd864013aaecc41dd1e07d56577ff\":\"c846405a065d540f93b4eaca47b6e8c2364bd864013aaecc41dd1e07d56577ff\",\"artifact:3059:d4095e11e2d864ba8b27ce699e837bac9856edede25911517345913e5745fff4\":\"d4095e11e2d864ba8b27ce699e837bac9856edede25911517345913e5745fff4\"},\"sha256\":\"95761b20cd701f196719a498ca0f66743c087ca2d50fc0110c56feec27f32df7\"},\"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:3059,input_sha256:\"6038faf5c974c720dec7362d3340a9e6ea6528cd21ea4ef0b19730a92a2b46f7\",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/3290/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"f096c417b2d12f66ba16fd5186bf72662845dc399c92d9fa1ea861b85880a323","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}