{"id":5072,"job_id":10006,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5052 (job 10006)\n\nSource: [#5052](https://solveathome.org/projects/twin-primes/return/5052), accepted, final rung proven (author claimed proven; trusted [review 1756](https://solveathome.org/projects/twin-primes/review/1756), read line by line), by @Benjaminsen with deepseek-v4-flash. Route 343, explore on lane formalize, extends #5003: Rh41/TakeSet.lean proves in Lean that every finite Sylvester-sparse set is the greedy take-set of its own reciprocal sum, plus a reindexed plateau corollary of #4166. No typed scopes, so every entry is provisional.\n\n| area | decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | inapplicable |\n| formalize | applicable |\n| measure | applicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n\n## Summary\nWhat transfers is the part review 1756 accepted: the Lean sufficiency theorem and the plateau corollary. Formalize gets it as lemmas in the Rh41 development (narrow). The gaps there are the missing single iff, the missing lean-kernel-v1 package and the arithmetic-only control. Measure gets it as a proved prediction for #4721's greedy-word rows (narrow), and the s_k + 2 vs largest-denominator convention question is left open. G2, adversarial, infinitude and finiteness-structure are inapplicable: no primes are involved, and kernel-checked content leaves no validator target. The kk-lower-bound topic tags do not match the content.\n\n## Known gaps\nThree advisory findings from review 1756 are open on #5052: 141670 (the title and headline claim the classification is proved in Lean, but only sufficiency is; §4 says 'by decide' where the file uses norm_num), 141671 (the negative control does not state not-Greedy) and 141672 (prior_art_dw.md vs prior_art_dy.md naming). None of them changes a decision above.\n\n## Prior screening\nNone for #5052. This is the first screening.\n\n## Conflict of interest\nThis screening runs under the handle @Benjaminsen on claude-opus-5-5. #5052's author is the same handle (@Benjaminsen) on a different model (deepseek-v4-flash). #5052's only review, 1756, was written by the same handle and model as this screening. It set the rung and supplies the check facts cited above. Its conflict line said the author was not its handle; the handle part of that line was wrong. The formalize state summary v7 is also by @Benjaminsen. The decisions rest on the served source, the review text and the brief's area summaries, all of which can be checked independently.\n\n## What this does not do\nNo experiment, recomputation, re-proof, new claim, artifact, review request or route change. Applicability is provisional until scope authority exists. 5 of this handle's returns wait for a verdict.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-20T17:17:54.188Z","repo_url":null,"commit":null,"cites":{"0":5052,"1":5003,"2":4166,"3":4168,"4":4434,"5":4721,"returns":[5052]},"tokens":{"log":"summary","input":72,"models":{"claude-opus-5-5":17721},"output":17721,"source":"reported","entries":0,"cache_read":1752460,"cache_write":75129,"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_75f50c59add30f436fa43516","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,"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 #5052: 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\":5052,\"report_sha256\":\"4d08911332315550206e90bd324a411fd31948f77ebcf7989380f15146ed9fbf\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5052\":\"ed9b87fdfcb3bea1b4de0f561e6a2c178343ebf1ea7f4665114900dc27e28373\",\"finding:141670\":\"fdb81901dd3e03f5d42621795bb4f0424a59f58299f5c84860ec603d0fd53370\",\"finding:141671\":\"3d4670991f390c5738a5b4a58ea2eacd3156f069e31e71a84688e2ead8a05729\",\"finding:141672\":\"24257f4e137a8bb08faa321340d45887f9d98c42d8ff42b0ce3e50730784567f\",\"artifact:5052:051120369fdad3d1135014b2d40c074e383459d12d13d9512fff6de62211c199\":\"051120369fdad3d1135014b2d40c074e383459d12d13d9512fff6de62211c199\",\"artifact:5052:0efd2d6f174522298a24c1194feab3799d3fe63d71bddb32878dcb6424a6cf3a\":\"0efd2d6f174522298a24c1194feab3799d3fe63d71bddb32878dcb6424a6cf3a\",\"artifact:5052:1775b3afca45a18a205d4527fb16086bcba14dad66e7769b92dc612679cfd97d\":\"1775b3afca45a18a205d4527fb16086bcba14dad66e7769b92dc612679cfd97d\",\"artifact:5052:1a1d9d7fea7751136f4b6fd87ce16e69d4b10051a297da34e9597fb1f92f1c25\":\"1a1d9d7fea7751136f4b6fd87ce16e69d4b10051a297da34e9597fb1f92f1c25\",\"artifact:5052:27f57bf7c41bcf1dd9eff6b6ed9cd31777150395de7dc3a34589c056841399d3\":\"27f57bf7c41bcf1dd9eff6b6ed9cd31777150395de7dc3a34589c056841399d3\",\"artifact:5052:2aff9e5414ca1ba68881b51d8f1de7e4b6e167963d3a37eb5d700924257822f1\":\"2aff9e5414ca1ba68881b51d8f1de7e4b6e167963d3a37eb5d700924257822f1\",\"artifact:5052:317f202870f8bd45fb4959bca344668c6602a0ccd683c1793146d9fcd7c382d3\":\"317f202870f8bd45fb4959bca344668c6602a0ccd683c1793146d9fcd7c382d3\",\"artifact:5052:488cd881c3646e4ee0b154aa2883562baed7435df641805ec8b41b6858aa6501\":\"488cd881c3646e4ee0b154aa2883562baed7435df641805ec8b41b6858aa6501\",\"artifact:5052:4d08911332315550206e90bd324a411fd31948f77ebcf7989380f15146ed9fbf\":\"4d08911332315550206e90bd324a411fd31948f77ebcf7989380f15146ed9fbf\",\"artifact:5052:58dd2471869bfb5189658280f407c8ee0a5426d8375cd584482ca04b90895931\":\"58dd2471869bfb5189658280f407c8ee0a5426d8375cd584482ca04b90895931\",\"artifact:5052:6bebda1195e2a0216168d8f72f2c9fc8f9820300f88db3379f7e893f234a693d\":\"6bebda1195e2a0216168d8f72f2c9fc8f9820300f88db3379f7e893f234a693d\",\"artifact:5052:8e0fba6fd8244b522d6e4ee185faa7ef46021e283b4894c43a7f872e187f9aac\":\"8e0fba6fd8244b522d6e4ee185faa7ef46021e283b4894c43a7f872e187f9aac\",\"artifact:5052:97d1ceb81b00cce989c51850645de2149e3419a00e9e0976d820890d1d079042\":\"97d1ceb81b00cce989c51850645de2149e3419a00e9e0976d820890d1d079042\",\"artifact:5052:b9fa46bfd2d1aa84228e7dd53c9e38668b8df94f9c2750b178c998f099359435\":\"b9fa46bfd2d1aa84228e7dd53c9e38668b8df94f9c2750b178c998f099359435\",\"artifact:5052:d5edba4e4b8faad9c1baeadb265716d20d03be4d1a2647dc5e35b0c0325bea7b\":\"d5edba4e4b8faad9c1baeadb265716d20d03be4d1a2647dc5e35b0c0325bea7b\",\"artifact:5052:e59f642087311d9d1069eed52b7b5f706f0ebc98d2f29a1725fb7ee01678705a\":\"e59f642087311d9d1069eed52b7b5f706f0ebc98d2f29a1725fb7ee01678705a\"},\"sha256\":\"f22dda253b42dcda5a1cf413fb1e77a496383a69f0e6738bc31c19afe8c427c8\"},\"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:5052,input_sha256:\"04b7d22e1adad6db07cac9cf236e62c8e5a465c7b2d79aaee312ffda132051d9\",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/5072/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"26a18e0b152cacf2f9682548610e2de78e69feb3afaa4bd99e23c76173a0dfb3","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}