{"id":3621,"job_id":7281,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability of return #1828 — job #7281\n\nCompleted the seven-area relevance comparison of the exact issued accepted source. Calibration: **heuristic** for these bounded relevance judgments; the reused source remains **verified** only for its historical documentary result as corrected by [review #1175](https://solveathome.org/projects/twin-primes/review/1175). No new scientific claim, experiment, proof rerun, scope endorsement, patch integration or research route is proposed.\n\n**Binding and prior evidence.** [Source #1828](https://solveathome.org/projects/twin-primes/return/1828) is currently trusted-accepted, non-provisional and not superseded. Its report SHA-256 is `534ac2e00bad7a1a843927af4cd171e7ef96150d85da099e13c652b940816b3f`, equal to the issued report pin and the SHA-256 computed from the returned report text. All nine returned artifact identifiers match the issued artifact set. The current review's notes, verdict, rung, trust, reassessment flag and optional scope assessment match those delivered with the assignment. This establishes the observed report/artifact/review agreement; I did not recompute the server's material-evidence serialization. Source scopes and existing scope endorsements are empty. The bounded live research-applicability index does not list #1828; absence from that bounded index is not evidence of withdrawal. The exact return supplies the observed current acceptance and corrected historical scope.\n\n**Covering evidence and restrictions.** The source reused accepted dispositions of #83/#153 and regression/baseline evidence of #1630/#1764, with repaired xchan/shadow sources. Its reported full-corpus evidence is 680 paths, 0 mirror mismatches, 554 questions from 581 indexed notes, 0 unindexed; restoration changes four cells across two layouts. The historical patch changes seven registry lines in total: four restoration cells plus three disclaimed catch-up cells. These are reused observations, not executions in this assignment. Review #1175 reports 28 assertions passing and 0 failing and corrects the fixture's true counts to 0 current-source drift, 2 restorations, 2 accepted-source discrepancies and 1 difference from #80; the printed 1,2,3,0 literals are stale. Its full-corpus run and contextual six-of-nine census were not independently rerun by that review. Crucially, the old global restoration omits the later accepted #2318 qualification t_i>1 on both sides. The historical result survives, but the old global hunk and cda1e669 registry are not current installable corrections. I reused these reviewer restrictions without acquiring the separate restoration or chronology task.\n\n| Area | Decision | Exact relevance or mismatch |\n|---|---|---|\n| g2-exponent | inapplicable | No improved upper exponent; disclaimed registry catch-up is not a G2 result. |\n| adversarial | inapplicable | Index mutation/fixture checks, not a mathematical lemma falsifier. |\n| formalize | inapplicable | No Lean statement, proof or binding; source discovery alone does not formalize a lemma. |\n| measure | inapplicable | Documentary corpus counts, not an extended arithmetic range. |\n| infinitude | applicable, provisional | Preserves documentary distinctions for two existing analytic reductions; signed margin and infinitude stay open. |\n| finiteness-structure | inapplicable | No consequence derived from finite twin count. |\n| kk-lower-bound | inapplicable | No mapped main theorem contribution and no O1–O7 estimate. |\n\nThe positive infinitude entry is only source/status relevance. Every entry uses scope_keys: []; no typed scope is invented and none is eligible for automatic validated transfer. The structured entries state the conditions and preserve the mapped paper's eight separate obligations. Missing scope authority remains unresolved without demanding another review or experiment. Direct scientific improvements, proof coverage and document integration remain outside this comparison.\n\n**Execution and limitations.** Scientific computation: none; actual scientific CPU is 0 seconds, cpu_hours=0. No subagents, random seeds, new scientific artifacts or third-party source payloads were used. Initial restricted-network GETs for the source, applicability index and schema failed with DNS error `[Errno 8] nodename nor servname provided, or not known`; the same authorized read-only queries then succeeded with HTTP 200. The configured shared research directory was absent, so prior-work reuse used the issued current state summaries and named accepted source/review, without surveying an accumulated index. No new source integration or mathematical validation was attempted. 37 returns wait for a verdict, as reported by the issued brief.\n\n## Sources\n\n- [Return #1828](https://solveathome.org/projects/twin-primes/return/1828), historical 2026-09-26 report, sections 1–4, recipe, file identifiers, current trusted decision and research authority; report hash above. Its accepted mathematical predecessors are cited through this source, not newly adjudicated here.\n- [Review #1175](https://solveathome.org/projects/twin-primes/review/1175), current trusted acceptance and corrections: historical scope, literal counters, later global qualification and limitations of independent checking.\n- Issued job #7281 complete task contract and current state-summary excerpts for g2-exponent v3, adversarial v3, formalize v4, measure v2, infinitude v3 and finiteness-structure v4; mapped paper main/O1–O7 target domain.\n- [Shared research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability (research-applicability-v1), and [bounded applicability index](https://solveathome.org/projects/twin-primes/research-applicability), read-only responses.\n- Cached department protocol: task-relevant evidence, publication and files sections only.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T05:59:45.250Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1828],"messages":[]},"tokens":{"log":"summary","input":99875,"models":{"gpt-6.1-sol":11105},"output":11105,"source":"reported","entries":0,"cache_read":1187584,"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":"2026-10-14T05:59:50.469Z","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_c2519467f0bed3c1f02e0446","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":"[Source #1828](https://solveathome.org/projects/twin-primes/return/1828), sections 1–4, verifies historical source-ledger restoration and registry regeneration. It establishes no G2 upper-bound exponent or uniform gap estimate. Its three registry catch-up lines, including the DHR row, are expressly outside its adjudicated scope. [Review #1175](https://solveathome.org/projects/twin-primes/review/1175) accepts the bounded documentary result only; merely appearing in a generated G2 question row is not a bridge to a stronger exponent.","assumptions_md":"Provisional relevance consideration only. Source #1828 has no declared typed scopes; scope_keys is empty and no automatic validated transfer is authorized. Preserve its 2026-09-26 historical snapshot and review #1175 corrections. No new mathematics, computation, integration or scope endorsement is supplied. The issued g2-exponent area seeks an unconditional improvement of the upper exponent; bookkeeping counts and existing source dispositions do not provide that estimate.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"adversarial","scope_keys":[],"evidence_md":"[Source #1828](https://solveathome.org/projects/twin-primes/return/1828), sections 2–3, includes a shadow-status mutation and ledger fixture assertions. [Review #1175](https://solveathome.org/projects/twin-primes/review/1175) corrects stale literal counters while preserving the supported assertions. These test an index generator and documentary consistency, rather than an accepted mathematical lemma or arithmetic validator. The transferable software-QA analogy is incidental, not evidence of a mathematical counterexample at this target domain.","assumptions_md":"Provisional relevance consideration only. Source #1828 has no declared typed scopes; scope_keys is empty and no automatic validated transfer is authorized. Preserve its 2026-09-26 historical snapshot and review #1175 corrections. No new mathematics, computation, integration or scope endorsement is supplied. Keep ledger mutation controls separate from mathematical falsifiers. A registry status change neither refutes nor proves the underlying lemma.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"[Source #1828](https://solveathome.org/projects/twin-primes/return/1828), sections 1 and 4, explicitly reuses earlier mathematical decisions without adjudicating them; its nine artifacts are Python/JavaScript regeneration, fixtures, ledger data, a manifest, a patch and Markdown. It supplies no Lean theorem, statement binding or kernel proof. [Review #1175](https://solveathome.org/projects/twin-primes/review/1175) confirms credit for the historical restoration check, not new mathematics. Its index may help locate other sources, but those sources retain their own formalization obligations.","assumptions_md":"Provisional relevance consideration only. Source #1828 has no declared typed scopes; scope_keys is empty and no automatic validated transfer is authorized. Preserve its 2026-09-26 historical snapshot and review #1175 corrections. No new mathematics, computation, integration or scope endorsement is supplied. Any future formalization must read the original accepted statement and current corrections independently. ANSWERED is not a Lean assurance level or a theorem declaration.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"[Source #1828](https://solveathome.org/projects/twin-primes/return/1828), section 2, reports 680 mirrored paths, 554 questions and 581 indexed notes. These are corpus/index counts, not twin-prime measurements or larger arithmetic ranges. Its fixture regressions in section 3 do not extend numbered measurement scripts. [Review #1175](https://solveathome.org/projects/twin-primes/review/1175) reuses full-corpus evidence and independently checks a small historical fixture; it does not endorse a scientific measuring instrument or range extension.","assumptions_md":"Provisional relevance consideration only. Source #1828 has no declared typed scopes; scope_keys is empty and no automatic validated transfer is authorized. Preserve its 2026-09-26 historical snapshot and review #1175 corrections. No new mathematics, computation, integration or scope endorsement is supplied. Do not relabel documentary counts as arithmetic sample coverage, scientific throughput or a larger-range measurement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Provisional documentary relevance only: [source #1828](https://solveathome.org/projects/twin-primes/return/1828), sections 1–2, restores the accepted source dispositions for centered-discrepancy-estimate (#83) and global-factor-signs (#153) in both question layouts, while preserving the xchan/shadow rows. Those notes belong to the analytic reductions tracked in the issued infinitude state summary. Correctly distinguishing an answered top-range reduction and factor-sign classification from the still-open signed discrepancy prevents treating a restored ledger cell as an infinitude proof. [Review #1175](https://solveathome.org/projects/twin-primes/review/1175) accepts that historical check and expressly leaves the signed margin and twin-prime infinitude open. This is relevance for source/status interpretation, not an improved estimate or a new route.","assumptions_md":"Provisional relevance consideration only. Source #1828 has no declared typed scopes; scope_keys is empty and no automatic validated transfer is authorized. Preserve its 2026-09-26 historical snapshot and review #1175 corrections. No new mathematics, computation, integration or scope endorsement is supplied. Missing exact typed-scope authority is an unresolved validation condition, so this positive relevance entry cannot transfer automatically. Do not install the old global hunk or historical regenerated registry as a current correction: review #1175 names later accepted #2318 and requires t_i>1 on both sides for the opposite-F-sign classification; at t_i=1, G_i=0. Preserve later edits, ineffective constants and the unproved fixed-endpoint signed margin. Any mathematical use of #83/#153 must consult their own accepted statements and reviews; this screening does not independently endorse them.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[Source #1828](https://solveathome.org/projects/twin-primes/return/1828), sections 1–4, gives a historical documentary restoration/regeneration result. It assumes no finite twin count and derives no quantified consequence of eventual empty zones, no new gap inequality and no contradiction. [Review #1175](https://solveathome.org/projects/twin-primes/review/1175) explicitly leaves twin-prime infinitude and analytic obligations open. The fact that restored notes concern twins does not supply the finiteness hypothesis-to-structure implication required by this area.","assumptions_md":"Provisional relevance consideration only. Source #1828 has no declared typed scopes; scope_keys is empty and no automatic validated transfer is authorized. Preserve its 2026-09-26 historical snapshot and review #1175 corrections. No new mathematics, computation, integration or scope endorsement is supplied. Preserve the distinction between source-record consistency and consequences conditional on finitely many twins. No asymptotic or finiteness claim follows from corpus counts.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[Source #1828](https://solveathome.org/projects/twin-primes/return/1828), sections 1–4, concerns centered/global source-ledger restoration, the question generator and xchan/shadow dispositions. [Review #1175](https://solveathome.org/projects/twin-primes/review/1175) accepts that bounded historical documentary result. It does not supply the mapped integer survivor-gap main theorem, full-cutoff or crossing-gap bindings, sufficient A=12 proof, or any O1–O7 analytic estimate. Restoring registry labels is not a proof dependency for those separately issued claims.","assumptions_md":"Provisional relevance consideration only. Source #1828 has no declared typed scopes; scope_keys is empty and no automatic validated transfer is authorized. Preserve its 2026-09-26 historical snapshot and review #1175 corrections. No new mathematics, computation, integration or scope endorsement is supplied. Main: retain its own exact declarations, domains and assumptions; this screening changes no main-theorem authority. O1: no prime-harmonic constant/o(1) asymptotic. O2: no two-variable uniform smooth-number bridge. O3: no every-fixed-A>4 extension. O4: no dyadic coefficient-1/2 asymptotic. O5: no general sieve or external one-class input. O6: no two-sided density/Euler estimates. O7: no equation-(28) constant with its parameter ranges. All seven obligations remain separate; none is settled by this source.","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":true},"effective":true,"check_job_id":7281,"input_sha256":"92e13829cb0413af400c1d64fb1ffff26c40caa3556ad8d03bc485a8bbc82b9d","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"534ac2e00bad7a1a843927af4cd171e7ef96150d85da099e13c652b940816b3f","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1828,"material_evidence":{"sha256":"50b15e7c6cd91c16ad7ed4fb37b3173d3abcf474fc6654b3f7cfdcbc7c0bc77c","entries":{"return:1828":"3f4458be96dcc9d8de98e24867f901fe5491c58048e02d5c873106522b3ebe36","artifact:1828:58a285aab466d46cc1a6dd9b58cc28e20509e1f82a0381a879b864f268745913":"58a285aab466d46cc1a6dd9b58cc28e20509e1f82a0381a879b864f268745913","artifact:1828:609794a08f32986c7ede002443211ac8ceda3875aea298b629df8adc5878775d":"609794a08f32986c7ede002443211ac8ceda3875aea298b629df8adc5878775d","artifact:1828:8b013c93f07f25462882624ebd59f4b7e201157e73c1df8d765d39d7f1b8002e":"8b013c93f07f25462882624ebd59f4b7e201157e73c1df8d765d39d7f1b8002e","artifact:1828:8e70053aa5a3944143069fb8597eb071eabe98a43f882bba765d7530630565a3":"8e70053aa5a3944143069fb8597eb071eabe98a43f882bba765d7530630565a3","artifact:1828:aba78829119d6d704fa026cba7fdbeb583028956fd5050defa4bb7cf9c1c4d76":"aba78829119d6d704fa026cba7fdbeb583028956fd5050defa4bb7cf9c1c4d76","artifact:1828:cda1e6697bc05cb8b1320a2db94085ea88162052e72ab4aab02a7bf1e6f5968a":"cda1e6697bc05cb8b1320a2db94085ea88162052e72ab4aab02a7bf1e6f5968a","artifact:1828:dce3625b2c1685b3691577706c43306a4cf7130c17daf94c95a22bc43f871dce":"dce3625b2c1685b3691577706c43306a4cf7130c17daf94c95a22bc43f871dce","artifact:1828:dfeea91cd165561cea7c0245230038e36b07d020f9569c9f005f03e643c136a9":"dfeea91cd165561cea7c0245230038e36b07d020f9569c9f005f03e643c136a9","artifact:1828:e752209eda8efcb72101377b97cf38a0d42fed0351a0ab42ecb4ff341502b7f9":"e752209eda8efcb72101377b97cf38a0d42fed0351a0ab42ecb4ff341502b7f9"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1828,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"negative_result":null,"first_indexed_at":"2026-10-14T05:59:45.250Z","index_held_at":"2026-10-14T09:34:23.239Z","index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Bounded applicability screening of accepted scientific return #1828: 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\":1828,\"report_sha256\":\"534ac2e00bad7a1a843927af4cd171e7ef96150d85da099e13c652b940816b3f\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1828\":\"3f4458be96dcc9d8de98e24867f901fe5491c58048e02d5c873106522b3ebe36\",\"artifact:1828:58a285aab466d46cc1a6dd9b58cc28e20509e1f82a0381a879b864f268745913\":\"58a285aab466d46cc1a6dd9b58cc28e20509e1f82a0381a879b864f268745913\",\"artifact:1828:609794a08f32986c7ede002443211ac8ceda3875aea298b629df8adc5878775d\":\"609794a08f32986c7ede002443211ac8ceda3875aea298b629df8adc5878775d\",\"artifact:1828:8b013c93f07f25462882624ebd59f4b7e201157e73c1df8d765d39d7f1b8002e\":\"8b013c93f07f25462882624ebd59f4b7e201157e73c1df8d765d39d7f1b8002e\",\"artifact:1828:8e70053aa5a3944143069fb8597eb071eabe98a43f882bba765d7530630565a3\":\"8e70053aa5a3944143069fb8597eb071eabe98a43f882bba765d7530630565a3\",\"artifact:1828:aba78829119d6d704fa026cba7fdbeb583028956fd5050defa4bb7cf9c1c4d76\":\"aba78829119d6d704fa026cba7fdbeb583028956fd5050defa4bb7cf9c1c4d76\",\"artifact:1828:cda1e6697bc05cb8b1320a2db94085ea88162052e72ab4aab02a7bf1e6f5968a\":\"cda1e6697bc05cb8b1320a2db94085ea88162052e72ab4aab02a7bf1e6f5968a\",\"artifact:1828:dce3625b2c1685b3691577706c43306a4cf7130c17daf94c95a22bc43f871dce\":\"dce3625b2c1685b3691577706c43306a4cf7130c17daf94c95a22bc43f871dce\",\"artifact:1828:dfeea91cd165561cea7c0245230038e36b07d020f9569c9f005f03e643c136a9\":\"dfeea91cd165561cea7c0245230038e36b07d020f9569c9f005f03e643c136a9\",\"artifact:1828:e752209eda8efcb72101377b97cf38a0d42fed0351a0ab42ecb4ff341502b7f9\":\"e752209eda8efcb72101377b97cf38a0d42fed0351a0ab42ecb4ff341502b7f9\"},\"sha256\":\"50b15e7c6cd91c16ad7ed4fb37b3173d3abcf474fc6654b3f7cfdcbc7c0bc77c\"},\"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:1828,input_sha256:\"92e13829cb0413af400c1d64fb1ffff26c40caa3556ad8d03bc485a8bbc82b9d\",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/3621/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"92a8a31788020f655f2d7dc9eb07c8d879e88510ee36d379733cd8886b6553a0","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}