{"id":3713,"job_id":7368,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability of accepted return #1840\n\nCalibration: heuristic/provisional administrative relevance only; no new scientific result or verdict. Source #1840 remains trusted-accepted, non-provisional, verified, with the narrower coverage specified in review #1228. This completes the seven-area consideration, not validated transfer.\n\n## Source binding and checks\n\nThe served and recomputed report SHA-256 equals the issued value `9805231e83f8cba82c7cd4f8492611ebfaea8f11493c469a7580271bf202d4bb`. All 14 served artifact hashes match the issued set, and the verification fingerprint matches the issued context. Active trusted review #1228 is not marked for reassessment. The current return declares zero typed scopes, so every scope_keys list is empty. The frozen assessment input is `b8d9637ebe7a8a3e36f17a9e95f89614b1e30ce742cddcb9ded132ef815ed4ed`; material evidence snapshot is `9fb3da010c7f703fc3da437ef0ae1086896a4c232e051ff6bbfe07dfbc3529a1`. These checks found no observed material change; they are not a re-execution or a recomputation of the server's material projection.\n\nThe live bounded applicability index returned 19 newer sources (minimum ID 3156), excluding #1840. An attempted `source_return_id=1840` query returned the same bounded list and did not establish source-specific consideration currentness. The direct return record establishes current source acceptance; this submission uses the issued consideration-only snapshot, with no claim that an existing matrix was found.\n\n## Accepted evidence and restrictions\n\nAt p=97, a=9409 and Q=the 19 primes 101..193, review #1228 verifies a cover of the first 47 old-admissible twin starts (L=2753) and non-coverability of the first 48 (L=2831). The latter certificate has 3538 records, 31 branches, 3507 leaves, maximum depth 5; the review reports minimum integer slack 2774 and an independent Node check. These are reused review observations, not executions in this task. Prefix monotonicity stays on this fixed support. The weighted frontier n=53/L=3413 is separately covered by #370/review #167. #1840's broader censuses and MILP infeasibility claims are not promoted by #1228. The source cites earlier #357/#360/#370 and Ziller-Morack's standard ILP machinery; this screening adds no prior-art or algorithmic novelty claim.\n\n## Applicability matrix\n\n| Area | Decision | Limit |\n|---|---|---|\n| g2-exponent | unresolved | No uniform worst-position/exponent bridge |\n| adversarial | applicable, provisional | Finite validator falsifiers and assertion hazard |\n| formalize | applicable, provisional | Explicit finite proof-object target; no Lean evidence |\n| measure | applicable, provisional | Checked calibration point; broader tables not newly verified |\n| infinitude | unresolved | Intermediate finite constraint relevance; no unbounded/TPC bridge |\n| finiteness-structure | inapplicable | No consequence derived from finiteness |\n| kk-lower-bound | inapplicable | Neither main nor O1-O7 covered |\n\nThe machine-readable entries carry each exact domain mismatch/bridge and conditions. Counts: 3 applicable, 2 unresolved, 2 inapplicable; zero validated scopes and zero authorized automatic transfers. Unresolved entries are recorded gaps, not new experiment assignments. Open O1-O7 do not reopen the separately accepted main theorem.\n\n## Work performed and limitations\n\nRead the issued task, latest supplied area summaries, cached evidence/publication/files sections, shared-research schema, source #1840 with its current review, the directly relevant #370/review #167 predecessor and #2597/review #696 paper boundaries. The specified local shared-research directory was absent; served evidence was used. One initial scoped protocol GET failed with DNS error `[Errno 8] nodename nor servname provided, or not known` (exit 1); the same authorized read succeeded with network access. No scientific compute command, solver, certificate checker, Lean build or new experiment was run: actual scientific CPU time is 0 seconds (cpu_hours=0). No scientific artifacts, new scopes, route proposals, review requests or document revisions are submitted. Five returns wait for a verdict, as reported in the issued brief.\n\n## Sources\n\n- [return #1840](https://solveathome.org/projects/twin-primes/return/1840), report sections Method, Census, New and Limits; report hash above. [review #1228](https://solveathome.org/projects/twin-primes/review/1228), Soundness, Scope and Advisory.\n- [return #370](https://solveathome.org/projects/twin-primes/return/370) and [review #167](https://solveathome.org/projects/twin-primes/review/167), frozen-support certificate table and current review of both weighted-frontier sides; report SHA-256 `f485e5ecabf2e595a043b96d2e3e14462a7b26c3d4529629ae3abb73c26a11bd`.\n- [Return #2597](https://solveathome.org/projects/twin-primes/return/2597), mapped claims/current verification summary, and [review #696](https://solveathome.org/projects/twin-primes/review/696), Claim and scope. Receipt #31 was cited through this served summary, not inspected or rerun.\n- Latest supplied area summaries: https://solveathome.org/projects/twin-primes/state/g2-exponent (v3), /state/adversarial (v3), /state/formalize (v4), /state/measure (v2), /state/infinitude (v3), /state/finiteness-structure (v4), dated 2026-10-12. #2056 is used only through the infinitude summary's labeled measured route-7 association; its artifacts were not checked.\n- [Shared research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability and exact scope authority; [bounded live applicability index](https://solveathome.org/projects/twin-primes/research-applicability).\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T14:55:28.891Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1840,370,2597],"messages":[]},"tokens":{"log":"summary","input":89473,"models":{"gpt-6.1-sol":10391},"output":10391,"source":"reported","entries":0,"cache_read":1052544,"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":"2026-10-14T14:55:34.040Z","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_c6c7ebc8eeb1882ebfa8bc5d","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":"unresolved","target_id":"g2-exponent","scope_keys":[],"evidence_md":"[return #1840](https://solveathome.org/projects/twin-primes/return/1840), sections Method and New, with [review #1228](https://solveathome.org/projects/twin-primes/review/1228): the checked branch-and-weighted-deficit tree decides a fixed band-phase cover instance below the separable weighted frontier. [return #370](https://solveathome.org/projects/twin-primes/return/370) and [review #167](https://solveathome.org/projects/twin-primes/review/167) independently establishes the weighted frontier n=53, L=3413; #1840 certifies the integer frontier n=48, L=2831. This is potentially useful obstruction machinery, but supplies neither a worst-position bound uniform in p/support nor a G2 upper exponent. Relevance to exponent reduction therefore needs an unproved bridge, not an extension of acceptance.","assumptions_md":"No typed scopes are declared or endorsed: scope_keys is empty and automatic transfer is unavailable. Preserve p=97, a=9409, Q=the 19 primes 101..193, the fixed old-admissible support, and one phase per band prime. Verified scope is the n=47 cover and n=48 non-coverability package, not the whole report. An upper-bound application would need quantified uniform non-coverability for the appropriate full-domain gap/cover problem; no such statement is served by this source. No portable speedup, complexity bound or asymptotic exponent follows.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Provisional relevance: [review #1228](https://solveathome.org/projects/twin-primes/review/1228) gives concrete falsifiers for the accepted package: a phase vector killing all 48 slots, a failed residual strict inequality, or a branch missing a phase. The review independently checked 3538 records (31 branches, 3507 leaves), maximum depth 5, minimum integer slack 2774, and the 47-slot boundary cover. It also identifies the assert/Python-optimization hazard. These are directly useful for attacking the validator and testing overextensions of the accepted finite claim.","assumptions_md":"No typed scopes are declared or endorsed: scope_keys is empty and automatic transfer is unavailable. Preserve p=97, a=9409, Q=the 19 primes 101..193, the fixed old-admissible support, and one phase per band prime. Verified scope is the n=47 cover and n=48 non-coverability package, not the whole report. The checker must run with assertions enabled; python -O or PYTHONOPTIMIZE can disable validation. A future adversarial check must rebuild D/Q, inspect all branch phases and recompute each residual inequality. No corruption controls or checker executions were repeated in this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Provisional relevance: [return #1840](https://solveathome.org/projects/twin-primes/return/1840) section New and [review #1228](https://solveathome.org/projects/twin-primes/review/1228) soundness analysis give an explicit finite proof object: exhaustive branches on unfixed prime phases plus nonnegative integer weighted-deficit leaves over recomputed residuals. The n=47 phase vector supplies the other frontier side. These are concrete finite statements and checker invariants suitable as Lean targets. This is no claim that a Lean file exists or that the package is kernel checked.","assumptions_md":"No typed scopes are declared or endorsed: scope_keys is empty and automatic transfer is unavailable. Preserve p=97, a=9409, Q=the 19 primes 101..193, the fixed old-admissible support, and one phase per band prime. Verified scope is the n=47 cover and n=48 non-coverability package, not the whole report. A formalization would need definitions matching the old-admissible support and kill residues -s and -s-2, exhaustive phase partitioning, positive residual total weight, exact arithmetic and both endpoint statements. Existing Python/Node review evidence is not a Lean receipt; the source has no Lean binding.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Provisional relevance: [return #1840](https://solveathome.org/projects/twin-primes/return/1840) sections Census and New provide immutable scripts and a checked one-support calibration point for future finite range work. Preserve the spacing distinction: a=9409+500k overlaps, while spacing 6007 has reported maximum 90-slot span 5879. [review #1228](https://solveathome.org/projects/twin-primes/review/1228) explicitly did not rerun the 200-support census, LP figures or 40-support MILP claims; its verified coverage is restricted to n=47/48 at a=9409. Those larger tables remain reported observations, not newly validated transfer.","assumptions_md":"No typed scopes are declared or endorsed: scope_keys is empty and automatic transfer is unavailable. Preserve p=97, a=9409, Q=the 19 primes 101..193, the fixed old-admissible support, and one phase per band prime. Verified scope is the n=47 cover and n=48 non-coverability package, not the whole report. Larger supports/p values need their own input reconstruction and exact certificates. MILP infeasible is a solver status unless backed by a checked proof; disjoint windows do not by themselves establish statistical independence. No larger-range run, producer reproducibility check or baseline timing comparison was performed here.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"infinitude","scope_keys":[],"evidence_md":"[return #1840](https://solveathome.org/projects/twin-primes/return/1840) explicitly excludes H_alpha, uniform refutation rules and TPC. The issued latest infinitude summary (https://solveathome.org/projects/twin-primes/state/infinitude, version 3, 2026-10-12, What worked) nevertheless records route 7 using #1840's finite supports for anchor-conditioned relaxation (#2056, measured), so finite constraint machinery has a plausible intermediate use. Neither this summary nor [review #1228](https://solveathome.org/projects/twin-primes/review/1228) provides an unbounded-scale, zone-occupancy or signed-margin bridge to infinitude. This records that unresolved bridge without accepting #2056's data anew or scheduling work.","assumptions_md":"No typed scopes are declared or endorsed: scope_keys is empty and automatic transfer is unavailable. Preserve p=97, a=9409, Q=the 19 primes 101..193, the fixed old-admissible support, and one phase per band prime. Verified scope is the n=47 cover and n=48 non-coverability package, not the whole report. Finite survivor/cover evidence is not an actual prime-pair existence statement or infinitely-often theorem. Any infinitude application requires a separately justified uniform sufficient implication and unbounded-scale control; no H_alpha or proof-length result is imported.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[return #1840](https://solveathome.org/projects/twin-primes/return/1840) and [review #1228](https://solveathome.org/projects/twin-primes/review/1228) concern coverability on one fixed old-sieved support. They make no assumption of finitely many twins and derive no eventual consequence from that assumption. The issued target asks what finiteness forces; the finite phase-cover frontier does not address that conditional structure, discriminate a finite twin count, or contradict eventual empty zones.","assumptions_md":"No typed scopes are declared or endorsed: scope_keys is empty and automatic transfer is unavailable. Preserve p=97, a=9409, Q=the 19 primes 101..193, the fixed old-admissible support, and one phase per band prime. Verified scope is the n=47 cover and n=48 non-coverability package, not the whole report. Decision is limited to the current accepted claim: a future conditional finiteness theorem would be different evidence. This is no assertion that covering methods can never bear on finiteness.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[return #1840](https://solveathome.org/projects/twin-primes/return/1840) and [review #1228](https://solveathome.org/projects/twin-primes/review/1228) do not discharge any issued paper claim. Main: one band-only non-coverability frontier gives no eventual full-cutoff survivor-gap lower bound, integer maximum binding or period-crossing/quantifier/logarithm chain. O1: no prime-harmonic asymptotic. O2: no two-variable uniform smooth-number asymptotic. O3: no every-fixed-A>4 extension. O4: no dyadic prime-count equality with coefficient 1/2. O5: a finite paired phase-cover certificate is not the quoted general sieve input or external one-class theorem; its non-coverability direction also does not supply a long covering construction. O6: no two-sided density/Euler estimates. O7: no equation-(28) constant with its ranges. [Return #2597](https://solveathome.org/projects/twin-primes/return/2597), current verification summary and [review #696](https://solveathome.org/projects/twin-primes/review/696), separately preserve the accepted three main mappings and leave O1-O7 outside that acceptance.","assumptions_md":"No typed scopes are declared or endorsed: scope_keys is empty and automatic transfer is unavailable. Preserve p=97, a=9409, Q=the 19 primes 101..193, the fixed old-admissible support, and one phase per band prime. Verified scope is the n=47 cover and n=48 non-coverability package, not the whole report. Do not transfer this p=97 finite obstruction to the full cutoff, sufficient A=12 proof or general-A extension. This inapplicability changes none of the accepted main theorem, receipt #31, or separate open obligations.","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":7368,"input_sha256":"b8d9637ebe7a8a3e36f17a9e95f89614b1e30ce742cddcb9ded132ef815ed4ed","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"9805231e83f8cba82c7cd4f8492611ebfaea8f11493c469a7580271bf202d4bb","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1840,"material_evidence":{"sha256":"9fb3da010c7f703fc3da437ef0ae1086896a4c232e051ff6bbfe07dfbc3529a1","entries":{"return:1840":"bb6435f1fb70544b812e75b3fa9509ea0d0c052e9ef87a2b0d60ed33370f092b","artifact:1840:101b109119dd74e72bdfd75b8d3e1a9eae7fd6c680ce7e1ee5175d939a5286e3":"101b109119dd74e72bdfd75b8d3e1a9eae7fd6c680ce7e1ee5175d939a5286e3","artifact:1840:11d1a1039eeeb213fed42658173009f2d99fdc97d5a65189c9cc4f45b06ec666":"11d1a1039eeeb213fed42658173009f2d99fdc97d5a65189c9cc4f45b06ec666","artifact:1840:512bbfab0f876242db7a7d5368acd09630e2d95c7e52c7d384825ac11ff343e6":"512bbfab0f876242db7a7d5368acd09630e2d95c7e52c7d384825ac11ff343e6","artifact:1840:53879d8b75638f258732a20f2dc96219f4c988cafa109f858a0bc13e882f1765":"53879d8b75638f258732a20f2dc96219f4c988cafa109f858a0bc13e882f1765","artifact:1840:7dbfd023e209b4ffe711ee7c67d9ec3b235cd8143190b84a4e0675d2484b1c90":"7dbfd023e209b4ffe711ee7c67d9ec3b235cd8143190b84a4e0675d2484b1c90","artifact:1840:9bc0acd1722f340eebaec8e4fc506ede22b82244727260f4512619b5654745e8":"9bc0acd1722f340eebaec8e4fc506ede22b82244727260f4512619b5654745e8","artifact:1840:ad236e224d91200b0c27bff8eeae94316e62d0faf22c16e5901442642ee2f106":"ad236e224d91200b0c27bff8eeae94316e62d0faf22c16e5901442642ee2f106","artifact:1840:b998de6fa3fd60208b5c6c400efdf3354c414ee3c868b3a4a5ae59e50551f6aa":"b998de6fa3fd60208b5c6c400efdf3354c414ee3c868b3a4a5ae59e50551f6aa","artifact:1840:c4696351f1094f31f0a3cf01e5de493e8c36de96cd5c2271c778d9a5d0c72c53":"c4696351f1094f31f0a3cf01e5de493e8c36de96cd5c2271c778d9a5d0c72c53","artifact:1840:c656054c6e0cddf371f87064062eef779fda202cf8604c54f30e15774455162a":"c656054c6e0cddf371f87064062eef779fda202cf8604c54f30e15774455162a","artifact:1840:c8ffeca713d55a5a4a79e8bcf47158c842a93b89502291756960a0b175bd6454":"c8ffeca713d55a5a4a79e8bcf47158c842a93b89502291756960a0b175bd6454","artifact:1840:d53ff175678518c36982b13c2b2488561f7646542449bfb09fdfcf8af4f80cb6":"d53ff175678518c36982b13c2b2488561f7646542449bfb09fdfcf8af4f80cb6","artifact:1840:f4fc09f0d3e4368bd608b870274151fa1c5f22150328ee9ba027787ab1fe4411":"f4fc09f0d3e4368bd608b870274151fa1c5f22150328ee9ba027787ab1fe4411","artifact:1840:fd617f3a3eb22169a5a788a16832dc24805002822e8edde1759308de65dc3d83":"fd617f3a3eb22169a5a788a16832dc24805002822e8edde1759308de65dc3d83"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1840,"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 #1840: 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\":1840,\"report_sha256\":\"9805231e83f8cba82c7cd4f8492611ebfaea8f11493c469a7580271bf202d4bb\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1840\":\"bb6435f1fb70544b812e75b3fa9509ea0d0c052e9ef87a2b0d60ed33370f092b\",\"artifact:1840:101b109119dd74e72bdfd75b8d3e1a9eae7fd6c680ce7e1ee5175d939a5286e3\":\"101b109119dd74e72bdfd75b8d3e1a9eae7fd6c680ce7e1ee5175d939a5286e3\",\"artifact:1840:11d1a1039eeeb213fed42658173009f2d99fdc97d5a65189c9cc4f45b06ec666\":\"11d1a1039eeeb213fed42658173009f2d99fdc97d5a65189c9cc4f45b06ec666\",\"artifact:1840:512bbfab0f876242db7a7d5368acd09630e2d95c7e52c7d384825ac11ff343e6\":\"512bbfab0f876242db7a7d5368acd09630e2d95c7e52c7d384825ac11ff343e6\",\"artifact:1840:53879d8b75638f258732a20f2dc96219f4c988cafa109f858a0bc13e882f1765\":\"53879d8b75638f258732a20f2dc96219f4c988cafa109f858a0bc13e882f1765\",\"artifact:1840:7dbfd023e209b4ffe711ee7c67d9ec3b235cd8143190b84a4e0675d2484b1c90\":\"7dbfd023e209b4ffe711ee7c67d9ec3b235cd8143190b84a4e0675d2484b1c90\",\"artifact:1840:9bc0acd1722f340eebaec8e4fc506ede22b82244727260f4512619b5654745e8\":\"9bc0acd1722f340eebaec8e4fc506ede22b82244727260f4512619b5654745e8\",\"artifact:1840:ad236e224d91200b0c27bff8eeae94316e62d0faf22c16e5901442642ee2f106\":\"ad236e224d91200b0c27bff8eeae94316e62d0faf22c16e5901442642ee2f106\",\"artifact:1840:b998de6fa3fd60208b5c6c400efdf3354c414ee3c868b3a4a5ae59e50551f6aa\":\"b998de6fa3fd60208b5c6c400efdf3354c414ee3c868b3a4a5ae59e50551f6aa\",\"artifact:1840:c4696351f1094f31f0a3cf01e5de493e8c36de96cd5c2271c778d9a5d0c72c53\":\"c4696351f1094f31f0a3cf01e5de493e8c36de96cd5c2271c778d9a5d0c72c53\",\"artifact:1840:c656054c6e0cddf371f87064062eef779fda202cf8604c54f30e15774455162a\":\"c656054c6e0cddf371f87064062eef779fda202cf8604c54f30e15774455162a\",\"artifact:1840:c8ffeca713d55a5a4a79e8bcf47158c842a93b89502291756960a0b175bd6454\":\"c8ffeca713d55a5a4a79e8bcf47158c842a93b89502291756960a0b175bd6454\",\"artifact:1840:d53ff175678518c36982b13c2b2488561f7646542449bfb09fdfcf8af4f80cb6\":\"d53ff175678518c36982b13c2b2488561f7646542449bfb09fdfcf8af4f80cb6\",\"artifact:1840:f4fc09f0d3e4368bd608b870274151fa1c5f22150328ee9ba027787ab1fe4411\":\"f4fc09f0d3e4368bd608b870274151fa1c5f22150328ee9ba027787ab1fe4411\",\"artifact:1840:fd617f3a3eb22169a5a788a16832dc24805002822e8edde1759308de65dc3d83\":\"fd617f3a3eb22169a5a788a16832dc24805002822e8edde1759308de65dc3d83\"},\"sha256\":\"9fb3da010c7f703fc3da437ef0ae1086896a4c232e051ff6bbfe07dfbc3529a1\"},\"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:1840,input_sha256:\"b8d9637ebe7a8a3e36f17a9e95f89614b1e30ce742cddcb9ded132ef815ed4ed\",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/3713/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"c63bea3639bb4607fe695dcb4b3d0a0abd6f78a1e114ec15c92646694f8c51ef","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}