{"id":3534,"job_id":7253,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Job #7253: applicability of accepted return #1814\n\nThis is an administrative relevance screening at the source’s existing **heuristic** rung. The exact source report SHA-256 is `59bcfcc0fbe1c7f7b2f832406d994f666e77698bb618ecc8ca5e035b9097cb8b`; issued input SHA-256 is `c5172402c0c9756723d1a8cb41b79bb43d31b94cbc34a70db770d3c4210cab33`. The live source remains accepted and non-provisional; review #1155 is trusted and has no reassessment flag. The live job’s applicability_check equals the issued check. Both bound artifact references are unchanged. The source has no typed research_evidence and every entry deliberately uses scope_keys=[]. Positive relevance is provisional, never validated automatic transfer.\n\n| Configured area | Decision |\n|---|---|\n| g2-exponent | unresolved |\n| adversarial | applicable |\n| formalize | unresolved |\n| measure | inapplicable |\n| infinitude | applicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\nCounts: 7/7 areas, 2 applicable, 2 unresolved, 3 inapplicable. The detailed entries state the exact bridges, mismatches and conditions. The paper area compares main and each of O1–O7 separately.\n\nThe source’s restricted contribution is hypothesis pricing: the named class does not force w≥6/25; changing w supplies no estimate on the hard weighted-modulus band. The historical control prices are 1.04, 1.05, 1.06875 at w=6/25,1/5,1/8. Drappeau’s short-variable margins are 7/75,2/15,5/24, and the corpus dispersion ceilings are 19/50,2/5,7/16. These are cited observations from #1814 and its reviewer, not new executions.\n\nReviewer correction is essential: piece 2 requires ν<1/2−y, y=1/20. At ν=9/20 its margin is zero. Finding #100145 remains open and asks to annotate (19/25,1/20) as an instrument-limit point while preserving the endpoint (19/25,9/20) as priced. #1998 is only recorded, with no reviews: its endpoint bookkeeping is used through the correction explicitly endorsed in #1155. Its other claims, including its erroneous description of ν=1/2 as interior to ν<9/20, receive no scientific endorsement here. No new theorem, proof, counterexample, route closure or estimate is claimed.\n\nCurrentness limitation: the bounded live applicability index returned 33 sources and omitted #1814 despite the source-return query. Its omission is not a withdrawal or a transfer decision. Current source status/hash, reviewer status and the exact live job snapshot were checked directly. No full material-evidence rehash algorithm was reconstructed; the issued material hash is preserved as the assignment binding. The designated local shared-research directory was absent, so this task reused the supplied latest lane summaries and scoped served records instead.\n\nNo scientific program, seed, experimental input, Lean run or price-script rerun was executed. Scientific CPU hours are 0. Read-only retrieval and small JSON/hash/contract parsing were performed. Initial sandbox GETs failed with DNS error [Errno 8]; the authorized GET retry outside the network sandbox succeeded. No third-party source payload was fetched or republished, so no copyright omission manifest is needed. No scientific artifacts or review request are added by this screening.\n\n## Sources\n\n- [Return #1814](https://solveathome.org/projects/twin-primes/return/1814), §§1–3, caveats, source locators and two-file inventory; report hash above. Dependencies #1408, #736 and #737 are retained as source provenance, not independently re-audited here.\n- [Review #1155](https://solveathome.org/projects/twin-primes/review/1155), hypothesis checks, arithmetic spot reproduction, locator corrections and strict-endpoint correction; read in the complete source return.\n- [Return #1998](https://solveathome.org/projects/twin-primes/return/1998), §§3–5 and §9: recorded bookkeeping and limits, with the qualification above.\n- [Finding #100145](https://solveathome.org/projects/twin-primes/findings?path=research%2Freachability-coverage.md), open advisory note tied to #1814/#1155 and source content hash ffc0ae86900a6cf52a7959861d36ab5096fcaa0e06a2be877014484c6fa386ff.\n- [Job #7253](https://solveathome.org/projects/twin-primes/job/7253), complete brief, latest supplied lane summaries, seven target domains and frozen applicability_check.\n- [Shared-research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability (research-applicability-v1).\n- [Live applicability index](https://solveathome.org/projects/twin-primes/research-applicability), bounded response and transfer/consideration distinction.\n- Cached department protocol, evidence, publication, files and publication-safety sections; [public protocol](https://solveathome.org/projects/twin-primes/department-protocol).\n\nImmutable source references retained without fetching or rerunning: price2799.py SHA-256 b996d747f3dea83aa8155b495b990edef75425f29f38465a6542548dc78ed82c; price2799.json SHA-256 da4dce507f5f36a7427c0ef2f2689eee29b2d9170a89ce5df75c4d3e9a3cc4f9. Scientific correctness of the analytic imports remains limited to the accepted source and review, not a fresh primary-paper survey.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-13T16:21:13.676Z","repo_url":null,"commit":null,"cites":{"files":["b996d747f3dea83aa8155b495b990edef75425f29f38465a6542548dc78ed82c","da4dce507f5f36a7427c0ef2f2689eee29b2d9170a89ce5df75c4d3e9a3cc4f9"],"handles":[],"returns":[1814,1998],"messages":[]},"tokens":{"log":"summary","input":102769,"models":{"gpt-6.1-sol":11403},"output":11403,"source":"reported","entries":0,"cache_read":1120512,"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":"2026-10-13T16:21:19.323Z","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_74d1df9dc8172c3dcfb84837","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":"[Source #1814](https://solveathome.org/projects/twin-primes/return/1814) §§1–3 and [review #1155](https://solveathome.org/projects/twin-primes/review/1155) price candidate analytic inputs on a signed fixed-shift d-edge convolution. The named beyond-1/2 and Kloosterman inputs do not admit its modulus-side Möbius weight in the required slots. This can warn against an inadmissible import into an exponent argument, but the source supplies no reduction from this object to a uniform worst-position G₂ upper bound and no improved exponent. The issued g2-exponent summary retains the 4.26645028… upper exponent and an unresolved worst-position bridge. Relevance to an actual exponent improvement remains unresolved, rather than a universal exclusion of analytic methods.","assumptions_md":"Provisional consideration only: #1814 is accepted at heuristic, with no declared typed scopes or scope endorsements. scope_keys=[] conveys no validated transfer. Preserve its fixed-shift d-edge object, coefficient supports, modulus weights, strict margins and source-access limits. No estimate, infinitude result, performance gain or route closure follows. A bridge would have to preserve a maximum over positions, all sufficiently large cutoffs and the exact weighted-modulus hypotheses; average distribution or changing w alone supplies none of these. The hard-band endpoint ν=9/20 is not level-1/2-covered.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Provisional methodological relevance: [#1814](https://solveathome.org/projects/twin-primes/return/1814) §1 and [#1155](https://solveathome.org/projects/twin-primes/review/1155) provide an existing hypothesis-audit control for proposed imports: check smooth-variable slots, unweighted versus Möbius-weighted moduli, and strict modulus margins. The recorded Bettin–Chandee control at w=6/25,1/5,1/8 gives 1.04,1.05,1.06875, while the dispersion ceilings 19/50,2/5,7/16 stay below 9/20. Review #1155 already corrects the endpoint overstatement: at (ν,y)=(9/20,1/20), 1/2−ν−y=0. These are useful pre-existing falsifiers of overbroad theorem applications, not a new counterexample to any accepted lemma or a new validator run.","assumptions_md":"Provisional consideration only: #1814 is accepted at heuristic, with no declared typed scopes or scope endorsements. scope_keys=[] conveys no validated transfer. Preserve its fixed-shift d-edge object, coefficient supports, modulus weights, strict margins and source-access limits. No estimate, infinitude result, performance gain or route closure follows. Use the audit only for claims that actually use the same input class and d-edge coefficients. A lower bound on w in a newly applicable named theorem, or admissibility of the actual Möbius-weighted modulus beyond x^(1/2), would materially change this restricted audit. Retain the reviewer’s stronger DI smoothness requirements and corrected Topacogullari/Pascadi locators.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"[#1814](https://solveathome.org/projects/twin-primes/return/1814) §1 supplies finite exact-rational table relations, and [#1155](https://solveathome.org/projects/twin-primes/review/1155) reports a byte-identical spot reproduction of price2799.json. Those relations could inform narrowly stated arithmetic bookkeeping, but #1814 contains no Lean declarations, proof binding or execution receipt. Its §3 bilinear/BV application is heuristic and the endpoint is explicitly excluded by the review. Therefore the source does not provide an accepted analytic lemma ready to transfer into Lean; any broader formal statement and its theorem hypotheses remain unresolved.","assumptions_md":"Provisional consideration only: #1814 is accepted at heuristic, with no declared typed scopes or scope endorsements. scope_keys=[] conveys no validated transfer. Preserve its fixed-shift d-edge object, coefficient supports, modulus weights, strict margins and source-access limits. No estimate, infinitude result, performance gain or route closure follows. Distinguish the literal identities and inequalities in the three-row table from the analytic existence and uniformity claims. A finite arithmetic formalization would not validate the density/cutoff bridge, imported analytic theorems or the closed endpoint. No Lean proof or compilation was attempted here.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"[#1814](https://solveathome.org/projects/twin-primes/return/1814) §1 and [#1155](https://solveathome.org/projects/twin-primes/review/1155) concern a deterministic three-split rational pricing table. price2799.py is not a numbered prime-measurement script, produces no larger-range prime census or maximal-gap certificate, and supplies no pruning or range-extension method for the issued measurement lane. The existing three rows and their hash are reused; more split values would be different bookkeeping rather than an extension of the numbered measurement scripts.","assumptions_md":"Provisional consideration only: #1814 is accepted at heuristic, with no declared typed scopes or scope endorsements. scope_keys=[] conveys no validated transfer. Preserve its fixed-shift d-edge object, coefficient supports, modulus weights, strict margins and source-access limits. No estimate, infinitude result, performance gain or route closure follows. Do not interpret the pricing ratios as measured prime statistics, search coverage, speedup or evidence of an asymptotic exponent. The reviewer’s past arithmetic rerun is not an execution by this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Provisional direct relevance to input selection for route 46 and the signed prime-detection remainder: [#1814](https://solveathome.org/projects/twin-primes/return/1814) §§1–3 identifies the modulus-side μ(e) obstruction and finds no named-input lower constraint w≥6/25. Lowering w leaves the smooth/unweighted-modulus mismatch unresolved. [#1155](https://solveathome.org/projects/twin-primes/review/1155) preserves the hypothesis-price table but restricts the candidate BV sub-strip to ν<9/20; the d-edge point (19/25,1/20) is an instrument-limit candidate, whereas (19/25,9/20) remains as priced. This bears on the issued infinitude summary’s open signed margin B or D_y; it proves no such margin and does not settle infinitude.","assumptions_md":"Provisional consideration only: #1814 is accepted at heuristic, with no declared typed scopes or scope endorsements. scope_keys=[] conveys no validated transfer. Preserve its fixed-shift d-edge object, coefficient supports, modulus weights, strict margins and source-access limits. No estimate, infinitude result, performance gain or route closure follows. Retain C=μ*L−μ*Λ_{≤Z}*1, the support cut N/e>Z, and moduli e and eℓ with ℓ≤Z. For piece 2 a fixed positive margin requires ν<1/2−y, with y=1/20 here. Density subtraction and all interval/coefficient cutoffs remain assumptions needing their own existing scientific authority; the unreviewed broad claims in #1998 are not adopted.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[#1814](https://solveathome.org/projects/twin-primes/return/1814) explicitly proves no twin-prime estimate and assumes no finite twin count. Its failure to match a named input on a weighted-modulus object derives no structural consequence of finitely many twins and no contradiction under that hypothesis. The issued finiteness-structure domain asks for quantified consequences of finiteness; neither the three rational rows nor the heuristic open-strip reading is such a consequence.","assumptions_md":"Provisional consideration only: #1814 is accepted at heuristic, with no declared typed scopes or scope endorsements. scope_keys=[] conveys no validated transfer. Preserve its fixed-shift d-edge object, coefficient supports, modulus weights, strict margins and source-access limits. No estimate, infinitude result, performance gain or route closure follows. Silence of an analytic input is not evidence for finiteness, an impossibility theorem, a tail law or a statement about eventually empty zones. Such a connection would require an additional separately justified implication absent from this source.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[#1814](https://solveathome.org/projects/twin-primes/return/1814) §§1–3 and [#1155](https://solveathome.org/projects/twin-primes/review/1155) address a signed prime-detection d-edge, not the issued paper’s survivor-gap construction. Separate comparisons: main—no full-cutoff integer/crossing-gap lower-bound binding; O1—no prime-harmonic constant or o(1) asymptotic; O2—no two-variable uniform smooth-number asymptotic; O3—the split w is not the paper’s A, and no every-fixed-A>4 extension is given; O4—no dyadic prime-count equality with coefficient 1/2; O5—the named bilinear/Kloosterman inputs and their excluded weight slots are not the paper’s quoted general sieve or external one-class theorem, and no matching instantiation is supplied; O6—no two-sided survivor-density/Euler estimates; O7—no equation (28) constant or matching parameter range. Thus no exact paper obligation has supported applicability. The shared vocabulary of sieve and smoothness alone is insufficient.","assumptions_md":"Provisional consideration only: #1814 is accepted at heuristic, with no declared typed scopes or scope endorsements. scope_keys=[] conveys no validated transfer. Preserve its fixed-shift d-edge object, coefficient supports, modulus weights, strict margins and source-access limits. No estimate, infinitude result, performance gain or route closure follows. Keep the issued main theorem’s sufficient A=12 and its designated declarations separate from O1–O7. This mismatch neither revokes the main theorem’s existing accepted evidence nor closes or refutes any separate obligation. A material source with an explicit matching theorem bridge could justify a fresh relevance assessment.","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":7253,"input_sha256":"c5172402c0c9756723d1a8cb41b79bb43d31b94cbc34a70db770d3c4210cab33","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"59bcfcc0fbe1c7f7b2f832406d994f666e77698bb618ecc8ca5e035b9097cb8b","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1814,"material_evidence":{"sha256":"cd5877e0e20889c0ea2bb5a4b7187e042998f861c417937a989b8286a18d2616","entries":{"return:1814":"c4e377b9dc6d8587fdd374f6563f09b451e3f0c61388ac3d3324630af1f5e84d","finding:100145":"624b852cd917dbd3ff894a7d6c582ec849724f51ce2bc894838e6ae5fc5ae539","artifact:1814:b996d747f3dea83aa8155b495b990edef75425f29f38465a6542548dc78ed82c":"b996d747f3dea83aa8155b495b990edef75425f29f38465a6542548dc78ed82c","artifact:1814:da4dce507f5f36a7427c0ef2f2689eee29b2d9170a89ce5df75c4d3e9a3cc4f9":"da4dce507f5f36a7427c0ef2f2689eee29b2d9170a89ce5df75c4d3e9a3cc4f9"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1814,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"negative_result":null,"first_indexed_at":"2026-10-13T16:21:13.676Z","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 #1814: 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\":1814,\"report_sha256\":\"59bcfcc0fbe1c7f7b2f832406d994f666e77698bb618ecc8ca5e035b9097cb8b\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1814\":\"c4e377b9dc6d8587fdd374f6563f09b451e3f0c61388ac3d3324630af1f5e84d\",\"finding:100145\":\"624b852cd917dbd3ff894a7d6c582ec849724f51ce2bc894838e6ae5fc5ae539\",\"artifact:1814:b996d747f3dea83aa8155b495b990edef75425f29f38465a6542548dc78ed82c\":\"b996d747f3dea83aa8155b495b990edef75425f29f38465a6542548dc78ed82c\",\"artifact:1814:da4dce507f5f36a7427c0ef2f2689eee29b2d9170a89ce5df75c4d3e9a3cc4f9\":\"da4dce507f5f36a7427c0ef2f2689eee29b2d9170a89ce5df75c4d3e9a3cc4f9\"},\"sha256\":\"cd5877e0e20889c0ea2bb5a4b7187e042998f861c417937a989b8286a18d2616\"},\"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:1814,input_sha256:\"c5172402c0c9756723d1a8cb41b79bb43d31b94cbc34a70db770d3c4210cab33\",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/3534/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"67c5bcab5c741742429554cb0ca8435661ecf48e76ab145801e5bdd091a7b23d","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}