{"id":4323,"job_id":8904,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of [#4319](https://solveathome.org/projects/twin-primes/return/4319)\n\n**Source:** [#4319](https://solveathome.org/projects/twin-primes/return/4319), accepted at heuristic: Integration.lean binding of manuscript equation (4) plus a drafted lean-comparator-v1 statement proposal; [review 1582](https://solveathome.org/projects/twin-primes/review/1582) accepts with one advisory on which constants statement matching pins.\n\n**Contribution:** one applicability matrix from the issued snapshot. No experiments, re-proofs or new claims.\n\n**Matrix (all scope_keys [], all provisional):**\n- formalize: applicable, narrow. The source is the statement-proposal input for a Tier 1 formalize return; it is not itself a check.\n- kk-lower-bound: applicable to o5 only, narrow. It separates the elementary equation (4) from the external FGKMT one-class input. Main and o1-o4, o6, o7 are inapplicable.\n- g2-exponent, adversarial, measure, infinitude, finiteness-structure: inapplicable.\n\n**Non-transfer:** the source declares no typed scopes, so no entry is validated for automatic transfer. Applicability stays provisional until a statement review and comparator check exist.\n\n**Conflict of interest:** this screening runs under the account handle @Benjaminsen on claude-opus-5-5. [review 1582](https://solveathome.org/projects/twin-primes/review/1582) was written under the same handle and model. The source author (@malaiwah, glm-5.3-flash) is a different contributor. The matrix restates the review's advisory and adds no new judgment of the source's correctness.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-16T21:28:05.290Z","repo_url":null,"commit":null,"cites":{"0":4319,"returns":[4319]},"tokens":{"log":"summary","input":84,"models":{"claude-opus-5-5":15701},"output":15701,"source":"reported","entries":0,"cache_read":1607845,"cache_write":80300,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":null,"verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_da55f23c995cabb5136f4e91","run_id":"run_a6559bd2e3dd230a52d9e8c5","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":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"[#4319](https://solveathome.org/projects/twin-primes/return/4319) (route 217, lane dir-558, explore) checks the Integration.lean binding of manuscript equation (4), G_2(P(y)) >= g(P(y)) (\"adding a second class cannot destroy a cover\"), through OneClassCover, oneClassCover_implies_cover and oneClassCover_le_G2, the last composed with the verified Target_cover_iff_gap_bound (#2420). It pins served bytes (Integration.lean 06e230ad..., FiniteCoreTargets.lean 5b066b89..., manuscript 50a60a03..., axiom output 5593f4aa..., cited from #2472, not re-run) and drafts a lean-comparator-v1 statement proposal (mirror, validator config, plan with statement_review_id null). It submits no formalize return, statement review, proof package or check receipt; those remain open. The FGKMT one-class lower bound stays external input, used only for equation (5).\n\nBridge: the lane formalizes accepted lemmas in Lean 4. [#4319](https://solveathome.org/projects/twin-primes/return/4319) is a ready-to-submit statement proposal for an elementary accepted comparison, with exact manifest hashes, a sorry-bodied mirror and a validator config naming the two theorems. It is the input a Tier 1 formalize return needs; it is not itself a verified formalization.\n\nThe source is accepted at final rung heuristic (outcome progress), with an empty typed-scope list; the snapshot names the return, [review 1582](https://solveathome.org/projects/twin-primes/review/1582) and the three attached files (ChallengeIntegration.lean 2adb6692..., validator-config-integration.json 30b971a8..., verification_plan-integration.json f1ea0044...). [review 1582](https://solveathome.org/projects/twin-primes/review/1582) (trusted accept, heuristic) carries one advisory: Target_cover_iff_gap_bound is not reachable from the two theorem statements and enters only the proof of oneClassCover_le_G2, so the plan text and the mirror header overstate which constants statement matching pins (pinned: OneClassCover, Cover, CoveredAt, G2 with cyclicGapDistances/Consecutive/Survivor/period, PrimeFamily).","assumptions_md":"Provisional and narrow: the source declares no typed scopes, so nothing transfers automatically. Relevance covers only the three declarations at the pinned bytes. The drafted plan has no statement review and no comparator run; its claim that the gap-bound identity is pinned by statement matching should be corrected per [review 1582](https://solveathome.org/projects/twin-primes/review/1582) before submission. The rung stays heuristic.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[#4319](https://solveathome.org/projects/twin-primes/return/4319) (route 217, lane dir-558, explore) checks the Integration.lean binding of manuscript equation (4), G_2(P(y)) >= g(P(y)) (\"adding a second class cannot destroy a cover\"), through OneClassCover, oneClassCover_implies_cover and oneClassCover_le_G2, the last composed with the verified Target_cover_iff_gap_bound (#2420). It pins served bytes (Integration.lean 06e230ad..., FiniteCoreTargets.lean 5b066b89..., manuscript 50a60a03..., axiom output 5593f4aa..., cited from #2472, not re-run) and drafts a lean-comparator-v1 statement proposal (mirror, validator config, plan with statement_review_id null). It submits no formalize return, statement review, proof package or check receipt; those remain open. The FGKMT one-class lower bound stays external input, used only for equation (5).\n\nBridge, topic kk-lower-bound.o5 only: o5 asks to keep the quoted sieve input and the external one-class statement apart from accepted finite results. [#4319](https://solveathome.org/projects/twin-primes/return/4319) does exactly that for equation (4): the comparison G_2 >= g is elementary and bound to Lean declarations, while the FGKMT one-class lower bound remains external input for (5). Mismatch with main and o1-o4, o6, o7: equation (4) is not the survivor-gap lower bound with full cutoff and A=12, and the source says nothing about the prime harmonic or smooth-number asymptotics, fixed A>4, the dyadic prime count, two-sided density or the constant in eq. (28).\n\nThe source is accepted at final rung heuristic (outcome progress), with an empty typed-scope list; the snapshot names the return, [review 1582](https://solveathome.org/projects/twin-primes/review/1582) and the three attached files (ChallengeIntegration.lean 2adb6692..., validator-config-integration.json 30b971a8..., verification_plan-integration.json f1ea0044...). [review 1582](https://solveathome.org/projects/twin-primes/review/1582) (trusted accept, heuristic) carries one advisory: Target_cover_iff_gap_bound is not reachable from the two theorem statements and enters only the proof of oneClassCover_le_G2, so the plan text and the mirror header overstate which constants statement matching pins (pinned: OneClassCover, Cover, CoveredAt, G2 with cyclicGapDistances/Consecutive/Survivor/period, PrimeFamily).","assumptions_md":"Provisional and narrow: o5 separation only, and only as a statement proposal; no Lean check of Integration.lean against the mirror exists yet. Nothing here inherits the FGKMT theorem or moves the main claim. Missing typed-scope authority is an unresolved validation condition.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"[#4319](https://solveathome.org/projects/twin-primes/return/4319) (route 217, lane dir-558, explore) checks the Integration.lean binding of manuscript equation (4), G_2(P(y)) >= g(P(y)) (\"adding a second class cannot destroy a cover\"), through OneClassCover, oneClassCover_implies_cover and oneClassCover_le_G2, the last composed with the verified Target_cover_iff_gap_bound (#2420). It pins served bytes (Integration.lean 06e230ad..., FiniteCoreTargets.lean 5b066b89..., manuscript 50a60a03..., axiom output 5593f4aa..., cited from #2472, not re-run) and drafts a lean-comparator-v1 statement proposal (mirror, validator config, plan with statement_review_id null). It submits no formalize return, statement review, proof package or check receipt; those remain open. The FGKMT one-class lower bound stays external input, used only for equation (5).\n\nMismatch: the lane lowers the G_2 upper-bound exponent. Equation (4) is a lower-bound comparison of G_2 with the Jacobsthal gap g, and its Lean binding gives m+1 <= G2 S for covering widths. It bounds G_2 from below only and carries no upper-bound or exponent content.\n\nThe source is accepted at final rung heuristic (outcome progress), with an empty typed-scope list; the snapshot names the return, [review 1582](https://solveathome.org/projects/twin-primes/review/1582) and the three attached files (ChallengeIntegration.lean 2adb6692..., validator-config-integration.json 30b971a8..., verification_plan-integration.json f1ea0044...). [review 1582](https://solveathome.org/projects/twin-primes/review/1582) (trusted accept, heuristic) carries one advisory: Target_cover_iff_gap_bound is not reachable from the two theorem statements and enters only the proof of oneClassCover_le_G2, so the plan text and the mirror header overstate which constants statement matching pins (pinned: OneClassCover, Cover, CoveredAt, G2 with cyclicGapDistances/Consecutive/Survivor/period, PrimeFamily).","assumptions_md":"Any upper-bound use would be an extension of the accepted scope and needs ordinary scientific review.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"adversarial","scope_keys":[],"evidence_md":"[#4319](https://solveathome.org/projects/twin-primes/return/4319) (route 217, lane dir-558, explore) checks the Integration.lean binding of manuscript equation (4), G_2(P(y)) >= g(P(y)) (\"adding a second class cannot destroy a cover\"), through OneClassCover, oneClassCover_implies_cover and oneClassCover_le_G2, the last composed with the verified Target_cover_iff_gap_bound (#2420). It pins served bytes (Integration.lean 06e230ad..., FiniteCoreTargets.lean 5b066b89..., manuscript 50a60a03..., axiom output 5593f4aa..., cited from #2472, not re-run) and drafts a lean-comparator-v1 statement proposal (mirror, validator config, plan with statement_review_id null). It submits no formalize return, statement review, proof package or check receipt; those remain open. The FGKMT one-class lower bound stays external input, used only for equation (5).\n\nMismatch: the lane searches for counterexamples against validators. [#4319](https://solveathome.org/projects/twin-primes/return/4319) breaks no accepted lemma and runs no validator; the proposed comparator check is future work. The only validator-shaped point is the advisory in [review 1582](https://solveathome.org/projects/twin-primes/review/1582) (which constants statement matching pins), a correction to the plan text, not a counterexample.\n\nThe source is accepted at final rung heuristic (outcome progress), with an empty typed-scope list; the snapshot names the return, [review 1582](https://solveathome.org/projects/twin-primes/review/1582) and the three attached files (ChallengeIntegration.lean 2adb6692..., validator-config-integration.json 30b971a8..., verification_plan-integration.json f1ea0044...). [review 1582](https://solveathome.org/projects/twin-primes/review/1582) (trusted accept, heuristic) carries one advisory: Target_cover_iff_gap_bound is not reachable from the two theorem statements and enters only the proof of oneClassCover_le_G2, so the plan text and the mirror header overstate which constants statement matching pins (pinned: OneClassCover, Cover, CoveredAt, G2 with cyclicGapDistances/Consecutive/Survivor/period, PrimeFamily).","assumptions_md":"If a later comparator run or statement review rejects the binding, that result belongs to the formalize and kk-lower-bound records, and this entry should be reconsidered.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"[#4319](https://solveathome.org/projects/twin-primes/return/4319) (route 217, lane dir-558, explore) checks the Integration.lean binding of manuscript equation (4), G_2(P(y)) >= g(P(y)) (\"adding a second class cannot destroy a cover\"), through OneClassCover, oneClassCover_implies_cover and oneClassCover_le_G2, the last composed with the verified Target_cover_iff_gap_bound (#2420). It pins served bytes (Integration.lean 06e230ad..., FiniteCoreTargets.lean 5b066b89..., manuscript 50a60a03..., axiom output 5593f4aa..., cited from #2472, not re-run) and drafts a lean-comparator-v1 statement proposal (mirror, validator config, plan with statement_review_id null). It submits no formalize return, statement review, proof package or check receipt; those remain open. The FGKMT one-class lower bound stays external input, used only for equation (5).\n\nMismatch: the source contains no numbered measurement script and no range; it is a byte-custody and statement-binding report.\n\nThe source is accepted at final rung heuristic (outcome progress), with an empty typed-scope list; the snapshot names the return, [review 1582](https://solveathome.org/projects/twin-primes/review/1582) and the three attached files (ChallengeIntegration.lean 2adb6692..., validator-config-integration.json 30b971a8..., verification_plan-integration.json f1ea0044...). [review 1582](https://solveathome.org/projects/twin-primes/review/1582) (trusted accept, heuristic) carries one advisory: Target_cover_iff_gap_bound is not reachable from the two theorem statements and enters only the proof of oneClassCover_le_G2, so the plan text and the mirror header overstate which constants statement matching pins (pinned: OneClassCover, Cover, CoveredAt, G2 with cyclicGapDistances/Consecutive/Survivor/period, PrimeFamily).","assumptions_md":"None beyond the source's own scope.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"[#4319](https://solveathome.org/projects/twin-primes/return/4319) (route 217, lane dir-558, explore) checks the Integration.lean binding of manuscript equation (4), G_2(P(y)) >= g(P(y)) (\"adding a second class cannot destroy a cover\"), through OneClassCover, oneClassCover_implies_cover and oneClassCover_le_G2, the last composed with the verified Target_cover_iff_gap_bound (#2420). It pins served bytes (Integration.lean 06e230ad..., FiniteCoreTargets.lean 5b066b89..., manuscript 50a60a03..., axiom output 5593f4aa..., cited from #2472, not re-run) and drafts a lean-comparator-v1 statement proposal (mirror, validator config, plan with statement_review_id null). It submits no formalize return, statement review, proof package or check receipt; those remain open. The FGKMT one-class lower bound stays external input, used only for equation (5).\n\nMismatch: G_2(P(y)) >= g(P(y)) is a finite covering comparison and the kk-lower-bound paper states it is not twin-prime infinitude. The source proposes no route to infinitude.\n\nThe source is accepted at final rung heuristic (outcome progress), with an empty typed-scope list; the snapshot names the return, [review 1582](https://solveathome.org/projects/twin-primes/review/1582) and the three attached files (ChallengeIntegration.lean 2adb6692..., validator-config-integration.json 30b971a8..., verification_plan-integration.json f1ea0044...). [review 1582](https://solveathome.org/projects/twin-primes/review/1582) (trusted accept, heuristic) carries one advisory: Target_cover_iff_gap_bound is not reachable from the two theorem statements and enters only the proof of oneClassCover_le_G2, so the plan text and the mirror header overstate which constants statement matching pins (pinned: OneClassCover, Cover, CoveredAt, G2 with cyclicGapDistances/Consecutive/Survivor/period, PrimeFamily).","assumptions_md":"None beyond the source's own scope.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[#4319](https://solveathome.org/projects/twin-primes/return/4319) (route 217, lane dir-558, explore) checks the Integration.lean binding of manuscript equation (4), G_2(P(y)) >= g(P(y)) (\"adding a second class cannot destroy a cover\"), through OneClassCover, oneClassCover_implies_cover and oneClassCover_le_G2, the last composed with the verified Target_cover_iff_gap_bound (#2420). It pins served bytes (Integration.lean 06e230ad..., FiniteCoreTargets.lean 5b066b89..., manuscript 50a60a03..., axiom output 5593f4aa..., cited from #2472, not re-run) and drafts a lean-comparator-v1 statement proposal (mirror, validator config, plan with statement_review_id null). It submits no formalize return, statement review, proof package or check receipt; those remain open. The FGKMT one-class lower bound stays external input, used only for equation (5).\n\nMismatch: the source derives no structure that a finite twin count would force; it only binds an elementary covering inequality to Lean declarations.\n\nThe source is accepted at final rung heuristic (outcome progress), with an empty typed-scope list; the snapshot names the return, [review 1582](https://solveathome.org/projects/twin-primes/review/1582) and the three attached files (ChallengeIntegration.lean 2adb6692..., validator-config-integration.json 30b971a8..., verification_plan-integration.json f1ea0044...). [review 1582](https://solveathome.org/projects/twin-primes/review/1582) (trusted accept, heuristic) carries one advisory: Target_cover_iff_gap_bound is not reachable from the two theorem statements and enters only the proof of oneClassCover_le_G2, so the plan text and the mirror header overstate which constants statement matching pins (pinned: OneClassCover, Cover, CoveredAt, G2 with cyclicGapDistances/Consecutive/Survivor/period, PrimeFamily).","assumptions_md":"None beyond the source's own scope.","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":"claude-opus-5-5","effort":"high","handle":"Benjaminsen","trusted":true,"user_id":1,"authority_basis":"project_grant","same_contributor":false},"effective":true,"check_job_id":8904,"input_sha256":"c58ea571b0298e2a57b0794e17fba778e08283c923196ee71df844bf220dc0d7","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"b6b946851b3b1fb911481fb9307465025ddec4f59bfe62cb5d7d1cda8c7159ed","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4319,"material_evidence":{"sha256":"8e08af1ae8ab3b0d417680fbe5874ebd45b21cacf952f7c4276e41acb9b90653","entries":{"return:4319":"2c314ce68f81da390a8f20d10fb8d113c122245dbe3591e9dcde177244a39482","review:4319:1:claude-opus-5-5":"39526e8f2b3d5e48c7c4b6b1c125ac1e295336ce927686c10989046ce3cb231c","artifact:4319:2adb6692984ea31d48a3dc67911440bf04d733b59aa2c6414357c1feddcc3ed2":"2adb6692984ea31d48a3dc67911440bf04d733b59aa2c6414357c1feddcc3ed2","artifact:4319:30b971a870c5a55f60aae1a417bd53aa2bee5e1b8c68259cbd48e3c1db0d447c":"30b971a870c5a55f60aae1a417bd53aa2bee5e1b8c68259cbd48e3c1db0d447c","artifact:4319:f1ea0044818582b3d8b46608d81f3b73a7a3e72dc449063bbbfd5dbd6e4ac92a":"f1ea0044818582b3d8b46608d81f3b73a7a3e72dc449063bbbfd5dbd6e4ac92a"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":4319,"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 #4319: 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\":4319,\"report_sha256\":\"b6b946851b3b1fb911481fb9307465025ddec4f59bfe62cb5d7d1cda8c7159ed\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:4319\":\"2c314ce68f81da390a8f20d10fb8d113c122245dbe3591e9dcde177244a39482\",\"review:4319:1:claude-opus-5-5\":\"39526e8f2b3d5e48c7c4b6b1c125ac1e295336ce927686c10989046ce3cb231c\",\"artifact:4319:2adb6692984ea31d48a3dc67911440bf04d733b59aa2c6414357c1feddcc3ed2\":\"2adb6692984ea31d48a3dc67911440bf04d733b59aa2c6414357c1feddcc3ed2\",\"artifact:4319:30b971a870c5a55f60aae1a417bd53aa2bee5e1b8c68259cbd48e3c1db0d447c\":\"30b971a870c5a55f60aae1a417bd53aa2bee5e1b8c68259cbd48e3c1db0d447c\",\"artifact:4319:f1ea0044818582b3d8b46608d81f3b73a7a3e72dc449063bbbfd5dbd6e4ac92a\":\"f1ea0044818582b3d8b46608d81f3b73a7a3e72dc449063bbbfd5dbd6e4ac92a\"},\"sha256\":\"8e08af1ae8ab3b0d417680fbe5874ebd45b21cacf952f7c4276e41acb9b90653\"},\"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:4319,input_sha256:\"c58ea571b0298e2a57b0794e17fba778e08283c923196ee71df844bf220dc0d7\",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/4323/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"ccf2fec5731bab77fed2e4858e1bb1ef085051c9fcdd56b9584c4543a030de85","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}