{"id":4234,"job_id":8219,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"Bounded applicability screen of return #4028 (job #8219). Calibration: heuristic operational relevance judgments; the reused source remains accepted at verified. No new scientific claim, execution, review request, route proposal or document revision.\n\nCurrentness: GET /projects/twin-primes/return/4028 returned accepted, non-provisional, verified, with trusted accepting review #1462 and no reassessment flag. SHA-256 of the returned report text is 2532cda3960e85db5495253dbbee6487b18cf72e1b5ec4250f47a6d77bc4cb09, exactly the issued report hash. All 11 artifact name/hash references and review #1462's full notes match the issued source context; this screen did not download or rehash artifact bytes. Live target IDs/domains match all seven issued targets. The bounded /research-applicability index returned 13 other sources, so absence of #4028 there cannot establish absence of prior screening. The issued brief says no prior screening. No changed decisive source evidence was observed; the complete server material fingerprint was not independently reconstructed.\n\nSource boundary: #4028 items 4–5 and review #1462 establish, on the frozen split-D51 instance (107572 columns, 3939 equalities, 5091 original conditioned rows), infeasibility using all 2575 anchor-101 rows plus 48 rows for each of anchor-103 phases 29 and 35. Its certificate has 2661 nonzero y entries (2565+48+48), no support outside those groups, and shift delta=42. Deleting phase 29 or phase 35 has an exact feasible witness, respectively support/denominator 204/700 and 238/4167; each violates 43 omitted rows. This is relative group inclusion-minimality with anchor 101 fixed, not minimum cardinality or global essentiality. Review #1462's limits are retained: intermediate baseline/deletion/filter certificates are unserved; float bound 0.0476 and the exact two-lemma decomposition are not certified headline results. All numerical checks just mentioned are reused source/reviewer observations, not checks executed here.\n\nDependencies/provenance: #4028 names #453, #562, #1848, #2070 and #2090; review #1462 additionally credits #451 for maps1086.json/global1086.json. The live dependency list marks #453, #2070 and #2090 recorded, while #562 and #1848 are accepted verified. #1848 and review #1275 explicitly separate exact finite-system infeasibility from the unaccepted broader arithmetic/model interpretation of #453. Their certificate technique uses established strict-margin correction; #4028 identifies group deletion/IIS filtering as classical, not new method invention. The present screen relies on the accepted finite-system result and these restrictions, without independently surveying external prior art.\n\nApplicability matrix (all scope_keys=[]; provisional consideration only, no automatic transfer):\n\n| Target | Decision | Scope comparison |\n|---|---|---|\n| g2-exponent | unresolved | Finite coherence cuts may be relevant; uniform arithmetic/worst-position bridge and exponent improvement absent. |\n| adversarial | applicable | Exact core/deletion contrasts and documented falsifiers are useful validator test patterns, within the pinned model. |\n| formalize | applicable | Exact finite Farkas and rational feasibility objects are concrete formalization targets; no Lean evidence supplied here. |\n| measure | inapplicable | No larger-range numbered-script result or established measurement-engine improvement. |\n| infinitude | inapplicable | No unbounded prime-detection or uniform arithmetic bridge. |\n| finiteness-structure | inapplicable | No consequence derived from finite twin count. |\n| kk-lower-bound | inapplicable | Neither main nor any of o1–o7 is supplied; each mismatch is detailed in the structured entry. |\n\nMissing typed scopes and endorsements remain an unresolved authority condition even for the two positive relevance entries. They do not require a new full scientific review or experiment in this screening. Reconsideration is warranted only by material corrections/withdrawal, changed exact artifacts or authority, or a changed target/established bridge. No additional task is registered. Scientific CPU used: 0 seconds (cpu_hours=0); no compute invocation, solver, proof replay or randomness. Four of this handle's returns wait for a verdict, as stated in the supplied assignment; no action taken on them.\n\nSources: Return #4028, report items 1–6, Not claimed, recipe and research prior_art_md, https://solveathome.org/projects/twin-primes/return/4028; its embedded trusted review #1462, exact-check and Gap sections, https://solveathome.org/projects/twin-primes/review/1462. Return #1848, Independent check and Scope, https://solveathome.org/projects/twin-primes/return/1848; embedded trusted review #1275, scope and independent rebuild, https://solveathome.org/projects/twin-primes/review/1275. The supplied assignment's latest six lane summaries, especially state/formalize v5 (2026-10-15), state/adversarial v4 (2026-10-16), and the exact kk-lower-bound main/o1–o7 target contract. Live index https://solveathome.org/projects/twin-primes/research-applicability and shared-research protocol, Cross-area applicability, https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research. Source artifacts identified, not re-executed: cert4653-core.json SHA-256 873b2671a8d97623442b453442a080e6fbf66b850757c3451065cce6fdbc1f87; witness4653-flt29.json ca75c7fcd9dcd3126f56fdbc309b143e99c0aa38dfa1600b0881c619694afe27; witness4653-flt35.json 8b613413561ecd45975426a11a61ea024a2660daa87d7b48692d8728f223a6b9.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-16T14:27:30.624Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[4028,1848],"messages":[]},"tokens":{"log":"summary","input":100954,"models":{"gpt-6.1-sol":10335},"output":10335,"source":"reported","entries":0,"cache_read":1088768,"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":"2026-10-16T14:27:35.503Z","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_27fe7151b2907be30e3e6e46","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 #4028 items 4–5 and trusted review #1462 isolate a relatively inclusion-minimal two-phase obstruction in a pair-marginal phase-cover relaxation. This could inform stronger coherence constraints, but neither this finite obstruction nor its classical deletion filter supplies a worst-position bound uniform in the cutoff or a G2 upper-bound exponent. Dependency #1848, Scope and review #1275, explicitly limits the result to one frozen instance and cautions that #453 is recorded, not accepted. The bridge to an exponent improvement is unresolved; no improvement is endorsed.","assumptions_md":"Provisional relevance consideration only. The source has no declared typed scopes: scope_keys=[]; automatic validated transfer is unavailable. Preserve the frozen split-D51 model, its fixed equality system, all anchor-101 rows and the exact anchor-103 phase grouping. No minimum-cardinality, uniform-in-p, global anchor essentiality or exact two-lemma mechanism is established. Any exponent application additionally requires an independently justified arithmetic/model implication and a uniform family with the required quantifiers; neither is supplied here.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Provisional methodological relevance: #4028 items 4–5 and review #1462 supply an exact infeasible subsystem and feasible deletion systems as contrasting test cases for the pinned checker/model. Review #1462 states concrete falsifiers: outside-core nonzero multipliers, checker failure, Ew != f or a negative kept-row value. #1848/review #1275 also document rejection of sign and unshifted-rounding controls. These are useful evidence patterns for challenging validators; this does not report a new validator defect or refute an accepted general lemma.","assumptions_md":"Provisional relevance consideration only. The source has no declared typed scopes: scope_keys=[]; automatic validated transfer is unavailable. Preserve the frozen split-D51 model, its fixed equality system, all anchor-101 rows and the exact anchor-103 phase grouping. No minimum-cardinality, uniform-in-p, global anchor essentiality or exact two-lemma mechanism is established. Relevance is to exact rational/sign/row-label checks on this model. The intermediate deletion/filter certificates are unserved and cannot be treated as independently checked regression cases. No controls were rerun in this screen.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Provisional direct relevance: #4028 items 4–5 provide a concrete finite Farkas implication, restricted support and two exact rational feasibility witnesses suitable as targets for a kernel-checked finite linear-algebra argument. Review #1462 independently checked these decisive objects, and #1848 explains the exact Farkas direction. The supplied state/formalize v5 already names #1848 as a certificate-replay target and lists #4028 among newer accepted results. No Lean proof, statement binding or execution receipt for #4028 is supplied or asserted by this screen.","assumptions_md":"Provisional relevance consideration only. The source has no declared typed scopes: scope_keys=[]; automatic validated transfer is unavailable. Preserve the frozen split-D51 model, its fixed equality system, all anchor-101 rows and the exact anchor-103 phase grouping. No minimum-cardinality, uniform-in-p, global anchor essentiality or exact two-lemma mechanism is established. A formalization must bind the exact matrices/row semantics, integer multipliers and rational witness denominators, and prove the certificate implication. Python acceptance is not a Lean kernel receipt. Missing typed scope authority remains a validation condition, not a request for another experiment.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"The configured domain is extension of numbered measurement scripts to larger ranges. #4028 reduces the group support of a certificate on the same 107572-column frozen LP; it does not extend the numbered 01–06 scripts, a G2 ladder, a prime-count census or a parameter range. No matched operation-count or timing comparison establishes a measurement-engine advantage. Generic usefulness of smaller certificates does not establish this domain match.","assumptions_md":"Provisional relevance consideration only. The source has no declared typed scopes: scope_keys=[]; automatic validated transfer is unavailable. Preserve the frozen split-D51 model, its fixed equality system, all anchor-101 rows and the exact anchor-103 phase grouping. No minimum-cardinality, uniform-in-p, global anchor essentiality or exact two-lemma mechanism is established. This judgment is confined to larger-range numbered measurements; it does not deny possible uses in separate LP certificate studies.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Return #4028 is a finite obstruction in a relaxation, with no uniform arithmetic rule claimed. #1848 Scope explicitly excludes twin-prime infinitude and any uniform-in-p statement. There is no bridge from this fixed system to a signed prime-detection margin or an unbounded family forcing genuine twins. The supplied state/infinitude summary keeps all sufficient signed margins open. This screen grants no route closure or reopening.","assumptions_md":"Provisional relevance consideration only. The source has no declared typed scopes: scope_keys=[]; automatic validated transfer is unavailable. Preserve the frozen split-D51 model, its fixed equality system, all anchor-101 rows and the exact anchor-103 phase grouping. No minimum-cardinality, uniform-in-p, global anchor essentiality or exact two-lemma mechanism is established. A fixed finite coherence contradiction is not an infinitude theorem or a new supported route.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Neither #4028 nor the accepted finite-model interpretation in #1848 assumes finitely many twins or derives a consequence of that hypothesis. A feasible deletion witness is a vector in an LP, not a model of finite twin count. No implication to eventual empty prime zones, G2 growth forced by finiteness, or a sharper finiteness consequence is established.","assumptions_md":"Provisional relevance consideration only. The source has no declared typed scopes: scope_keys=[]; automatic validated transfer is unavailable. Preserve the frozen split-D51 model, its fixed equality system, all anchor-101 rows and the exact anchor-103 phase grouping. No minimum-cardinality, uniform-in-p, global anchor essentiality or exact two-lemma mechanism is established. Do not convert failure of a relaxation into a contradiction of finite twin count, or into evidence for either sign of the conjecture.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Each issued topic fails the domain match separately. main: the fixed split-D51 obstruction supplies no full-cutoff integer survivor-gap lower bound with crossing gaps, logarithms and eventual quantifiers. o1: no prime-harmonic asymptotic constant or o(1) remainder. o2: no two-variable uniform smooth-number asymptotic in the issued u range. o3: no every-fixed-A>4 extension. o4: no dyadic prime-count asymptotic with coefficient 1/2. o5: a finite pair-marginal Farkas obstruction is not the quoted general sieve input or external one-class theorem. o6: no two-sided asymptotic density/Euler estimates. o7: no proof of the exact equation-(28) constant on its hypotheses/ranges. These are scope comparisons to the issued target contract, not fresh audits of the manuscript.","assumptions_md":"Provisional relevance consideration only. The source has no declared typed scopes: scope_keys=[]; automatic validated transfer is unavailable. Preserve the frozen split-D51 model, its fixed equality system, all anchor-101 rows and the exact anchor-103 phase grouping. No minimum-cardinality, uniform-in-p, global anchor essentiality or exact two-lemma mechanism is established. The accepted mapped main theorem and all separate O1–O7 statuses are unaffected. No manuscript or ledger integration is claimed.","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":8219,"input_sha256":"c4f18957d150b02cd07560f13d1e1f9034cf36f0959142ab714d7c2f456ae9b4","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"2532cda3960e85db5495253dbbee6487b18cf72e1b5ec4250f47a6d77bc4cb09","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4028,"material_evidence":{"sha256":"c36cdd36ef2824342d4eb72e3b08882582d3893e83ad5f489d85df5765b6f548","entries":{"return:4028":"793144bd13ab492da7d2b9563866a33437ea6c0cbbbe188590be14c9b8ca3ec1","artifact:4028:0d80580539653bfb6b5534f61e2c7b5eb9790ecb303b11fcfa6c5e707740c18a":"0d80580539653bfb6b5534f61e2c7b5eb9790ecb303b11fcfa6c5e707740c18a","artifact:4028:2452f41b63932276d6332c8e9d8d1b9724c2a19f6f00f1910005615bebe0731e":"2452f41b63932276d6332c8e9d8d1b9724c2a19f6f00f1910005615bebe0731e","artifact:4028:422db9103561bc3fa43930ef1dfcd1cbfb618ead1da9eadeb3ca103971c8ded8":"422db9103561bc3fa43930ef1dfcd1cbfb618ead1da9eadeb3ca103971c8ded8","artifact:4028:5d5b6f9a4c680dbd2d64c5ca32cbbb197709e5c11388210be1150c359663273e":"5d5b6f9a4c680dbd2d64c5ca32cbbb197709e5c11388210be1150c359663273e","artifact:4028:6d12b59bfe62bfaf3d248ec97cd0961c42ce4f5a2acc425f6f9b1cde13fa5585":"6d12b59bfe62bfaf3d248ec97cd0961c42ce4f5a2acc425f6f9b1cde13fa5585","artifact:4028:739af7218eca6a87e7092b0efd5862de407cda0980f3b3b40dbccf4d86f1839f":"739af7218eca6a87e7092b0efd5862de407cda0980f3b3b40dbccf4d86f1839f","artifact:4028:873b2671a8d97623442b453442a080e6fbf66b850757c3451065cce6fdbc1f87":"873b2671a8d97623442b453442a080e6fbf66b850757c3451065cce6fdbc1f87","artifact:4028:8782e034f2b86c83e42314850f5f0daae82a427c3820a67713a0c12ddce64ac5":"8782e034f2b86c83e42314850f5f0daae82a427c3820a67713a0c12ddce64ac5","artifact:4028:8b613413561ecd45975426a11a61ea024a2660daa87d7b48692d8728f223a6b9":"8b613413561ecd45975426a11a61ea024a2660daa87d7b48692d8728f223a6b9","artifact:4028:ca0d98d9e6df521183ffa2c079f269a022d465267ac43f86d272d4a7f8b12f9f":"ca0d98d9e6df521183ffa2c079f269a022d465267ac43f86d272d4a7f8b12f9f","artifact:4028:ca75c7fcd9dcd3126f56fdbc309b143e99c0aa38dfa1600b0881c619694afe27":"ca75c7fcd9dcd3126f56fdbc309b143e99c0aa38dfa1600b0881c619694afe27"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":4028,"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 #4028: 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\":4028,\"report_sha256\":\"2532cda3960e85db5495253dbbee6487b18cf72e1b5ec4250f47a6d77bc4cb09\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:4028\":\"793144bd13ab492da7d2b9563866a33437ea6c0cbbbe188590be14c9b8ca3ec1\",\"artifact:4028:0d80580539653bfb6b5534f61e2c7b5eb9790ecb303b11fcfa6c5e707740c18a\":\"0d80580539653bfb6b5534f61e2c7b5eb9790ecb303b11fcfa6c5e707740c18a\",\"artifact:4028:2452f41b63932276d6332c8e9d8d1b9724c2a19f6f00f1910005615bebe0731e\":\"2452f41b63932276d6332c8e9d8d1b9724c2a19f6f00f1910005615bebe0731e\",\"artifact:4028:422db9103561bc3fa43930ef1dfcd1cbfb618ead1da9eadeb3ca103971c8ded8\":\"422db9103561bc3fa43930ef1dfcd1cbfb618ead1da9eadeb3ca103971c8ded8\",\"artifact:4028:5d5b6f9a4c680dbd2d64c5ca32cbbb197709e5c11388210be1150c359663273e\":\"5d5b6f9a4c680dbd2d64c5ca32cbbb197709e5c11388210be1150c359663273e\",\"artifact:4028:6d12b59bfe62bfaf3d248ec97cd0961c42ce4f5a2acc425f6f9b1cde13fa5585\":\"6d12b59bfe62bfaf3d248ec97cd0961c42ce4f5a2acc425f6f9b1cde13fa5585\",\"artifact:4028:739af7218eca6a87e7092b0efd5862de407cda0980f3b3b40dbccf4d86f1839f\":\"739af7218eca6a87e7092b0efd5862de407cda0980f3b3b40dbccf4d86f1839f\",\"artifact:4028:873b2671a8d97623442b453442a080e6fbf66b850757c3451065cce6fdbc1f87\":\"873b2671a8d97623442b453442a080e6fbf66b850757c3451065cce6fdbc1f87\",\"artifact:4028:8782e034f2b86c83e42314850f5f0daae82a427c3820a67713a0c12ddce64ac5\":\"8782e034f2b86c83e42314850f5f0daae82a427c3820a67713a0c12ddce64ac5\",\"artifact:4028:8b613413561ecd45975426a11a61ea024a2660daa87d7b48692d8728f223a6b9\":\"8b613413561ecd45975426a11a61ea024a2660daa87d7b48692d8728f223a6b9\",\"artifact:4028:ca0d98d9e6df521183ffa2c079f269a022d465267ac43f86d272d4a7f8b12f9f\":\"ca0d98d9e6df521183ffa2c079f269a022d465267ac43f86d272d4a7f8b12f9f\",\"artifact:4028:ca75c7fcd9dcd3126f56fdbc309b143e99c0aa38dfa1600b0881c619694afe27\":\"ca75c7fcd9dcd3126f56fdbc309b143e99c0aa38dfa1600b0881c619694afe27\"},\"sha256\":\"c36cdd36ef2824342d4eb72e3b08882582d3893e83ad5f489d85df5765b6f548\"},\"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:4028,input_sha256:\"c4f18957d150b02cd07560f13d1e1f9034cf36f0959142ab714d7c2f456ae9b4\",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/4234/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"e8648c90a0c90451b316a05c62b9be03966721cd96b95750f41b6467de52ec40","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}