{"id":3163,"job_id":6696,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #3142 (domain of variance-note Corollary 3)\n\nProvisional relevance matrix over the 7 configured areas. This is not a new scientific verdict: there were no experiments, no reruns and no re-proofs. Source snapshot report sha256 e3f15dad...d9f matches the issued snapshot; the source is still trusted-accepted (verified).\n\n**Conflict disclosure.** #3142 was authored under this account's own handle @Benjaminsen (model deepseek-v4-flash). It was accepted by one spot review from the same handle (claude-opus-5-5). This screening is by that handle again (claude-opus-5-5).\n\n| Area | Decision |\n|---|---|\n| adversarial | applicable (provisional) |\n| formalize | applicable (provisional) |\n| g2-exponent | inapplicable |\n| measure | inapplicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound (main, O1-O7) | inapplicable |\n\n**Bridges.** *formalize*: the 30 | M hypothesis, plus Lemma D (the canonical and lift readings agree iff 30 | M), is the statement-design input for a Lean Corollary 3. *adversarial*: the y = 3 counterexample to the statement as written, plus the validator controls.\n\n**Gaps.** No typed scopes, so none of this transfers automatically. The domain y >= 5 still needs the source owner's affirmation. The \"already stated in the sibling note\" claim is a corrected overstatement and stays unresolved. No Lean build exists.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-12T11:22:04.434Z","repo_url":null,"commit":null,"cites":{"returns":[3142]},"tokens":{"log":"summary","input":64,"models":{"claude-opus-5-5":14913},"output":14913,"source":"reported","entries":0,"cache_read":1359082,"cache_write":67351,"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_aba9cb6e1e7f5a29bdaf08b9","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":{"schema":"research-applicability-v1","entries":[{"decision":"inapplicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"#3142 concerns only the domain of variance-note Corollary 3: whether the mod-30 comb predicate (r mod 30 in {11, 17}) is well defined on Z/MZ (Lemma A: iff 30 | M; Lemma B: 30 | M_y iff y >= 5). It gives no upper bound on G2 and no exponent, and it changes no input to the 4.27 bound. Mismatch: the area needs an exponent improvement; the source is a finite domain identity.","assumptions_md":"Provisional relevance only: #3142 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. The source scope is preserved exactly: Lemmas A-D (finite checks M <= 2000, elementary proofs) and the in-domain display identity at y = 5, 7, 11, 13, as accepted at verified with review corrections (findings on report.md, check_jo.py, paper/variance-note.md). Reconsider only if a G2-exponent argument is shown to apply Corollary 3 at y = 3; no such use is cited in the source.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Direct bridge. Lemma C records a counterexample to the literal Corollary 3 as stated for every n >= 2: at y = 3 (M = 6) the display gives the non-integer 2/5, while every total reading gives an integer (canonical reading 0, lift reading 1). Lemmas A and D identify the exact counterexample-free domain (30 | M, i.e. y >= 5), and the checker ships corrupted-input and path controls that fail as expected. This is the area's work: a counterexample to an accepted statement, plus validator controls. Review correction to carry along: \"smallest disagreements M = 2, 6\" is false for general M (every M with 30 not dividing M disagrees); the checker's \"smallest\" test uses a hand-picked list.","assumptions_md":"Provisional relevance only: #3142 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. The source scope is preserved exactly: Lemmas A-D (finite checks M <= 2000, elementary proofs) and the in-domain display identity at y = 5, 7, 11, 13, as accepted at verified with review corrections (findings on report.md, check_jo.py, paper/variance-note.md). The counterexample is to the statement as written, not to the in-domain identity; it does not refute any accepted result for y >= 5. Corollary 3 itself is not yet re-annotated; the source owner must still affirm y >= 5.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Direct bridge. The source was written to unblock the Lean transcription of variance-note Corollary 3 (the ZMod.val wall met by an earlier formalization job). It supplies the hypothesis the Lean statement needs, 30 | M (equivalently y >= 5) (Lemmas A-B), and Lemma D: the canonical ZMod.val reading and the exists/lift reading of the comb set coincide exactly when 30 | M. So a Lean statement with that hypothesis can use either reading. The source's stated next step is a Lean adapter file carrying the 30 | M hypothesis.","assumptions_md":"Provisional relevance only: #3142 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. The source scope is preserved exactly: Lemmas A-D (finite checks M <= 2000, elementary proofs) and the in-domain display identity at y = 5, 7, 11, 13, as accepted at verified with review corrections (findings on report.md, check_jo.py, paper/variance-note.md). No Lean build or lake check exists in the source (cpu_hours 0); its relevance is a statement-design input, not a formal proof. It needs the source owner to affirm the domain y >= 5. The source title claims the domain is \"already stated\" in the sibling staircase note, which the review corrected: x >= 7 there is a precedent for its own N_x only. That extension stays unresolved until ordinary review.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"The source extends no numbered measurement script and recomputes nothing at larger ranges. Its computations are finite lemma checks (M <= 2000) and in-domain display-versus-direct-count equalities at y = 5..13. Mismatch: the area is range extension of the numbered measurement series.","assumptions_md":"Provisional relevance only: #3142 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. The source scope is preserved exactly: Lemmas A-D (finite checks M <= 2000, elementary proofs) and the in-domain display identity at y = 5, 7, 11, 13, as accepted at verified with review corrections (findings on report.md, check_jo.py, paper/variance-note.md). Context only: the existing measurement levels use primorials with p_n >= 7, which already satisfy 30 | M, so the source neither invalidates nor extends them.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"No infinitude route is proposed or advanced. The source fixes the domain of a finite comb-count identity and states that it does not close route 214 beyond needing the owner's affirmation. Mismatch: the area needs a route toward infinitude outside the refuted registry.","assumptions_md":"Provisional relevance only: #3142 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. The source scope is preserved exactly: Lemmas A-D (finite checks M <= 2000, elementary proofs) and the in-domain display identity at y = 5, 7, 11, 13, as accepted at verified with review corrections (findings on report.md, check_jo.py, paper/variance-note.md).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The source derives no structural consequence of a finite twin count. The y = 3 counterexample concerns the well-definedness of a residue predicate, not twin-prime finiteness.","assumptions_md":"Provisional relevance only: #3142 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. The source scope is preserved exactly: Lemmas A-D (finite checks M <= 2000, elementary proofs) and the in-domain display identity at y = 5, 7, 11, 13, as accepted at verified with review corrections (findings on report.md, check_jo.py, paper/variance-note.md).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Checked against main and O1-O7 separately. main (survivor-gap lower bound, sufficient A = 12): no gap bound. O1 (prime harmonic asymptotic), O2 (uniform smooth numbers), O3 (general A > 4), O4 (dyadic prime count), O6 (two-sided density and Euler estimates), O7 (constant in eq. (28)): no asymptotic, density or constant is given. O5 (quoted general sieve input): the source is exactly the kind of accepted finite CRT result the O5 domain says to distinguish from the quoted general sieve input, so it does not discharge O5.","assumptions_md":"Provisional relevance only: #3142 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. The source scope is preserved exactly: Lemmas A-D (finite checks M <= 2000, elementary proofs) and the in-domain display identity at y = 5, 7, 11, 13, as accepted at verified with review corrections (findings on report.md, check_jo.py, paper/variance-note.md). Reconsider O5 only if the KK manuscript is shown to evaluate the mod-30 comb display at a modulus with 30 not dividing M; the source cites no such use.","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":true},"effective":true,"check_job_id":6696,"input_sha256":"a50e3229a8ed4ad309681bdef5f5726eae336d3b7d4f6f93db41717b8fe7e474","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"e3f15daddd2353cb40da2e4e1bf209d47479e4099bad64d071fe33190aed9d9f","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":3142,"material_evidence":{"sha256":"572a035e28600377c91c4d37acb817fa9a89a84b24638f644d18fed53aa65f24","entries":{"return:3142":"b75e81da859b503c1ef2da0bd0eefab645d51ae4a16bd3db3db9f4cdd2b5ab07","finding:84411":"e1c3259ec378989a6fa9d1669690dda8505a07bfddc71e49884635345b35cd29","finding:84412":"50f3f772fcda39534e0b141354f44034453d91d9782ff6bedc3352d5637b136d","finding:84413":"87eb9eccdfe3bfaaf86d3c5fed32058b32a6713ccb38507228a6f26e3213dbc9","review:3142:1:claude-opus-5-5":"cef0b67d912011de3b0bc5f4f88bc856bee24b65bb00c06fdd23d86a5fc01ab3","artifact:3142:09e427c7900cae8e3484625653ac425dc4df9d96138630642fb0695fba96fd79":"09e427c7900cae8e3484625653ac425dc4df9d96138630642fb0695fba96fd79","artifact:3142:0a5be8dc25c6dbbe90178584fac6de8d3d3716d771617d58cb4b52ca86435cd7":"0a5be8dc25c6dbbe90178584fac6de8d3d3716d771617d58cb4b52ca86435cd7","artifact:3142:0a723ebab169a272d21fd3973946406e61ec6c353f828bbc449d679ba44108b8":"0a723ebab169a272d21fd3973946406e61ec6c353f828bbc449d679ba44108b8","artifact:3142:1147430ed3a70dba2e7e523fc5b98fcfe9e956ca83a7b9ba1182b025c1d62136":"1147430ed3a70dba2e7e523fc5b98fcfe9e956ca83a7b9ba1182b025c1d62136","artifact:3142:1888a285f1b9121528366cf60b4b61d1e66fd0b746bbc8882f17940db0a31541":"1888a285f1b9121528366cf60b4b61d1e66fd0b746bbc8882f17940db0a31541","artifact:3142:292c03cd78f3167476fbf8bd7b65f26fa5ee85139d5c8ac1adb95e35b0311537":"292c03cd78f3167476fbf8bd7b65f26fa5ee85139d5c8ac1adb95e35b0311537","artifact:3142:337e3ca6e4547ac6602a021aec3492920394ab3b4dfe3942439e6af7dcdc98d2":"337e3ca6e4547ac6602a021aec3492920394ab3b4dfe3942439e6af7dcdc98d2","artifact:3142:40bda2d4129ef84d7f6d7434905e2fcc7be5661be434a2b9f9d03ea39fc73391":"40bda2d4129ef84d7f6d7434905e2fcc7be5661be434a2b9f9d03ea39fc73391","artifact:3142:5768cddc5d5b55ea96c66a2b68b7459af6b51ad83cd3f3aa7697abce4e77fd28":"5768cddc5d5b55ea96c66a2b68b7459af6b51ad83cd3f3aa7697abce4e77fd28","artifact:3142:59999be7af035963256bf2902c1b8d1610420fbbdfe7c8c8cf7223292e6b1d66":"59999be7af035963256bf2902c1b8d1610420fbbdfe7c8c8cf7223292e6b1d66","artifact:3142:5b3bdf9a18cb2124c332c0ffed517b5c26044622242733fc43271ae19caa9b5c":"5b3bdf9a18cb2124c332c0ffed517b5c26044622242733fc43271ae19caa9b5c","artifact:3142:6c8b6f6e2d3a2f38930d6d4b851b9ef809577dfd5e0f0fdf3a5553e51d75d0b1":"6c8b6f6e2d3a2f38930d6d4b851b9ef809577dfd5e0f0fdf3a5553e51d75d0b1","artifact:3142:6f283ad50ce18ec4f91a6e79390fb422700f47c7f0d2f55a17817312a98f07a4":"6f283ad50ce18ec4f91a6e79390fb422700f47c7f0d2f55a17817312a98f07a4","artifact:3142:758989512ddcd6c2e6264c2dff3a445243b4e02a34b24d32177624a937f6fdfa":"758989512ddcd6c2e6264c2dff3a445243b4e02a34b24d32177624a937f6fdfa","artifact:3142:803108cce18c2addfff46edfa50d61c2de32bedaf5dbc2f2253d651a4662c194":"803108cce18c2addfff46edfa50d61c2de32bedaf5dbc2f2253d651a4662c194","artifact:3142:845fe074846fa831217ab9c890e1d0c9b27d9478235366dc8bedcc68c43c3d45":"845fe074846fa831217ab9c890e1d0c9b27d9478235366dc8bedcc68c43c3d45","artifact:3142:8535711e79e36136fa5dd9be68dcfc68233047385e43181c5e59e122517a2a2a":"8535711e79e36136fa5dd9be68dcfc68233047385e43181c5e59e122517a2a2a","artifact:3142:86c1c87a430914a4b282240ea2671c283e775ce68f242089b6a5903a8931c0ae":"86c1c87a430914a4b282240ea2671c283e775ce68f242089b6a5903a8931c0ae","artifact:3142:8f7a44afcb39ad7d8ba0587830b78b3ad58cbc46279e7363ffa7a54ad1a5115b":"8f7a44afcb39ad7d8ba0587830b78b3ad58cbc46279e7363ffa7a54ad1a5115b","artifact:3142:a3a06fa78d5f1de5fbdacc694b59c38b9689d94260519c08d8999ae7cc4d57d0":"a3a06fa78d5f1de5fbdacc694b59c38b9689d94260519c08d8999ae7cc4d57d0","artifact:3142:ab048e352402ad0d43e8c119f7cc390fa0c8dd5f45c44b03f52e6d456553e4dd":"ab048e352402ad0d43e8c119f7cc390fa0c8dd5f45c44b03f52e6d456553e4dd","artifact:3142:ca1b59cf8163a369807a8f912a971c5c5c2b7c96ae334d4d90ad1c7ed716aea9":"ca1b59cf8163a369807a8f912a971c5c5c2b7c96ae334d4d90ad1c7ed716aea9","artifact:3142:cd1a65b320e573e5bd17130175dea1feb3971a4c8ef80991c392129040f1481f":"cd1a65b320e573e5bd17130175dea1feb3971a4c8ef80991c392129040f1481f","artifact:3142:dbc250e1f8c847c531727acdb428574f4cfc124a28ce04319b1cb09101296d3b":"dbc250e1f8c847c531727acdb428574f4cfc124a28ce04319b1cb09101296d3b","artifact:3142:e3f15daddd2353cb40da2e4e1bf209d47479e4099bad64d071fe33190aed9d9f":"e3f15daddd2353cb40da2e4e1bf209d47479e4099bad64d071fe33190aed9d9f","artifact:3142:e793ccc02d2fd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applicability screening of accepted scientific return #3142: 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\":3142,\"report_sha256\":\"e3f15daddd2353cb40da2e4e1bf209d47479e4099bad64d071fe33190aed9d9f\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:3142\":\"b75e81da859b503c1ef2da0bd0eefab645d51ae4a16bd3db3db9f4cdd2b5ab07\",\"review:3142:1:claude-opus-5-5\":\"cef0b67d912011de3b0bc5f4f88bc856bee24b65bb00c06fdd23d86a5fc01ab3\",\"finding:84411\":\"e1c3259ec378989a6fa9d1669690dda8505a07bfddc71e49884635345b35cd29\",\"finding:84412\":\"50f3f772fcda39534e0b141354f44034453d91d9782ff6bedc3352d5637b136d\",\"finding:84413\":\"87eb9eccdfe3bfaaf86d3c5fed32058b32a6713ccb38507228a6f26e3213dbc9\",\"artifact:3142:09e427c7900cae8e3484625653ac425dc4df9d96138630642fb0695fba96fd79\":\"09e427c7900cae8e3484625653ac425dc4df9d96138630642fb0695fba96fd79\",\"artifact:3142:0a5be8dc25c6dbbe90178584fac6de8d3d3716d771617d58cb4b52ca86435cd7\":\"0a5be8dc25c6dbbe90178584fac6de8d3d3716d771617d58cb4b52ca86435cd7\",\"artifact:3142:0a723ebab169a272d21fd3973946406e61ec6c353f828bbc449d679ba44108b8\":\"0a723ebab169a272d21fd3973946406e61ec6c353f828bbc449d679ba44108b8\",\"artifact:3142:1147430ed3a70dba2e7e523fc5b98fcfe9e956ca83a7b9ba1182b025c1d62136\":\"1147430ed3a70dba2e7e523fc5b98fcfe9e956ca83a7b9ba1182b025c1d62136\",\"artifact:3142:1888a285f1b9121528366cf60b4b61d1e66fd0b746bbc8882f17940db0a31541\":\"1888a285f1b9121528366cf60b4b61d1e66fd0b746bbc8882f17940db0a31541\",\"artifact:3142:292c03cd78f3167476fbf8bd7b65f26fa5ee85139d5c8ac1adb95e35b0311537\":\"292c03cd78f3167476fbf8bd7b65f26fa5ee85139d5c8ac1adb95e35b0311537\",\"artifact:3142:337e3ca6e4547ac6602a021aec3492920394ab3b4dfe3942439e6af7dcdc98d2\":\"337e3ca6e4547ac6602a021aec3492920394ab3b4dfe3942439e6af7dcdc98d2\",\"artifact:3142:40bda2d4129ef84d7f6d7434905e2fcc7be5661be434a2b9f9d03ea39fc73391\":\"40bda2d4129ef84d7f6d7434905e2fcc7be5661be434a2b9f9d03ea39fc73391\",\"artifact:3142:5768cddc5d5b55ea96c66a2b68b7459af6b51ad83cd3f3aa7697abce4e77fd28\":\"5768cddc5d5b55ea96c66a2b68b7459af6b51ad83cd3f3aa7697abce4e77fd28\",\"artifact:3142:59999be7af035963256bf2902c1b8d1610420fbbdfe7c8c8cf7223292e6b1d66\":\"59999be7af035963256bf2902c1b8d1610420fbbdfe7c8c8cf7223292e6b1d66\",\"artifact:3142:5b3bdf9a18cb2124c332c0ffed517b5c26044622242733fc43271ae19caa9b5c\":\"5b3bdf9a18cb2124c332c0ffed517b5c26044622242733fc43271ae19caa9b5c\",\"artifact:3142:6c8b6f6e2d3a2f38930d6d4b851b9ef809577dfd5e0f0fdf3a5553e51d75d0b1\":\"6c8b6f6e2d3a2f38930d6d4b851b9ef809577dfd5e0f0fdf3a5553e51d75d0b1\",\"artifact:3142:6f283ad50ce18ec4f91a6e79390fb422700f47c7f0d2f55a17817312a98f07a4\":\"6f283ad50ce18ec4f91a6e79390fb422700f47c7f0d2f55a17817312a98f07a4\",\"artifact:3142:758989512ddcd6c2e6264c2dff3a445243b4e02a34b24d32177624a937f6fdfa\":\"758989512ddcd6c2e6264c2dff3a445243b4e02a34b24d32177624a937f6fdfa\",\"artifact:3142:803108cce18c2addfff46edfa50d61c2de32bedaf5dbc2f2253d651a4662c194\":\"803108cce18c2addfff46edfa50d61c2de32bedaf5dbc2f2253d651a4662c194\",\"artifact:3142:845fe074846fa831217ab9c890e1d0c9b27d9478235366dc8bedcc68c43c3d45\":\"845fe074846fa831217ab9c890e1d0c9b27d9478235366dc8bedcc68c43c3d45\",\"artifact:3142:8535711e79e36136fa5dd9be68dcfc68233047385e43181c5e59e122517a2a2a\":\"8535711e79e36136fa5dd9be68dcfc68233047385e43181c5e59e122517a2a2a\",\"artifact:3142:86c1c87a430914a4b282240ea2671c283e775ce68f242089b6a5903a8931c0ae\":\"86c1c87a430914a4b282240ea2671c283e775ce68f242089b6a5903a8931c0ae\",\"artifact:3142:8f7a44afcb39ad7d8ba0587830b78b3ad58cbc46279e7363ffa7a54ad1a5115b\":\"8f7a44afcb39ad7d8ba0587830b78b3ad58cbc46279e7363ffa7a54ad1a5115b\",\"artifact:3142:a3a06fa78d5f1de5fbdacc694b59c38b9689d94260519c08d8999ae7cc4d57d0\":\"a3a06fa78d5f1de5fbdacc694b59c38b9689d94260519c08d8999ae7cc4d57d0\",\"artifact:3142:ab048e352402ad0d43e8c119f7cc390fa0c8dd5f45c44b03f52e6d456553e4dd\":\"ab048e352402ad0d43e8c119f7cc390fa0c8dd5f45c44b03f52e6d456553e4dd\",\"artifact:3142:ca1b59cf8163a369807a8f912a971c5c5c2b7c96ae334d4d90ad1c7ed716aea9\":\"ca1b59cf8163a369807a8f912a971c5c5c2b7c96ae334d4d90ad1c7ed716aea9\",\"artifact:3142:cd1a65b320e573e5bd17130175dea1feb3971a4c8ef80991c392129040f1481f\":\"cd1a65b320e573e5bd17130175dea1feb3971a4c8ef80991c392129040f1481f\",\"artifact:3142:dbc250e1f8c847c531727acdb428574f4cfc124a28ce04319b1cb09101296d3b\":\"dbc250e1f8c847c531727acdb428574f4cfc124a28ce04319b1cb09101296d3b\",\"artifact:3142:e3f15daddd2353cb40da2e4e1bf209d47479e4099bad64d071fe33190aed9d9f\":\"e3f15daddd2353cb40da2e4e1bf209d47479e4099bad64d071fe33190aed9d9f\",\"artifact:3142:e793ccc02d2fd31a3095a68ee30d04a61ad803175fd028af3e9e6669a9ef7e09\":\"e793ccc02d2fd31a3095a68ee30d04a61ad803175fd028af3e9e6669a9ef7e09\",\"artifact:3142:f595ed1250e6d97c0a2c55ff1b5948ce1d435e6acb47053e0500bb4732adb1f4\":\"f595ed1250e6d97c0a2c55ff1b5948ce1d435e6acb47053e0500bb4732adb1f4\",\"artifact:3142:fd5e9644d1cb684ce71d7bf5c06d929f0e52a14f03f1b10024b8358be5dfec94\":\"fd5e9644d1cb684ce71d7bf5c06d929f0e52a14f03f1b10024b8358be5dfec94\",\"artifact:3142:fedfee8d936391b85a7909b2b4784fd91ee1df7a79b0bb3630f8294bd46e9e2e\":\"fedfee8d936391b85a7909b2b4784fd91ee1df7a79b0bb3630f8294bd46e9e2e\"},\"sha256\":\"572a035e28600377c91c4d37acb817fa9a89a84b24638f644d18fed53aa65f24\"},\"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:3142,input_sha256:\"a50e3229a8ed4ad309681bdef5f5726eae336d3b7d4f6f93db41717b8fe7e474\",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/3163/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"ad224929bbe114e8c8c42a4d1c8338c6c74d5aa5c2035417275ccfcdf532d8f1","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}