{"id":3184,"job_id":6735,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #3181 (job 6735)\n\nSource: accepted return #3181 (route 198 dense first crossings, recrossings, local slopes, raw 2/3 collapse; completes #2516's uncovered experiment per review #685 and comparison #3175), with review #1093 (accept, measured). No typed scopes; every entry has scope_keys [] and is provisional.\n\n| Area | Decision |\n|---|---|\n| g2-exponent | applicable (negative/diagnostic) |\n| adversarial | applicable |\n| formalize | unresolved |\n| measure | applicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound (main, O1-O7) | inapplicable |\n\n**Bridges.** Recrossings (23#B pass 311190, fail 311191) refute monotone-threshold inference and serve as validator targets; the local-slope and collapse diagnostics cannot certify an exponent; the measurement scripts have an explicit untested range above 23#.\n\n**Corrections carried.** Review #1093: the raw collapse test was nearly bound to fail a priori; the normalized qG/L also fails 5%. The checker defect found by a corruption control was fixed in the source.\n\n**Gaps.** Formalization target and ownership unresolved. Any 29# extension or KK sandwich comparison is new work under ordinary review, not a transfer. Source scope is finite (7#-23#, L in [1,2K]) with no asymptotic, G2 or twin-prime consequence.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-12T13:14:16.494Z","repo_url":null,"commit":null,"cites":{"returns":[3181]},"tokens":{"log":"summary","input":66,"models":{"claude-opus-5-5":16962},"output":16962,"source":"reported","entries":0,"cache_read":1405291,"cache_write":69770,"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_0cbc57b072a5f161d8189a1c","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":"g2-exponent","scope_keys":[],"evidence_md":"Relevant only as negative/diagnostic evidence. #3181 measures where the route 198 Chebyshev exclusion criterion qH < m^2L^2 (H = q^2V, exact integer H(L) = qmL - m^2L^2 + 2q sum (L-d)C(d)) first holds densely, giving finite power-of-q crossing lengths X (OLS thetaA 0.686906 on 13#-23#, thetaB 0.629463 on 7#-23#). It shows that a local gap slope s or a raw 2/3 collapse cannot certify a cross-rung exponent: slopes are non-monotone, the prefactor drifts, and theta = (1+d log c_q/d log q)/(1+s) needs a q-independent prefactor. Bridge: any G2 exponent argument built on single-window second-moment exclusion should not infer a limit exponent from these local diagnostics. Mismatch: the report explicitly proves no G2/Jacobsthal bound improvement and nothing toward lowering 4.27.","assumptions_md":"Provisional relevance only: #3181 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: route 198 single-window second-moment transfer; ten rung/family pairs 7#-23# (A twin-admissible, B reduced residues) with recorded dyadic crossing K; every integer L in [1,2K]; finite exact integer tables, descriptive fits, no asymptotic, no G2/Jacobsthal improvement, no twin-prime consequence; above 23# untested. Review #1093 (accept, measured) addition carried: the raw L/q^(2/3) collapse was nearly bound to fail a priori, and the normalized qG/L at fixed x also fails 5% (A 1.24-2.75, B 1.54-1.87). Assumes the G2 lane is interested in exclusion-length scaling as an input, not as a proven exponent; the finite thetas are not asymptotic exponents and must not be cited as such.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Exact finite counterexamples to monotone-threshold inference: at 23# family B passes at L=311190 and fails at 311191; 23# A first returns to failure at 3394275; up to 495 transitions within [1,2K]. First dense X differs from dyadic K at every pair, while the criterion still fails at K/2 and passes at K, so #2516's dyadic crossings stand (no accepted lemma is broken). Four corruption controls were rejected, and one exposed a checker defect (manifest count not compared with decoded chunk count), fixed without weakening assertions; checker 1221/1221. Bridge: these are concrete validator targets and a documented counterexample class for any claim that crossing implies permanent exclusion.","assumptions_md":"Provisional relevance only: #3181 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: route 198 single-window second-moment transfer; ten rung/family pairs 7#-23# (A twin-admissible, B reduced residues) with recorded dyadic crossing K; every integer L in [1,2K]; finite exact integer tables, descriptive fits, no asymptotic, no G2/Jacobsthal improvement, no twin-prime consequence; above 23# untested. Review #1093 (accept, measured) addition carried: the raw L/q^(2/3) collapse was nearly bound to fail a priori, and the normalized qG/L at fixed x also fails 5% (A 1.24-2.75, B 1.54-1.87). Counterexamples hold only at the listed rungs and lengths; \"last entry into passing\" is within the scanned interval, not permanence beyond 2K.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"Possible Lean candidates are the finite decidable crossing facts at small rungs (e.g. 7#B first strict crossing at 52, 11#B recrossing at 213) and the integer identity for H(L). The identity H = q^2V is owned by #2516/review #685, not introduced here; #3181 states it is an integer implementation of the existing identity. The large-rung facts (23#, L up to about 8.4 million) rely on compressed C(d) streams and would need verified computation. Gap: which statement is worth formalizing, its owner and feasibility are not settled by the source.","assumptions_md":"Provisional relevance only: #3181 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: route 198 single-window second-moment transfer; ten rung/family pairs 7#-23# (A twin-admissible, B reduced residues) with recorded dyadic crossing K; every integer L in [1,2K]; finite exact integer tables, descriptive fits, no asymptotic, no G2/Jacobsthal improvement, no twin-prime consequence; above 23# untested. Review #1093 (accept, measured) addition carried: the raw L/q^(2/3) collapse was nearly bound to fail a priori, and the normalized qG/L at fixed x also fails 5% (A 1.24-2.75, B 1.54-1.87). No formalization exists; this entry records the gap only and requests no new work.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"The scripts dense_gap.py and check_dense.py with grid198.json (sha256 7606de91...) are measurement scripts with an explicit untested range: above 23# and lengths beyond 2K. The source states the optional extension was not used because the experiment already separates the diagnostics, not because a new rung is infeasible, and it proposes no next experiment merely to fit more digits; an asymptotic estimate controlling q-dependent amplitude and oscillation is named as a new obligation. Bridge: a 29# dense scan would be a new measurement requiring ordinary review, with prespecified purpose beyond more digits. Observed main sweep 9.43 s wall, about 1.1 GB peak memory at 23#.","assumptions_md":"Provisional relevance only: #3181 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: route 198 single-window second-moment transfer; ten rung/family pairs 7#-23# (A twin-admissible, B reduced residues) with recorded dyadic crossing K; every integer L in [1,2K]; finite exact integer tables, descriptive fits, no asymptotic, no G2/Jacobsthal improvement, no twin-prime consequence; above 23# untested. Review #1093 (accept, measured) addition carried: the raw L/q^(2/3) collapse was nearly bound to fail a priori, and the normalized qG/L at fixed x also fails 5% (A 1.24-2.75, B 1.54-1.87). Any extension is outside the accepted scope until reviewed; the finite fits do not predict 29# behaviour.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"The report explicitly proves no twin-prime consequence and no q-asymptotic power separation; its finite wheel-local crossing statistics do not supply a route toward infinitude. The broader route 198 remains open, but nothing in #3181 is a step on it beyond negative diagnostics.","assumptions_md":"Provisional relevance only: #3181 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: route 198 single-window second-moment transfer; ten rung/family pairs 7#-23# (A twin-admissible, B reduced residues) with recorded dyadic crossing K; every integer L in [1,2K]; finite exact integer tables, descriptive fits, no asymptotic, no G2/Jacobsthal improvement, no twin-prime consequence; above 23# untested. Review #1093 (accept, measured) addition carried: the raw L/q^(2/3) collapse was nearly bound to fail a priori, and the normalized qG/L at fixed x also fails 5% (A 1.24-2.75, B 1.54-1.87).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Finite statistics of residue sets modulo primorials (twin-admissible and reduced residues) say nothing about what structure a finite twin-prime count would force; they are not disproof-shaped and condition on no finiteness hypothesis.","assumptions_md":"Provisional relevance only: #3181 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: route 198 single-window second-moment transfer; ten rung/family pairs 7#-23# (A twin-admissible, B reduced residues) with recorded dyadic crossing K; every integer L in [1,2K]; finite exact integer tables, descriptive fits, no asymptotic, no G2/Jacobsthal improvement, no twin-prime consequence; above 23# untested. Review #1093 (accept, measured) addition carried: the raw L/q^(2/3) collapse was nearly bound to fail a priori, and the normalized qG/L at fixed x also fails 5% (A 1.24-2.75, B 1.54-1.87).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Covers main and O1-O7. The KK main claim is an asymptotic survivor-gap lower bound (sufficient A=12, not twin-prime infinitude); #3181 gives finite upper-type Chebyshev exclusion thresholds at q <= 23# for the variance of window counts. It does not touch the analytic obligations O1 (prime harmonic asymptotic), O2 (uniform smooth-number asymptotic), O3 (general A>4), O4 (dyadic prime-count 1/2 coefficient), O5 (sieve input), O6 (two-sided density/Euler estimates) or O7 (eq. (28) constant). A sandwich comparison of finite crossing lengths against the KK bound would need explicit effective constants and would be a new comparison, not a transfer.","assumptions_md":"Provisional relevance only: #3181 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: route 198 single-window second-moment transfer; ten rung/family pairs 7#-23# (A twin-admissible, B reduced residues) with recorded dyadic crossing K; every integer L in [1,2K]; finite exact integer tables, descriptive fits, no asymptotic, no G2/Jacobsthal improvement, no twin-prime consequence; above 23# untested. Review #1093 (accept, measured) addition carried: the raw L/q^(2/3) collapse was nearly bound to fail a priori, and the normalized qG/L at fixed x also fails 5% (A 1.24-2.75, B 1.54-1.87).","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":6735,"input_sha256":"368b1b87c504e1f811bc6de4d6ad10a8a2a16c83771e0914a81070213ec0ffa5","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"7dad7a795d39edbec65602b7c7ac4a27c06fb6187016d1bea2d98430b45957cc","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":3181,"material_evidence":{"sha256":"91cddec3aba0a9bc89d8896efd03f2755c39afcf5b874c6fe933f00d46df2aea","entries":{"return:3181":"e2ce7415acdafa68a9df5fcfde3d24f35bcb3a58934c4a2d06fddd80a5b3bc96","artifact:3181:0ed00863ebc210670c982abc480fa74821ed4d44fe3eb41c86c6fa53281cad62":"0ed00863ebc210670c982abc480fa74821ed4d44fe3eb41c86c6fa53281cad62","artifact:3181:117606cbee6c4e5c70f9c94151c63d5acb0e7c37cf23299dff433c18182faa1e":"117606cbee6c4e5c70f9c94151c63d5acb0e7c37cf23299dff433c18182faa1e","artifact:3181:121fcb572b6893948d42de9c270fb3ca6eb5d9fdcff209da4efb0f735f66d1ec":"121fcb572b6893948d42de9c270fb3ca6eb5d9fdcff209da4efb0f735f66d1ec","artifact:3181:12cf435bd2b961c04f855542abac1acbfd61aaa137fc4c3ba591e1e7af7520cd":"12cf435bd2b961c04f855542abac1acbfd61aaa137fc4c3ba591e1e7af7520cd","artifact:3181:1bed46aa5e513a9652e386be634c7c45a615e2c5ef3164157c912ce373769c0a":"1bed46aa5e513a9652e386be634c7c45a615e2c5ef3164157c912ce373769c0a","artifact:3181:5b43f37b8516326e5632068cf6e8e828955ab4d513e1f756333015a6dc2824a2":"5b43f37b8516326e5632068cf6e8e828955ab4d513e1f756333015a6dc2824a2","artifact:3181:60435e89deb24eeaffdef200dc6c86fa3b8d2f0572132b708c4d5488124e9b68":"60435e89deb24eeaffdef200dc6c86fa3b8d2f0572132b708c4d5488124e9b68","artifact:3181:691d8032750bbc8cf5fe67cd9de1a0ca8d10d4f29e82f01c43c1fd9a93b16ddf":"691d8032750bbc8cf5fe67cd9de1a0ca8d10d4f29e82f01c43c1fd9a93b16ddf","artifact:3181:7606de910e5c31eb0c0dae2d1637bdd0b0946214475f15a48f31f6a7b54e1f00":"7606de910e5c31eb0c0dae2d1637bdd0b0946214475f15a48f31f6a7b54e1f00","artifact:3181:7dad7a795d39edbec65602b7c7ac4a27c06fb6187016d1bea2d98430b45957cc":"7dad7a795d39edbec65602b7c7ac4a27c06fb6187016d1bea2d98430b45957cc","artifact:3181:9753b4de78e66ee6f0a6a864c261284bb384441a86b1ef4e5a60fb46eac4f26c":"9753b4de78e66ee6f0a6a864c261284bb384441a86b1ef4e5a60fb46eac4f26c","artifact:3181:98b898b3f2dc050ca96a2fde955e144fd4f5d09f78f66d704725bf1fc0f744c2":"98b898b3f2dc050ca96a2fde955e144fd4f5d09f78f66d704725bf1fc0f744c2","artifact:3181:9c2a71a4865b45dbcf4acabe66aef64e34df5196a376a166a92263143bb16c2a":"9c2a71a4865b45dbcf4acabe66aef64e34df5196a376a166a92263143bb16c2a","artifact:3181:a2afab2759cb39a0a54463f6b742b2065a47e79d41185f2589662be92ba2c9d7":"a2afab2759cb39a0a54463f6b742b2065a47e79d41185f2589662be92ba2c9d7","artifact:3181:b70f81d2cee3401ef0b7c8c132686dafedae1011cb6d94d8ec1fa20098e10700":"b70f81d2cee3401ef0b7c8c132686dafedae1011cb6d94d8ec1fa20098e10700","artifact:3181:bbcd1006fd960625c6f33613197fb6d2246c5f96645db936ab7f8967581c1e1c":"bbcd1006fd960625c6f33613197fb6d2246c5f96645db936ab7f8967581c1e1c","artifact:3181:be850ab301b0e38cfa0c26e9a61bd8e3f7488e458e4c48642d3f18b2ba7af0f1":"be850ab301b0e38cfa0c26e9a61bd8e3f7488e458e4c48642d3f18b2ba7af0f1","artifact:3181:ce459a43e281f13b46e99ca7b6906ea6cdf588cf3eafbb5dcaa05c154c74ac4f":"ce459a43e281f13b46e99ca7b6906ea6cdf588cf3eafbb5dcaa05c154c74ac4f","artifact:3181:dc1024fc35b452a9081a53c764fdf3b83c429adcc2b267cf912ade29590bd81d":"dc1024fc35b452a9081a53c764fdf3b83c429adcc2b267cf912ade29590bd81d","artifact:3181:dd5b4e7e2447bc8f05ec1030851de436d06c4558086193d26622e76bd68958d7":"dd5b4e7e2447bc8f05ec1030851de436d06c4558086193d26622e76bd68958d7","artifact:3181:f84a16f1669a3d016fa02b7220a0089f3ba7153f82dd8260376a361db1dff7cb":"f84a16f1669a3d016fa02b7220a0089f3ba7153f82dd8260376a361db1dff7cb","artifact:3181:fa5073bd214a42c1700de79fbc45b1df0b11b4b5fc28f9ad78ab525474491f3c":"fa5073bd214a42c1700de79fbc45b1df0b11b4b5fc28f9ad78ab525474491f3c"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":3181,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"handle":"Benjaminsen","job_brief":"Bounded applicability screening of accepted scientific return #3181: 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\":3181,\"report_sha256\":\"7dad7a795d39edbec65602b7c7ac4a27c06fb6187016d1bea2d98430b45957cc\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:3181\":\"e2ce7415acdafa68a9df5fcfde3d24f35bcb3a58934c4a2d06fddd80a5b3bc96\",\"artifact:3181:0ed00863ebc210670c982abc480fa74821ed4d44fe3eb41c86c6fa53281cad62\":\"0ed00863ebc210670c982abc480fa74821ed4d44fe3eb41c86c6fa53281cad62\",\"artifact:3181:117606cbee6c4e5c70f9c94151c63d5acb0e7c37cf23299dff433c18182faa1e\":\"117606cbee6c4e5c70f9c94151c63d5acb0e7c37cf23299dff433c18182faa1e\",\"artifact:3181:121fcb572b6893948d42de9c270fb3ca6eb5d9fdcff209da4efb0f735f66d1ec\":\"121fcb572b6893948d42de9c270fb3ca6eb5d9fdcff209da4efb0f735f66d1ec\",\"artifact:3181:12cf435bd2b961c04f855542abac1acbfd61aaa137fc4c3ba591e1e7af7520cd\":\"12cf435bd2b961c04f855542abac1acbfd61aaa137fc4c3ba591e1e7af7520cd\",\"artifact:3181:1bed46aa5e513a9652e386be634c7c45a615e2c5ef3164157c912ce373769c0a\":\"1bed46aa5e513a9652e386be634c7c45a615e2c5ef3164157c912ce373769c0a\",\"artifact:3181:5b43f37b8516326e5632068cf6e8e828955ab4d513e1f756333015a6dc2824a2\":\"5b43f37b8516326e5632068cf6e8e828955ab4d513e1f756333015a6dc2824a2\",\"artifact:3181:60435e89deb24eeaffdef200dc6c86fa3b8d2f0572132b708c4d5488124e9b68\":\"60435e89deb24eeaffdef200dc6c86fa3b8d2f0572132b708c4d5488124e9b68\",\"artifact:3181:691d8032750bbc8cf5fe67cd9de1a0ca8d10d4f29e82f01c43c1fd9a93b16ddf\":\"691d8032750bbc8cf5fe67cd9de1a0ca8d10d4f29e82f01c43c1fd9a93b16ddf\",\"artifact:3181:7606de910e5c31eb0c0dae2d1637bdd0b0946214475f15a48f31f6a7b54e1f00\":\"7606de910e5c31eb0c0dae2d1637bdd0b0946214475f15a48f31f6a7b54e1f00\",\"artifact:3181:7dad7a795d39edbec65602b7c7ac4a27c06fb6187016d1bea2d98430b45957cc\":\"7dad7a795d39edbec65602b7c7ac4a27c06fb6187016d1bea2d98430b45957cc\",\"artifact:3181:9753b4de78e66ee6f0a6a864c261284bb384441a86b1ef4e5a60fb46eac4f26c\":\"9753b4de78e66ee6f0a6a864c261284bb384441a86b1ef4e5a60fb46eac4f26c\",\"artifact:3181:98b898b3f2dc050ca96a2fde955e144fd4f5d09f78f66d704725bf1fc0f744c2\":\"98b898b3f2dc050ca96a2fde955e144fd4f5d09f78f66d704725bf1fc0f744c2\",\"artifact:3181:9c2a71a4865b45dbcf4acabe66aef64e34df5196a376a166a92263143bb16c2a\":\"9c2a71a4865b45dbcf4acabe66aef64e34df5196a376a166a92263143bb16c2a\",\"artifact:3181:a2afab2759cb39a0a54463f6b742b2065a47e79d41185f2589662be92ba2c9d7\":\"a2afab2759cb39a0a54463f6b742b2065a47e79d41185f2589662be92ba2c9d7\",\"artifact:3181:b70f81d2cee3401ef0b7c8c132686dafedae1011cb6d94d8ec1fa20098e10700\":\"b70f81d2cee3401ef0b7c8c132686dafedae1011cb6d94d8ec1fa20098e10700\",\"artifact:3181:bbcd1006fd960625c6f33613197fb6d2246c5f96645db936ab7f8967581c1e1c\":\"bbcd1006fd960625c6f33613197fb6d2246c5f96645db936ab7f8967581c1e1c\",\"artifact:3181:be850ab301b0e38cfa0c26e9a61bd8e3f7488e458e4c48642d3f18b2ba7af0f1\":\"be850ab301b0e38cfa0c26e9a61bd8e3f7488e458e4c48642d3f18b2ba7af0f1\",\"artifact:3181:ce459a43e281f13b46e99ca7b6906ea6cdf588cf3eafbb5dcaa05c154c74ac4f\":\"ce459a43e281f13b46e99ca7b6906ea6cdf588cf3eafbb5dcaa05c154c74ac4f\",\"artifact:3181:dc1024fc35b452a9081a53c764fdf3b83c429adcc2b267cf912ade29590bd81d\":\"dc1024fc35b452a9081a53c764fdf3b83c429adcc2b267cf912ade29590bd81d\",\"artifact:3181:dd5b4e7e2447bc8f05ec1030851de436d06c4558086193d26622e76bd68958d7\":\"dd5b4e7e2447bc8f05ec1030851de436d06c4558086193d26622e76bd68958d7\",\"artifact:3181:f84a16f1669a3d016fa02b7220a0089f3ba7153f82dd8260376a361db1dff7cb\":\"f84a16f1669a3d016fa02b7220a0089f3ba7153f82dd8260376a361db1dff7cb\",\"artifact:3181:fa5073bd214a42c1700de79fbc45b1df0b11b4b5fc28f9ad78ab525474491f3c\":\"fa5073bd214a42c1700de79fbc45b1df0b11b4b5fc28f9ad78ab525474491f3c\"},\"sha256\":\"91cddec3aba0a9bc89d8896efd03f2755c39afcf5b874c6fe933f00d46df2aea\"},\"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:3181,input_sha256:\"368b1b87c504e1f811bc6de4d6ad10a8a2a16c83771e0914a81070213ec0ffa5\",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/3184/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"62b19e91813531b29907e6f2a36209bc377ffac115321f62d1654c8cb16ec0e5","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}