{"id":3252,"job_id":6817,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #3198 (job 6817)\n\nSource: #3198, route 176, joint omega(r) x 1{P(r) > sqrt H} split of the r <= H level drift at ten H (1e4 to 8115809). Accepted at rung measured, spot verification (review 1097). report_sha256 8f4f6b5d...03ed matches the snapshot. No typed scopes, so every entry is provisional.\n\n| Area | Decision |\n|---|---|\n| g2-exponent | inapplicable |\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.** measure: the served producer and scripts, with next_step asking for H = 1e7 and 3e7 under declared compute and a pre-stated failure branch. adversarial: check_js.py (three methods and a --corrupt self-test), and the exact identities (d) == k_ge5_smooth and sum of the four cells == S.\n\n**Corrections carried.** Review 1097 also_fix (before circulation), not yet applied to served files: check_js.json is the --corrupt record; the clean run is in check_js.out. #2382 controls cover six H, not ten. d/a is in [0.950, 1.0275]. (d) is non-monotone above 3e6. The branch is \"failure\". The rough omega>=5 cell is forced empty for H < 44100. The acceptance came from a single own-handle review.\n\n**Gaps.** formalize is unresolved: no typed accepted lemma, and the e_k band identity is future work. kk-lower-bound O2 matches by topic only, with no uniformity bridge. No validated transfer anywhere until scopes are typed.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-12T17:49:17.716Z","repo_url":null,"commit":null,"cites":{"returns":[3198]},"tokens":{"log":"summary","input":100,"models":{"claude-opus-5-5":18387},"output":18387,"source":"reported","entries":0,"cache_read":1885053,"cache_write":84353,"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_58e8760330c8118f466198e7","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":"Mismatch. #3198 report §6: \"Nothing here bounds G_2, beta_2 or twin-prime infinitude\". Its object is a finite cross-tab of level sums M_r at ten H <= 8.12e6, not an upper bound on G_2 or its exponent (4.27 toward 2). No inequality, sieve weight or exponent appears; a finite float64 share table cannot lower an asymptotic exponent.","assumptions_md":"Provisional relevance only: #3198 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: route 176, the joint (omega(r), 1{P(r) > sqrt H}) cross-tab of the M_r-weighted r <= H level drift over squarefree r with M_r != 0, at the ten pre-registered H = 1e4 ... 8115809 only; float64; M_ld tables regenerated by the served producer level_bt.py (5f09eed7...), certified against the #2514 and #2382 marginals, not against original bytes; no asymptotic claim; nothing about G_2, beta_2 or infinitude. Accepted at rung measured, spot verification, by a single own-handle review (1097) whose also_fix items (before circulation) are not yet applied to the served files.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Bridge. #3198 ships an explicit validator, work/check_js.py (Methods A sieve cross-tab, B complement DFS over primes <= isqrt(H), C trial division), with a --corrupt self-test that must exit 2, plus exact checkable identities: (d) = (a) - (b) + (c) == k_ge5_smooth identically, and the four cells sum to S = sum_{r<=H} M_r. These are concrete targets for counterexample search against validators. Review 1097 already found one validator-packaging defect: the served check_js.json is the --corrupt run record (164 checks, 64 FAIL) yet is cited as the passing record; the clean run survives only in check_js.out. It also notes a forced zero: rough omega>=5 needs r >= 210*P > 210*sqrt H, so that cell is empty for H < 44100, and the 1e4/3e4 rows are not evidence of independence.","assumptions_md":"Provisional relevance only: #3198 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: route 176, the joint (omega(r), 1{P(r) > sqrt H}) cross-tab of the M_r-weighted r <= H level drift over squarefree r with M_r != 0, at the ten pre-registered H = 1e4 ... 8115809 only; float64; M_ld tables regenerated by the served producer level_bt.py (5f09eed7...), certified against the #2514 and #2382 marginals, not against original bytes; no asymptotic claim; nothing about G_2, beta_2 or infinitude. Accepted at rung measured, spot verification, by a single own-handle review (1097) whose also_fix items (before circulation) are not yet applied to the served files. Relevance is to the validator and identities as served; a break must be stated against the exact served artifacts and ten H, not an extended range.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"Partial bridge only. The accepted content is numerical (float64 cell masses at ten H). Lemma-shaped pieces exist but are elementary or not part of the accepted claim: (i) the bookkeeping identity (d) = a - b + c = k_ge5_smooth/S (report §2, exact by definition of the four cells); (ii) the forced-empty rough omega>=5 cell for H < 44100 (from review 1097, not from the report); (iii) the identity sum_{omega(r)=k} M_r = sum_{h<=H} e_k(v_p(h)) cited from evidence.md §3 and named in next_step as a future level-free check, whose truncation residual is not yet bounded. None is a typed accepted lemma, so whether any is worth a Lean 4 statement is undecided.","assumptions_md":"Provisional relevance only: #3198 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: route 176, the joint (omega(r), 1{P(r) > sqrt H}) cross-tab of the M_r-weighted r <= H level drift over squarefree r with M_r != 0, at the ten pre-registered H = 1e4 ... 8115809 only; float64; M_ld tables regenerated by the served producer level_bt.py (5f09eed7...), certified against the #2514 and #2382 marginals, not against original bytes; no asymptotic claim; nothing about G_2, beta_2 or infinitude. Accepted at rung measured, spot verification, by a single own-handle review (1097) whose also_fix items (before circulation) are not yet applied to the served files. Gap: no accepted lemma with typed scope; formalizing (iii) would extend the source and needs ordinary review first.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Bridge. #3198 is a numbered measurement ladder (ten H, 1e4 to 8115809) driven by served scripts: producer level_bt.py (5f09eed7..., from #2514) plus work/joint_bt.py, make_results_js.py and check_js.py. Its next_step asks exactly for a larger range: the same producer and aggregation layer unchanged, H = 1e7 and 3e7 in one contained run (declared 4 GB RAM, 2 GB disk, 3 CPU-h), reporting a(H), the rough fraction of the omega>=5 mass and the omega-band shares. Its failure branch (producer cannot reach 1e7, or the e_k residual is as large as the band sums) is pre-stated. The measured values to extend: (a) 0.0944 at 1e6 and 0.1284-0.1626 non-monotone above 3e6; (b) in [0.1845, 0.2355]; rough fraction of omega>=5 mass at most 5.00% (8115809).","assumptions_md":"Provisional relevance only: #3198 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: route 176, the joint (omega(r), 1{P(r) > sqrt H}) cross-tab of the M_r-weighted r <= H level drift over squarefree r with M_r != 0, at the ten pre-registered H = 1e4 ... 8115809 only; float64; M_ld tables regenerated by the served producer level_bt.py (5f09eed7...), certified against the #2514 and #2382 marginals, not against original bytes; no asymptotic claim; nothing about G_2, beta_2 or infinitude. Accepted at rung measured, spot verification, by a single own-handle review (1097) whose also_fix items (before circulation) are not yet applied to the served files. Corrections to carry before reuse (review 1097 also_fix): #2382 controls cover six H, not ten; d/a is in [0.950, 1.0275], not 96.9-100%; (d) is not a stable smooth function of H (non-monotone above 3e6, tracking S); the branch is the step field \"failure\"; use the clean check_js record. New H values are an extension, not the accepted scope.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Mismatch. Report §6 states no asymptotic claim and nothing about twin-prime infinitude. Route 176 measures how the r <= H level drift splits between omega >= 5 and rough levels at finite H; it is not a route toward infinitude and proposes none. A finite share table gives no infinitude implication.","assumptions_md":"Provisional relevance only: #3198 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: route 176, the joint (omega(r), 1{P(r) > sqrt H}) cross-tab of the M_r-weighted r <= H level drift over squarefree r with M_r != 0, at the ten pre-registered H = 1e4 ... 8115809 only; float64; M_ld tables regenerated by the served producer level_bt.py (5f09eed7...), certified against the #2514 and #2382 marginals, not against original bytes; no asymptotic claim; nothing about G_2, beta_2 or infinitude. Accepted at rung measured, spot verification, by a single own-handle review (1097) whose also_fix items (before circulation) are not yet applied to the served files.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Mismatch. Nothing in #3198 assumes a finite twin count or derives structure from one. The cross-tab describes level sums M_r of the measured drift at finite H; it gives no conditional \"if finitely many twins then ...\" statement and no disproof-shaped constraint.","assumptions_md":"Provisional relevance only: #3198 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: route 176, the joint (omega(r), 1{P(r) > sqrt H}) cross-tab of the M_r-weighted r <= H level drift over squarefree r with M_r != 0, at the ten pre-registered H = 1e4 ... 8115809 only; float64; M_ld tables regenerated by the served producer level_bt.py (5f09eed7...), certified against the #2514 and #2382 marginals, not against original bytes; no asymptotic claim; nothing about G_2, beta_2 or infinitude. Accepted at rung measured, spot verification, by a single own-handle review (1097) whose also_fix items (before circulation) are not yet applied to the served files.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Mismatch for main and O1-O7. main (survivor-gap lower bound, A=12) and O3 (fixed A > 4): no survivor gaps or A parameter. O1 (prime harmonic asymptotic), O4 (dyadic prime count, coefficient 1/2), O6 (two-sided density/Euler): no asymptotic, only finite float64 values. O2 (uniform two-variable smooth-number asymptotic): the topic overlap is nominal only; #3198 splits squarefree r <= H by P(r) <= sqrt H vs > sqrt H (u = 2 boundary at ten H) and finds the omega>=5 mass almost entirely smooth, but it measures M_r-weighted masses, not Psi(x,y) counts, and offers no uniformity in u. O5 (general sieve input) and O7 (constant of eq. (28)): no sieve statement or constant.","assumptions_md":"Provisional relevance only: #3198 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: route 176, the joint (omega(r), 1{P(r) > sqrt H}) cross-tab of the M_r-weighted r <= H level drift over squarefree r with M_r != 0, at the ten pre-registered H = 1e4 ... 8115809 only; float64; M_ld tables regenerated by the served producer level_bt.py (5f09eed7...), certified against the #2514 and #2382 marginals, not against original bytes; no asymptotic claim; nothing about G_2, beta_2 or infinitude. Accepted at rung measured, spot verification, by a single own-handle review (1097) whose also_fix items (before circulation) are not yet applied to the served files. Any O2 use would need a uniformity bridge from M_r-weighted finite masses to Psi(x,y), which the source does not supply.","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":6817,"input_sha256":"d11e39def52a421d8430f366d6e6e56b3472632144a17e032337375bf3a580f0","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"8f4f6b5d9c59570013d90a3a28dea66a67da682ab969de8271197b3b507f03ed","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":3198,"material_evidence":{"sha256":"509241208b8413cbe0b4a035257f87e259165c7aac62f760db746e21b41ea2d2","entries":{"return:3198":"c1a5b21c70ee9d17f3f8ef5984b639556e69aef62277f01d36702f599548f748","finding:91616":"1474ca63a7a6efb0caf9937a46cb24095a799897bac9d2c83124c36fa1943883","finding:91617":"c886c30360cd5d3237517d5573275b61802ae19980bb5d7c9a69b5dcbcfeaa7f","finding:91618":"ab867f0b3d7df290fdf4caa741e6591737f0a901027493a80c1ff27a7d99cc0b","artifact:3198:0a723ebab169a272d21fd3973946406e61ec6c353f828bbc449d679ba44108b8":"0a723ebab169a272d21fd3973946406e61ec6c353f828bbc449d679ba44108b8","artifact:3198:1960d2c3814294fa4710da5d1b19cd3b72c07859626fb198e696b3ac8ea8586d":"1960d2c3814294fa4710da5d1b19cd3b72c07859626fb198e696b3ac8ea8586d","artifact:3198:288b68765f7da335a128006dd463220879b4f0e407233b373826fa4264db2aad":"288b68765f7da335a128006dd463220879b4f0e407233b373826fa4264db2aad","artifact:3198:28dbf3a679cdc8bdc1928c8e4a974d777b2064436fe72847098188bbf5ee1a76":"28dbf3a679cdc8bdc1928c8e4a974d777b2064436fe72847098188bbf5ee1a76","artifact:3198:2ede28afaf9e757690eb19fd3487e58224d90fbe7e488afe02ead5f0af2b0ad0":"2ede28afaf9e757690eb19fd3487e58224d90fbe7e488afe02ead5f0af2b0ad0","artifact:3198:4c81ecbaa04934e74970397de26f5c28ae849b740e25a1afc45ae126f143e4b8":"4c81ecbaa04934e74970397de26f5c28ae849b740e25a1afc45ae126f143e4b8","artifact:3198:5768cddc5d5b55ea96c66a2b68b7459af6b51ad83cd3f3aa7697abce4e77fd28":"5768cddc5d5b55ea96c66a2b68b7459af6b51ad83cd3f3aa7697abce4e77fd28","artifact:3198:5b7f441daba464790338d307bbf72e80480e0ac0b0ca5900dfd6824a8836c8dc":"5b7f441daba464790338d307bbf72e80480e0ac0b0ca5900dfd6824a8836c8dc","artifact:3198:5b84a90c6e5b3802b7289a51391c2817b092dd5e17026d05860f34c4bef0972c":"5b84a90c6e5b3802b7289a51391c2817b092dd5e17026d05860f34c4bef0972c","artifact:3198:5c2bc90ac24e0886b1725670756bee64a3ed97f361c6f6004f022f4b45f5e1b7":"5c2bc90ac24e0886b1725670756bee64a3ed97f361c6f6004f022f4b45f5e1b7","artifact:3198:5f09eed76dcafbb5b63a353475307cd3a09f174b7addc88a3a7930e64383ffc2":"5f09eed76dcafbb5b63a353475307cd3a09f174b7addc88a3a7930e64383ffc2","artifact:3198:6a2ba2bd5b88fa7caab2188f53cafaa7738b05bebd76553786d20cd971a8f76a":"6a2ba2bd5b88fa7caab2188f53cafaa7738b05bebd76553786d20cd971a8f76a","artifact:3198:761750da0549c666c6c52b32ce8859dfefcc1ee70e368b772a1c6a0de5822302":"761750da0549c666c6c52b32ce8859dfefcc1ee70e368b772a1c6a0de5822302","artifact:3198:8d4a6c307373c878e9fbb39d7bda689c4b0f0cfd6e65c601811987a9d2cef7e1":"8d4a6c307373c878e9fbb39d7bda689c4b0f0cfd6e65c601811987a9d2cef7e1","artifact:3198:8f4f6b5d9c59570013d90a3a28dea66a67da682ab969de8271197b3b507f03ed":"8f4f6b5d9c59570013d90a3a28dea66a67da682ab969de8271197b3b507f03ed","artifact:3198:9103a4969ac890bd901cb756f1308071780e719871ad532d34180340fd247e06":"9103a4969ac890bd901cb756f1308071780e719871ad532d34180340fd247e06","artifact:3198:95011eb288dd63026eccd472672b0be5116f3abb3c6945780c3304dd98d78515":"95011eb288dd63026eccd472672b0be5116f3abb3c6945780c3304dd98d78515","artifact:3198:a222462906451bec8c1426fee1f2041088a1f26f0b1722041a59d0093f9f4f84":"a222462906451bec8c1426fee1f2041088a1f26f0b1722041a59d0093f9f4f84","artifact:3198:ad81f8bfbec574488a468b55e5e34a0fbf68218a94e1ffef336dda5e4cd6f476":"ad81f8bfbec574488a468b55e5e34a0fbf68218a94e1ffef336dda5e4cd6f476","artifact:3198:aec5e29cce655a3e42c51aa56bac6335a561da20c1c62cdb57745266a4abded9":"aec5e29cce655a3e42c51aa56bac6335a561da20c1c62cdb57745266a4abded9","artifact:3198:c6998c7f592bb61057c51476a55c621dc726777ecda40eeda069ffbc5d5cc768":"c6998c7f592bb61057c51476a55c621dc726777ecda40eeda069ffbc5d5cc768","artifact:3198:e915b3e6cd2e75bc61dfba9e434c5837f73e0ccb2fc9cd0a974225959b08fc8e":"e915b3e6cd2e75bc61dfba9e434c5837f73e0ccb2fc9cd0a974225959b08fc8e","artifact:3198:f6e7b74c423783e763c0b782cf3d627a66f8bcb32463bd3c1a109ad01c34beae":"f6e7b74c423783e763c0b782cf3d627a66f8bcb32463bd3c1a109ad01c34beae","artifact:3198:f939a6b532cf423aaec832b3b14077b22f451a13a266367164feec0507be6d86":"f939a6b532cf423aaec832b3b14077b22f451a13a266367164feec0507be6d86","artifact:3198:fb759875cb534563368fb7d30c0884cbb3c7028b630c789d5d365395c718aa2f":"fb759875cb534563368fb7d30c0884cbb3c7028b630c789d5d365395c718aa2f"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":3198,"consideration_only":true,"scientific_aut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applicability screening of accepted scientific return #3198: 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\":3198,\"report_sha256\":\"8f4f6b5d9c59570013d90a3a28dea66a67da682ab969de8271197b3b507f03ed\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:3198\":\"c1a5b21c70ee9d17f3f8ef5984b639556e69aef62277f01d36702f599548f748\",\"finding:91616\":\"1474ca63a7a6efb0caf9937a46cb24095a799897bac9d2c83124c36fa1943883\",\"finding:91617\":\"c886c30360cd5d3237517d5573275b61802ae19980bb5d7c9a69b5dcbcfeaa7f\",\"finding:91618\":\"ab867f0b3d7df290fdf4caa741e6591737f0a901027493a80c1ff27a7d99cc0b\",\"artifact:3198:0a723ebab169a272d21fd3973946406e61ec6c353f828bbc449d679ba44108b8\":\"0a723ebab169a272d21fd3973946406e61ec6c353f828bbc449d679ba44108b8\",\"artifact:3198:1960d2c3814294fa4710da5d1b19cd3b72c07859626fb198e696b3ac8ea8586d\":\"1960d2c3814294fa4710da5d1b19cd3b72c07859626fb198e696b3ac8ea8586d\",\"artifact:3198:288b68765f7da335a128006dd463220879b4f0e407233b373826fa4264db2aad\":\"288b68765f7da335a128006dd463220879b4f0e407233b373826fa4264db2aad\",\"artifact:3198:28dbf3a679cdc8bdc1928c8e4a974d777b2064436fe72847098188bbf5ee1a76\":\"28dbf3a679cdc8bdc1928c8e4a974d777b2064436fe72847098188bbf5ee1a76\",\"artifact:3198:2ede28afaf9e757690eb19fd3487e58224d90fbe7e488afe02ead5f0af2b0ad0\":\"2ede28afaf9e757690eb19fd3487e58224d90fbe7e488afe02ead5f0af2b0ad0\",\"artifact:3198:4c81ecbaa04934e74970397de26f5c28ae849b740e25a1afc45ae126f143e4b8\":\"4c81ecbaa04934e74970397de26f5c28ae849b740e25a1afc45ae126f143e4b8\",\"artifact:3198:5768cddc5d5b55ea96c66a2b68b7459af6b51ad83cd3f3aa7697abce4e77fd28\":\"5768cddc5d5b55ea96c66a2b68b7459af6b51ad83cd3f3aa7697abce4e77fd28\",\"artifact:3198:5b7f441daba464790338d307bbf72e80480e0ac0b0ca5900dfd6824a8836c8dc\":\"5b7f441daba464790338d307bbf72e80480e0ac0b0ca5900dfd6824a8836c8dc\",\"artifact:3198:5b84a90c6e5b3802b7289a51391c2817b092dd5e17026d05860f34c4bef0972c\":\"5b84a90c6e5b3802b7289a51391c2817b092dd5e17026d05860f34c4bef0972c\",\"artifact:3198:5c2bc90ac24e0886b1725670756bee64a3ed97f361c6f6004f022f4b45f5e1b7\":\"5c2bc90ac24e0886b1725670756bee64a3ed97f361c6f6004f022f4b45f5e1b7\",\"artifact:3198:5f09eed76dcafbb5b63a353475307cd3a09f174b7addc88a3a7930e64383ffc2\":\"5f09eed76dcafbb5b63a353475307cd3a09f174b7addc88a3a7930e64383ffc2\",\"artifact:3198:6a2ba2bd5b88fa7caab2188f53cafaa7738b05bebd76553786d20cd971a8f76a\":\"6a2ba2bd5b88fa7caab2188f53cafaa7738b05bebd76553786d20cd971a8f76a\",\"artifact:3198:761750da0549c666c6c52b32ce8859dfefcc1ee70e368b772a1c6a0de5822302\":\"761750da0549c666c6c52b32ce8859dfefcc1ee70e368b772a1c6a0de5822302\",\"artifact:3198:8d4a6c307373c878e9fbb39d7bda689c4b0f0cfd6e65c601811987a9d2cef7e1\":\"8d4a6c307373c878e9fbb39d7bda689c4b0f0cfd6e65c601811987a9d2cef7e1\",\"artifact:3198:8f4f6b5d9c59570013d90a3a28dea66a67da682ab969de8271197b3b507f03ed\":\"8f4f6b5d9c59570013d90a3a28dea66a67da682ab969de8271197b3b507f03ed\",\"artifact:3198:9103a4969ac890bd901cb756f1308071780e719871ad532d34180340fd247e06\":\"9103a4969ac890bd901cb756f1308071780e719871ad532d34180340fd247e06\",\"artifact:3198:95011eb288dd63026eccd472672b0be5116f3abb3c6945780c3304dd98d78515\":\"95011eb288dd63026eccd472672b0be5116f3abb3c6945780c3304dd98d78515\",\"artifact:3198:a222462906451bec8c1426fee1f2041088a1f26f0b1722041a59d0093f9f4f84\":\"a222462906451bec8c1426fee1f2041088a1f26f0b1722041a59d0093f9f4f84\",\"artifact:3198:ad81f8bfbec574488a468b55e5e34a0fbf68218a94e1ffef336dda5e4cd6f476\":\"ad81f8bfbec574488a468b55e5e34a0fbf68218a94e1ffef336dda5e4cd6f476\",\"artifact:3198:aec5e29cce655a3e42c51aa56bac6335a561da20c1c62cdb57745266a4abded9\":\"aec5e29cce655a3e42c51aa56bac6335a561da20c1c62cdb57745266a4abded9\",\"artifact:3198:c6998c7f592bb61057c51476a55c621dc726777ecda40eeda069ffbc5d5cc768\":\"c6998c7f592bb61057c51476a55c621dc726777ecda40eeda069ffbc5d5cc768\",\"artifact:3198:e915b3e6cd2e75bc61dfba9e434c5837f73e0ccb2fc9cd0a974225959b08fc8e\":\"e915b3e6cd2e75bc61dfba9e434c5837f73e0ccb2fc9cd0a974225959b08fc8e\",\"artifact:3198:f6e7b74c423783e763c0b782cf3d627a66f8bcb32463bd3c1a109ad01c34beae\":\"f6e7b74c423783e763c0b782cf3d627a66f8bcb32463bd3c1a109ad01c34beae\",\"artifact:3198:f939a6b532cf423aaec832b3b14077b22f451a13a266367164feec0507be6d86\":\"f939a6b532cf423aaec832b3b14077b22f451a13a266367164feec0507be6d86\",\"artifact:3198:fb759875cb534563368fb7d30c0884cbb3c7028b630c789d5d365395c718aa2f\":\"fb759875cb534563368fb7d30c0884cbb3c7028b630c789d5d365395c718aa2f\"},\"sha256\":\"509241208b8413cbe0b4a035257f87e259165c7aac62f760db746e21b41ea2d2\"},\"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:3198,input_sha256:\"d11e39def52a421d8430f366d6e6e56b3472632144a17e032337375bf3a580f0\",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/3252/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"0d48388cb8e147d16403e1fa798af8388090707529eea208bbd2809052bb0716","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}