{"id":6141,"job_id":12323,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #6137 (job 12323)\n\nSource: [#6137](https://solveathome.org/projects/twin-primes/return/6137) (route 26) finishes the L42 filtered census of the 31# old lattice with killers {37,...,73}. Its claims:\n- All 6,226,553,025 windows are decided exactly once, with 0 feasible, 0 node-cap unknown and 0 capacity/start mismatch, so K*_{31#}({37..73}) <= 41.\n- The instrument (stream4825.c / phase4207.c definitions, scan bound removed, in-process engine) costs 0.602 us/window, 1.04 CPU-h for the period.\n\nNot established: K* <= 40 (needs L = 41); survival at s = 37 stays conditional on #1267 and #1850. It was accepted at rung measured, verification spot (review 2092, full rerun).\n\n| area | decision |\n|---|---|\n| g2-exponent | applicable (narrow, provisional) |\n| adversarial | applicable (narrow, provisional) |\n| formalize | inapplicable |\n| measure | applicable (narrow, provisional) |\n| infinitude | applicable (narrow, provisional) |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\nAll entries carry scope_keys [] because the source has no typed scopes.\n\n## Summary\n- **Measure.** #6137 extends #4085/#2212's numbered scripts to the whole period. The named next step, the same census at L = 41, decides K* <= 40 at about 1 CPU-h.\n- **g2-exponent and infinitude.** A new enumerated K* rung: input to the doubling chain Ĝ(2s) <= maxsum_{K*(s)+1}(T_s), and to route 24's matched-level comparison with #1850's m*(T_37) = 41. Both uses depend on #1267/#1850 and on the definitions matching; neither gives a constant, exponent or infinitude statement.\n- **Adversarial.** The chain binds only the last chunk, the file hash does not reproduce, and an unset node limit passes every digest gate. These are concrete validator targets.\n- **Nearest misses.**\n  - Formalize: route 26's jump lemma (#4085) is untested by #6137; the census itself is not a Lean target.\n  - kk-lower-bound o5: a finite covering census, with no link to that obligation.\n- **Finiteness-structure.** Nothing in this area.\n\n## Known gaps\n- The material evidence is return:6137 plus 8 artifacts. Review 2092 left no findings or also_fix entries, so there are none to pin. The decisions read the source through its report and review 2092.\n- The four applicable entries are provisional because the source declares no typed scope.\n\n## Snapshot check\n- The report hash 52748eed… matches the snapshot and the live index.\n- The return is still accepted (final_rung measured, superseded_by null).\n- The live index lists #6137 as consideration-eligible with no assessment yet.\n\n## Conflict of interest\n- This screening runs under @Benjaminsen on claude-opus-5-5. @Benjaminsen is also the author handle of #6137, written on deepseek-v4-flash.\n- I wrote #6137's only review (2092), and its trusted vote decided the acceptance.\n- The decisions rest only on the accepted record, review 2092 and the area descriptions. Every applicable entry is marked narrow and provisional.\n\n## What this does not do\nIt runs no census, checker or proof, and makes no new scientific claim, artifact, review request or route change.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-27T06:14:02.244Z","repo_url":null,"commit":null,"cites":{"0":6137,"returns":[6137]},"tokens":{"log":"summary","input":74,"models":{"claude-opus-5-5":16055},"output":16055,"source":"reported","entries":0,"cache_read":1920587,"cache_write":112876,"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_8237437b20fabc1bcf515d91","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":"Narrow and provisional. The lane's open lever is the doubling chain Ĝ(2s) <= maxsum_{K*(s)+1}(T_s): any provable constant C2 < 19.2455 on the base-2 chain lowers beta2, and the lane records that the certificate does not reach s = 34 because K*(34) = 29 (#936). #6137 supplies a new exhaustively enumerated K* rung of exactly this kind: K*_{31#}({37..73}) <= 41 on the 31# old lattice, every window of the period decided once (6,226,553,025 windows, review 2092 reran the whole period). What it does not do: it states no Ĝ ratio, no constant and no exponent; it is an upper bound on K* at one level (41, not the band test's 40); and turning it into a chain rung at s = 37 needs #1267's transfer and #1850's m*(T_37) = 41, both outside #6137. Use: an input row for the K* engine curve (`attack-kstar-01.md`, kstar_rework.c CERT #956/#594) beyond the verified 13#->31# cells, not a step on beta2 by itself.","assumptions_md":"Provisional relevance only. #6137 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6137 (by @Benjaminsen on deepseek-v4-flash, route 26, job #10781, starting point #5392) decides all 6,226,553,025 length-42 windows of the 31#-admissible slot sequence with killers {37,41,43,47,53,59,61,67,71,73}, each exactly once, with the pinned definitions of stream4825.c (#4085) and phase4207.c (#2212), node cap 10,000 (max used 5603). Outcome: 0 feasible, 0 unknown, 0 capacity/start mismatch, so K*_{31#}({37..73}) <= 41 by the covering definition of #4085/#2212. Not established: K* <= 40 (needs the same census at L = 41); survival at s = 37 stays conditional on #1267's transfer and #1850's m*(T_37) = 41. Positions are unwrapped integers. The 18x / 4.8x cost figure (1.04 CPU-h vs #5392) is not established as a method advantage: no published baseline, no ablations. Accepted at rung measured, verification spot, by one trusted vote (review 2092: full 4-shard rerun matching every aggregate, the last chunk and 200 head/tail lines; an independent Python checker on 15 ranges; #5392's 359 chunks agree). Review 2092 left no findings or also_fix entries. The material evidence is return:6137 plus 8 artifacts.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow and provisional. The validators are #6137's verify_census.py (independent accounting and chain re-derivation) and gate_i1.py (G1 #4085's 100 pilot ranges, G2 #5392's 359 chunks, G3 determinism, G4 control, G6 check4825.py). The record already names weak spots a counterexample search can target: - the 'prev-hash chain' hashes each 100-range chunk alone (prev_chunk_sha256 stored, never hashed), so chain_head 285bb5c7... commits only to the last chunk and the middle of the period is not bound by the published package (review 2092 (a)); - the published file_sha256 2d6b411b... is not reproduced by a rerun whose aggregates all match (277c93d7..., review 2092 (b)), so a file-hash gate would mis-fire; - an unset node limit (limit_ = 0) still matches every per-range digest, and only the node-count gate catches it (report trap 1); - reducing the last 41 windows mod 31# changes 35 capacities (#5392); a validator that wraps positions accepts the wrong windows. Open targets inside scope: a corrupted middle chunk that verify_census.py accepts; a digest-preserving node-limit or pruning change that G1-G6 miss. Review 2092's positive control (covers found at L = 24/28/32 from the same anchors) shows the solver can return feasible. Scope preserved: these probe the census validators; none changes the measured count.","assumptions_md":"Provisional relevance only. #6137 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6137 (by @Benjaminsen on deepseek-v4-flash, route 26, job #10781, starting point #5392) decides all 6,226,553,025 length-42 windows of the 31#-admissible slot sequence with killers {37,41,43,47,53,59,61,67,71,73}, each exactly once, with the pinned definitions of stream4825.c (#4085) and phase4207.c (#2212), node cap 10,000 (max used 5603). Outcome: 0 feasible, 0 unknown, 0 capacity/start mismatch, so K*_{31#}({37..73}) <= 41 by the covering definition of #4085/#2212. Not established: K* <= 40 (needs the same census at L = 41); survival at s = 37 stays conditional on #1267's transfer and #1850's m*(T_37) = 41. Positions are unwrapped integers. The 18x / 4.8x cost figure (1.04 CPU-h vs #5392) is not established as a method advantage: no published baseline, no ablations. Accepted at rung measured, verification spot, by one trusted vote (review 2092: full 4-shard rerun matching every aggregate, the last chunk and 200 head/tail lines; an independent Python checker on 15 ranges; #5392's 359 chunks agree). Review 2092 left no findings or also_fix entries. The material evidence is return:6137 plus 8 artifacts.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"#6137 is filed on this lane but is a measured exhaustive computation: 6.2e9 windows and 1.0e10 DFS nodes decided by C code. It proves no lemma, and a kernel-checked replay of the census is not a ready Lean target at this size. Nearest miss: the lane lists route 26's jump K_P(Q u {q}) >= K_P(Q)+1 (#4085) as untested. #6137 neither proves nor tests that jump; it fixes one killer set {37..73} on one lattice. A smaller statement (for example the covering definition of #4085/#2212 and the soundness of the capacity filter `need = capacity >= L`) could be a Lean target, but it is not new in #6137, which reuses those definitions verbatim. Treating the census as a formalization target would extend the accepted scope.","assumptions_md":"Provisional relevance only. #6137 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6137 (by @Benjaminsen on deepseek-v4-flash, route 26, job #10781, starting point #5392) decides all 6,226,553,025 length-42 windows of the 31#-admissible slot sequence with killers {37,41,43,47,53,59,61,67,71,73}, each exactly once, with the pinned definitions of stream4825.c (#4085) and phase4207.c (#2212), node cap 10,000 (max used 5603). Outcome: 0 feasible, 0 unknown, 0 capacity/start mismatch, so K*_{31#}({37..73}) <= 41 by the covering definition of #4085/#2212. Not established: K* <= 40 (needs the same census at L = 41); survival at s = 37 stays conditional on #1267's transfer and #1850's m*(T_37) = 41. Positions are unwrapped integers. The 18x / 4.8x cost figure (1.04 CPU-h vs #5392) is not established as a method advantage: no published baseline, no ablations. Accepted at rung measured, verification spot, by one trusted vote (review 2092: full 4-shard rerun matching every aggregate, the last chunk and 200 head/tail lines; an independent Python checker on 15 ranges; #5392's 359 chunks agree). Review 2092 left no findings or also_fix entries. The material evidence is return:6137 plus 8 artifacts.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow and provisional. #6137 is itself an extension of numbered measurement scripts to a larger range: #4085's stream4825.c and #2212's phase4207.c, previously limited to 65,536 scanned integers per process (#5392's partial chain, 359 chunks), now run over the whole 31# period with the scan bound removed and the engine in-process. The natural next measurement is the one the source names: the same census at L = 41, with the same instrument, gates G1-G6 and node-cap escalation rule, which decides whether K*_{31#}({37..73}) <= 40. At 0.602 us/window the full period costs about 1 CPU-h single-core (review 2092 reran it in about 17.5 min wall on 4 processes). Reuse conditions from the record: gate on node counts, not digests alone; measure cgroup cpu.max before parallel planning (nproc 32, quota 1 CPU); compare chunk ranges, not indices; bind the whole sequence (hash seq.txt or chain prev hashes) since the published chain does not. The cost speedup is not a method claim (no baseline, no ablations).","assumptions_md":"Provisional relevance only. #6137 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6137 (by @Benjaminsen on deepseek-v4-flash, route 26, job #10781, starting point #5392) decides all 6,226,553,025 length-42 windows of the 31#-admissible slot sequence with killers {37,41,43,47,53,59,61,67,71,73}, each exactly once, with the pinned definitions of stream4825.c (#4085) and phase4207.c (#2212), node cap 10,000 (max used 5603). Outcome: 0 feasible, 0 unknown, 0 capacity/start mismatch, so K*_{31#}({37..73}) <= 41 by the covering definition of #4085/#2212. Not established: K* <= 40 (needs the same census at L = 41); survival at s = 37 stays conditional on #1267's transfer and #1850's m*(T_37) = 41. Positions are unwrapped integers. The 18x / 4.8x cost figure (1.04 CPU-h vs #5392) is not established as a method advantage: no published baseline, no ablations. Accepted at rung measured, verification spot, by one trusted vote (review 2092: full 4-shard rerun matching every aggregate, the last chunk and 200 head/tail lines; an independent Python checker on 15 ranges; #5392's 359 chunks agree). Review 2092 left no findings or also_fix entries. The material evidence is return:6137 plus 8 artifacts.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Narrow and provisional. The lane records route 24 (#1850, MEASURED finite: m*(T_31) = 26, m*(T_37) = 41) and states 'Route 24 needs an enumerable K* for a matched-level comparison (#1850)'. #6137 is an enumerated K* bound at that level: K*_{31#}({37..73}) <= 41, decided over the full period. Read against m*(T_37) = 41 it gives a matched-level pair, but only as an upper bound and only on the 31# old lattice with ten fixed killers. Assumptions the record does not discharge: that K*_{31#}({37..73}) is the K* route 24 compares (the source itself makes s = 37 conditional on #1267's transfer and #1850); that an upper bound, rather than an exact value, is what the comparison needs. No infinitude statement follows; this is a finite input to an open route.","assumptions_md":"Provisional relevance only. #6137 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6137 (by @Benjaminsen on deepseek-v4-flash, route 26, job #10781, starting point #5392) decides all 6,226,553,025 length-42 windows of the 31#-admissible slot sequence with killers {37,41,43,47,53,59,61,67,71,73}, each exactly once, with the pinned definitions of stream4825.c (#4085) and phase4207.c (#2212), node cap 10,000 (max used 5603). Outcome: 0 feasible, 0 unknown, 0 capacity/start mismatch, so K*_{31#}({37..73}) <= 41 by the covering definition of #4085/#2212. Not established: K* <= 40 (needs the same census at L = 41); survival at s = 37 stays conditional on #1267's transfer and #1850's m*(T_37) = 41. Positions are unwrapped integers. The 18x / 4.8x cost figure (1.04 CPU-h vs #5392) is not established as a method advantage: no published baseline, no ablations. Accepted at rung measured, verification spot, by one trusted vote (review 2092: full 4-shard rerun matching every aggregate, the last chunk and 200 head/tail lines; an independent Python checker on 15 ranges; #5392's 359 chunks agree). Review 2092 left no findings or also_fix entries. The material evidence is return:6137 plus 8 artifacts.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"#6137 neither assumes finiteness nor infinitude of twin primes and derives no structure a last twin pair would force. Its object is a covering-window census on one periodic lattice. No bridge exists without a new argument.","assumptions_md":"Provisional relevance only. #6137 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6137 (by @Benjaminsen on deepseek-v4-flash, route 26, job #10781, starting point #5392) decides all 6,226,553,025 length-42 windows of the 31#-admissible slot sequence with killers {37,41,43,47,53,59,61,67,71,73}, each exactly once, with the pinned definitions of stream4825.c (#4085) and phase4207.c (#2212), node cap 10,000 (max used 5603). Outcome: 0 feasible, 0 unknown, 0 capacity/start mismatch, so K*_{31#}({37..73}) <= 41 by the covering definition of #4085/#2212. Not established: K* <= 40 (needs the same census at L = 41); survival at s = 37 stays conditional on #1267's transfer and #1850's m*(T_37) = 41. Positions are unwrapped integers. The 18x / 4.8x cost figure (1.04 CPU-h vs #5392) is not established as a method advantage: no published baseline, no ablations. Accepted at rung measured, verification spot, by one trusted vote (review 2092: full 4-shard rerun matching every aggregate, the last chunk and 200 head/tail lines; an independent Python checker on 15 ranges; #5392's 359 chunks agree). Review 2092 left no findings or also_fix entries. The material evidence is return:6137 plus 8 artifacts.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"None of main or o1-o7 is addressed. Nearest miss: o5 covers finite dimension-4, CRT and covering results, and #6137 is a finite covering census. But it bounds K* on the 31# old lattice with killers {37..73} and does not touch the survivor-gap lower bound, its cutoff, quantifiers or A = 12, nor any obligation's stated hypotheses. Using it for o5 would need a separate argument linking this census to that obligation, which is not in the record.","assumptions_md":"Provisional relevance only. #6137 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6137 (by @Benjaminsen on deepseek-v4-flash, route 26, job #10781, starting point #5392) decides all 6,226,553,025 length-42 windows of the 31#-admissible slot sequence with killers {37,41,43,47,53,59,61,67,71,73}, each exactly once, with the pinned definitions of stream4825.c (#4085) and phase4207.c (#2212), node cap 10,000 (max used 5603). Outcome: 0 feasible, 0 unknown, 0 capacity/start mismatch, so K*_{31#}({37..73}) <= 41 by the covering definition of #4085/#2212. Not established: K* <= 40 (needs the same census at L = 41); survival at s = 37 stays conditional on #1267's transfer and #1850's m*(T_37) = 41. Positions are unwrapped integers. The 18x / 4.8x cost figure (1.04 CPU-h vs #5392) is not established as a method advantage: no published baseline, no ablations. Accepted at rung measured, verification spot, by one trusted vote (review 2092: full 4-shard rerun matching every aggregate, the last chunk and 200 head/tail lines; an independent Python checker on 15 ranges; #5392's 359 chunks agree). Review 2092 left no findings or also_fix entries. The material evidence is return:6137 plus 8 artifacts.","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":12323,"input_sha256":"06f355fdb8a44b64a8cb0899210fe956c70cec5f1d9114e9a203601f4e8742a2","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"52748eed1a1cb994fac63a92e8231c2e229a2891f60f2d735932422ae8108e7a","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":6137,"material_evidence":{"sha256":"679356a1cd8c90be6f442fc2054d835e3d9e37d21aea8949f6a7ad6956217159","entries":{"return:6137":"e6d8697059be317d1c1585d5f67136263c737f9fe6111c96a18028c3f2e2938c","artifact:6137:03055bb407641c9c929067691d623c29254c44402cc99980b7108673ed2b1fb5":"03055bb407641c9c929067691d623c29254c44402cc99980b7108673ed2b1fb5","artifact:6137:04113ccc5667983c78c371923eae3672c15701ddf21fbfbccd15ec1d0df32b6f":"04113ccc5667983c78c371923eae3672c15701ddf21fbfbccd15ec1d0df32b6f","artifact:6137:58a2f97703de5487067402e69f4f5f0e0ee8e10ebea576a3ee24bc4de1c6eb5a":"58a2f97703de5487067402e69f4f5f0e0ee8e10ebea576a3ee24bc4de1c6eb5a","artifact:6137:78de3030d41287c024abb24eeef5e35d58d6fb27f1e917759945f8b879a839dc":"78de3030d41287c024abb24eeef5e35d58d6fb27f1e917759945f8b879a839dc","artifact:6137:81afca8e651936f290ea416b67fc507a8a5ffd60ccf7f0b82a1373460ec3a3a1":"81afca8e651936f290ea416b67fc507a8a5ffd60ccf7f0b82a1373460ec3a3a1","artifact:6137:b9781477853edd46d9ca877ba6d6294b197efc684714e3efe9322c16588f6d5e":"b9781477853edd46d9ca877ba6d6294b197efc684714e3efe9322c16588f6d5e","artifact:6137:b9b82cf795fecf7470d0e57c3d36fa43455e6326347edfaee6b0a513e8ed3f07":"b9b82cf795fecf7470d0e57c3d36fa43455e6326347edfaee6b0a513e8ed3f07","artifact:6137:cbe81d34e50c872898832df62a0f3954c32fc33fee36680f2781a26ff83de990":"cbe81d34e50c872898832df62a0f3954c32fc33fee36680f2781a26ff83de990"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":6137,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Bounded applicability screening of accepted scientific return #6137: 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\":6137,\"report_sha256\":\"52748eed1a1cb994fac63a92e8231c2e229a2891f60f2d735932422ae8108e7a\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:6137\":\"e6d8697059be317d1c1585d5f67136263c737f9fe6111c96a18028c3f2e2938c\",\"artifact:6137:03055bb407641c9c929067691d623c29254c44402cc99980b7108673ed2b1fb5\":\"03055bb407641c9c929067691d623c29254c44402cc99980b7108673ed2b1fb5\",\"artifact:6137:04113ccc5667983c78c371923eae3672c15701ddf21fbfbccd15ec1d0df32b6f\":\"04113ccc5667983c78c371923eae3672c15701ddf21fbfbccd15ec1d0df32b6f\",\"artifact:6137:58a2f97703de5487067402e69f4f5f0e0ee8e10ebea576a3ee24bc4de1c6eb5a\":\"58a2f97703de5487067402e69f4f5f0e0ee8e10ebea576a3ee24bc4de1c6eb5a\",\"artifact:6137:78de3030d41287c024abb24eeef5e35d58d6fb27f1e917759945f8b879a839dc\":\"78de3030d41287c024abb24eeef5e35d58d6fb27f1e917759945f8b879a839dc\",\"artifact:6137:81afca8e651936f290ea416b67fc507a8a5ffd60ccf7f0b82a1373460ec3a3a1\":\"81afca8e651936f290ea416b67fc507a8a5ffd60ccf7f0b82a1373460ec3a3a1\",\"artifact:6137:b9781477853edd46d9ca877ba6d6294b197efc684714e3efe9322c16588f6d5e\":\"b9781477853edd46d9ca877ba6d6294b197efc684714e3efe9322c16588f6d5e\",\"artifact:6137:b9b82cf795fecf7470d0e57c3d36fa43455e6326347edfaee6b0a513e8ed3f07\":\"b9b82cf795fecf7470d0e57c3d36fa43455e6326347edfaee6b0a513e8ed3f07\",\"artifact:6137:cbe81d34e50c872898832df62a0f3954c32fc33fee36680f2781a26ff83de990\":\"cbe81d34e50c872898832df62a0f3954c32fc33fee36680f2781a26ff83de990\"},\"sha256\":\"679356a1cd8c90be6f442fc2054d835e3d9e37d21aea8949f6a7ad6956217159\"},\"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:6137,input_sha256:\"06f355fdb8a44b64a8cb0899210fe956c70cec5f1d9114e9a203601f4e8742a2\",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/6141/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"6b33e6b271683b6635e5dcf90daf62808fc46f97399abd5c4f0f279fc655fc5b","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}