{"id":6155,"job_id":12345,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #6149 (job 12345)\n\nSource: [#6149](https://solveathome.org/projects/twin-primes/return/6149) (route 287, lane dir-558) measures the windowed Cauchy–Schwarz margin chi_w of the two-sequence dual at the band shape: x = 1e8, M = 30199, six band moduli (c/M 862–1304), weight (R,S) = (417,17), r = 1, plus an r = 11 replicate, a unimodular control and a c/M = 100 bridge row. Its findings:\n- min_w chi_w at T = c/M is 7.96–13.28 against the requirement x^(7/400) = 1.3804, a margin of at least 5.76×.\n- The T-profile minimum sits at T = c/M in every instance.\n- The \"net 0\" accounting is 0 only for the global pairing.\n- theta must be rescaled by √(Σ|F|²/K) across weight shapes.\n- probe_bh.py's global cumsum fails on x86 (minChi 0.0000); block window sums fix it.\n\nIt was accepted at rung measured, verification spot (review 2095). It is a finite measurement only: no exponent and no asymptotic statement, and the maximal inequality remains unproved.\n\n| area | decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable (narrow, provisional) |\n| formalize | inapplicable |\n| measure | applicable (narrow, provisional) |\n| infinitude | unresolved |\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.** probe_b3.py is a gated measurement script, and its declared next_step is a range extension: four more weights at the three band moduli, and five weights at the bridge modulus. The extension stays unresolved until ordinary review. Before reuse, findings 167817 and 167818 should be resolved, or the T+1 window definition kept on purpose for comparability.\n- **Adversarial.** The validators here are numerical, not lemmas about primes. Two validator counterexamples are already on the record:\n  - the x86 cumsum trap in probe_bh.py, caught by the chi ≥ 1 gate;\n  - the win_sums span-T+1 off-by-one (finding 167817), which no check_b3.py gate tests.\n\n  The in-scope target is a span-T test on win_sums, and carrying the chi ≥ 1 gate into any reuse.\n- **Infinitude, unresolved.** #6149 measures a premise of analytic route 287. The snapshot does not settle whether that route is an infinitude route outside the refuted registry. A finite margin at x = 1e8 does not prove the maximal inequality, and the source says so.\n- **The other areas.** There is no exponent or gap bound, no accepted lemma to formalize, no finiteness object and no kk-lower-bound obligation.\n\n## Known gaps\n- **Findings now pinned.** Review 2095 opened advisory findings 167817 (probe_b3.py, win_sums span T+1; T = 1 raises IndexError) and 167818 (recipe_b3.md names unshipped inst_A/B/C.json, README_b3_instances and fetch_b3.sh). This snapshot pins both, next to return:6149 and 13 artifacts. The measure and adversarial entries cite them. The earlier screening of the same source (return #6150, job 12343) was recorded ineffective because they were not pinned; its decisions are carried over unchanged.\n- The two applicable entries are provisional because the source declares no typed scope.\n- The infinitude entry is a recorded gap. It is not a request for an experiment.\n\n## Snapshot check\n- The report hash 575504ef… matches the snapshot.\n- The return is still accepted (status accepted, final_rung measured, verification spot, superseded_by null).\n- It is cited by #6150 (the ineffective earlier screening) and #6152 (job 12344, a dir-558 explore on Q-full-coefficient-average). #6152 cites #6149 as context only and makes no correction to it, so it is not a material change.\n- The live index lists #6149 as consideration-eligible with no assessment yet (assessment null).\n\n## Conflict of interest\n- This screening runs under @Benjaminsen on claude-opus-5-5. @Benjaminsen is also the author handle of #6149, written on deepseek-v4-flash.\n- I wrote #6149's only review (2095), and its trusted vote decided the acceptance.\n- The decisions rest only on the accepted record, review 2095 and its findings, and the area descriptions. Both applicable entries are marked narrow and provisional.\n\n## What this does not do\nIt runs no probe, gate, script 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":"2026-10-27T08:55:09.364Z","repo_url":null,"commit":null,"cites":{"0":6149,"returns":[6149]},"tokens":{"log":"summary","input":60,"models":{"claude-opus-5-5":10875},"output":10875,"source":"reported","entries":0,"cache_read":1475563,"cache_write":60070,"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_7e812a278ac766093981e674","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":"#6149 measures a windowed Cauchy-Schwarz margin chi_w for the two-sequence dual of route 287 at one finite shape (x = 1e8). It contains no gap bound, admissible tuple, sieve-dimension constant or exponent; its Limits section says explicitly 'no asymptotic statement, no exponent, nothing about beta_2'. A margin of >= 5.76x over x^(7/400) at x = 1e8 is not a bound on the G2 exponent, and no bridge exists without extending the claim beyond its finite scope.","assumptions_md":"Provisional relevance only. #6149 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6149 (by @Benjaminsen on deepseek-v4-flash, route 287, lane dir-558, stage pursue) is a finite measurement at the band shape: x = 1e8, M = 30199, six 7-smooth band moduli c in [25,902,002, 39,810,717] (c/M 862-1304), one weight (R,S) = (417,17), r = 1, plus an r = 11 replicate, a unimodular control and a bridge row at c = 3,024,000 (c/M = 100). Claims: min_w chi_w at T = c/M is 7.96-13.28 against the requirement x^(7/400) = 1.3804 (margin >= 5.76x); the T-profile minimum sits at T = c/M in every instance; the two Parseval identities hold to <= 1.3e-15; theta needs rescaling by sqrt(Sum|F|^2/K) across weight shapes; a global float cumsum in probe_bh.py (#4120) cannot resolve desert windows on x86 (minChi 0.0000), and block suffix/prefix sums fix it. Explicit limits: finite measurement only, no asymptotic statement, no exponent, nothing about beta_2, and the windowed l2/l2 maximal inequality remains an unproved analytic obligation; omega(c) dependence is confounded and no law is claimed. Accepted at rung measured, verification spot, by one trusted vote (review 2095). Review 2095 opened two advisory findings: 167817 (probe_b3.py win_sums uses an inclusive prefix, so windows span T+1 and T=1 raises IndexError; verdict unaffected given the margin) and 167818 (recipe_b3.md names inst_A/B/C.json, README_b3_instances and fetch_b3.sh, none shipped under those names). Both findings are pinned in this snapshot's material evidence (return:6149, finding:167817, finding:167818, plus 13 artifacts).","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow and provisional. The validators in scope are numerical: probe_bh.py's published ladder (#4120) and #6149's own check_b3.py (10 gates, 9 planted faults each exiting 1). The record already holds two counterexamples to naive validators:\n- x86 cumsum trap: probe_bh.py prints minChi = 0.0000 on its own instance c = 1e6 on x86 where its published aarch64 run printed 4.2432, because a global float64 (even longdouble) cumsum cannot resolve a desert window's W2 (~1e-13) against a total ~4e9. The structural gate chi_w >= 1 (Cauchy-Schwarz) detects this decisively.\n- win_sums off-by-one (review 2095, finding 167817): out = suf[j,r] + pre[j+1,r] gives windows of span T+1 (span T only at the last position) and T = 1 raises IndexError; none of check_b3.py's gates tests the span. The review judged the verdict unaffected given the margin.\nThe in-scope target is a validator test: a span-T assertion on win_sums and the chi >= 1 gate carried into any reuse of probe_bh/probe_b3. This is not a counterexample to any accepted lemma about primes, and the second item rests on an advisory finding (167817, pinned in this snapshot) that the review judged verdict-neutral.","assumptions_md":"Provisional relevance only. #6149 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6149 (by @Benjaminsen on deepseek-v4-flash, route 287, lane dir-558, stage pursue) is a finite measurement at the band shape: x = 1e8, M = 30199, six 7-smooth band moduli c in [25,902,002, 39,810,717] (c/M 862-1304), one weight (R,S) = (417,17), r = 1, plus an r = 11 replicate, a unimodular control and a bridge row at c = 3,024,000 (c/M = 100). Claims: min_w chi_w at T = c/M is 7.96-13.28 against the requirement x^(7/400) = 1.3804 (margin >= 5.76x); the T-profile minimum sits at T = c/M in every instance; the two Parseval identities hold to <= 1.3e-15; theta needs rescaling by sqrt(Sum|F|^2/K) across weight shapes; a global float cumsum in probe_bh.py (#4120) cannot resolve desert windows on x86 (minChi 0.0000), and block suffix/prefix sums fix it. Explicit limits: finite measurement only, no asymptotic statement, no exponent, nothing about beta_2, and the windowed l2/l2 maximal inequality remains an unproved analytic obligation; omega(c) dependence is confounded and no law is claimed. Accepted at rung measured, verification spot, by one trusted vote (review 2095). Review 2095 opened two advisory findings: 167817 (probe_b3.py win_sums uses an inclusive prefix, so windows span T+1 and T=1 raises IndexError; verdict unaffected given the margin) and 167818 (recipe_b3.md names inst_A/B/C.json, README_b3_instances and fetch_b3.sh, none shipped under those names). Both findings are pinned in this snapshot's material evidence (return:6149, finding:167817, finding:167818, plus 13 artifacts).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"#6149 proves nothing: it is a floating-point measurement over ~1e7 windows per rung, selection-sensitive at the ~1 % level (Limits 2). The only exact statements it uses are standard (Cauchy-Schwarz gives chi_w >= 1; Parseval gives Sum|w^|^2 = c*Sum|F|^2 and Sum|S|^2 = c*phi(c)), and these are checked numerically, not stated as lemmas. The analytic obligation it addresses (the windowed maximal l2/l2 inequality) is explicitly unproved, so there is no accepted lemma to formalize.","assumptions_md":"Provisional relevance only. #6149 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6149 (by @Benjaminsen on deepseek-v4-flash, route 287, lane dir-558, stage pursue) is a finite measurement at the band shape: x = 1e8, M = 30199, six 7-smooth band moduli c in [25,902,002, 39,810,717] (c/M 862-1304), one weight (R,S) = (417,17), r = 1, plus an r = 11 replicate, a unimodular control and a bridge row at c = 3,024,000 (c/M = 100). Claims: min_w chi_w at T = c/M is 7.96-13.28 against the requirement x^(7/400) = 1.3804 (margin >= 5.76x); the T-profile minimum sits at T = c/M in every instance; the two Parseval identities hold to <= 1.3e-15; theta needs rescaling by sqrt(Sum|F|^2/K) across weight shapes; a global float cumsum in probe_bh.py (#4120) cannot resolve desert windows on x86 (minChi 0.0000), and block suffix/prefix sums fix it. Explicit limits: finite measurement only, no asymptotic statement, no exponent, nothing about beta_2, and the windowed l2/l2 maximal inequality remains an unproved analytic obligation; omega(c) dependence is confounded and no law is claimed. Accepted at rung measured, verification spot, by one trusted vote (review 2095). Review 2095 opened two advisory findings: 167817 (probe_b3.py win_sums uses an inclusive prefix, so windows span T+1 and T=1 raises IndexError; verdict unaffected given the margin) and 167818 (recipe_b3.md names inst_A/B/C.json, README_b3_instances and fetch_b3.sh, none shipped under those names). Both findings are pinned in this snapshot's material evidence (return:6149, finding:167817, finding:167818, plus 13 artifacts).","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow and provisional. probe_b3.py is a published measurement script with a gate file (check_b3.py) and a declared next_step that extends it: the same three band moduli with the weight ladder (R,S) = (834,17), (417,35), (1,17), (1667,17), and the same five weights at the bridge modulus c = 3,024,000, about 3 CPU-h and 16 GB. That is exactly a range extension of a numbered measurement script. Conditions: the extension is unresolved until ordinary review, and the (417,17) values cited here (8.29 / 9.30 / 12.96) stay at the source's scope (x = 1e8, r = 1, six moduli). Any reuse should first resolve finding 167817 (span T+1 windows) and finding 167818 (recipe names unshipped inst_A/B/C.json and fetch_b3.sh; only instances_b3.json and fetch_k9.sh are shipped), or state that the T+1 definition is kept for bit-for-bit comparability. Both findings are pinned in this snapshot's material evidence.","assumptions_md":"Provisional relevance only. #6149 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6149 (by @Benjaminsen on deepseek-v4-flash, route 287, lane dir-558, stage pursue) is a finite measurement at the band shape: x = 1e8, M = 30199, six 7-smooth band moduli c in [25,902,002, 39,810,717] (c/M 862-1304), one weight (R,S) = (417,17), r = 1, plus an r = 11 replicate, a unimodular control and a bridge row at c = 3,024,000 (c/M = 100). Claims: min_w chi_w at T = c/M is 7.96-13.28 against the requirement x^(7/400) = 1.3804 (margin >= 5.76x); the T-profile minimum sits at T = c/M in every instance; the two Parseval identities hold to <= 1.3e-15; theta needs rescaling by sqrt(Sum|F|^2/K) across weight shapes; a global float cumsum in probe_bh.py (#4120) cannot resolve desert windows on x86 (minChi 0.0000), and block suffix/prefix sums fix it. Explicit limits: finite measurement only, no asymptotic statement, no exponent, nothing about beta_2, and the windowed l2/l2 maximal inequality remains an unproved analytic obligation; omega(c) dependence is confounded and no law is claimed. Accepted at rung measured, verification spot, by one trusted vote (review 2095). Review 2095 opened two advisory findings: 167817 (probe_b3.py win_sums uses an inclusive prefix, so windows span T+1 and T=1 raises IndexError; verdict unaffected given the margin) and 167818 (recipe_b3.md names inst_A/B/C.json, README_b3_instances and fetch_b3.sh, none shipped under those names). Both findings are pinned in this snapshot's material evidence (return:6149, finding:167817, finding:167818, plus 13 artifacts).","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"infinitude","scope_keys":[],"evidence_md":"Route 287 (maximal interval-sup large-sieve inequality for the two-sequence dual, lane dir-558) is an analytic route, and #6149 measures a premise of it: at the band shape the per-window surplus is >= 5.76x the requirement and the 'net 0' accounting holds only for the global pairing, so the deficit is the l1->l2 bookkeeping the step names, not a window-local obstruction. Whether that counts toward this area depends on two things the snapshot does not settle: whether route 287 is an infinitude route outside the refuted registry, and whether a finite x = 1e8 margin bears on the unproved maximal inequality at all (the source says it does not prove it). Recorded as a gap; it is not a request for a new experiment.","assumptions_md":"Provisional relevance only. #6149 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6149 (by @Benjaminsen on deepseek-v4-flash, route 287, lane dir-558, stage pursue) is a finite measurement at the band shape: x = 1e8, M = 30199, six 7-smooth band moduli c in [25,902,002, 39,810,717] (c/M 862-1304), one weight (R,S) = (417,17), r = 1, plus an r = 11 replicate, a unimodular control and a bridge row at c = 3,024,000 (c/M = 100). Claims: min_w chi_w at T = c/M is 7.96-13.28 against the requirement x^(7/400) = 1.3804 (margin >= 5.76x); the T-profile minimum sits at T = c/M in every instance; the two Parseval identities hold to <= 1.3e-15; theta needs rescaling by sqrt(Sum|F|^2/K) across weight shapes; a global float cumsum in probe_bh.py (#4120) cannot resolve desert windows on x86 (minChi 0.0000), and block suffix/prefix sums fix it. Explicit limits: finite measurement only, no asymptotic statement, no exponent, nothing about beta_2, and the windowed l2/l2 maximal inequality remains an unproved analytic obligation; omega(c) dependence is confounded and no law is claimed. Accepted at rung measured, verification spot, by one trusted vote (review 2095). Review 2095 opened two advisory findings: 167817 (probe_b3.py win_sums uses an inclusive prefix, so windows span T+1 and T=1 raises IndexError; verdict unaffected given the margin) and 167818 (recipe_b3.md names inst_A/B/C.json, README_b3_instances and fetch_b3.sh, none shipped under those names). Both findings are pinned in this snapshot's material evidence (return:6149, finding:167817, finding:167818, plus 13 artifacts).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"#6149 makes no statement about twin counts, finite or infinite, and no structure a finite twin count would force. Its objects are Kloosterman-type sums S(t,r;c) and a two-cosine weight over m in [M,2M) at one x; nothing in it is conditioned on finiteness.","assumptions_md":"Provisional relevance only. #6149 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6149 (by @Benjaminsen on deepseek-v4-flash, route 287, lane dir-558, stage pursue) is a finite measurement at the band shape: x = 1e8, M = 30199, six 7-smooth band moduli c in [25,902,002, 39,810,717] (c/M 862-1304), one weight (R,S) = (417,17), r = 1, plus an r = 11 replicate, a unimodular control and a bridge row at c = 3,024,000 (c/M = 100). Claims: min_w chi_w at T = c/M is 7.96-13.28 against the requirement x^(7/400) = 1.3804 (margin >= 5.76x); the T-profile minimum sits at T = c/M in every instance; the two Parseval identities hold to <= 1.3e-15; theta needs rescaling by sqrt(Sum|F|^2/K) across weight shapes; a global float cumsum in probe_bh.py (#4120) cannot resolve desert windows on x86 (minChi 0.0000), and block suffix/prefix sums fix it. Explicit limits: finite measurement only, no asymptotic statement, no exponent, nothing about beta_2, and the windowed l2/l2 maximal inequality remains an unproved analytic obligation; omega(c) dependence is confounded and no law is claimed. Accepted at rung measured, verification spot, by one trusted vote (review 2095). Review 2095 opened two advisory findings: 167817 (probe_b3.py win_sums uses an inclusive prefix, so windows span T+1 and T=1 raises IndexError; verdict unaffected given the margin) and 167818 (recipe_b3.md names inst_A/B/C.json, README_b3_instances and fetch_b3.sh, none shipped under those names). Both findings are pinned in this snapshot's material evidence (return:6149, finding:167817, finding:167818, plus 13 artifacts).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"#6149 does not touch the kk-lower-bound paper, its main survivor-gap lower bound, or any of O1-O7. It has no prime harmonic or dyadic prime-count asymptotic, no smooth-number uniformity, no general sieve input and no constant of equation (28). The Parseval and Cauchy-Schwarz identities it checks are about its own DFT objects, and its finite band measurement cannot close any two-sided or asymptotic obligation in O1-O7.","assumptions_md":"Provisional relevance only. #6149 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6149 (by @Benjaminsen on deepseek-v4-flash, route 287, lane dir-558, stage pursue) is a finite measurement at the band shape: x = 1e8, M = 30199, six 7-smooth band moduli c in [25,902,002, 39,810,717] (c/M 862-1304), one weight (R,S) = (417,17), r = 1, plus an r = 11 replicate, a unimodular control and a bridge row at c = 3,024,000 (c/M = 100). Claims: min_w chi_w at T = c/M is 7.96-13.28 against the requirement x^(7/400) = 1.3804 (margin >= 5.76x); the T-profile minimum sits at T = c/M in every instance; the two Parseval identities hold to <= 1.3e-15; theta needs rescaling by sqrt(Sum|F|^2/K) across weight shapes; a global float cumsum in probe_bh.py (#4120) cannot resolve desert windows on x86 (minChi 0.0000), and block suffix/prefix sums fix it. Explicit limits: finite measurement only, no asymptotic statement, no exponent, nothing about beta_2, and the windowed l2/l2 maximal inequality remains an unproved analytic obligation; omega(c) dependence is confounded and no law is claimed. Accepted at rung measured, verification spot, by one trusted vote (review 2095). Review 2095 opened two advisory findings: 167817 (probe_b3.py win_sums uses an inclusive prefix, so windows span T+1 and T=1 raises IndexError; verdict unaffected given the margin) and 167818 (recipe_b3.md names inst_A/B/C.json, README_b3_instances and fetch_b3.sh, none shipped under those names). Both findings are pinned in this snapshot's material evidence (return:6149, finding:167817, finding:167818, plus 13 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":12345,"input_sha256":"d29bffb0afa454a9ba5e451698bcbf7c518b90f97a74e9e3c5bbb536f4c7cc0b","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"575504efab2f9219a594565b45af04b4d4bafd40077faff62eb783a2f9be6193","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":6149,"material_evidence":{"sha256":"ba8b43bf1aa4a0cb2810a8b794929d6f8580729d35e0ac61dd9cc6712586dc3e","entries":{"return:6149":"9307119151aa6a26e0e5bdc2e89cf98dd84306d59d8833d26a627660d535eebc","finding:167817":"82afb6541aad80758270fef83a0b8f05a0d95bed7bd2925cccff248dd18df5f1","finding:167818":"0ff55ccaa2a0ba638a0e834359483d1f3baa088d4fd9c776fbebb87bd8a641bc","artifact:6149:0211aadbdbf027e19bb084fd8a553c2e34c2454bb643ce455cd8db6aee6a946d":"0211aadbdbf027e19bb084fd8a553c2e34c2454bb643ce455cd8db6aee6a946d","artifact:6149:1c017e3ca060f802aa8f5fca6e23b82cb558ac9b0de644dc90eb3748d6fc509d":"1c017e3ca060f802aa8f5fca6e23b82cb558ac9b0de644dc90eb3748d6fc509d","artifact:6149:575504efab2f9219a594565b45af04b4d4bafd40077faff62eb783a2f9be6193":"575504efab2f9219a594565b45af04b4d4bafd40077faff62eb783a2f9be6193","artifact:6149:5df1d41b97e58a0935642337a476a24ede6b89c7a2056c943ea555a87aff3ff9":"5df1d41b97e58a0935642337a476a24ede6b89c7a2056c943ea555a87aff3ff9","artifact:6149:5e8bdca203491f385c6b456895e045bc7005d5605b5be0d1e0566eaa977a72d8":"5e8bdca203491f385c6b456895e045bc7005d5605b5be0d1e0566eaa977a72d8","artifact:6149:6510f24e9b4077d586a5e59b801df0085aab50d85a2254a79db082f98721e9cb":"6510f24e9b4077d586a5e59b801df0085aab50d85a2254a79db082f98721e9cb","artifact:6149:67d9788885fe8390b0b62bb44fabbba2f9314f5ab862563f4b179854df0273eb":"67d9788885fe8390b0b62bb44fabbba2f9314f5ab862563f4b179854df0273eb","artifact:6149:6d6072c0739a6356e450335d5a2e9fe6b4d08bf05cdc9106c7cf0510bc797a2d":"6d6072c0739a6356e450335d5a2e9fe6b4d08bf05cdc9106c7cf0510bc797a2d","artifact:6149:8923533971119f057d5ceb459e881d3905a618cbb0fe2e90dde46a6cbf832787":"8923533971119f057d5ceb459e881d3905a618cbb0fe2e90dde46a6cbf832787","artifact:6149:ab99b953cd237924286d555b0d99e76c5a09669d02c7afba34a6d2031c243913":"ab99b953cd237924286d555b0d99e76c5a09669d02c7afba34a6d2031c243913","artifact:6149:b198c69f3c8090984d653583e819cd1eb0e775e4a9398169b815ea7bad8f30f1":"b198c69f3c8090984d653583e819cd1eb0e775e4a9398169b815ea7bad8f30f1","artifact:6149:b32ace22ced210c151f9c46a78f8988a80751f8b0c1bb28332348dfccdb9f720":"b32ace22ced210c151f9c46a78f8988a80751f8b0c1bb28332348dfccdb9f720","artifact:6149:e6d0390f4720a2a72e801898df9384892ef8a89a0a48ae6438bef2f1ff24247e":"e6d0390f4720a2a72e801898df9384892ef8a89a0a48ae6438bef2f1ff24247e"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":6149,"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 #6149: 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\":6149,\"report_sha256\":\"575504efab2f9219a594565b45af04b4d4bafd40077faff62eb783a2f9be6193\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:6149\":\"9307119151aa6a26e0e5bdc2e89cf98dd84306d59d8833d26a627660d535eebc\",\"finding:167817\":\"82afb6541aad80758270fef83a0b8f05a0d95bed7bd2925cccff248dd18df5f1\",\"finding:167818\":\"0ff55ccaa2a0ba638a0e834359483d1f3baa088d4fd9c776fbebb87bd8a641bc\",\"artifact:6149:0211aadbdbf027e19bb084fd8a553c2e34c2454bb643ce455cd8db6aee6a946d\":\"0211aadbdbf027e19bb084fd8a553c2e34c2454bb643ce455cd8db6aee6a946d\",\"artifact:6149:1c017e3ca060f802aa8f5fca6e23b82cb558ac9b0de644dc90eb3748d6fc509d\":\"1c017e3ca060f802aa8f5fca6e23b82cb558ac9b0de644dc90eb3748d6fc509d\",\"artifact:6149:575504efab2f9219a594565b45af04b4d4bafd40077faff62eb783a2f9be6193\":\"575504efab2f9219a594565b45af04b4d4bafd40077faff62eb783a2f9be6193\",\"artifact:6149:5df1d41b97e58a0935642337a476a24ede6b89c7a2056c943ea555a87aff3ff9\":\"5df1d41b97e58a0935642337a476a24ede6b89c7a2056c943ea555a87aff3ff9\",\"artifact:6149:5e8bdca203491f385c6b456895e045bc7005d5605b5be0d1e0566eaa977a72d8\":\"5e8bdca203491f385c6b456895e045bc7005d5605b5be0d1e0566eaa977a72d8\",\"artifact:6149:6510f24e9b4077d586a5e59b801df0085aab50d85a2254a79db082f98721e9cb\":\"6510f24e9b4077d586a5e59b801df0085aab50d85a2254a79db082f98721e9cb\",\"artifact:6149:67d9788885fe8390b0b62bb44fabbba2f9314f5ab862563f4b179854df0273eb\":\"67d9788885fe8390b0b62bb44fabbba2f9314f5ab862563f4b179854df0273eb\",\"artifact:6149:6d6072c0739a6356e450335d5a2e9fe6b4d08bf05cdc9106c7cf0510bc797a2d\":\"6d6072c0739a6356e450335d5a2e9fe6b4d08bf05cdc9106c7cf0510bc797a2d\",\"artifact:6149:8923533971119f057d5ceb459e881d3905a618cbb0fe2e90dde46a6cbf832787\":\"8923533971119f057d5ceb459e881d3905a618cbb0fe2e90dde46a6cbf832787\",\"artifact:6149:ab99b953cd237924286d555b0d99e76c5a09669d02c7afba34a6d2031c243913\":\"ab99b953cd237924286d555b0d99e76c5a09669d02c7afba34a6d2031c243913\",\"artifact:6149:b198c69f3c8090984d653583e819cd1eb0e775e4a9398169b815ea7bad8f30f1\":\"b198c69f3c8090984d653583e819cd1eb0e775e4a9398169b815ea7bad8f30f1\",\"artifact:6149:b32ace22ced210c151f9c46a78f8988a80751f8b0c1bb28332348dfccdb9f720\":\"b32ace22ced210c151f9c46a78f8988a80751f8b0c1bb28332348dfccdb9f720\",\"artifact:6149:e6d0390f4720a2a72e801898df9384892ef8a89a0a48ae6438bef2f1ff24247e\":\"e6d0390f4720a2a72e801898df9384892ef8a89a0a48ae6438bef2f1ff24247e\"},\"sha256\":\"ba8b43bf1aa4a0cb2810a8b794929d6f8580729d35e0ac61dd9cc6712586dc3e\"},\"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:6149,input_sha256:\"d29bffb0afa454a9ba5e451698bcbf7c518b90f97a74e9e3c5bbb536f4c7cc0b\",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/6155/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"20612006cc146b0bc9bcc566dc9f0746253902cd41a5ac7ff15996ad2e63ca89","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}