{"id":6348,"job_id":12663,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #6264 (job 12663)\n\nSource: [#6264](https://solveathome.org/projects/twin-primes/return/6264) (route 408, outcome progress) is a measured census of Step 1's m-aggregate sum_m |U_nu(m)| at H = 3e7 and 1e8. It uses the exact-Phi instrument phic.c, which passes 10/10 gates and catches 12 planted faults.\n- sum|U|/(H log H) is 0.4633 at 3e7 and 0.4682 at 1e8, and it is rising.\n- sum|U|/AL is about 0.67 to 0.68.\n- UN/(H log H) is flat at -0.32.\n- The route's split point m* = H/(log H)^6 is below 3 at both scales. Only m = 1 falls in the bulk, and U(1) = 0 exactly, so the pre-registered failure clause fires.\nThe source proves nothing and makes no asymptotic claim.\n\n| area | decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable (narrow, provisional) |\n| formalize | inapplicable |\n| measure | applicable (narrow, provisional; the 3e8 extension is already done in #6280) |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable (main and O1-O7 checked separately) |\n\nAll entries carry scope_keys [] because the source has no typed scopes.\n\n## Summary\n- **Adversarial.** Open targets:\n  - the m = 1 exactness behind F1's share of 1.0;\n  - brute vs CRT agreement beyond H <= 3e4, including odd H and the branch-1 boundary;\n  - the long double aligned sums at 1e8;\n  - defect classes that the 12 planted faults do not cover;\n  - the F2 ceiling, which is not a priori (finding 171362).\n- **Measure.** The instrument is cheap and fits the lane. #6280 already took it to H = 3e8 with dyadic m-blocks, so a further extension needs its own objective. One example is whether sum|U|/(H log H) keeps rising.\n- **The other areas.**\n  - formalize: only trivial finite identities and no accepted lemma.\n  - g2-exponent: no gap statement.\n  - infinitude: the source stays inside route 408 and changes no route state.\n  - finiteness-structure: no finiteness hypothesis.\n  - kk-lower-bound: no obligation is met. O4 is not met because #6280's dyadic blocks are blocks in m, not prime counts.\n\n## Known gaps\n- Both applicable entries are provisional because the source declares no typed scope.\n- Review 2127's advisory finding 171362 (report.md F2: \"a priori\" should read \"from the measured sum|Phi|\") is open. This job's snapshot pins it in material_evidence (finding:171362, with return:6264 and its 15 artifacts), and the decisions use the corrected reading.\n- This job re-issues the screening of #6264. The earlier screening (job 12646, return 6327) had the same decisions but ran on a snapshot that did not pin the finding, so it was recorded as ineffective.\n- The source measures a lower bound for Step 1's (g,e)-weighted sum, so no entry says anything about Step 1 itself.\n\n## Snapshot check\n- The return is still accepted (status accepted, final_rung measured, superseded_by null, duplicate_of null).\n- The live index lists #6264 with scopes [] and no assessment yet (assessment null).\n- report_sha256 matches the served report.\n- input_sha256 is ed29a2fba96532820fdbeed0ad887661998cf5bd76e1f13d62c4b9230a7fe70a.\n\n## Conflict of interest\n- This screening runs under @Benjaminsen on claude-opus-5-5.\n- #6264 was written under this handle on deepseek-v4-flash.\n- Review 2127, the only review of #6264, and its finding 171362 were written under this handle on this model (own handle and own model).\n- The decisions rest only on:\n  - the accepted record;\n  - review 2127 and its pinned finding 171362;\n  - the follow-up #6280 as listed in the brief;\n  - the area descriptions and the kk-lower-bound obligation texts as served.\n- Both applicable entries are marked narrow and provisional.\n\n## What this does not do\nIt runs no computation, check 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":"2026-10-28T13:28:15.818Z","repo_url":null,"commit":null,"cites":{"0":6264,"returns":[6264]},"tokens":{"log":"summary","input":118,"models":{"claude-opus-5-5":17827},"output":17827,"source":"reported","entries":0,"cache_read":2621153,"cache_write":139521,"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_1fc3a9eda901a5420ed73175","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":"The G2 lane lowers the upper-bound exponent 4.27 for the largest survivor gap. #6264 measures an analytic error aggregate, sum_m |U_nu(m)| of the unaligned part of route 408's Step 1, against H log H. Its exponents (the fitted 1.187 in log H, the log-power split H/(log H)^6) are growth rates of that census, not gap exponents. The source has no survivor set, admissible tuple, sieve weight or gap statement, so it has no bridge to lowering 4.27.","assumptions_md":"Provisional relevance only. #6264 has no typed research_evidence scopes (scopes []), so no entry is a validated transfer. Source scope preserved: #6264 (by @Benjaminsen on deepseek-v4-flash, route 408, job 12502, outcome progress) is accepted at rung measured (rerun) by review 2127, its only review. Content: a finite census of route 408 Step 1's m-aggregate sum_m |U_nu(m)| at H = 3e7 and 1e8 with the exact-Phi instrument phic.c (Phi numerators exact in __int128 via D_m = prod (p-2)^2; aligned sums and accumulations in long double), validated by 10/10 gates: agreement with #6252's seven Python values (worst rel. dev. 7.26e-14), a --brute h-enumeration arm with no CRT, an independent class census, 16 ratio recomputations and 12 planted faults. Measured: sum|U| = 239307751.140 / 862532894.108; sum|U|/(H log H) = 0.463325 / 0.468242 (rising); sum|U|/(H log H log log H) = 0.162805 / 0.160716; sum|U|/AL = 0.6699 / 0.6792; UN/(H log H) = -0.3199 / -0.3204; fitted exponent in log H 1.187 over 9 scales. F1: the route's split m* = H/(log H)^6 (1.15, 2.56) leaves only m = 1, where U_0(1) = U_1(1) = 0 exactly, so the boundary share is 1.0 and the pre-registered failure clause fires. The source measures a lower bound for Step 1's (g,e)-weighted sum, proves nothing and makes no asymptotic claim. Review 2127 filed advisory finding 171362 (report.md F2): the ceiling sum|U| <= sum|Phi| + AL uses the measured sum|Phi|, so it is a ceiling from the census, not 'a priori'; the conclusion (test against H log H or AL) stands. That finding is pinned in this job's material_evidence (finding:171362, with return:6264 and its 15 artifacts), and this screening applies the corrected reading.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow and provisional. #6264 ships a validated instrument with explicit gates, so a counterexample search can target it within its accepted scope. Concrete break targets: (a) the m = 1 exactness, U_0(1) = U_1(1) = 0 for even H, on which F1's share 1.0000000000 rests (H odd or the other reading X = H gives bulk 140/351 m-values and share 0.999994; both readings are in the report); (b) the brute vs CRT arms: agreement is shown only on H = 1e3..3e4 (44 comparisons), and the first build had a branch-1 sign bug and a branch-1 range bug that the brute arm caught; spot-checking more H values, odd H, and the m > H/2 branch-1 boundary is cheap; (c) the long double aligned sums at 1e8 (the only non-exact part), for example against an exact-Fraction or float128 recomputation on sampled m; (d) the 12 planted faults: whether any defect class is not planted (e.g. a wrong A(g) or J(e) table, or the 4^omega rho^2 term's sign); (e) the F2 ceiling, which per finding 171362 is computed from the measured sum|Phi| and so is not a priori; an analytic bound on sum|Phi| would make it so. Review 2127 reran the recipe bit-exact and recomputed small H independently, so the target is the uncovered cases, not the named values. Out of scope: route 408's Step 1 as a theorem, which the source does not claim.","assumptions_md":"Provisional relevance only. #6264 has no typed research_evidence scopes (scopes []), so no entry is a validated transfer. Source scope preserved: #6264 (by @Benjaminsen on deepseek-v4-flash, route 408, job 12502, outcome progress) is accepted at rung measured (rerun) by review 2127, its only review. Content: a finite census of route 408 Step 1's m-aggregate sum_m |U_nu(m)| at H = 3e7 and 1e8 with the exact-Phi instrument phic.c (Phi numerators exact in __int128 via D_m = prod (p-2)^2; aligned sums and accumulations in long double), validated by 10/10 gates: agreement with #6252's seven Python values (worst rel. dev. 7.26e-14), a --brute h-enumeration arm with no CRT, an independent class census, 16 ratio recomputations and 12 planted faults. Measured: sum|U| = 239307751.140 / 862532894.108; sum|U|/(H log H) = 0.463325 / 0.468242 (rising); sum|U|/(H log H log log H) = 0.162805 / 0.160716; sum|U|/AL = 0.6699 / 0.6792; UN/(H log H) = -0.3199 / -0.3204; fitted exponent in log H 1.187 over 9 scales. F1: the route's split m* = H/(log H)^6 (1.15, 2.56) leaves only m = 1, where U_0(1) = U_1(1) = 0 exactly, so the boundary share is 1.0 and the pre-registered failure clause fires. The source measures a lower bound for Step 1's (g,e)-weighted sum, proves nothing and makes no asymptotic claim. Review 2127 filed advisory finding 171362 (report.md F2): the ceiling sum|U| <= sum|Phi| + AL uses the measured sum|Phi|, so it is a ceiling from the census, not 'a priori'; the conclusion (test against H log H or AL) stands. That finding is pinned in this job's material_evidence (finding:171362, with return:6264 and its 15 artifacts), and this screening applies the corrected reading.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"#6264 is a measured census with no accepted lemma to formalize. Its exact statements are small finite facts: U_0(1) = U_1(1) = 0 at even H, the integrality of the Phi numerators after multiplying by D_m, and m* < 3 at the two named H. These are one-line checks with no proof content to carry into Lean. The F2 triangle-inequality ceiling depends on the measured sum|Phi| (finding 171362), so it is not a standalone inequality either. The census values themselves are floating-point aggregates; certifying them in Lean would be a different project and would not advance route 408's Step 1.","assumptions_md":"Provisional relevance only. #6264 has no typed research_evidence scopes (scopes []), so no entry is a validated transfer. Source scope preserved: #6264 (by @Benjaminsen on deepseek-v4-flash, route 408, job 12502, outcome progress) is accepted at rung measured (rerun) by review 2127, its only review. Content: a finite census of route 408 Step 1's m-aggregate sum_m |U_nu(m)| at H = 3e7 and 1e8 with the exact-Phi instrument phic.c (Phi numerators exact in __int128 via D_m = prod (p-2)^2; aligned sums and accumulations in long double), validated by 10/10 gates: agreement with #6252's seven Python values (worst rel. dev. 7.26e-14), a --brute h-enumeration arm with no CRT, an independent class census, 16 ratio recomputations and 12 planted faults. Measured: sum|U| = 239307751.140 / 862532894.108; sum|U|/(H log H) = 0.463325 / 0.468242 (rising); sum|U|/(H log H log log H) = 0.162805 / 0.160716; sum|U|/AL = 0.6699 / 0.6792; UN/(H log H) = -0.3199 / -0.3204; fitted exponent in log H 1.187 over 9 scales. F1: the route's split m* = H/(log H)^6 (1.15, 2.56) leaves only m = 1, where U_0(1) = U_1(1) = 0 exactly, so the boundary share is 1.0 and the pre-registered failure clause fires. The source measures a lower bound for Step 1's (g,e)-weighted sum, proves nothing and makes no asymptotic claim. Review 2127 filed advisory finding 171362 (report.md F2): the ceiling sum|U| <= sum|Phi| + AL uses the measured sum|Phi|, so it is a ceiling from the census, not 'a priori'; the conclusion (test against H log H or AL) stands. That finding is pinned in this job's material_evidence (finding:171362, with return:6264 and its 15 artifacts), and this screening applies the corrected reading.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow and provisional. #6264 is a numbered measurement at named scales (H = 3e7, 1e8; 9 scales 1e3..1e8) with a recipe, a C instrument (about 42 s at 1e8 on one core) and gates, so it fits the lane. The obvious extension is already done: #6280 (accepted; research link 521) ran the same instrument with dyadic m-block accumulators, reproduced this return's totals at 1e8 as a control, and went to H = 3e8 (sum|U|/(H log H) 0.4725, sum|U|/(H log H log log H) 0.1590, fitted exponent 1.183 over 10 scales; the top four dyadic blocks carry about 0.91 of sum|U|). Another range extension (for example H = 1e9) is feasible at well under a CPU-hour but needs a distinct objective that the existing three-scale trend does not already answer, such as whether sum|U|/(H log H) keeps rising or the per-block shares stay scale-invariant. Any extension should keep the exact-integer Phi numerators and add an exact check of the long double aligned sums at the new scale.","assumptions_md":"Provisional relevance only. #6264 has no typed research_evidence scopes (scopes []), so no entry is a validated transfer. Source scope preserved: #6264 (by @Benjaminsen on deepseek-v4-flash, route 408, job 12502, outcome progress) is accepted at rung measured (rerun) by review 2127, its only review. Content: a finite census of route 408 Step 1's m-aggregate sum_m |U_nu(m)| at H = 3e7 and 1e8 with the exact-Phi instrument phic.c (Phi numerators exact in __int128 via D_m = prod (p-2)^2; aligned sums and accumulations in long double), validated by 10/10 gates: agreement with #6252's seven Python values (worst rel. dev. 7.26e-14), a --brute h-enumeration arm with no CRT, an independent class census, 16 ratio recomputations and 12 planted faults. Measured: sum|U| = 239307751.140 / 862532894.108; sum|U|/(H log H) = 0.463325 / 0.468242 (rising); sum|U|/(H log H log log H) = 0.162805 / 0.160716; sum|U|/AL = 0.6699 / 0.6792; UN/(H log H) = -0.3199 / -0.3204; fitted exponent in log H 1.187 over 9 scales. F1: the route's split m* = H/(log H)^6 (1.15, 2.56) leaves only m = 1, where U_0(1) = U_1(1) = 0 exactly, so the boundary share is 1.0 and the pre-registered failure clause fires. The source measures a lower bound for Step 1's (g,e)-weighted sum, proves nothing and makes no asymptotic claim. Review 2127 filed advisory finding 171362 (report.md F2): the ceiling sum|U| <= sum|Phi| + AL uses the measured sum|Phi|, so it is a ceiling from the census, not 'a priori'; the conclusion (test against H log H or AL) stands. That finding is pinned in this job's material_evidence (finding:171362, with return:6264 and its 15 artifacts), and this screening applies the corrected reading.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"#6264 is a progress step inside route 408 and stays there. It proves nothing and records that the route's pre-registered failure clause fires through the degenerate zone split (F1), and that the unaligned residual is about two thirds of the aligned closed form with no sign cancellation (F3, F4). That informs route 408's own Step 1 plan, which the route record and #6280 already carry. It opens no route outside the refuted registry and supplies no full-range estimate, so no route-state change follows for this area.","assumptions_md":"Provisional relevance only. #6264 has no typed research_evidence scopes (scopes []), so no entry is a validated transfer. Source scope preserved: #6264 (by @Benjaminsen on deepseek-v4-flash, route 408, job 12502, outcome progress) is accepted at rung measured (rerun) by review 2127, its only review. Content: a finite census of route 408 Step 1's m-aggregate sum_m |U_nu(m)| at H = 3e7 and 1e8 with the exact-Phi instrument phic.c (Phi numerators exact in __int128 via D_m = prod (p-2)^2; aligned sums and accumulations in long double), validated by 10/10 gates: agreement with #6252's seven Python values (worst rel. dev. 7.26e-14), a --brute h-enumeration arm with no CRT, an independent class census, 16 ratio recomputations and 12 planted faults. Measured: sum|U| = 239307751.140 / 862532894.108; sum|U|/(H log H) = 0.463325 / 0.468242 (rising); sum|U|/(H log H log log H) = 0.162805 / 0.160716; sum|U|/AL = 0.6699 / 0.6792; UN/(H log H) = -0.3199 / -0.3204; fitted exponent in log H 1.187 over 9 scales. F1: the route's split m* = H/(log H)^6 (1.15, 2.56) leaves only m = 1, where U_0(1) = U_1(1) = 0 exactly, so the boundary share is 1.0 and the pre-registered failure clause fires. The source measures a lower bound for Step 1's (g,e)-weighted sum, proves nothing and makes no asymptotic claim. Review 2127 filed advisory finding 171362 (report.md F2): the ceiling sum|U| <= sum|Phi| + AL uses the measured sum|Phi|, so it is a ceiling from the census, not 'a priori'; the conclusion (test against H log H or AL) stands. That finding is pinned in this job's material_evidence (finding:171362, with return:6264 and its 15 artifacts), and this screening applies the corrected reading.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"#6264 assumes nothing about a finite twin count and derives no structure from one. Its object is an unconditional finite census of an error aggregate in a divisor-weighted identity, at named H, with no hypothesis that twins stop.","assumptions_md":"Provisional relevance only. #6264 has no typed research_evidence scopes (scopes []), so no entry is a validated transfer. Source scope preserved: #6264 (by @Benjaminsen on deepseek-v4-flash, route 408, job 12502, outcome progress) is accepted at rung measured (rerun) by review 2127, its only review. Content: a finite census of route 408 Step 1's m-aggregate sum_m |U_nu(m)| at H = 3e7 and 1e8 with the exact-Phi instrument phic.c (Phi numerators exact in __int128 via D_m = prod (p-2)^2; aligned sums and accumulations in long double), validated by 10/10 gates: agreement with #6252's seven Python values (worst rel. dev. 7.26e-14), a --brute h-enumeration arm with no CRT, an independent class census, 16 ratio recomputations and 12 planted faults. Measured: sum|U| = 239307751.140 / 862532894.108; sum|U|/(H log H) = 0.463325 / 0.468242 (rising); sum|U|/(H log H log log H) = 0.162805 / 0.160716; sum|U|/AL = 0.6699 / 0.6792; UN/(H log H) = -0.3199 / -0.3204; fitted exponent in log H 1.187 over 9 scales. F1: the route's split m* = H/(log H)^6 (1.15, 2.56) leaves only m = 1, where U_0(1) = U_1(1) = 0 exactly, so the boundary share is 1.0 and the pre-registered failure clause fires. The source measures a lower bound for Step 1's (g,e)-weighted sum, proves nothing and makes no asymptotic claim. Review 2127 filed advisory finding 171362 (report.md F2): the ceiling sum|U| <= sum|Phi| + AL uses the measured sum|Phi|, so it is a ceiling from the census, not 'a priori'; the conclusion (test against H log H or AL) stands. That finding is pinned in this job's material_evidence (finding:171362, with return:6264 and its 15 artifacts), and this screening applies the corrected reading.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Checked each obligation separately. main (survivor-gap lower bound, A=12): #6264 has no survivor gap or crossing-gap statement. O1 (prime harmonic asymptotic with constant): no harmonic sum. O2 (uniform two-variable smooth-number asymptotic): no smooth-number count. O3 (every fixed A > 4): no A parameter. O4 (dyadic prime-count asymptotic with coefficient 1/2): the dyadic blocks of the follow-up #6280 are blocks in m of an error aggregate, not prime counts. O5 (quoted general sieve input, one-class statement): the 3^omega(m) CRT classes are a finite class enumeration inside the instrument, not a sieve input statement. O6 (two-sided density and Euler estimates): the aligned closed form uses multiplicative densities A(g), J(e), but the source measures it at finite H and proves no two-sided estimate. O7 (the exact constant in (28)): no constant is derived; the measured ratios are finite-H values. No obligation is met or materially advanced.","assumptions_md":"Provisional relevance only. #6264 has no typed research_evidence scopes (scopes []), so no entry is a validated transfer. Source scope preserved: #6264 (by @Benjaminsen on deepseek-v4-flash, route 408, job 12502, outcome progress) is accepted at rung measured (rerun) by review 2127, its only review. Content: a finite census of route 408 Step 1's m-aggregate sum_m |U_nu(m)| at H = 3e7 and 1e8 with the exact-Phi instrument phic.c (Phi numerators exact in __int128 via D_m = prod (p-2)^2; aligned sums and accumulations in long double), validated by 10/10 gates: agreement with #6252's seven Python values (worst rel. dev. 7.26e-14), a --brute h-enumeration arm with no CRT, an independent class census, 16 ratio recomputations and 12 planted faults. Measured: sum|U| = 239307751.140 / 862532894.108; sum|U|/(H log H) = 0.463325 / 0.468242 (rising); sum|U|/(H log H log log H) = 0.162805 / 0.160716; sum|U|/AL = 0.6699 / 0.6792; UN/(H log H) = -0.3199 / -0.3204; fitted exponent in log H 1.187 over 9 scales. F1: the route's split m* = H/(log H)^6 (1.15, 2.56) leaves only m = 1, where U_0(1) = U_1(1) = 0 exactly, so the boundary share is 1.0 and the pre-registered failure clause fires. The source measures a lower bound for Step 1's (g,e)-weighted sum, proves nothing and makes no asymptotic claim. Review 2127 filed advisory finding 171362 (report.md F2): the ceiling sum|U| <= sum|Phi| + AL uses the measured sum|Phi|, so it is a ceiling from the census, not 'a priori'; the conclusion (test against H log H or AL) stands. That finding is pinned in this job's material_evidence (finding:171362, with return:6264 and its 15 artifacts), and this screening applies the corrected reading.","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":12663,"input_sha256":"ed29a2fba96532820fdbeed0ad887661998cf5bd76e1f13d62c4b9230a7fe70a","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"6ab58b80e07ba7a80fd46fba44683763cf983f9556e6cc194ab1811d19a3be31","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":6264,"material_evidence":{"sha256":"2d07d9bf7ec08124f4df58e67b1e80ab2fdb401ebc56ea9e7a72a9aaa94ab98d","entries":{"return:6264":"6a2d4ebc1ce7ae10be936c21ac1aca86e9947932be442259ea2a910530535be5","finding:171362":"95aadeafe334f364f8ee7174db7b2a8e96698c72114a28f806223d80b2f1b3b6","artifact:6264:0a7de483db19857467c6c50f4b7aaed55c70de043c61e05f8426e708c0de69fc":"0a7de483db19857467c6c50f4b7aaed55c70de043c61e05f8426e708c0de69fc","artifact:6264:32902a22a3e73db9ceac555e3710d24926b83b7922c291288285f3d8e7287c4f":"32902a22a3e73db9ceac555e3710d24926b83b7922c291288285f3d8e7287c4f","artifact:6264:46358509e5b319c42fe7a5226049a11d8d08c6f4db60cdbbf86aa507ceaa60a0":"46358509e5b319c42fe7a5226049a11d8d08c6f4db60cdbbf86aa507ceaa60a0","artifact:6264:4b74399414b2fe9b03a7ccbfb4c277fec2966d6e09eb110fc46ce466315f0062":"4b74399414b2fe9b03a7ccbfb4c277fec2966d6e09eb110fc46ce466315f0062","artifact:6264:55f6f57d9b1567201de912827064c30529f8eeaf1e4841b3d504467099a52447":"55f6f57d9b1567201de912827064c30529f8eeaf1e4841b3d504467099a52447","artifact:6264:62cb4edd02ddafe139cc6d5ceaaab9e30be2c5bedc2a69beb4b4b4c0613fc511":"62cb4edd02ddafe139cc6d5ceaaab9e30be2c5bedc2a69beb4b4b4c0613fc511","artifact:6264:6ab58b80e07ba7a80fd46fba44683763cf983f9556e6cc194ab1811d19a3be31":"6ab58b80e07ba7a80fd46fba44683763cf983f9556e6cc194ab1811d19a3be31","artifact:6264:722dd2b8da77a4d7a50f2ee4460f3e59e3707908aa04ec2e86b45d9d6bc39027":"722dd2b8da77a4d7a50f2ee4460f3e59e3707908aa04ec2e86b45d9d6bc39027","artifact:6264:9cb264c69de4d01b2898110386c16337035523f9a831422ef9f4afa2aca04239":"9cb264c69de4d01b2898110386c16337035523f9a831422ef9f4afa2aca04239","artifact:6264:9d6360ce9c9928e28d424909ffaa2e56c1e86643c5c1b05d7c4f8337580b0697":"9d6360ce9c9928e28d424909ffaa2e56c1e86643c5c1b05d7c4f8337580b0697","artifact:6264:a4f426070c779c70e2bbfa32062c212733c4a6fd9f4dee7325bfdb85c950ae93":"a4f426070c779c70e2bbfa32062c212733c4a6fd9f4dee7325bfdb85c950ae93","artifact:6264:b8c57de63d421cd70c928e3868c80a811564a81a91d0b0976a7ca79580c2695c":"b8c57de63d421cd70c928e3868c80a811564a81a91d0b0976a7ca79580c2695c","artifact:6264:dd8e43715b64da425616937e5dc6d9ffbb9c7ec4e661ecfab241510c7d1adc91":"dd8e43715b64da425616937e5dc6d9ffbb9c7ec4e661ecfab241510c7d1adc91","artifact:6264:e96c0a1e99f5ea3b5d85899ea17656a73111e6f352eeea30b0eb114b03859ba1":"e96c0a1e99f5ea3b5d85899ea17656a73111e6f352eeea30b0eb114b03859ba1","artifact:6264:ee2b04056c4a0fe01b89f3ad93e0f5a3deb03ca77af4c2da2e97da1b834e6761":"ee2b04056c4a0fe01b89f3ad93e0f5a3deb03ca77af4c2da2e97da1b834e6761"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":6264,"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 #6264: 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. 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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:6264,input_sha256:\"ed29a2fba96532820fdbeed0ad887661998cf5bd76e1f13d62c4b9230a7fe70a\",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. 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