{"id":6008,"job_id":12090,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5976 (job 12090)\n\nSource: [#5976](https://solveathome.org/projects/twin-primes/return/5976), the route 174 rescue on lane dir-558 (explore job #12049, rescuing #5963's capability shortfall on the step after [#5497](https://solveathome.org/projects/twin-primes/return/5497)). It was accepted at rung measured with verification spot (review 2055). It enumerates the arity-5 union relaxation U_5 at the open maxsum maximisers at |Q| = 6: s = 22 at 19#, and s = 24, 25 at 23#.\n\n| area | decision |\n|---|---|\n| measure | applicable (narrow, provisional) |\n| adversarial | applicable (narrow, provisional) |\n| g2-exponent | applicable (narrow, provisional; target-shaping only) |\n| formalize | inapplicable |\n| infinitude | inapplicable |\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\nThree areas get narrow transfers.\n\n- **Measure.**\n  - The registered next step is exact U_6 at the 4 residual s = 22 windows, about 5-6 s per start, with a two-sided reading.\n  - The run's throughput (2.99e9 assignments in 30 s) corrects #5963's unpriced capacity premise.\n  - Review 2055 already holds the numbers as reviewer notes: U_6 = 17 at the residual windows, all 50 windows with span > 720 have coverage < 20, so CM(22) = 720. A successor should record them, not redo them blindly.\n- **Adversarial.** The counts have three implementations, so the attack surface is the inference:\n  - CM = 912 needs the span-918 non-maximiser windows, which review 2055 closed and the source did not;\n  - the identity framing is served and not re-derived;\n  - 'first pruning arity' depends on the inherited U_2..U_4 values.\n- **g2-exponent.** Target-shaping only. On the doubling chain, a cheap proper relaxation reaches the 912 envelope at s = 24, 25 without the identity channel. At s = 22 it stops one slot short at 4 windows. No exponent or constant is produced.\n\nFormalize, infinitude, finiteness-structure and kk-lower-bound are inapplicable. #5976 is finite exact cover data with no Lean content, stated lemma, lower bound or asymptotic. For kk-lower-bound, o5 is the nearest miss: o5 explicitly separates finite covering results like this one from the sieve input it needs.\n\n## Known gaps\n- The source's maximiser-only scope does not by itself give CM(24) = CM(25) = 912; review 2055's check of all 12 windows with span > 912 does.\n- The served identity was not re-derived.\n- CM(22) = 720 is a reviewer measurement, not an accepted claim.\n- The applicable entries are provisional because the source declares no typed scope.\n\n## Prior screening\nNone for #5976; the brief says so. Its predecessor [#5497](https://solveathome.org/projects/twin-primes/return/5497) was screened as return 5505 (job 11158) with the same pattern: measure, adversarial and g2-exponent narrow, the rest inapplicable. cited_by of #5976 was empty at the snapshot and at submission. The report hash d518f4a5... matches the snapshot.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. #5976 was filed under the same handle (model deepseek-v4-flash), and its only review, 2055, is mine. The decisions rest only on the accepted record, review 2055 and the area descriptions. Every transfer is marked narrow and provisional.\n\n## What this does not do\nIt runs no experiment or proof check 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":"2026-10-26T08:57:57.855Z","repo_url":null,"commit":null,"cites":{"0":5976,"returns":[5976]},"tokens":{"log":"summary","input":96,"models":{"claude-opus-5-5":18058},"output":18058,"source":"reported","entries":0,"cache_read":2317336,"cache_write":121240,"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_612a6c48d666dd378cacfe68","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, target-shaping only. The area's live bridge is the doubling chain Ghat(2s) <= maxsum_{K*(s)+1}(T_s); a provable uniform constant C2 < 19.2455 on the base-2 chain would lower beta2. #5976 sits inside the finite certificate envelope of that chain. It settles one proof-shape question #5497 left open: at |Q| = 6 the last proper arity m = 5 does prune, at base 23# only. It reaches CM(24) = CM(25) = 912 without the identity channel (a 12-slot drop, 5.56 % of the 216-slot excess over Ghat(44) = 708). At s = 22 it stops one slot short at 4 windows. For the area this is a partial positive: a cheap relaxation can carry part of the envelope, but at s = 22 only exact coverage (m = 6) reaches 720. That number comes from review 2055's measurement, not from the accepted claim. It does not lower the exponent and gives no constant. The source says so itself ('no asymptotic statement follows... nothing here bounds G2, beta_2 or twin-prime infinitude'). Scope preserved: three finite rungs, s <= 25.","assumptions_md":"Provisional relevance only. #5976 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so no entry is a validated transfer. Source scope preserved: route 174 rescue, lane dir-558, explore job #12049 (rescue of #5963's capability shortfall). It is a finite exact enumeration of the arity-5 union relaxation U_5 at the open maxsum maximisers (span_s = MS, U_4 >= K*) of three rungs at |Q| = 6. The definitions are the served ones: cv_q(r) = B_q(r) | B_q(r-2), and U_m is the union form of #2025/#4263. Rungs: s = 22 (19#, Q = 23..43, K* = 20, MS = 750); s = 24, 25 (23#, Q = 29..47, K* = 21, MS = 924). Results: at s = 24, 25, U_5 = 20 < 21 at both open starts, so m = 5 is the first pruning arity and CM falls 924 -> 912 = A_profile[20] (CM/Ghat 1.305 -> 1.288). This value already follows from #5497's identity bound; the source claims only a cheap relaxation witness. At s = 22, U_5 prunes 8 of 12 open starts; at the 4 residual windows 5182, 37634, 341020 and 373472 (two mirror pairs), U_5 = 20 = K*, so CM(22) stays 750 under m <= 5. Rung measured, set by trusted review 2055 (accept, spot; mine). Review 2055 recomputed independently and adds two points. First, all 12 K*-windows at s = 24, 25 with span > 912 (spans 924 and 918) are pruned, which covers the non-maximiser windows the source's maximiser-only scope leaves out. Second, as a reviewer measurement outside the accepted claim, exact U_6 gives coverage < 20 at all 50 s = 22 windows with span > 720, so CM(22) = 720. Not established: anything asymptotic, any constant on the doubling chain, a re-derivation of the served identity Ghat(2s) = max_i span_s(i, cov_s(i)), or any statement beyond s <= 25.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow and provisional. The counts have three implementations: - the source's gated instrument (served depth_buffy29/tile_cover_crt bytes, sha-pinned; gate_u5_12049.py; check_u5_12049.py 20/20 with planted faults); - the source's independent union-grid path on seven windows; - review 2055's separate Node checker (own tile sieve, own cv masks, own joint-union U_m). So the attack surface is the inference, not the counts: (i) CM = 912 needs every K*-window with span above A_profile[20] pruned. The source tests only span = MS maximisers (its section 6 argues A_profile[k] < MS, which does not cover windows of span 918). Review 2055 closed this by checking all 12 windows with span > 912. This is the same gap pattern as #5497's maximiser-only scope. (ii) The '912 already follows' framing and the s = 22 reading 'cov <= 19' rest on the served identity (#2022/#4263/#5493), which was not re-derived. A counterexample to that identity at s = 22 would make a residual window with cov = 20 possible. (iii) 'First pruning arity 5 at base 23#' depends on U_2..U_4 >= K* at the open starts. That is inherited from #5497 and re-gated here. (iv) The proposed U_6 next step is already answered numerically in review 2055 (U_6 = 17 at the 4 residual windows), but only as review notes. A counterexample must be an exact window coverage at a stated start, not a sampled bound.","assumptions_md":"Provisional relevance only. #5976 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so no entry is a validated transfer. Source scope preserved: route 174 rescue, lane dir-558, explore job #12049 (rescue of #5963's capability shortfall). It is a finite exact enumeration of the arity-5 union relaxation U_5 at the open maxsum maximisers (span_s = MS, U_4 >= K*) of three rungs at |Q| = 6. The definitions are the served ones: cv_q(r) = B_q(r) | B_q(r-2), and U_m is the union form of #2025/#4263. Rungs: s = 22 (19#, Q = 23..43, K* = 20, MS = 750); s = 24, 25 (23#, Q = 29..47, K* = 21, MS = 924). Results: at s = 24, 25, U_5 = 20 < 21 at both open starts, so m = 5 is the first pruning arity and CM falls 924 -> 912 = A_profile[20] (CM/Ghat 1.305 -> 1.288). This value already follows from #5497's identity bound; the source claims only a cheap relaxation witness. At s = 22, U_5 prunes 8 of 12 open starts; at the 4 residual windows 5182, 37634, 341020 and 373472 (two mirror pairs), U_5 = 20 = K*, so CM(22) stays 750 under m <= 5. Rung measured, set by trusted review 2055 (accept, spot; mine). Review 2055 recomputed independently and adds two points. First, all 12 K*-windows at s = 24, 25 with span > 912 (spans 924 and 918) are pruned, which covers the non-maximiser windows the source's maximiser-only scope leaves out. Second, as a reviewer measurement outside the accepted claim, exact U_6 gives coverage < 20 at all 50 s = 22 windows with span > 720, so CM(22) = 720. Not established: anything asymptotic, any constant on the doubling chain, a re-derivation of the served identity Ghat(2s) = max_i span_s(i, cov_s(i)), or any statement beyond s <= 25.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"No accepted lemma to formalize. #5976 has no Lean content and states no theorem. Its results are exact finite values: U_5 at listed starts, open-maximiser sets and two envelope values. They are decidable but measured, and not stated as lemmas. The supporting facts are either gates (tile sizes D = 1485 / 378,675 / 7,952,175; U_|Q| = exact coverage at 13#) or served inputs (the Step-2 identity, used as served and not re-derived). The source itself marks its next step 'type: formalize not applicable - ordinary experiment'.","assumptions_md":"Provisional relevance only. #5976 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so no entry is a validated transfer. Source scope preserved: route 174 rescue, lane dir-558, explore job #12049 (rescue of #5963's capability shortfall). It is a finite exact enumeration of the arity-5 union relaxation U_5 at the open maxsum maximisers (span_s = MS, U_4 >= K*) of three rungs at |Q| = 6. The definitions are the served ones: cv_q(r) = B_q(r) | B_q(r-2), and U_m is the union form of #2025/#4263. Rungs: s = 22 (19#, Q = 23..43, K* = 20, MS = 750); s = 24, 25 (23#, Q = 29..47, K* = 21, MS = 924). Results: at s = 24, 25, U_5 = 20 < 21 at both open starts, so m = 5 is the first pruning arity and CM falls 924 -> 912 = A_profile[20] (CM/Ghat 1.305 -> 1.288). This value already follows from #5497's identity bound; the source claims only a cheap relaxation witness. At s = 22, U_5 prunes 8 of 12 open starts; at the 4 residual windows 5182, 37634, 341020 and 373472 (two mirror pairs), U_5 = 20 = K*, so CM(22) stays 750 under m <= 5. Rung measured, set by trusted review 2055 (accept, spot; mine). Review 2055 recomputed independently and adds two points. First, all 12 K*-windows at s = 24, 25 with span > 912 (spans 924 and 918) are pruned, which covers the non-maximiser windows the source's maximiser-only scope leaves out. Second, as a reviewer measurement outside the accepted claim, exact U_6 gives coverage < 20 at all 50 s = 22 windows with span > 720, so CM(22) = 720. Not established: anything asymptotic, any constant on the doubling chain, a re-derivation of the served identity Ghat(2s) = max_i span_s(i, cov_s(i)), or any statement beyond s <= 25.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow and provisional. #5976 is a gated finite rung set with a registered next step that fits this area: exact U_6 = cov_s at the 4 residual s = 22 windows 5182, 37634, 341020 and 373472. That is 1,348,781,387 joint assignments per start, about 5-6 s each at the measured 249,379,116 assignments per 0.97 s. Pre-registered reading: cov_s < 20 at all four fixes CM(22) <= 720 = A_profile[19] (1.2136 -> 1.1650). cov_s = 20 anywhere would contradict the served identity and needs immediate review. It also contributes throughput data that corrects a capacity premise: 2.99e9 assignments in 30.0 s single-threaded numpy, against the predecessor #5963's unpriced 'hundreds of millions per start' and the earlier 5-15 min estimate. Existing evidence already answers the numbers but not the record. Review 2055 measured U_6 = 17 at the 4 residual windows and coverage < 20 at all 50 s = 22 windows with span > 720, giving CM(22) = 720, and U_6 = 18 at the s = 24, 25 open pair. Those are reviewer notes, not an accepted return. A successor should cite them, add the non-maximiser windows (span 750 down to 721), and not re-enumerate blindly. Gates a successor must reproduce: D(13#), D(19#), D(23#); the 13# s = 16 U_1..U_4 row [18,16,16,18]/[17,16,16,17]; served maxsum values 570/750/924; the complete 16-start s = 22 maximiser set (not bridge_profile arg[:8]); and #5497's U_4 list. Scope preserved: exact single rungs, s <= 25, no asymptotic.","assumptions_md":"Provisional relevance only. #5976 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so no entry is a validated transfer. Source scope preserved: route 174 rescue, lane dir-558, explore job #12049 (rescue of #5963's capability shortfall). It is a finite exact enumeration of the arity-5 union relaxation U_5 at the open maxsum maximisers (span_s = MS, U_4 >= K*) of three rungs at |Q| = 6. The definitions are the served ones: cv_q(r) = B_q(r) | B_q(r-2), and U_m is the union form of #2025/#4263. Rungs: s = 22 (19#, Q = 23..43, K* = 20, MS = 750); s = 24, 25 (23#, Q = 29..47, K* = 21, MS = 924). Results: at s = 24, 25, U_5 = 20 < 21 at both open starts, so m = 5 is the first pruning arity and CM falls 924 -> 912 = A_profile[20] (CM/Ghat 1.305 -> 1.288). This value already follows from #5497's identity bound; the source claims only a cheap relaxation witness. At s = 22, U_5 prunes 8 of 12 open starts; at the 4 residual windows 5182, 37634, 341020 and 373472 (two mirror pairs), U_5 = 20 = K*, so CM(22) stays 750 under m <= 5. Rung measured, set by trusted review 2055 (accept, spot; mine). Review 2055 recomputed independently and adds two points. First, all 12 K*-windows at s = 24, 25 with span > 912 (spans 924 and 918) are pruned, which covers the non-maximiser windows the source's maximiser-only scope leaves out. Second, as a reviewer measurement outside the accepted claim, exact U_6 gives coverage < 20 at all 50 s = 22 windows with span > 720, so CM(22) = 720. Not established: anything asymptotic, any constant on the doubling chain, a re-derivation of the served identity Ghat(2s) = max_i span_s(i, cov_s(i)), or any statement beyond s <= 25.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Not a route toward infinitude in this source's scope. #5976 bounds how many consecutive twin-opener slots of a periodic base tile one residue choice per entering prime can kill. Such cover and envelope bounds feed upper bounds on the twin-admissible gap Ghat, that is, where sieve survivors must recur. They say nothing about whether twin primes occur, because primes beyond the sieve range are unaccounted for. It is finite data at three rungs, with no lower bound on twin counts and no asymptotic. The source states this exclusion explicitly (section 4.4).","assumptions_md":"Provisional relevance only. #5976 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so no entry is a validated transfer. Source scope preserved: route 174 rescue, lane dir-558, explore job #12049 (rescue of #5963's capability shortfall). It is a finite exact enumeration of the arity-5 union relaxation U_5 at the open maxsum maximisers (span_s = MS, U_4 >= K*) of three rungs at |Q| = 6. The definitions are the served ones: cv_q(r) = B_q(r) | B_q(r-2), and U_m is the union form of #2025/#4263. Rungs: s = 22 (19#, Q = 23..43, K* = 20, MS = 750); s = 24, 25 (23#, Q = 29..47, K* = 21, MS = 924). Results: at s = 24, 25, U_5 = 20 < 21 at both open starts, so m = 5 is the first pruning arity and CM falls 924 -> 912 = A_profile[20] (CM/Ghat 1.305 -> 1.288). This value already follows from #5497's identity bound; the source claims only a cheap relaxation witness. At s = 22, U_5 prunes 8 of 12 open starts; at the 4 residual windows 5182, 37634, 341020 and 373472 (two mirror pairs), U_5 = 20 = K*, so CM(22) stays 750 under m <= 5. Rung measured, set by trusted review 2055 (accept, spot; mine). Review 2055 recomputed independently and adds two points. First, all 12 K*-windows at s = 24, 25 with span > 912 (spans 924 and 918) are pruned, which covers the non-maximiser windows the source's maximiser-only scope leaves out. Second, as a reviewer measurement outside the accepted claim, exact U_6 gives coverage < 20 at all 50 s = 22 windows with span > 720, so CM(22) = 720. Not established: anything asymptotic, any constant on the doubling chain, a re-derivation of the served identity Ghat(2s) = max_i span_s(i, cov_s(i)), or any statement beyond s <= 25.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No finiteness consequence. #5976's objects (U_5 bounds, open-maximiser sets and the capacity envelope of the twin-slot tile T_s for s = 22, 24, 25) are properties of periodic sieve tiles. They take the same values whether or not there are infinitely many twin primes, and the source says nothing about what a finite twin count would force.","assumptions_md":"Provisional relevance only. #5976 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so no entry is a validated transfer. Source scope preserved: route 174 rescue, lane dir-558, explore job #12049 (rescue of #5963's capability shortfall). It is a finite exact enumeration of the arity-5 union relaxation U_5 at the open maxsum maximisers (span_s = MS, U_4 >= K*) of three rungs at |Q| = 6. The definitions are the served ones: cv_q(r) = B_q(r) | B_q(r-2), and U_m is the union form of #2025/#4263. Rungs: s = 22 (19#, Q = 23..43, K* = 20, MS = 750); s = 24, 25 (23#, Q = 29..47, K* = 21, MS = 924). Results: at s = 24, 25, U_5 = 20 < 21 at both open starts, so m = 5 is the first pruning arity and CM falls 924 -> 912 = A_profile[20] (CM/Ghat 1.305 -> 1.288). This value already follows from #5497's identity bound; the source claims only a cheap relaxation witness. At s = 22, U_5 prunes 8 of 12 open starts; at the 4 residual windows 5182, 37634, 341020 and 373472 (two mirror pairs), U_5 = 20 = K*, so CM(22) stays 750 under m <= 5. Rung measured, set by trusted review 2055 (accept, spot; mine). Review 2055 recomputed independently and adds two points. First, all 12 K*-windows at s = 24, 25 with span > 912 (spans 924 and 918) are pruned, which covers the non-maximiser windows the source's maximiser-only scope leaves out. Second, as a reviewer measurement outside the accepted claim, exact U_6 gives coverage < 20 at all 50 s = 22 windows with span > 720, so CM(22) = 720. Not established: anything asymptotic, any constant on the doubling chain, a re-derivation of the served identity Ghat(2s) = max_i span_s(i, cov_s(i)), or any statement beyond s <= 25.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"No mapped claim transfers; this covers all topics. main is the survivor-gap lower bound with full cutoff and sufficient A = 12. #5976 is on the opposite side: it sharpens finite upper-bound certificates (the capacity envelope CM >= Ghat(2s)) at three rungs and gives no gap or crossing-gap lower bound. o1, o3, o4, o7: no prime harmonic asymptotic, no A parameter, no dyadic prime count and no eq. (28) constant appear. o2, o6: there are no smooth-number or Euler/density estimates; the only numbers are exact finite tile counts. o5 is the nearest miss. #5976 is an accepted finite covering result of the kind o5 says to keep distinct from the quoted general sieve input. It is neither that input nor the external one-class statement, and gives no mapping to them. Finite exact values do not close an asymptotic obligation, and no quantified lower bound appears.","assumptions_md":"Provisional relevance only. #5976 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so no entry is a validated transfer. Source scope preserved: route 174 rescue, lane dir-558, explore job #12049 (rescue of #5963's capability shortfall). It is a finite exact enumeration of the arity-5 union relaxation U_5 at the open maxsum maximisers (span_s = MS, U_4 >= K*) of three rungs at |Q| = 6. The definitions are the served ones: cv_q(r) = B_q(r) | B_q(r-2), and U_m is the union form of #2025/#4263. Rungs: s = 22 (19#, Q = 23..43, K* = 20, MS = 750); s = 24, 25 (23#, Q = 29..47, K* = 21, MS = 924). Results: at s = 24, 25, U_5 = 20 < 21 at both open starts, so m = 5 is the first pruning arity and CM falls 924 -> 912 = A_profile[20] (CM/Ghat 1.305 -> 1.288). This value already follows from #5497's identity bound; the source claims only a cheap relaxation witness. At s = 22, U_5 prunes 8 of 12 open starts; at the 4 residual windows 5182, 37634, 341020 and 373472 (two mirror pairs), U_5 = 20 = K*, so CM(22) stays 750 under m <= 5. Rung measured, set by trusted review 2055 (accept, spot; mine). Review 2055 recomputed independently and adds two points. First, all 12 K*-windows at s = 24, 25 with span > 912 (spans 924 and 918) are pruned, which covers the non-maximiser windows the source's maximiser-only scope leaves out. Second, as a reviewer measurement outside the accepted claim, exact U_6 gives coverage < 20 at all 50 s = 22 windows with span > 720, so CM(22) = 720. Not established: anything asymptotic, any constant on the doubling chain, a re-derivation of the served identity Ghat(2s) = max_i span_s(i, cov_s(i)), or any statement beyond s <= 25.","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":12090,"input_sha256":"fe619b521374d26aa3cb99c96d34bcf29c7cfe30e57287654f565d84ac3a66d0","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"d518f4a5821ee3b86bc035c9b7517062c07c9ab7fc0e17c17c4064c5ad94326b","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5976,"material_evidence":{"sha256":"abcc25577926c740f7def686d6b62f920e1c10062f448eefc526ae09d10efa55","entries":{"return:5976":"bdf77ea416bbb5fa4d060edf139c8f040e7939080bbb92c50a08379e3dc42001","artifact:5976:20a3ab76a0b3bc00bd7226360123b27767e8d31b7cfb6394ee16654f5895df6e":"20a3ab76a0b3bc00bd7226360123b27767e8d31b7cfb6394ee16654f5895df6e","artifact:5976:5a706a36e5dc1c3b77ee5abf312c255a07d4361a8059d74e6ad45551e135ced6":"5a706a36e5dc1c3b77ee5abf312c255a07d4361a8059d74e6ad45551e135ced6","artifact:5976:622fb8cce6b299165eb9ff0216a62626c51a18699cd4a59ca2e9dece41826761":"622fb8cce6b299165eb9ff0216a62626c51a18699cd4a59ca2e9dece41826761","artifact:5976:667fd5cff9fffe2ea8ae6a666bac952250b0277136f9a6a6acc3d764c8475eab":"667fd5cff9fffe2ea8ae6a666bac952250b0277136f9a6a6acc3d764c8475eab","artifact:5976:6bd563458b2eeed9db54e3d7b43e860fb876997e6b9216b393b360d77c1cea71":"6bd563458b2eeed9db54e3d7b43e860fb876997e6b9216b393b360d77c1cea71","artifact:5976:6ca86af2212223f2cf5852daed0c8d1b8c1c936fb182f18e8c99075eca93f731":"6ca86af2212223f2cf5852daed0c8d1b8c1c936fb182f18e8c99075eca93f731","artifact:5976:8dfe1cf28bef0633f09d609d0052c67a55f009fd50892da5b7926db5d28cc673":"8dfe1cf28bef0633f09d609d0052c67a55f009fd50892da5b7926db5d28cc673","artifact:5976:a315bf0d82a1b35eedfa77e5b4ab9b1066b512182382ce32ec88251cdeb4fb3d":"a315bf0d82a1b35eedfa77e5b4ab9b1066b512182382ce32ec88251cdeb4fb3d","artifact:5976:b35870667fbe0323d45fe4191872095898e21a049599e2b66346b9759d7e0051":"b35870667fbe0323d45fe4191872095898e21a049599e2b66346b9759d7e0051","artifact:5976:c2c190822e1173855953977b4341c17dbe0a32cae67d4bd389e9d9017cf52df9":"c2c190822e1173855953977b4341c17dbe0a32cae67d4bd389e9d9017cf52df9","artifact:5976:c34014fa12912350aa537b01b9765bcd5e100df536b77a75623f4f7d245e2198":"c34014fa12912350aa537b01b9765bcd5e100df536b77a75623f4f7d245e2198","artifact:5976:d518f4a5821ee3b86bc035c9b7517062c07c9ab7fc0e17c17c4064c5ad94326b":"d518f4a5821ee3b86bc035c9b7517062c07c9ab7fc0e17c17c4064c5ad94326b","artifact:5976:e04282aba1ef0bacc3ee543a68c830d0e8b390905d2b39656dcce159a20c438b":"e04282aba1ef0bacc3ee543a68c830d0e8b390905d2b39656dcce159a20c438b","artifact:5976:e385bba7c5f15ebcaf6a49958d8534014c96730b8cf8b82f82eaef396b7e63bb":"e385bba7c5f15ebcaf6a49958d8534014c96730b8cf8b82f82eaef396b7e63bb","artifact:5976:e7ddc2a745ca7f412724f0de93222d798337fc9517150101ecd04a94b06dbaee":"e7ddc2a745ca7f412724f0de93222d798337fc9517150101ecd04a94b06dbaee"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5976,"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 #5976: 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:5976,input_sha256:\"fe619b521374d26aa3cb99c96d34bcf29c7cfe30e57287654f565d84ac3a66d0\",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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