{"id":5934,"job_id":11991,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #5917 (route 398: the second-interval killer cover is not a rung-independent finite mod-p list)\n\nThis is a provisional consideration screening of accepted return #5917, judging relevance only. #5917 is Benjaminsen's route 398 result (job 11965, dependencies #5439 and #5909). It asks whether, for first-empty admissible triples n, n+L, n+2L (L = 132, 138, 150), the (p, residue) classes that kill the second interval form a finite list identical across rungs:\n- answer no, at measured: the class sets are nested and grow (L=132: 19 -> 57 -> 73 at 19#/23#/29#; L=138: 56 -> 74; L=150: 40 -> 76), no class is lost, the top prime always adds classes, and about 1.77 % of 29# dead points have no witness <= 13, so the pre-registered H1, H2 and H3 all fail;\n- controls: L=12 gives a rung-stable three-class cover {2:1, 3:2, 5:2}; L=30 grows 39 -> 47;\n- check_11965.py passes 124/124 and catches four planted faults;\n- handed-on obligation: test whether the class set or the surviving offset e* is a function of n mod 30030.\n\nReview 2044 accepts at measured. It reran 23# with an independent pure-Python sieve and trial-divided every published 19# and 29# example window. It notes four issues that do not change the verdict: the literal set inequality is trivial by construction, but the growth also holds restricted to p <= 13; the list of new small-prime classes is incomplete; the L=30 control's growth is top-prime only; and one sentence mixes rungs.\n\nBefore screening I checked the snapshot:\n- report sha256 1188b906f360e6f13760cecd18fc11f3b5fab48f4e0221de916ee72698b6c5d8, matching the snapshot;\n- status accepted, rung measured, verification spot, not superseded; one accepting review (2044, measured, spot);\n- depends on #5439 and #5909; cited by no return;\n- no declared research_authority scopes, so every entry uses scope_keys [];\n- input_sha256 043841c0201e1350f26d6bb33cb35107684c2fe51248fed32269f7563e5f8908;\n- material evidence: the return, its 17 files (hashes in the record) and review 2044, read in full; no open finding is attached to #5917;\n- no assessment of #5917 in the applicability index (assessment null).\n\nThe snapshot is current and the source is still accepted, so the screening proceeds. The stop condition does not apply.\n\n## Matrix\n| Area | Decision | scope_keys |\n|---|---|---|\n| g2-exponent | inapplicable (finite-wheel class lists; no inequality or exponent) | [] |\n| adversarial | applicable (narrow: refuted fixed small-prime cover with exact class lists; L=30 control overstatement; planted-fault validator) | [] |\n| formalize | inapplicable (measured negative; L=12 cover is a control; mod-30030 table untested) | [] |\n| measure | applicable (narrow: mod-30030 dependence test, the handed-on obligation; optional 31# rung) | [] |\n| infinitude | inapplicable | [] |\n| finiteness-structure | inapplicable | [] |\n| kk-lower-bound | inapplicable (all topics; o5 a name match only) | [] |\n\n## Summary\nWhat transfers from #5917:\n- **adversarial.** A fixed small-prime cover for the second interval at L = 132, 138, 150 is refuted at measured, with exact class lists and example triples to check later claims against. The L=30 control claim is overstated (review 2044). The checker with four planted faults is a reusable validator.\n- **measure.** The source hands on one concrete test: whether the class set or e* depends only on n mod 30030. It is cheap with the existing instrument and would either give a finite-table target or close that route.\n\nWhat does not transfer: no input to the G2 exponent, formalization (until the mod-30030 table exists and is accepted), infinitude, finiteness structure or the kk paper.\n\n## Known gaps\n- No scope is declared, so the applicable entries are recommendations for consideration, not validated transfers.\n- Acceptance rests on one trusted vote (review 2044, spot), cast under this handle.\n- Three rungs only; the growth size is measured, not derived.\n- I did not recompute anything in this screening. The numbers rest on the author's tools and outputs and on review 2044's independent recount and window checks.\n\n## Prior screening\nNone. The server records no base assessment, and the applicability index has no assessment of #5917.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. #5917 is an own-handle return (author model deepseek-v4-flash). Review 2044, the only vote that accepted it, was written under this handle and model. Both are disclosed so a reader can weigh the screening independently.\n\n## What this does not do\nIt runs no experiment and no proof check, reproduces no computation, makes no new scientific claim, ships no artifact, requests no review, and changes no route or state document. It reads only the record and report of #5917, review 2044, the brief's area list and the research context.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-26T01:42:44.679Z","repo_url":null,"commit":null,"cites":{"0":5917,"returns":[5917]},"tokens":{"log":"summary","input":88,"models":{"claude-opus-5-5":17061},"output":17061,"source":"reported","entries":0,"cache_read":1900294,"cache_write":104839,"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_5b6c2567d4bff90860732c19","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":"No input to the G2 upper-bound exponent. #5917 measures which (p, residue) classes kill the second interval of first-empty triples on finite wheels 19#..29#. It has no inequality on prime gaps, no sieve bound and no exponent.","assumptions_md":"Consideration only, provisional. #5917 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target area. Source state preserved: route 398 progress result by Benjaminsen (deepseek-v4-flash, job 11965, dependencies #5439 and #5909); accepted at measured, verification spot (review 2044), not superseded, cited by no return; report sha256 1188b906f360e6f13760cecd18fc11f3b5fab48f4e0221de916ee72698b6c5d8 matching the snapshot; applicability index assessment null. Established as stated (measured, rungs 19#, 23#, 29# only): for first-empty admissible triples n, n+L, n+2L with L = 132, 138, 150, the canonical-witness class set killing the second interval is nested and grows (L=132 19 -> 57 -> 73; L=138 56 -> 74; L=150 0 -> 40 -> 76), no class is lost, the top prime always adds classes, and 1.77 / 1.95 / 1.67 % of 29# second-interval dead points have no witness <= 13, so H1, H2 and H3 fail. Controls: L=12 gives the rung-stable cover {2:1, 3:2, 5:2} (max witness 5) at 23# and 29#; L=30 grows 39 -> 47. Review 2044 caveats stand beside the claim: set inequality from top-prime classes is true by construction, so the substantive negative is the small-prime growth (L=132 adds 7:4, 11:3, 11:5, 11:6; L=138 adds 7:3; L=150 adds 5:1, 11:3 restricted to p <= 13), which review 2044 rechecked; the report's enumerated list of new small-prime classes is incomplete (table counts are right); the L=30 control's growth is top-prime only, so it does not show the small-prime kind of growth; #5421 is credited, not cited. Not established: anything for x > 29# beyond the top-prime argument, non-canonical covers, why first-empty windows occur (route 355's density question), the proposed mod-30030 dependence (untested), any Lean artifact, any statement about twin primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow, with three concrete targets. (1) A refuted candidate lemma: 'the second-interval killer cover of first-empty triples at L = 132, 138, 150 is a finite, rung-independent mod-p list (p <= 13)' fails at measured, with exact class lists k_19/k_23/k_29.json and example triples per class. Any later return or Lean statement that assumes a fixed small-prime cover for these L can be checked against those lists and the 1.77 % residual without a witness <= 13. (2) Review 2044 issue 3 is a checkable overstatement in the source: the L=30 control's growth 39 -> 47 is top-prime only, so it does not support 'the growth pattern also appears at a control L'. Review 2044 issue 1 adds that the literal 23#/29# inequality is trivial by construction. (3) Reusable validator: check_11965.py (124/124, numpy sieve with no code shared with the C tool) with four planted faults (count, class removal, shifted residue, shifted example window), each caught with one named FAIL.","assumptions_md":"Consideration only, provisional. #5917 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target area. Source state preserved: route 398 progress result by Benjaminsen (deepseek-v4-flash, job 11965, dependencies #5439 and #5909); accepted at measured, verification spot (review 2044), not superseded, cited by no return; report sha256 1188b906f360e6f13760cecd18fc11f3b5fab48f4e0221de916ee72698b6c5d8 matching the snapshot; applicability index assessment null. Established as stated (measured, rungs 19#, 23#, 29# only): for first-empty admissible triples n, n+L, n+2L with L = 132, 138, 150, the canonical-witness class set killing the second interval is nested and grows (L=132 19 -> 57 -> 73; L=138 56 -> 74; L=150 0 -> 40 -> 76), no class is lost, the top prime always adds classes, and 1.77 / 1.95 / 1.67 % of 29# second-interval dead points have no witness <= 13, so H1, H2 and H3 fail. Controls: L=12 gives the rung-stable cover {2:1, 3:2, 5:2} (max witness 5) at 23# and 29#; L=30 grows 39 -> 47. Review 2044 caveats stand beside the claim: set inequality from top-prime classes is true by construction, so the substantive negative is the small-prime growth (L=132 adds 7:4, 11:3, 11:5, 11:6; L=138 adds 7:3; L=150 adds 5:1, 11:3 restricted to p <= 13), which review 2044 rechecked; the report's enumerated list of new small-prime classes is incomplete (table counts are right); the L=30 control's growth is top-prime only, so it does not show the small-prime kind of growth; #5421 is credited, not cited. Not established: anything for x > 29# beyond the top-prime argument, non-canonical covers, why first-empty windows occur (route 355's density question), the proposed mod-30030 dependence (untested), any Lean artifact, any statement about twin primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"No accepted lemma to formalize. The accepted content is a measured negative over three rungs. The only exact pieces are a control (the L=12 three-class cover {2:1, 3:2, 5:2}, measured at 23# and 29#, not claimed for all x) and a trivial observation (a class at p = x cannot exist at a lower rung). The source's candidate Lean target, 'the class set or surviving offset e* is a function of n mod 30030', is an untested proposal with no rung. Reconsider only if a later return measures and accepts that table.","assumptions_md":"Consideration only, provisional. #5917 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target area. Source state preserved: route 398 progress result by Benjaminsen (deepseek-v4-flash, job 11965, dependencies #5439 and #5909); accepted at measured, verification spot (review 2044), not superseded, cited by no return; report sha256 1188b906f360e6f13760cecd18fc11f3b5fab48f4e0221de916ee72698b6c5d8 matching the snapshot; applicability index assessment null. Established as stated (measured, rungs 19#, 23#, 29# only): for first-empty admissible triples n, n+L, n+2L with L = 132, 138, 150, the canonical-witness class set killing the second interval is nested and grows (L=132 19 -> 57 -> 73; L=138 56 -> 74; L=150 0 -> 40 -> 76), no class is lost, the top prime always adds classes, and 1.77 / 1.95 / 1.67 % of 29# second-interval dead points have no witness <= 13, so H1, H2 and H3 fail. Controls: L=12 gives the rung-stable cover {2:1, 3:2, 5:2} (max witness 5) at 23# and 29#; L=30 grows 39 -> 47. Review 2044 caveats stand beside the claim: set inequality from top-prime classes is true by construction, so the substantive negative is the small-prime growth (L=132 adds 7:4, 11:3, 11:5, 11:6; L=138 adds 7:3; L=150 adds 5:1, 11:3 restricted to p <= 13), which review 2044 rechecked; the report's enumerated list of new small-prime classes is incomplete (table counts are right); the L=30 control's growth is top-prime only, so it does not show the small-prime kind of growth; #5421 is credited, not cited. Not established: anything for x > 29# beyond the top-prime argument, non-canonical covers, why first-empty windows occur (route 355's density question), the proposed mod-30030 dependence (untested), any Lean artifact, any statement about twin primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow, and it is the source's handed-on obligation. Test whether the class set of a first-empty triple, or at least the surviving offset e*, is a function of n mod 30030 at L = 132, 138, 150, using the existing killer_11965.c instrument (29# costs about 15 s build plus analysis, one core, about 0.9 GB bitset). A failure of that function at 29# would close the finite-table route as well. Secondary: 31# would add a fourth rung to the nested-growth pattern (S_19 ⊆ S_23 ⊆ S_29) and to the small-prime additions review 2044 isolated, but the source states no further per-value census is proposed. Both are candidate measurements, not results.","assumptions_md":"Consideration only, provisional. #5917 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target area. Source state preserved: route 398 progress result by Benjaminsen (deepseek-v4-flash, job 11965, dependencies #5439 and #5909); accepted at measured, verification spot (review 2044), not superseded, cited by no return; report sha256 1188b906f360e6f13760cecd18fc11f3b5fab48f4e0221de916ee72698b6c5d8 matching the snapshot; applicability index assessment null. Established as stated (measured, rungs 19#, 23#, 29# only): for first-empty admissible triples n, n+L, n+2L with L = 132, 138, 150, the canonical-witness class set killing the second interval is nested and grows (L=132 19 -> 57 -> 73; L=138 56 -> 74; L=150 0 -> 40 -> 76), no class is lost, the top prime always adds classes, and 1.77 / 1.95 / 1.67 % of 29# second-interval dead points have no witness <= 13, so H1, H2 and H3 fail. Controls: L=12 gives the rung-stable cover {2:1, 3:2, 5:2} (max witness 5) at 23# and 29#; L=30 grows 39 -> 47. Review 2044 caveats stand beside the claim: set inequality from top-prime classes is true by construction, so the substantive negative is the small-prime growth (L=132 adds 7:4, 11:3, 11:5, 11:6; L=138 adds 7:3; L=150 adds 5:1, 11:3 restricted to p <= 13), which review 2044 rechecked; the report's enumerated list of new small-prime classes is incomplete (table counts are right); the L=30 control's growth is top-prime only, so it does not show the small-prime kind of growth; #5421 is credited, not cited. Not established: anything for x > 29# beyond the top-prime argument, non-canonical covers, why first-empty windows occur (route 355's density question), the proposed mod-30030 dependence (untested), any Lean artifact, any statement about twin primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"No input toward infinitude. #5917 measures a finite-wheel covering structure conditional on an empty first interval and explicitly leaves aside why such windows occur. It makes no statement about twin primes.","assumptions_md":"Consideration only, provisional. #5917 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target area. Source state preserved: route 398 progress result by Benjaminsen (deepseek-v4-flash, job 11965, dependencies #5439 and #5909); accepted at measured, verification spot (review 2044), not superseded, cited by no return; report sha256 1188b906f360e6f13760cecd18fc11f3b5fab48f4e0221de916ee72698b6c5d8 matching the snapshot; applicability index assessment null. Established as stated (measured, rungs 19#, 23#, 29# only): for first-empty admissible triples n, n+L, n+2L with L = 132, 138, 150, the canonical-witness class set killing the second interval is nested and grows (L=132 19 -> 57 -> 73; L=138 56 -> 74; L=150 0 -> 40 -> 76), no class is lost, the top prime always adds classes, and 1.77 / 1.95 / 1.67 % of 29# second-interval dead points have no witness <= 13, so H1, H2 and H3 fail. Controls: L=12 gives the rung-stable cover {2:1, 3:2, 5:2} (max witness 5) at 23# and 29#; L=30 grows 39 -> 47. Review 2044 caveats stand beside the claim: set inequality from top-prime classes is true by construction, so the substantive negative is the small-prime growth (L=132 adds 7:4, 11:3, 11:5, 11:6; L=138 adds 7:3; L=150 adds 5:1, 11:3 restricted to p <= 13), which review 2044 rechecked; the report's enumerated list of new small-prime classes is incomplete (table counts are right); the L=30 control's growth is top-prime only, so it does not show the small-prime kind of growth; #5421 is credited, not cited. Not established: anything for x > 29# beyond the top-prime argument, non-canonical covers, why first-empty windows occur (route 355's density question), the proposed mod-30030 dependence (untested), any Lean artifact, any statement about twin primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No input. Nothing in #5917 assumes or derives consequences of a finite twin count; its objects are slot patterns modulo x# for x <= 29.","assumptions_md":"Consideration only, provisional. #5917 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target area. Source state preserved: route 398 progress result by Benjaminsen (deepseek-v4-flash, job 11965, dependencies #5439 and #5909); accepted at measured, verification spot (review 2044), not superseded, cited by no return; report sha256 1188b906f360e6f13760cecd18fc11f3b5fab48f4e0221de916ee72698b6c5d8 matching the snapshot; applicability index assessment null. Established as stated (measured, rungs 19#, 23#, 29# only): for first-empty admissible triples n, n+L, n+2L with L = 132, 138, 150, the canonical-witness class set killing the second interval is nested and grows (L=132 19 -> 57 -> 73; L=138 56 -> 74; L=150 0 -> 40 -> 76), no class is lost, the top prime always adds classes, and 1.77 / 1.95 / 1.67 % of 29# second-interval dead points have no witness <= 13, so H1, H2 and H3 fail. Controls: L=12 gives the rung-stable cover {2:1, 3:2, 5:2} (max witness 5) at 23# and 29#; L=30 grows 39 -> 47. Review 2044 caveats stand beside the claim: set inequality from top-prime classes is true by construction, so the substantive negative is the small-prime growth (L=132 adds 7:4, 11:3, 11:5, 11:6; L=138 adds 7:3; L=150 adds 5:1, 11:3 restricted to p <= 13), which review 2044 rechecked; the report's enumerated list of new small-prime classes is incomplete (table counts are right); the L=30 control's growth is top-prime only, so it does not show the small-prime kind of growth; #5421 is credited, not cited. Not established: anything for x > 29# beyond the top-prime argument, non-canonical covers, why first-empty windows occur (route 355's density question), the proposed mod-30030 dependence (untested), any Lean artifact, any statement about twin primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Inapplicable on all topics. main (survivor-gap lower bound, full cutoff, crossing gaps, A = 12) needs a gap lower bound with logarithmic quantifiers; #5917 has no gap bound. o1, o2, o4 (prime harmonic, uniform smooth-number and dyadic prime-count asymptotics), o6 (two-sided density and Euler estimates) and o7 (the exact constant in eq. (28)) are untouched. o3 has no A. o5 (quoted general sieve input, one-class statement; finite dimension-4, CRT and covering results) is a name match at most: #5917's 'killer cover' is a measured canonical-witness class list that grows with the rung, which is not a finite covering result and says nothing about the quoted sieve input.","assumptions_md":"Consideration only, provisional. #5917 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target area. Source state preserved: route 398 progress result by Benjaminsen (deepseek-v4-flash, job 11965, dependencies #5439 and #5909); accepted at measured, verification spot (review 2044), not superseded, cited by no return; report sha256 1188b906f360e6f13760cecd18fc11f3b5fab48f4e0221de916ee72698b6c5d8 matching the snapshot; applicability index assessment null. Established as stated (measured, rungs 19#, 23#, 29# only): for first-empty admissible triples n, n+L, n+2L with L = 132, 138, 150, the canonical-witness class set killing the second interval is nested and grows (L=132 19 -> 57 -> 73; L=138 56 -> 74; L=150 0 -> 40 -> 76), no class is lost, the top prime always adds classes, and 1.77 / 1.95 / 1.67 % of 29# second-interval dead points have no witness <= 13, so H1, H2 and H3 fail. Controls: L=12 gives the rung-stable cover {2:1, 3:2, 5:2} (max witness 5) at 23# and 29#; L=30 grows 39 -> 47. Review 2044 caveats stand beside the claim: set inequality from top-prime classes is true by construction, so the substantive negative is the small-prime growth (L=132 adds 7:4, 11:3, 11:5, 11:6; L=138 adds 7:3; L=150 adds 5:1, 11:3 restricted to p <= 13), which review 2044 rechecked; the report's enumerated list of new small-prime classes is incomplete (table counts are right); the L=30 control's growth is top-prime only, so it does not show the small-prime kind of growth; #5421 is credited, not cited. Not established: anything for x > 29# beyond the top-prime argument, non-canonical covers, why first-empty windows occur (route 355's density question), the proposed mod-30030 dependence (untested), any Lean artifact, any statement about twin primes.","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":11991,"input_sha256":"043841c0201e1350f26d6bb33cb35107684c2fe51248fed32269f7563e5f8908","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"1188b906f360e6f13760cecd18fc11f3b5fab48f4e0221de916ee72698b6c5d8","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5917,"material_evidence":{"sha256":"916e56a67331b5d0df68d2853809cf6acc24a67468d32407686849d8ad7a0446","entries":{"return:5917":"8bf27e400b71494bae7b0b29a604dcf2b7a688e1360e60a9be5f3020cf4386b3","artifact:5917:0b72dfcb407c3fd76a7325fd1746c02b4553626fea8e26b1f91e814d60ea1c13":"0b72dfcb407c3fd76a7325fd1746c02b4553626fea8e26b1f91e814d60ea1c13","artifact:5917:1188b906f360e6f13760cecd18fc11f3b5fab48f4e0221de916ee72698b6c5d8":"1188b906f360e6f13760cecd18fc11f3b5fab48f4e0221de916ee72698b6c5d8","artifact:5917:25133e0caf740996ec018b30345579ac5b049338be3cdcef84e5a706a9cf094a":"25133e0caf740996ec018b30345579ac5b049338be3cdcef84e5a706a9cf094a","artifact:5917:58b8992cb62f29c231688e269c2e4831a5e32d7fe5667a447bf4cdf69c08fca1":"58b8992cb62f29c231688e269c2e4831a5e32d7fe5667a447bf4cdf69c08fca1","artifact:5917:6c97872581b02cc4909097513eab2385283266b0b0dc7f59ca3133f27307b7f7":"6c97872581b02cc4909097513eab2385283266b0b0dc7f59ca3133f27307b7f7","artifact:5917:7d69bc071ebd9dd347d2719127e3de23f82905e20afd950fe6f2bf985c7ccaa5":"7d69bc071ebd9dd347d2719127e3de23f82905e20afd950fe6f2bf985c7ccaa5","artifact:5917:9b49b1f576af609a65adea5997214d4728645a7e6f0e5b542b7698fcf1f1a00e":"9b49b1f576af609a65adea5997214d4728645a7e6f0e5b542b7698fcf1f1a00e","artifact:5917:a4e9d1ed21931d4e7b11c1014ba0d15105cc7714bf5b5d6f5f8a99fcaf8eb057":"a4e9d1ed21931d4e7b11c1014ba0d15105cc7714bf5b5d6f5f8a99fcaf8eb057","artifact:5917:abdad5b19eba1cb64de5d2c5d3b2d674967794b850d263da71e39bc9658195a6":"abdad5b19eba1cb64de5d2c5d3b2d674967794b850d263da71e39bc9658195a6","artifact:5917:ac84dd30ce794fa33a5a86c90382722f8a07a72a4f4f66cc05ca8a495f9c3a35":"ac84dd30ce794fa33a5a86c90382722f8a07a72a4f4f66cc05ca8a495f9c3a35","artifact:5917:b59cd995ba4a43667ce992c56a1785ef43f9443d376de6808bf8f83d6f87ae9b":"b59cd995ba4a43667ce992c56a1785ef43f9443d376de6808bf8f83d6f87ae9b","artifact:5917:c3951a44525f83e83c97e02f323c89c2e5cb2fe7d029ee9801aa7c9b0372a896":"c3951a44525f83e83c97e02f323c89c2e5cb2fe7d029ee9801aa7c9b0372a896","artifact:5917:d6dcc3e1104bf88eb7b9ea6fa657a18cef32672634eaf8cab4c72995de42ee32":"d6dcc3e1104bf88eb7b9ea6fa657a18cef32672634eaf8cab4c72995de42ee32","artifact:5917:de474eefb22c6503cccc7e0f234d75d4403d691264be44b5f3bc2273d616fbcb":"de474eefb22c6503cccc7e0f234d75d4403d691264be44b5f3bc2273d616fbcb","artifact:5917:df0f312f834d7a8501510ed578589cb02aeaf1b14cfb86b00495db19adc31545":"df0f312f834d7a8501510ed578589cb02aeaf1b14cfb86b00495db19adc31545","artifact:5917:e48a0915cad08215fdbaba87f0e5c7c877e07c2e8d1d2f5c06898beda761e6a3":"e48a0915cad08215fdbaba87f0e5c7c877e07c2e8d1d2f5c06898beda761e6a3","artifact:5917:f57bc6fec9894bfe83c38cac488e6f0ffb50c2c1c345c945421eefc250084f7e":"f57bc6fec9894bfe83c38cac488e6f0ffb50c2c1c345c945421eefc250084f7e"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5917,"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 #5917: 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\":5917,\"report_sha256\":\"1188b906f360e6f13760cecd18fc11f3b5fab48f4e0221de916ee72698b6c5d8\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5917\":\"8bf27e400b71494bae7b0b29a604dcf2b7a688e1360e60a9be5f3020cf4386b3\",\"artifact:5917:0b72dfcb407c3fd76a7325fd1746c02b4553626fea8e26b1f91e814d60ea1c13\":\"0b72dfcb407c3fd76a7325fd1746c02b4553626fea8e26b1f91e814d60ea1c13\",\"artifact:5917:1188b906f360e6f13760cecd18fc11f3b5fab48f4e0221de916ee72698b6c5d8\":\"1188b906f360e6f13760cecd18fc11f3b5fab48f4e0221de916ee72698b6c5d8\",\"artifact:5917:25133e0caf740996ec018b30345579ac5b049338be3cdcef84e5a706a9cf094a\":\"25133e0caf740996ec018b30345579ac5b049338be3cdcef84e5a706a9cf094a\",\"artifact:5917:58b8992cb62f29c231688e269c2e4831a5e32d7fe5667a447bf4cdf69c08fca1\":\"58b8992cb62f29c231688e269c2e4831a5e32d7fe5667a447bf4cdf69c08fca1\",\"artifact:5917:6c97872581b02cc4909097513eab2385283266b0b0dc7f59ca3133f27307b7f7\":\"6c97872581b02cc4909097513eab2385283266b0b0dc7f59ca3133f27307b7f7\",\"artifact:5917:7d69bc071ebd9dd347d2719127e3de23f82905e20afd950fe6f2bf985c7ccaa5\":\"7d69bc071ebd9dd347d2719127e3de23f82905e20afd950fe6f2bf985c7ccaa5\",\"artifact:5917:9b49b1f576af609a65adea5997214d4728645a7e6f0e5b542b7698fcf1f1a00e\":\"9b49b1f576af609a65adea5997214d4728645a7e6f0e5b542b7698fcf1f1a00e\",\"artifact:5917:a4e9d1ed21931d4e7b11c1014ba0d15105cc7714bf5b5d6f5f8a99fcaf8eb057\":\"a4e9d1ed21931d4e7b11c1014ba0d15105cc7714bf5b5d6f5f8a99fcaf8eb057\",\"artifact:5917:abdad5b19eba1cb64de5d2c5d3b2d674967794b850d263da71e39bc9658195a6\":\"abdad5b19eba1cb64de5d2c5d3b2d674967794b850d263da71e39bc9658195a6\",\"artifact:5917:ac84dd30ce794fa33a5a86c90382722f8a07a72a4f4f66cc05ca8a495f9c3a35\":\"ac84dd30ce794fa33a5a86c90382722f8a07a72a4f4f66cc05ca8a495f9c3a35\",\"artifact:5917:b59cd995ba4a43667ce992c56a1785ef43f9443d376de6808bf8f83d6f87ae9b\":\"b59cd995ba4a43667ce992c56a1785ef43f9443d376de6808bf8f83d6f87ae9b\",\"artifact:5917:c3951a44525f83e83c97e02f323c89c2e5cb2fe7d029ee9801aa7c9b0372a896\":\"c3951a44525f83e83c97e02f323c89c2e5cb2fe7d029ee9801aa7c9b0372a896\",\"artifact:5917:d6dcc3e1104bf88eb7b9ea6fa657a18cef32672634eaf8cab4c72995de42ee32\":\"d6dcc3e1104bf88eb7b9ea6fa657a18cef32672634eaf8cab4c72995de42ee32\",\"artifact:5917:de474eefb22c6503cccc7e0f234d75d4403d691264be44b5f3bc2273d616fbcb\":\"de474eefb22c6503cccc7e0f234d75d4403d691264be44b5f3bc2273d616fbcb\",\"artifact:5917:df0f312f834d7a8501510ed578589cb02aeaf1b14cfb86b00495db19adc31545\":\"df0f312f834d7a8501510ed578589cb02aeaf1b14cfb86b00495db19adc31545\",\"artifact:5917:e48a0915cad08215fdbaba87f0e5c7c877e07c2e8d1d2f5c06898beda761e6a3\":\"e48a0915cad08215fdbaba87f0e5c7c877e07c2e8d1d2f5c06898beda761e6a3\",\"artifact:5917:f57bc6fec9894bfe83c38cac488e6f0ffb50c2c1c345c945421eefc250084f7e\":\"f57bc6fec9894bfe83c38cac488e6f0ffb50c2c1c345c945421eefc250084f7e\"},\"sha256\":\"916e56a67331b5d0df68d2853809cf6acc24a67468d32407686849d8ad7a0446\"},\"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:5917,input_sha256:\"043841c0201e1350f26d6bb33cb35107684c2fe51248fed32269f7563e5f8908\",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/5934/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"ce71762763a32c22c12b5fc78b0ad974c62dbf33ac22a9e769c590c2cd8ac45f","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}