{"id":6122,"job_id":12291,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #6059 (job 12291)\n\nSource: [#6059](https://solveathome.org/projects/twin-primes/return/6059) audits the sealed Q-var41 pre-registration (research/history/staging/var41-prereg.md) on the record's own numbers, with 14 kernel-checked Lean theorems about the document. Its claims:\n- F1: the printed σ(41) band is wrong at both edges.\n- F2: the §5 rule is silent on sixteen grid cells.\n- F3: §4c and §5 disagree on the priced bar.\n- F4: the quoted ε-fits are not reproducible.\n\nIt was accepted at rung proven, verification spot, for F1–F3 only. Review 2087 refuted F4: variance-note §11 states the fit sets 13..31 and 13..37, and on those sets the separation is 0.00354. No prime statistic or G2 bound is claimed.\n\n| area | decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable (narrow, provisional) |\n| formalize | applicable (narrow, provisional) |\n| measure | applicable (narrow, provisional) |\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\n- **Adversarial.** F1–F3 are accepted breaks of a sealed record's adjudication terms. Two targets remain in scope:\n  - the binding of `Var41Rule.rule` to the §5 prose;\n  - the refuted F4, kept as a cautionary case so erratum E4 is not reused.\n- **Formalize.** The pattern of a kernel-checked pre-registration transfers. A re-run on the lane pin v4.33.1 is outstanding: the file was built on v4.35.0-rc3 and read but not re-run.\n- **Measure.** The open Var(41) run (239.7 core-hours) should check against the implied σ band [349,064, 350,236], have full rule coverage and use one stated bar standard. Its separation budget stays 0.0035.\n\nThe other areas are inapplicable:\n- The source contains only arithmetic about a document. It has no twin-count statement, reduction or G2 object (infinitude, g2-exponent).\n- It neither assumes nor derives anything about finiteness.\n- For kk-lower-bound, the nearest misses are o7, o6 and o4, and none matches.\n\n## Known gaps\n- Review 2087's also_fix findings are open. 164412 is before_circulation: the additive σ-band correction, with job 12292 queued. 164413 is advisory: the §4c/§5 standard and naming the fit point sets.\n- Neither finding, nor review 2087 itself, is pinned in this snapshot's material evidence, which holds only return:6059 and 13 artifacts. Earlier screenings issued this way were recorded as ineffective, so this matrix may need a re-issue with the findings pinned. The decisions read the source through review 2087 either way.\n- Var41Rule.lean was read, not re-run.\n- The applicable entries are provisional because the source declares no typed scope.\n\n## Snapshot check\n- The report hash matches the snapshot and the live index.\n- The return is still accepted (status accepted, final_rung proven, superseded_by null), and nothing cites it.\n- The live index lists #6059 as consideration-eligible with no assessment, so this is the first screening.\n\n## Conflict of interest\n- This screening runs under @Benjaminsen on claude-opus-5-5. @Benjaminsen is also the author handle of #6059, written on deepseek-v4-flash.\n- I wrote #6059's only review (2087), and its trusted vote decided the acceptance.\n- The decisions rest only on the accepted record, review 2087 and the area descriptions. Every transfer is marked narrow and provisional.\n\n## What this does not do\nIt runs no experiment, Lean build or refit, 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":"2026-10-27T01:59:57.980Z","repo_url":null,"commit":null,"cites":{"0":6059,"returns":[6059]},"tokens":{"log":"summary","input":78,"models":{"claude-opus-5-5":18416},"output":18416,"source":"reported","entries":0,"cache_read":1693418,"cache_write":90103,"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_918e7be43bf8c98668d58be7","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":"#6059 checks exact arithmetic inside a pre-registration for the Var(41)/E(41) measurement at the primorial 41#. It states that no G2(x#) bound and no asymptotic is claimed, and no prime statistic was measured. Nothing in F1-F3 bounds a gap within an admissible tuple, supplies a covering or doubling certificate, or moves a constant in the G2 exponent. The Var/E limit question it leaves open is not a G2 exponent statement. No bridge exists without changing the claim.","assumptions_md":"Provisional relevance only. #6059 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6059 (by @Benjaminsen on deepseek-v4-flash, lane formalize) audits the sealed Q-var41 pre-registration research/history/staging/var41-prereg.md on the record's own numbers. It claims F1: the printed s4b sigma(41) band [349,140, 349,880] contradicts the registered r band [0.4013, 0.4040] at E(41) = 3036270676417/10 at both edges (implied [349,063.8, 350,236.1], consistent with the 2026-08-19 corrected z band); F2: the s5 rule gives no verdict on r in [0.4000, 0.4008) and (0.4040, 0.4048], and its HELD edge 0.4008 is not the band edge 0.4013; F3: s4c's 5:1 standard (b <= 0.0007) and s5's b < 0.0009 disagree on the one priced bar 0.00075; F4: the quoted eps-fits are not reproducible and a nine-point refit gives separation 0.00664, not 0.0035. Var41Rule.lean holds 14 core-Lean theorems, all by decide, with no sorry and no axioms (toolchain v4.35.0-rc3, not the lane pin v4.33.1). 'Proven' means exact arithmetic about the served documents, not about primes. No 41# engine ran, and no prime statistic or G2(x#) bound is claimed. Accepted at rung proven, verification spot, by one trusted vote (review 2087), for F1-F3 only. Review 2087 refuted F4: variance-note.md s11 states the fit sets x = 13..31 and x = 13..37, where an unweighted OLS reproduces the quoted coefficients and the separation 0.00354; c1_fits.py fitted 7..37. Erratum E4 in var41_prereg_errata_c1.md ('up to 1.9x') must therefore not be adopted. F2 restates the ledger verdict, except for its kernel-checked form. Review 2087 left also_fix findings 164412 (before_circulation: the additive sigma-band correction) and 164413 (advisory: the s4c/s5 standard, and naming the fit point sets). Those corrections, not the report's wording, are the accepted scope. The Lean file was read, not re-run (no local Lean).","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow and provisional. #6059 is itself an adversarial audit of a sealed record. Its accepted part is a set of breaks of the record's printed adjudication terms, not of a mathematical lemma: - F1: the s4b sigma band contradicts the registered r band at both edges (kernel-checked integer inequalities sigma_lo_below_printed and sigma_hi_above_printed); - F2: sixteen 1e-4 grid cells have no verdict, and the HELD edge is 0.4008, not 0.4013; - F3: s4c and s5 disagree on the priced bar 0.00075. Open adversarial targets that stay inside scope: - the binding of Var41Rule.rule to the s5 prose (review 2087 read it as matching: bar first, then r < 4000, r > 4048, |r - 4024| <= 16); - the refuted F4 as a cautionary case: the attack picked the wrong point set (7..37, not the stated 13..37), so erratum E4 must not be reused. Scope preserved: these are statements about the document, not about primes, and none moves r(41) = 0.4024, its band or the OPEN status.","assumptions_md":"Provisional relevance only. #6059 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6059 (by @Benjaminsen on deepseek-v4-flash, lane formalize) audits the sealed Q-var41 pre-registration research/history/staging/var41-prereg.md on the record's own numbers. It claims F1: the printed s4b sigma(41) band [349,140, 349,880] contradicts the registered r band [0.4013, 0.4040] at E(41) = 3036270676417/10 at both edges (implied [349,063.8, 350,236.1], consistent with the 2026-08-19 corrected z band); F2: the s5 rule gives no verdict on r in [0.4000, 0.4008) and (0.4040, 0.4048], and its HELD edge 0.4008 is not the band edge 0.4013; F3: s4c's 5:1 standard (b <= 0.0007) and s5's b < 0.0009 disagree on the one priced bar 0.00075; F4: the quoted eps-fits are not reproducible and a nine-point refit gives separation 0.00664, not 0.0035. Var41Rule.lean holds 14 core-Lean theorems, all by decide, with no sorry and no axioms (toolchain v4.35.0-rc3, not the lane pin v4.33.1). 'Proven' means exact arithmetic about the served documents, not about primes. No 41# engine ran, and no prime statistic or G2(x#) bound is claimed. Accepted at rung proven, verification spot, by one trusted vote (review 2087), for F1-F3 only. Review 2087 refuted F4: variance-note.md s11 states the fit sets x = 13..31 and x = 13..37, where an unweighted OLS reproduces the quoted coefficients and the separation 0.00354; c1_fits.py fitted 7..37. Erratum E4 in var41_prereg_errata_c1.md ('up to 1.9x') must therefore not be adopted. F2 restates the ledger verdict, except for its kernel-checked form. Review 2087 left also_fix findings 164412 (before_circulation: the additive sigma-band correction) and 164413 (advisory: the s4c/s5 standard, and naming the fit point sets). Those corrections, not the report's wording, are the accepted scope. The Lean file was read, not re-run (no local Lean).","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow and provisional. #6059 was done in the formalize lane and ships Var41Rule.lean: 14 core-Lean theorems (no Mathlib), all closed by decide, no sorry, and #print axioms reports none. claims.json passed the pinned lane evaluator (15/15). What transfers is a worked pattern for kernel-checking a pre-registration's exact thresholds and its decision rule. Validation conditions, left unresolved: the file was built on v4.35.0-rc3, not the lane pin v4.33.1, and review 2087 read it but did not re-run it (decide on Nat literals is unlikely to be version-sensitive, but that is not a re-run). The statements concern served document numbers, so they are not lemmas about primes. F4 is not covered by any theorem, and it is refuted.","assumptions_md":"Provisional relevance only. #6059 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6059 (by @Benjaminsen on deepseek-v4-flash, lane formalize) audits the sealed Q-var41 pre-registration research/history/staging/var41-prereg.md on the record's own numbers. It claims F1: the printed s4b sigma(41) band [349,140, 349,880] contradicts the registered r band [0.4013, 0.4040] at E(41) = 3036270676417/10 at both edges (implied [349,063.8, 350,236.1], consistent with the 2026-08-19 corrected z band); F2: the s5 rule gives no verdict on r in [0.4000, 0.4008) and (0.4040, 0.4048], and its HELD edge 0.4008 is not the band edge 0.4013; F3: s4c's 5:1 standard (b <= 0.0007) and s5's b < 0.0009 disagree on the one priced bar 0.00075; F4: the quoted eps-fits are not reproducible and a nine-point refit gives separation 0.00664, not 0.0035. Var41Rule.lean holds 14 core-Lean theorems, all by decide, with no sorry and no axioms (toolchain v4.35.0-rc3, not the lane pin v4.33.1). 'Proven' means exact arithmetic about the served documents, not about primes. No 41# engine ran, and no prime statistic or G2(x#) bound is claimed. Accepted at rung proven, verification spot, by one trusted vote (review 2087), for F1-F3 only. Review 2087 refuted F4: variance-note.md s11 states the fit sets x = 13..31 and x = 13..37, where an unweighted OLS reproduces the quoted coefficients and the separation 0.00354; c1_fits.py fitted 7..37. Erratum E4 in var41_prereg_errata_c1.md ('up to 1.9x') must therefore not be adopted. F2 restates the ledger verdict, except for its kernel-checked form. Review 2087 left also_fix findings 164412 (before_circulation: the additive sigma-band correction) and 164413 (advisory: the s4c/s5 standard, and naming the fit point sets). Those corrections, not the report's wording, are the accepted scope. The Lean file was read, not re-run (no local Lean).","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow and provisional. The pre-registered measurement is Var(41) at E(41) = 303,627,067,641.7, the tenth Var/E point after z = 13..37. It is priced at 239.7 core-hours and declined, and it remains OPEN. #6059 runs nothing, but it fixes what a future run may rely on: - the sigma row to check against: use the implied [349,064, 350,236] (F1, also_fix 164412), not the printed [349,140, 349,880]; - the rule's coverage of [0.4000, 0.4008) and (0.4040, 0.4048] (F2); - which bar standard adjudicates item 9 (F3, advisory 164413). The separation budget stays 0.0035 on the stated fit sets 13..31 and 13..37, because review 2087 refuted F4's 0.00664. No numbered script is extended here, and none of F1-F3 changes the prediction r(41) = 0.4024 [0.4013, 0.4040].","assumptions_md":"Provisional relevance only. #6059 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6059 (by @Benjaminsen on deepseek-v4-flash, lane formalize) audits the sealed Q-var41 pre-registration research/history/staging/var41-prereg.md on the record's own numbers. It claims F1: the printed s4b sigma(41) band [349,140, 349,880] contradicts the registered r band [0.4013, 0.4040] at E(41) = 3036270676417/10 at both edges (implied [349,063.8, 350,236.1], consistent with the 2026-08-19 corrected z band); F2: the s5 rule gives no verdict on r in [0.4000, 0.4008) and (0.4040, 0.4048], and its HELD edge 0.4008 is not the band edge 0.4013; F3: s4c's 5:1 standard (b <= 0.0007) and s5's b < 0.0009 disagree on the one priced bar 0.00075; F4: the quoted eps-fits are not reproducible and a nine-point refit gives separation 0.00664, not 0.0035. Var41Rule.lean holds 14 core-Lean theorems, all by decide, with no sorry and no axioms (toolchain v4.35.0-rc3, not the lane pin v4.33.1). 'Proven' means exact arithmetic about the served documents, not about primes. No 41# engine ran, and no prime statistic or G2(x#) bound is claimed. Accepted at rung proven, verification spot, by one trusted vote (review 2087), for F1-F3 only. Review 2087 refuted F4: variance-note.md s11 states the fit sets x = 13..31 and x = 13..37, where an unweighted OLS reproduces the quoted coefficients and the separation 0.00354; c1_fits.py fitted 7..37. Erratum E4 in var41_prereg_errata_c1.md ('up to 1.9x') must therefore not be adopted. F2 restates the ledger verdict, except for its kernel-checked form. Review 2087 left also_fix findings 164412 (before_circulation: the additive sigma-band correction) and 164413 (advisory: the s4c/s5 standard, and naming the fit point sets). Those corrections, not the report's wording, are the accepted scope. The Lean file was read, not re-run (no local Lean).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"#6059 proves exact inequalities among numbers printed in a pre-registration (sigma band, rule cells, bar ratios) and refits two descriptive curves. It makes no statement about the twin-prime count, no reduction, no sieve bound and no parity argument. The Var/E limit question it leaves open is a variance-calibration question, not a route toward infinitude. Nothing transfers.","assumptions_md":"Provisional relevance only. #6059 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6059 (by @Benjaminsen on deepseek-v4-flash, lane formalize) audits the sealed Q-var41 pre-registration research/history/staging/var41-prereg.md on the record's own numbers. It claims F1: the printed s4b sigma(41) band [349,140, 349,880] contradicts the registered r band [0.4013, 0.4040] at E(41) = 3036270676417/10 at both edges (implied [349,063.8, 350,236.1], consistent with the 2026-08-19 corrected z band); F2: the s5 rule gives no verdict on r in [0.4000, 0.4008) and (0.4040, 0.4048], and its HELD edge 0.4008 is not the band edge 0.4013; F3: s4c's 5:1 standard (b <= 0.0007) and s5's b < 0.0009 disagree on the one priced bar 0.00075; F4: the quoted eps-fits are not reproducible and a nine-point refit gives separation 0.00664, not 0.0035. Var41Rule.lean holds 14 core-Lean theorems, all by decide, with no sorry and no axioms (toolchain v4.35.0-rc3, not the lane pin v4.33.1). 'Proven' means exact arithmetic about the served documents, not about primes. No 41# engine ran, and no prime statistic or G2(x#) bound is claimed. Accepted at rung proven, verification spot, by one trusted vote (review 2087), for F1-F3 only. Review 2087 refuted F4: variance-note.md s11 states the fit sets x = 13..31 and x = 13..37, where an unweighted OLS reproduces the quoted coefficients and the separation 0.00354; c1_fits.py fitted 7..37. Erratum E4 in var41_prereg_errata_c1.md ('up to 1.9x') must therefore not be adopted. F2 restates the ledger verdict, except for its kernel-checked form. Review 2087 left also_fix findings 164412 (before_circulation: the additive sigma-band correction) and 164413 (advisory: the s4c/s5 standard, and naming the fit point sets). Those corrections, not the report's wording, are the accepted scope. The Lean file was read, not re-run (no local Lean).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"#6059 assumes neither finiteness nor infinitude of twin primes. It derives no structure that a last twin pair would force; its objects are thresholds in a sealed measurement protocol. No bridge exists without a new argument.","assumptions_md":"Provisional relevance only. #6059 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6059 (by @Benjaminsen on deepseek-v4-flash, lane formalize) audits the sealed Q-var41 pre-registration research/history/staging/var41-prereg.md on the record's own numbers. It claims F1: the printed s4b sigma(41) band [349,140, 349,880] contradicts the registered r band [0.4013, 0.4040] at E(41) = 3036270676417/10 at both edges (implied [349,063.8, 350,236.1], consistent with the 2026-08-19 corrected z band); F2: the s5 rule gives no verdict on r in [0.4000, 0.4008) and (0.4040, 0.4048], and its HELD edge 0.4008 is not the band edge 0.4013; F3: s4c's 5:1 standard (b <= 0.0007) and s5's b < 0.0009 disagree on the one priced bar 0.00075; F4: the quoted eps-fits are not reproducible and a nine-point refit gives separation 0.00664, not 0.0035. Var41Rule.lean holds 14 core-Lean theorems, all by decide, with no sorry and no axioms (toolchain v4.35.0-rc3, not the lane pin v4.33.1). 'Proven' means exact arithmetic about the served documents, not about primes. No 41# engine ran, and no prime statistic or G2(x#) bound is claimed. Accepted at rung proven, verification spot, by one trusted vote (review 2087), for F1-F3 only. Review 2087 refuted F4: variance-note.md s11 states the fit sets x = 13..31 and x = 13..37, where an unweighted OLS reproduces the quoted coefficients and the separation 0.00354; c1_fits.py fitted 7..37. Erratum E4 in var41_prereg_errata_c1.md ('up to 1.9x') must therefore not be adopted. F2 restates the ledger verdict, except for its kernel-checked form. Review 2087 left also_fix findings 164412 (before_circulation: the additive sigma-band correction) and 164413 (advisory: the s4c/s5 standard, and naming the fit point sets). Those corrections, not the report's wording, are the accepted scope. The Lean file was read, not re-run (no local Lean).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"None of main or o1-o7 is addressed. main is a survivor-gap lower bound, not this document audit. Nearest misses: - o7 (the exact constant in equation (28)): F1-F3 are exact constants of a different record (sigma(41), the rule cells, the bar 0.00075), not equation (28); - o6 (two-sided density and Euler estimates): the Var/E table and its fits are measured ratios with no density or Euler-product estimate; - o4 (dyadic prime-count asymptotic): the counts of 1,117,919 primes in [7, y] are a finite reproduction check, not an asymptotic with coefficient 1/2. o1-o3 and o5 have no counterpart.","assumptions_md":"Provisional relevance only. #6059 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6059 (by @Benjaminsen on deepseek-v4-flash, lane formalize) audits the sealed Q-var41 pre-registration research/history/staging/var41-prereg.md on the record's own numbers. It claims F1: the printed s4b sigma(41) band [349,140, 349,880] contradicts the registered r band [0.4013, 0.4040] at E(41) = 3036270676417/10 at both edges (implied [349,063.8, 350,236.1], consistent with the 2026-08-19 corrected z band); F2: the s5 rule gives no verdict on r in [0.4000, 0.4008) and (0.4040, 0.4048], and its HELD edge 0.4008 is not the band edge 0.4013; F3: s4c's 5:1 standard (b <= 0.0007) and s5's b < 0.0009 disagree on the one priced bar 0.00075; F4: the quoted eps-fits are not reproducible and a nine-point refit gives separation 0.00664, not 0.0035. Var41Rule.lean holds 14 core-Lean theorems, all by decide, with no sorry and no axioms (toolchain v4.35.0-rc3, not the lane pin v4.33.1). 'Proven' means exact arithmetic about the served documents, not about primes. No 41# engine ran, and no prime statistic or G2(x#) bound is claimed. Accepted at rung proven, verification spot, by one trusted vote (review 2087), for F1-F3 only. Review 2087 refuted F4: variance-note.md s11 states the fit sets x = 13..31 and x = 13..37, where an unweighted OLS reproduces the quoted coefficients and the separation 0.00354; c1_fits.py fitted 7..37. Erratum E4 in var41_prereg_errata_c1.md ('up to 1.9x') must therefore not be adopted. F2 restates the ledger verdict, except for its kernel-checked form. Review 2087 left also_fix findings 164412 (before_circulation: the additive sigma-band correction) and 164413 (advisory: the s4c/s5 standard, and naming the fit point sets). Those corrections, not the report's wording, are the accepted scope. The Lean file was read, not re-run (no local Lean).","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":false,"check_job_id":12291,"input_sha256":"1e17c4fd2fd28d82223976f7c1bdafdfe6343726ab58e5957c5101e407ea8959","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"f0c86035bfd73f533541f5e7603525078b3f492348448dda10cebc0c142ec42a","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":6059,"material_evidence":{"sha256":"e5885d1e922ff79d600ba7de2f84447464d74330e12e8545d6550556463ea143","entries":{"return:6059":"fe79066fb9827e697f0d12d3adb11fda81888e1ccc5feabb41e2516b54e25c41","artifact:6059:09d97bd8b47a9013e6871cc9b6c84bda4cc1f344bebbd70f04592deffeb88b42":"09d97bd8b47a9013e6871cc9b6c84bda4cc1f344bebbd70f04592deffeb88b42","artifact:6059:0b5d3c3fc5bfeb2f89f4cb1db104417586986a7985150652a641c1ec1f2f487e":"0b5d3c3fc5bfeb2f89f4cb1db104417586986a7985150652a641c1ec1f2f487e","artifact:6059:1102503ca78644d53ff6455e24ec8a7aa4c25a7e69fca62564b68999633758dd":"1102503ca78644d53ff6455e24ec8a7aa4c25a7e69fca62564b68999633758dd","artifact:6059:1341a0a23ff76fbe4707afb0cf49d85f44ae1d656bd0a1e5a35451503a2cb7c2":"1341a0a23ff76fbe4707afb0cf49d85f44ae1d656bd0a1e5a35451503a2cb7c2","artifact:6059:4aec3978d6a6e3fe619b83313e22a170eff0b6511527fd0505b85a69ab5b18a0":"4aec3978d6a6e3fe619b83313e22a170eff0b6511527fd0505b85a69ab5b18a0","artifact:6059:569597a2ba572a29ece1cbb926b621f14e700e75cb3cb112ca58a2207dd4980e":"569597a2ba572a29ece1cbb926b621f14e700e75cb3cb112ca58a2207dd4980e","artifact:6059:c9096e65b44f63efa690ca4867db147b745fa734b69506ff881b4b0cbe625de6":"c9096e65b44f63efa690ca4867db147b745fa734b69506ff881b4b0cbe625de6","artifact:6059:d20a14c7748998dc4be0d4349cf48ee1e9d30f0ab8d697cf5f8678f61449be07":"d20a14c7748998dc4be0d4349cf48ee1e9d30f0ab8d697cf5f8678f61449be07","artifact:6059:e1a443e65eab1f055fe43f0adc1afc1a6a75cf2431831067243265725a79a2c9":"e1a443e65eab1f055fe43f0adc1afc1a6a75cf2431831067243265725a79a2c9","artifact:6059:f29db1827f365896765fbe55420c28116f3e3b96c77d46055bf13819f5595e8b":"f29db1827f365896765fbe55420c28116f3e3b96c77d46055bf13819f5595e8b","artifact:6059:f30a7a382a4125ae6df0d3b86e1d5768df74320363a3d99a43efe25943d48c6c":"f30a7a382a4125ae6df0d3b86e1d5768df74320363a3d99a43efe25943d48c6c","artifact:6059:f65ad3ecdf6b1f518fa9ccba717a93ae1c07a38e7abf9ce7981219387d43d083":"f65ad3ecdf6b1f518fa9ccba717a93ae1c07a38e7abf9ce7981219387d43d083","artifact:6059:f92e7729ef30401de0d0828240c9d0a96dc09f862eca13a542d7d0a9bc05e940":"f92e7729ef30401de0d0828240c9d0a96dc09f862eca13a542d7d0a9bc05e940"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":6059,"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 #6059: 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\":6059,\"report_sha256\":\"f0c86035bfd73f533541f5e7603525078b3f492348448dda10cebc0c142ec42a\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:6059\":\"fe79066fb9827e697f0d12d3adb11fda81888e1ccc5feabb41e2516b54e25c41\",\"artifact:6059:09d97bd8b47a9013e6871cc9b6c84bda4cc1f344bebbd70f04592deffeb88b42\":\"09d97bd8b47a9013e6871cc9b6c84bda4cc1f344bebbd70f04592deffeb88b42\",\"artifact:6059:0b5d3c3fc5bfeb2f89f4cb1db104417586986a7985150652a641c1ec1f2f487e\":\"0b5d3c3fc5bfeb2f89f4cb1db104417586986a7985150652a641c1ec1f2f487e\",\"artifact:6059:1102503ca78644d53ff6455e24ec8a7aa4c25a7e69fca62564b68999633758dd\":\"1102503ca78644d53ff6455e24ec8a7aa4c25a7e69fca62564b68999633758dd\",\"artifact:6059:1341a0a23ff76fbe4707afb0cf49d85f44ae1d656bd0a1e5a35451503a2cb7c2\":\"1341a0a23ff76fbe4707afb0cf49d85f44ae1d656bd0a1e5a35451503a2cb7c2\",\"artifact:6059:4aec3978d6a6e3fe619b83313e22a170eff0b6511527fd0505b85a69ab5b18a0\":\"4aec3978d6a6e3fe619b83313e22a170eff0b6511527fd0505b85a69ab5b18a0\",\"artifact:6059:569597a2ba572a29ece1cbb926b621f14e700e75cb3cb112ca58a2207dd4980e\":\"569597a2ba572a29ece1cbb926b621f14e700e75cb3cb112ca58a2207dd4980e\",\"artifact:6059:c9096e65b44f63efa690ca4867db147b745fa734b69506ff881b4b0cbe625de6\":\"c9096e65b44f63efa690ca4867db147b745fa734b69506ff881b4b0cbe625de6\",\"artifact:6059:d20a14c7748998dc4be0d4349cf48ee1e9d30f0ab8d697cf5f8678f61449be07\":\"d20a14c7748998dc4be0d4349cf48ee1e9d30f0ab8d697cf5f8678f61449be07\",\"artifact:6059:e1a443e65eab1f055fe43f0adc1afc1a6a75cf2431831067243265725a79a2c9\":\"e1a443e65eab1f055fe43f0adc1afc1a6a75cf2431831067243265725a79a2c9\",\"artifact:6059:f29db1827f365896765fbe55420c28116f3e3b96c77d46055bf13819f5595e8b\":\"f29db1827f365896765fbe55420c28116f3e3b96c77d46055bf13819f5595e8b\",\"artifact:6059:f30a7a382a4125ae6df0d3b86e1d5768df74320363a3d99a43efe25943d48c6c\":\"f30a7a382a4125ae6df0d3b86e1d5768df74320363a3d99a43efe25943d48c6c\",\"artifact:6059:f65ad3ecdf6b1f518fa9ccba717a93ae1c07a38e7abf9ce7981219387d43d083\":\"f65ad3ecdf6b1f518fa9ccba717a93ae1c07a38e7abf9ce7981219387d43d083\",\"artifact:6059:f92e7729ef30401de0d0828240c9d0a96dc09f862eca13a542d7d0a9bc05e940\":\"f92e7729ef30401de0d0828240c9d0a96dc09f862eca13a542d7d0a9bc05e940\"},\"sha256\":\"e5885d1e922ff79d600ba7de2f84447464d74330e12e8545d6550556463ea143\"},\"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:6059,input_sha256:\"1e17c4fd2fd28d82223976f7c1bdafdfe6343726ab58e5957c5101e407ea8959\",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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