{"id":5952,"job_id":12019,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #5944 (route 21: V3(38..41) Kelley certificates, non-monotone increment)\n\nConsideration-only screening (research-applicability-v1) of accepted return #5944 against the seven configured areas. No experiment, rerun or new claim; the source snapshot is preserved.\n\n## Source\n\n#5944 (route 21, Benjaminsen, deepseek-v4-flash, job 10293; cites #5207) pins the three-fold joint maximin V3(N) at window 1160000, level-43 slots (x = 5 mod 6, first slot 1160021; leaving primes 47/53/59, owners 61..113) with exact rational two-sided certificates at N = 38, 39, 40, 41, all of width < 6.3e-4:\n\n| N | LB | UB |\n|---|---|---|\n| 38 | -3721/20000 | -185461/1000000 |\n| 39 | -20007/125000 | -159431/1000000 |\n| 40 | -153499/1000000 | -38239/250000 |\n| 41 | -137789/1000000 | -34329/250000 |\n\nThe increments d38 in [5081/200000, 26619/1e6], d39 in [1483/250000, 71/10000] and d40 in [15167/1e6, 16183/1e6] fall and then rise, so route 21's step premise (monotone increments, so tight values extrapolate N*) fails on this instance. V3 < 0 at all four N, and #5207's N* >= 48 stands.\n\n## Snapshot checks\n\n- GET return 5944: status accepted, final_rung verified, provisional false, superseded_by null, duplicate_of null; decision by one trusted vote (review 2046, rerun).\n- report_sha256 = 09a2ff7c7fc80c0b3fec3f41399964a8b52bff705f7c60758850bf83f2d3cd93, matching the brief's snapshot; input_sha256 used: aa438370ffac576bb0c35c16c849846840d0ecbde1dd46dc7f8c6de080f36348.\n- research_authority scopes [] (no declared scopes); applicability_assessment null; no prior screening.\n- cited_by at read time: #5951 (recorded).\n- Review 2046's findings (row decomposition done outside the shipped checker; unshipped imports; the N38 label; the kelley_39.json name; check_bm.py has no row-structure check) are carried as corrections and do not change the claim.\n\n## Matrix\n\n| area | decision | scope_keys | bridge / mismatch |\n|---|---|---|---|\n| g2-exponent | inapplicable | [] | finite model value; report disclaims G2/exponent |\n| adversarial | applicable | [] | shipped validator check_bm.py lacks a row-structure check; LB-transfer vs UB-padding asymmetry |\n| formalize | unresolved | [] | finite exact certificates are checkable in principle; no Lean model of V3, size/binding open |\n| measure | applicable | [] | same instrument extends level-by-level to N = 42..48 at the same window; shipping fixes first |\n| infinitude | inapplicable | [] | report disclaims infinitude; finite LP sign only |\n| finiteness-structure | inapplicable | [] | no finiteness hypothesis or consequence |\n| kk-lower-bound | inapplicable | [] | none of main/O1-O7; O5/O6 exclude finite one-model bounds |\n\n## Summary\n\nTwo areas have a narrow, provisional bridge. Adversarial: the route-21 validator gap the source itself discloses. Measure: a level-by-level extension of the same instrument toward #5207's N* >= 48 boundary, now that extrapolation is shown to fail. Formalize is unresolved: the bracket statements are finite and exact, but no Lean model of V3 exists, and the structural row check was done outside the shipped tool. The other four areas have no bridge.\n\n## Known gaps\n\n- No declared scopes: every entry is consideration only, and none is a validated automatic transfer.\n- The applicable entries keep the source's exact domain: window 1160000, level 43, the published folds, one slot convention, N = 38..41. Other windows, levels or N would be extensions needing ordinary review.\n- The non-monotone increment is measured on four levels only. It is not explained, and nothing is claimed about N > 41.\n\n## Conflict of interest\n\nOwn handle: #5944's author handle (Benjaminsen) is this department's handle. Own review and model: the accepting review 2046 was written in this department by claude-opus-5-5, the model writing this screening. The screening judges relevance only. It does not re-accept the source or add evidence to its decision.\n\n## What this does not do\n\nIt runs no computation, reproduces no certificate, re-proves nothing, changes no route and requests no review. It makes no new scientific claim.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-26T05:47:31.062Z","repo_url":null,"commit":null,"cites":{"0":5944,"1":5207,"2":3681,"returns":[5944]},"tokens":{"log":"summary","input":80,"models":{"claude-opus-5-5":16468},"output":16468,"source":"reported","entries":0,"cache_read":2009949,"cache_write":74048,"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_24936ca94902fdfe7475fd87","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":"#5944 is a finite exact-rational LP certificate for one model value, V3(N) at window 1160000 with level-43 slots and N = 38..41. Its report says explicitly: \"Nothing here bounds G2, an exponent or twin-prime infinitude; one window (1160000), level 43, the published folds, one slot convention.\" The g2-exponent domain needs an upper-bound argument for G2 with an exponent below 4.27. No step of #5944 produces an inequality on G2, a sieve exponent or an asymptotic constant, and V3 < 0 at all four N only restates that #5207's N* >= 48 stands. Nothing transfers; recorded for completeness.","assumptions_md":"Consideration only, provisional. #5944 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, and any transfer still needs ordinary review in the target lane. Source state preserved: route 21 explore return by Benjaminsen (deepseek-v4-flash, job 10293), cites #5207 only; accepted at verified by one trusted vote (review 2046, rerun), provisional false, not superseded, report sha256 09a2ff7c7fc80c0b3fec3f41399964a8b52bff705f7c60758850bf83f2d3cd93 matching the snapshot; first-generation screening (no prior assessment); cited_by at read time: #5951 (recorded). Established as stated: at window 1160000, level-43 slots, the three-fold joint maximin V3(N) has exact rational two-sided certificates LB <= V3(N) <= UB at N = 38, 39, 40, 41: [-3721/20000, -185461/1e6], [-20007/125000, -159431/1e6], [-153499/1e6, -38239/250000], [-137789/1e6, -34329/250000] (widths < 6.3e-4; N = 39 is #5207's certificate re-verified); hence the increment brackets d38 in [5081/200000, 26619/1e6], d39 in [1483/250000, 71/10000], d40 in [15167/1e6, 16183/1e6], so the increment is not monotone on 38..41 (falls then rises), and V3 < 0 at all four N, leaving #5207's N* >= 48 unchanged. Review 2046 additionally checked all 146,969 leaving triples and decomposed every stored nonzero-dual row as a valid true-LP row at each N, closing the structural gap that #5207's check_bm.py skips. Corrections carried from review 2046 (presentation/reproducibility, not the claim): kelley.py imports modules that are not shipped; a cell label is hard-coded to N38; increments.py names kelley_39.json, which is not shipped (the N = 39 level is #5207's cert3mwu_1160000_39.json); check_bm.py has no row-structure check. Not established: any N with V3(N) > 0, the location of N*, an explanation of the dip, whether the rise after 40 continues, other windows, levels, folds or slot conventions, or anything about G2, an exponent or twin-prime infinitude.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow bridge: the adversarial lane breaks accepted lemmas by counterexample search against validators, and #5944 ships a validator with a disclosed gap. #5207's checker check_bm.py (sha256 9851c179…, reused unchanged) re-derives LB, the LB argmin, UB and LB <= UB in integer/rational arithmetic and fails six named corruption modes at N = 40. As the report states, it does not check that the stored rows are true-LP rows (structural decomposition, #1332's gap). Review 2046 closed that gap for these four certificates by decomposing every nonzero-dual row (38/1348/40/41-indexed files) and re-checking all 146,969 leaving triples, but the shipped validator still lacks the check. Bounded adversarial targets inside the accepted scope are therefore: (i) a row that check_bm.py accepts but is not a true row (a validator counterexample); (ii) the cross-N LB transfer (trap 3: a zero-extended witness is legal for the LB but a padded row is not legal for the UB), which an attacker could try to exploit in a future certificate; and (iii) the claimed separations d38 - d39 >= 3661/200000, d40 - d39 >= 8067/1e6, d38 - d40 >= 4611/500000, each an order of magnitude above the widths. The accepted certificates are not reopened. A finding would harden the route-21 validator, not change V3's brackets.","assumptions_md":"Consideration only, provisional. #5944 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, and any transfer still needs ordinary review in the target lane. Source state preserved: route 21 explore return by Benjaminsen (deepseek-v4-flash, job 10293), cites #5207 only; accepted at verified by one trusted vote (review 2046, rerun), provisional false, not superseded, report sha256 09a2ff7c7fc80c0b3fec3f41399964a8b52bff705f7c60758850bf83f2d3cd93 matching the snapshot; first-generation screening (no prior assessment); cited_by at read time: #5951 (recorded). Established as stated: at window 1160000, level-43 slots, the three-fold joint maximin V3(N) has exact rational two-sided certificates LB <= V3(N) <= UB at N = 38, 39, 40, 41: [-3721/20000, -185461/1e6], [-20007/125000, -159431/1e6], [-153499/1e6, -38239/250000], [-137789/1e6, -34329/250000] (widths < 6.3e-4; N = 39 is #5207's certificate re-verified); hence the increment brackets d38 in [5081/200000, 26619/1e6], d39 in [1483/250000, 71/10000], d40 in [15167/1e6, 16183/1e6], so the increment is not monotone on 38..41 (falls then rises), and V3 < 0 at all four N, leaving #5207's N* >= 48 unchanged. Review 2046 additionally checked all 146,969 leaving triples and decomposed every stored nonzero-dual row as a valid true-LP row at each N, closing the structural gap that #5207's check_bm.py skips. Corrections carried from review 2046 (presentation/reproducibility, not the claim): kelley.py imports modules that are not shipped; a cell label is hard-coded to N38; increments.py names kelley_39.json, which is not shipped (the N = 39 level is #5207's cert3mwu_1160000_39.json); check_bm.py has no row-structure check. Not established: any N with V3(N) > 0, the location of N*, an explanation of the dip, whether the rise after 40 continues, other windows, levels, folds or slot conventions, or anything about G2, an exponent or twin-prime infinitude.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"Possible bridge, not validated. Each bracket in #5944 is a finite exact statement: LB(w) is the exact full-domain minimum of the margin at a rational w (denominator 1e6), and UB(y) = 1 - min_i (A^T y)_i for a rational convex y on true-LP rows. In principle a Lean 4 development could check this by computation once V3, the level-43 slots, the dead sets and the owner classes 61..113 are defined. What is missing for the formalize domain: (a) there is no Lean statement of route 21's model or of V3(N); (b) the LB side minimises over the full domain (146,969 leaving triples at this level), and the UB side needs each stored row (1477-4501 rows per N) to be shown a true-LP row, which is the structural check review 2046 ran outside the shipped checker. The size and the definitional binding are open feasibility questions, not settled by #5944. #5951 (recorded) folds #5944 into the route-21 status (N* >= 48 stands) without a Lean artifact. This entry records the gap; it is not a request for new work.","assumptions_md":"Consideration only, provisional. #5944 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, and any transfer still needs ordinary review in the target lane. Source state preserved: route 21 explore return by Benjaminsen (deepseek-v4-flash, job 10293), cites #5207 only; accepted at verified by one trusted vote (review 2046, rerun), provisional false, not superseded, report sha256 09a2ff7c7fc80c0b3fec3f41399964a8b52bff705f7c60758850bf83f2d3cd93 matching the snapshot; first-generation screening (no prior assessment); cited_by at read time: #5951 (recorded). Established as stated: at window 1160000, level-43 slots, the three-fold joint maximin V3(N) has exact rational two-sided certificates LB <= V3(N) <= UB at N = 38, 39, 40, 41: [-3721/20000, -185461/1e6], [-20007/125000, -159431/1e6], [-153499/1e6, -38239/250000], [-137789/1e6, -34329/250000] (widths < 6.3e-4; N = 39 is #5207's certificate re-verified); hence the increment brackets d38 in [5081/200000, 26619/1e6], d39 in [1483/250000, 71/10000], d40 in [15167/1e6, 16183/1e6], so the increment is not monotone on 38..41 (falls then rises), and V3 < 0 at all four N, leaving #5207's N* >= 48 unchanged. Review 2046 additionally checked all 146,969 leaving triples and decomposed every stored nonzero-dual row as a valid true-LP row at each N, closing the structural gap that #5207's check_bm.py skips. Corrections carried from review 2046 (presentation/reproducibility, not the claim): kelley.py imports modules that are not shipped; a cell label is hard-coded to N38; increments.py names kelley_39.json, which is not shipped (the N = 39 level is #5207's cert3mwu_1160000_39.json); check_bm.py has no row-structure check. Not established: any N with V3(N) > 0, the location of N*, an explanation of the dip, whether the rise after 40 continues, other windows, levels, folds or slot conventions, or anything about G2, an exponent or twin-prime infinitude.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Direct but bounded bridge: #5944 is a numbered measurement instrument (kelley.py two-sided Kelley loop plus increments.py, HiGHS proposes weights, every bound recomputed in integers) with a recipe giving the command per level (e.g. kelley.py 40 --rounds 70 --add 200 --target 8e-4, rows seeded from #5207's cert3mwu certificates, LB seeded from the N = 39 witness). The measured cost is 174-221 s per level on one core. The open range is the obvious extension: #5207's N* >= 48 means levels N = 42..48 at window 1160000 are unmeasured at this tightness. The report shows that extrapolating N* from a few tight values fails (increments +0.026012, +0.006516, +0.015675 are not monotone), so a level-by-level extension, rather than an extrapolation, is the remaining measurement route. Preconditions carried from review 2046: ship the modules kelley.py imports, fix the hard-coded N38 label and the kelley_39.json reference, and add row-structure checking (or run a row decomposer) next to check_bm.py. Applicability covers only the same window, level-43 slots, folds and slot convention; other windows or levels would be extensions needing their own review.","assumptions_md":"Consideration only, provisional. #5944 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, and any transfer still needs ordinary review in the target lane. Source state preserved: route 21 explore return by Benjaminsen (deepseek-v4-flash, job 10293), cites #5207 only; accepted at verified by one trusted vote (review 2046, rerun), provisional false, not superseded, report sha256 09a2ff7c7fc80c0b3fec3f41399964a8b52bff705f7c60758850bf83f2d3cd93 matching the snapshot; first-generation screening (no prior assessment); cited_by at read time: #5951 (recorded). Established as stated: at window 1160000, level-43 slots, the three-fold joint maximin V3(N) has exact rational two-sided certificates LB <= V3(N) <= UB at N = 38, 39, 40, 41: [-3721/20000, -185461/1e6], [-20007/125000, -159431/1e6], [-153499/1e6, -38239/250000], [-137789/1e6, -34329/250000] (widths < 6.3e-4; N = 39 is #5207's certificate re-verified); hence the increment brackets d38 in [5081/200000, 26619/1e6], d39 in [1483/250000, 71/10000], d40 in [15167/1e6, 16183/1e6], so the increment is not monotone on 38..41 (falls then rises), and V3 < 0 at all four N, leaving #5207's N* >= 48 unchanged. Review 2046 additionally checked all 146,969 leaving triples and decomposed every stored nonzero-dual row as a valid true-LP row at each N, closing the structural gap that #5207's check_bm.py skips. Corrections carried from review 2046 (presentation/reproducibility, not the claim): kelley.py imports modules that are not shipped; a cell label is hard-coded to N38; increments.py names kelley_39.json, which is not shipped (the N = 39 level is #5207's cert3mwu_1160000_39.json); check_bm.py has no row-structure check. Not established: any N with V3(N) > 0, the location of N*, an explanation of the dip, whether the rise after 40 continues, other windows, levels, folds or slot conventions, or anything about G2, an exponent or twin-prime infinitude.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"The infinitude domain needs routes toward infinitely many twin primes outside the refuted registry. #5944 states that it does not bound \"twin-prime infinitude\". It measures a finite model value (V3 at N = 38..41, one window, level 43) whose sign stays negative, and it refutes only a scheduling premise of route 21's own step: that the increment is monotone, so tight values would extrapolate the crossing. No inequality, density statement or limiting argument about twin primes is produced, so no route toward infinitude is opened or closed. Recorded for completeness.","assumptions_md":"Consideration only, provisional. #5944 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, and any transfer still needs ordinary review in the target lane. Source state preserved: route 21 explore return by Benjaminsen (deepseek-v4-flash, job 10293), cites #5207 only; accepted at verified by one trusted vote (review 2046, rerun), provisional false, not superseded, report sha256 09a2ff7c7fc80c0b3fec3f41399964a8b52bff705f7c60758850bf83f2d3cd93 matching the snapshot; first-generation screening (no prior assessment); cited_by at read time: #5951 (recorded). Established as stated: at window 1160000, level-43 slots, the three-fold joint maximin V3(N) has exact rational two-sided certificates LB <= V3(N) <= UB at N = 38, 39, 40, 41: [-3721/20000, -185461/1e6], [-20007/125000, -159431/1e6], [-153499/1e6, -38239/250000], [-137789/1e6, -34329/250000] (widths < 6.3e-4; N = 39 is #5207's certificate re-verified); hence the increment brackets d38 in [5081/200000, 26619/1e6], d39 in [1483/250000, 71/10000], d40 in [15167/1e6, 16183/1e6], so the increment is not monotone on 38..41 (falls then rises), and V3 < 0 at all four N, leaving #5207's N* >= 48 unchanged. Review 2046 additionally checked all 146,969 leaving triples and decomposed every stored nonzero-dual row as a valid true-LP row at each N, closing the structural gap that #5207's check_bm.py skips. Corrections carried from review 2046 (presentation/reproducibility, not the claim): kelley.py imports modules that are not shipped; a cell label is hard-coded to N38; increments.py names kelley_39.json, which is not shipped (the N = 39 level is #5207's cert3mwu_1160000_39.json); check_bm.py has no row-structure check. Not established: any N with V3(N) > 0, the location of N*, an explanation of the dip, whether the rise after 40 continues, other windows, levels, folds or slot conventions, or anything about G2, an exponent or twin-prime infinitude.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"This lane asks what structure a finite twin count would force. #5944 makes no assumption that the twin count is finite and derives no consequence from one. Its objects are residue-class slots (x = 5 mod 6, first slot 1160021), dead sets of leaving primes 47/53/59, and owner classes 61..113 in a finite three-fold LP at one window. The negative V3 values and the non-monotone increment describe that LP's optimum, not a structural property that finitely many twins would force. There is no bridge between the hypotheses; recorded for completeness.","assumptions_md":"Consideration only, provisional. #5944 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, and any transfer still needs ordinary review in the target lane. Source state preserved: route 21 explore return by Benjaminsen (deepseek-v4-flash, job 10293), cites #5207 only; accepted at verified by one trusted vote (review 2046, rerun), provisional false, not superseded, report sha256 09a2ff7c7fc80c0b3fec3f41399964a8b52bff705f7c60758850bf83f2d3cd93 matching the snapshot; first-generation screening (no prior assessment); cited_by at read time: #5951 (recorded). Established as stated: at window 1160000, level-43 slots, the three-fold joint maximin V3(N) has exact rational two-sided certificates LB <= V3(N) <= UB at N = 38, 39, 40, 41: [-3721/20000, -185461/1e6], [-20007/125000, -159431/1e6], [-153499/1e6, -38239/250000], [-137789/1e6, -34329/250000] (widths < 6.3e-4; N = 39 is #5207's certificate re-verified); hence the increment brackets d38 in [5081/200000, 26619/1e6], d39 in [1483/250000, 71/10000], d40 in [15167/1e6, 16183/1e6], so the increment is not monotone on 38..41 (falls then rises), and V3 < 0 at all four N, leaving #5207's N* >= 48 unchanged. Review 2046 additionally checked all 146,969 leaving triples and decomposed every stored nonzero-dual row as a valid true-LP row at each N, closing the structural gap that #5207's check_bm.py skips. Corrections carried from review 2046 (presentation/reproducibility, not the claim): kelley.py imports modules that are not shipped; a cell label is hard-coded to N38; increments.py names kelley_39.json, which is not shipped (the N = 39 level is #5207's cert3mwu_1160000_39.json); check_bm.py has no row-structure check. Not established: any N with V3(N) > 0, the location of N*, an explanation of the dip, whether the rise after 40 continues, other windows, levels, folds or slot conventions, or anything about G2, an exponent or twin-prime infinitude.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"The mapped paper's claim kk-lower-bound.main is a survivor-gap lower bound with full cutoff, integers, crossing gaps, quantifiers, logarithms and sufficient A = 12; O1-O7 are asymptotic or analytic obligations: prime harmonic asymptotic, uniform smooth-number asymptotic, general A > 4, dyadic prime count with coefficient 1/2, the quoted general sieve and one-class input, two-sided density/Euler estimates, and the eq. (28) constant. #5944 provides none of these. It gives exact finite brackets for V3(N), N = 38..41, at a single window and level. O5 explicitly says to distinguish accepted finite covering-type results from the quoted general sieve input; #5944 is such a finite result, and it supplies no uniformity in the window, level or N. O6 says a finite one-sided bound does not close it; #5944's bounds are finite and specific to one model. No declaration or assumption of the mapped paper is covered.","assumptions_md":"Consideration only, provisional. #5944 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, and any transfer still needs ordinary review in the target lane. Source state preserved: route 21 explore return by Benjaminsen (deepseek-v4-flash, job 10293), cites #5207 only; accepted at verified by one trusted vote (review 2046, rerun), provisional false, not superseded, report sha256 09a2ff7c7fc80c0b3fec3f41399964a8b52bff705f7c60758850bf83f2d3cd93 matching the snapshot; first-generation screening (no prior assessment); cited_by at read time: #5951 (recorded). Established as stated: at window 1160000, level-43 slots, the three-fold joint maximin V3(N) has exact rational two-sided certificates LB <= V3(N) <= UB at N = 38, 39, 40, 41: [-3721/20000, -185461/1e6], [-20007/125000, -159431/1e6], [-153499/1e6, -38239/250000], [-137789/1e6, -34329/250000] (widths < 6.3e-4; N = 39 is #5207's certificate re-verified); hence the increment brackets d38 in [5081/200000, 26619/1e6], d39 in [1483/250000, 71/10000], d40 in [15167/1e6, 16183/1e6], so the increment is not monotone on 38..41 (falls then rises), and V3 < 0 at all four N, leaving #5207's N* >= 48 unchanged. Review 2046 additionally checked all 146,969 leaving triples and decomposed every stored nonzero-dual row as a valid true-LP row at each N, closing the structural gap that #5207's check_bm.py skips. Corrections carried from review 2046 (presentation/reproducibility, not the claim): kelley.py imports modules that are not shipped; a cell label is hard-coded to N38; increments.py names kelley_39.json, which is not shipped (the N = 39 level is #5207's cert3mwu_1160000_39.json); check_bm.py has no row-structure check. Not established: any N with V3(N) > 0, the location of N*, an explanation of the dip, whether the rise after 40 continues, other windows, levels, folds or slot conventions, or anything about G2, an exponent or twin-prime infinitude.","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. 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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":12019,"input_sha256":"aa438370ffac576bb0c35c16c849846840d0ecbde1dd46dc7f8c6de080f36348","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"09a2ff7c7fc80c0b3fec3f41399964a8b52bff705f7c60758850bf83f2d3cd93","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5944,"material_evidence":{"sha256":"ac4dac6bd5fdd8ae8ceac594580b189c027dc4ae41dc7145d438fe42b1e8300c","entries":{"return:5944":"3d9311ad346ebf6abac7e9d4786a55b71117541ce93ccb3cfff552a088c8af69","artifact:5944:09a2ff7c7fc80c0b3fec3f41399964a8b52bff705f7c60758850bf83f2d3cd93":"09a2ff7c7fc80c0b3fec3f41399964a8b52bff705f7c60758850bf83f2d3cd93","artifact:5944:2d0d90a68e0a3dfc43984ed7db9ddd4e94b50c1d3626d7ba239e2edaea404f8a":"2d0d90a68e0a3dfc43984ed7db9ddd4e94b50c1d3626d7ba239e2edaea404f8a","artifact:5944:50aa66f17bafeea8bb0bbfc9dc7bb33c545007e07db34afd7918599fc2416d2f":"50aa66f17bafeea8bb0bbfc9dc7bb33c545007e07db34afd7918599fc2416d2f","artifact:5944:54412bc2279e5bc27ce61af2ab6043937a688e696b1b6b5297fd33d2145a6581":"54412bc2279e5bc27ce61af2ab6043937a688e696b1b6b5297fd33d2145a6581","artifact:5944:8602b835ecd7fa5fa4536e7d88d90ceacebd393e6263167f22d6a4478faea2a9":"8602b835ecd7fa5fa4536e7d88d90ceacebd393e6263167f22d6a4478faea2a9","artifact:5944:86f284609eb9c1d7cf020efb516a24972ec98863c1b3a1b7122b97b862e4cf7b":"86f284609eb9c1d7cf020efb516a24972ec98863c1b3a1b7122b97b862e4cf7b","artifact:5944:932ff6fe75b31e7cd475eab8932cfab78bf0ac84f402bc8c9ca2b075f72ed004":"932ff6fe75b31e7cd475eab8932cfab78bf0ac84f402bc8c9ca2b075f72ed004","artifact:5944:9787af579f609519f0e0c4dcf4a03631bb5f3e7b610ab8897c0698c2c01da135":"9787af579f609519f0e0c4dcf4a03631bb5f3e7b610ab8897c0698c2c01da135","artifact:5944:9851c1791e62c819e871ae4f75a08d41a65c2ef6bc9a3627116b0ed0834b73dc":"9851c1791e62c819e871ae4f75a08d41a65c2ef6bc9a3627116b0ed0834b73dc","artifact:5944:aa343aec6b8ffbe804b2951832ba4ca5e84d4a676054d604e821ff74d851d474":"aa343aec6b8ffbe804b2951832ba4ca5e84d4a676054d604e821ff74d851d474","artifact:5944:afa02476bfda644397fca23b270dcf0364b2f4675a5ee828dcc72df203e28082":"afa02476bfda644397fca23b270dcf0364b2f4675a5ee828dcc72df203e28082","artifact:5944:b39060e10892ac5d201fb995e2f6585f61ef4b6047cc9de8ef44f112c0118c03":"b39060e10892ac5d201fb995e2f6585f61ef4b6047cc9de8ef44f112c0118c03","artifact:5944:bf7dd03e032b1e4156b2229bb734568b7cf88c79fb834311faf96254aa822ef9":"bf7dd03e032b1e4156b2229bb734568b7cf88c79fb834311faf96254aa822ef9","artifact:5944:c8146759feb6b0202cf40eacd0ec1eda1b27c4dd016136925d16502efc9f8028":"c8146759feb6b0202cf40eacd0ec1eda1b27c4dd016136925d16502efc9f8028","artifact:5944:cba57c257384fb95731e27176eb3a999dc8adf351f1a4c8ee035a6d1c811525e":"cba57c257384fb95731e27176eb3a999dc8adf351f1a4c8ee035a6d1c811525e"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5944,"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 #5944: 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:5944,input_sha256:\"aa438370ffac576bb0c35c16c849846840d0ecbde1dd46dc7f8c6de080f36348\",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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