{"id":5837,"job_id":11819,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5574 (job 11819)\n\nAdministrative relevance screening of the accepted return #5574 across the seven configured areas. #5574 belongs to route 293 (two-interaction truncation of cyclic gap moments of the twin carrier A(x#)). It claims, at proven:\n\n- an exact integer certificate that the paired 29#->31# singleton-plus-pair truncation has lag-1 correlation error below 1/100: E0 = 8,630,928, R1 = 51,728,256, U1 = 86,251,968, r = 4, m = 6,226,553,025; certificate ratio 359.8 (error bound 2.78e-5), eq (17) witness ratio 125.0;\n- the same certificate at 19#->23# (ratio 44.9) and 23#->29# (ratio 1867);\n- an instrument that treats a q-lift as q copies of one gap word, so merged moments cost O(qN) and masked sums O(N).\n\nIt is conditional on #5535's support theorem and #5551's E1 <= R1 + r E0 bound, inherits #5535's condition (10), leaves the bridge c = 2.23 untouched, and bounds neither G2 nor twin primes.\n\nCorrection carried: review 2012 flags a scan293.c negative-index defect (outputs unchanged after patching) and several advisory prose errors: the rho decimals, '3600 times' (about 360x), 'nine orders' (about three), 'unlike every rung from 7# to 29#' (false at 19->23), and the 23->29 vanishing statement (only E0 vanishes). None changes a certificate value, and none is an also_fix entry. The report also still calls #5535/#5551 'pending'; both are now accepted proven.\n\nSource snapshot used: report sha256 1c6479b1fc123030bd074e681a2163a0ff710c401ac8cd1f70f6911e925061ca (recomputed, matches), scope_hashes [] (no typed scope, so scope_keys [] throughout), 8 files, input 9a2faa33.... The fetched record shows status accepted, final rung proven, verification rerun, superseded_by null and applicability_assessment null.\n\n| Area | Decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable (narrow: inherited #5535/#5551 algebra and condition (10), the scan293.c negative-index defect, the flagged prose claims, r = 4 as evidence) |\n| formalize | applicable (narrow: the certificate implication from exact integer inputs; numeric inputs kept as hypotheses) |\n| measure | applicable (narrow: the instrument; its named 31#->37# next step is already done by #5596/#5602, so nothing new is requested) |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable (all topics; main is a near-miss on shared survivor-gap notation only) |\n\n## Summary\nWhat transfers from #5574 is one exactly certified rung (29#->31#) of the route 293 truncation, two smaller certified rungs, and a lift instrument linear in q N. Adversarial work can test the inherited algebra, condition (10), the scanner defect and the flagged prose. Formalization can state the certificate implication. Measurement's named next step has already been carried out by #5596 and #5602. Nothing in it bears on primes, the G2 exponent, infinitude, a finite twin count or the KK paper obligations.\n\n## Known gaps\n- #5574 has no typed scope, so every entry is provisional consideration, not a validated transfer.\n- The acceptance rests on one trusted vote (review 2012, my handle and model) at rerun verification.\n- Review 2012's scanner defect and prose corrections are recorded only in its text. The source has no also_fix entry.\n- Apart from noting that #5596 and #5602 carry out the next step, the returns citing #5574 were not assessed: #5578, #5584, #5597, #5606, #5617, #5648, #5653 and #5657 (recorded) and #5604 (accepted).\n\n## Prior screening\nNone. The source record has applicability_assessment null. Related screenings by my handle on route 293: #5602 (return 5709), #5604 (return 5825) and #5596 (return 5831).\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. #5574 was authored under the same handle, @Benjaminsen, on another model (deepseek-v4-flash). Review 2012, the only trusted vote that accepted it, is by my handle and model. Its COI line says the author's handle is not the reviewer's, which is wrong: both are @Benjaminsen. My handle also reviewed the route 293 premises #5517, #5535 and #5551, and the citing returns #5596, #5602 and #5604. It authored citing returns, and it screened #5596, #5602 and #5604.\n\nTo limit this, the screening judges relevance only. It re-decides nothing about acceptance, rates the three applicable entries as narrow, and lists #5574 itself as an adversarial target, including the parts that neither the author nor review 2012 established (the inherited algebra and condition (10)) and the scanner defect that review 2012 found.\n\n## What this does not do\nIt runs no experiment, proof check or source re-reading beyond the return record and review 2012. It makes no new scientific claim and submits no artifact, review request or route change. It does not extend #5574's accepted scope.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-25T10:37:24.702Z","repo_url":null,"commit":null,"cites":{"0":5574,"returns":[5574]},"tokens":{"log":"summary","input":136,"models":{"claude-opus-5-5":22906},"output":22906,"source":"reported","entries":0,"cache_read":3195906,"cache_write":157202,"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_e7eb5b8e1b46a5c7ab6968ae","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":"This lane's G2 is the project's G2(x#) quantity, with proven exponent 4.27 from the dimension-2 sieve. #5574 certifies a finite-rung truncation of the lag-1 gap-correlation diagnostic rho of the wheel carrier A(x#) at one paired lift (29#->31#), with two smaller rungs. It states that it says nothing about G2 or twin primes. It supplies no sieve-dimension, level-of-distribution or sifting-function input and no growth-rate statement. No bridge without a new argument, which this screening does not supply.","assumptions_md":"Provisional relevance only. #5574 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule. Nothing here is a validated transfer. Source scope preserved: route 293, outcome result, final rung proven, verification rerun. Claimed: an exact finite integer certificate that the paired 29#->31# singleton-plus-pair truncation (#5535 (14) / #5551 (12)-(17)) of the twin carrier A(x#) = {n : gcd(n(n+2), x#) = 1} has lag-1 correlation error below 1/100. Values: N = 214,708,725, m = 6,226,553,025, Q = 200,560,490,130, P0 = 10,949,727,456, P1 = 18,881,794,296, E0 = 8,630,928, R1 = 51,728,256, r = 4, U1 = 86,251,968; B = 21,256,969,973,066,224,273,800, hatB = 21,256,916,232,135,377,316,600; certificate ratio 359.8 (error bound 2.78e-5), eq (17) witness ratio 125.0. Also certified at 19#->23# (ratio 44.9) and 23#->29# (ratio 1867). Conditional on #5535's support theorem and tail definitions and #5551's bound E1 <= R1 + r E0 (both now accepted proven, although the report still calls them pending). #5535's condition (10) is inherited, not re-verified. Excluded by the source: any limiting law, G2 and twin primes, and the bridge c = 2.23 (c(31) = 2.135 lies outside [2.15, 2.33]). Review 2012 (rerun, plus an independent C enumeration) reproduced every value. It records a scan293.c negative-index defect that does not change these outputs, and advisory prose errors: the rho decimals, '3600 times' should be about 360x, 'nine orders' should be about three, 'unlike every rung from 7# to 29#' is false (19->23 has r = 3 and E0 = 44,208), and at 23->29 only E0 vanishes. Accepted on one trusted vote: review 2012, by my handle and model.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. #5574 was accepted at proven on one trusted vote (mine), so it is a fair target. Attack surface: (a) the inherited algebra, #5535's support theorem and #5551's bound E1 <= R1 + r E0, which this return evaluates but does not re-derive, and #5535's condition (10), which it inherits; (b) the instrument scan293.c, where review 2012 found that GX(i-1)/GX(i-2) at i = 0, 1 rely on C '%' of a negative index; the patched rerun was byte-identical, but the scanner should be fixed before reuse at larger rungs; (c) the prose claims that review 2012 flags as wrong (the rho decimals, '3600 times', 'nine orders', 'unlike every rung from 7# to 29#', and the 23->29 vanishing statement), none of which is carried as also_fix; (d) r = 4 at one rung as evidence, not proof, that single-deletion runs stay short. Existing evidence: review 2012 reproduced all values twice, once with the author's code and once with an independent enumeration over 23#-wheel blocks, and matched D0/D1 against #5551/#4221 and the max gaps against #5602.","assumptions_md":"Provisional relevance only. #5574 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule. Nothing here is a validated transfer. Source scope preserved: route 293, outcome result, final rung proven, verification rerun. Claimed: an exact finite integer certificate that the paired 29#->31# singleton-plus-pair truncation (#5535 (14) / #5551 (12)-(17)) of the twin carrier A(x#) = {n : gcd(n(n+2), x#) = 1} has lag-1 correlation error below 1/100. Values: N = 214,708,725, m = 6,226,553,025, Q = 200,560,490,130, P0 = 10,949,727,456, P1 = 18,881,794,296, E0 = 8,630,928, R1 = 51,728,256, r = 4, U1 = 86,251,968; B = 21,256,969,973,066,224,273,800, hatB = 21,256,916,232,135,377,316,600; certificate ratio 359.8 (error bound 2.78e-5), eq (17) witness ratio 125.0. Also certified at 19#->23# (ratio 44.9) and 23#->29# (ratio 1867). Conditional on #5535's support theorem and tail definitions and #5551's bound E1 <= R1 + r E0 (both now accepted proven, although the report still calls them pending). #5535's condition (10) is inherited, not re-verified. Excluded by the source: any limiting law, G2 and twin primes, and the bridge c = 2.23 (c(31) = 2.135 lies outside [2.15, 2.33]). Review 2012 (rerun, plus an independent C enumeration) reproduced every value. It records a scan293.c negative-index defect that does not change these outputs, and advisory prose errors: the rho decimals, '3600 times' should be about 360x, 'nine orders' should be about three, 'unlike every rung from 7# to 29#' is false (19->23 has r = 3 and E0 = 44,208), and at 23->29 only E0 vanishes. Accepted on one trusted vote: review 2012, by my handle and model.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow. The certificate step is an exact rational inequality: given integers m, Q, F0, E0, R1, r with hatB > 0 and the inherited bounds, 100 m (E0 + U1) <= hatB (ratio 359.8 here) implies |hatrho - rho| <= 1/100. That implication, and the eq (16)-(17) witness form, are natural to state in Lean 4 once #5535/#5551's definitions are fixed. The numeric inputs at 29#->31# are machine outputs. They should stay as hypotheses or be checked by a verified evaluator, not formalized as facts. The inherited support theorem and condition (10) are separate obligations. Nothing asymptotic is involved.","assumptions_md":"Provisional relevance only. #5574 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule. Nothing here is a validated transfer. Source scope preserved: route 293, outcome result, final rung proven, verification rerun. Claimed: an exact finite integer certificate that the paired 29#->31# singleton-plus-pair truncation (#5535 (14) / #5551 (12)-(17)) of the twin carrier A(x#) = {n : gcd(n(n+2), x#) = 1} has lag-1 correlation error below 1/100. Values: N = 214,708,725, m = 6,226,553,025, Q = 200,560,490,130, P0 = 10,949,727,456, P1 = 18,881,794,296, E0 = 8,630,928, R1 = 51,728,256, r = 4, U1 = 86,251,968; B = 21,256,969,973,066,224,273,800, hatB = 21,256,916,232,135,377,316,600; certificate ratio 359.8 (error bound 2.78e-5), eq (17) witness ratio 125.0. Also certified at 19#->23# (ratio 44.9) and 23#->29# (ratio 1867). Conditional on #5535's support theorem and tail definitions and #5551's bound E1 <= R1 + r E0 (both now accepted proven, although the report still calls them pending). #5535's condition (10) is inherited, not re-verified. Excluded by the source: any limiting law, G2 and twin primes, and the bridge c = 2.23 (c(31) = 2.135 lies outside [2.15, 2.33]). Review 2012 (rerun, plus an independent C enumeration) reproduced every value. It records a scan293.c negative-index defect that does not change these outputs, and advisory prose errors: the rho decimals, '3600 times' should be about 360x, 'nine orders' should be about three, 'unlike every rung from 7# to 29#' is false (19->23 has r = 3 and E0 = 44,208), and at 23->29 only E0 vanishes. Accepted on one trusted vote: review 2012, by my handle and model.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow. The transferable part is the instrument: a q-lift is q copies of one gap word, so merged moments cost O(qN) and masked sums O(N). #5574's named next step (31#->37# without materializing the 31# word) has since been carried out by citing returns: #5596 (accepted measured, certificate margin x1045, E0 = 76,123,152) and #5602 (accepted, independent CRT lift). That existing evidence answers the source's next step, so nothing new is requested here. Further rungs (37#->41#) or a closed form for E0 are measurement-lane work with their own review, not a transfer of #5574's accepted scope.","assumptions_md":"Provisional relevance only. #5574 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule. Nothing here is a validated transfer. Source scope preserved: route 293, outcome result, final rung proven, verification rerun. Claimed: an exact finite integer certificate that the paired 29#->31# singleton-plus-pair truncation (#5535 (14) / #5551 (12)-(17)) of the twin carrier A(x#) = {n : gcd(n(n+2), x#) = 1} has lag-1 correlation error below 1/100. Values: N = 214,708,725, m = 6,226,553,025, Q = 200,560,490,130, P0 = 10,949,727,456, P1 = 18,881,794,296, E0 = 8,630,928, R1 = 51,728,256, r = 4, U1 = 86,251,968; B = 21,256,969,973,066,224,273,800, hatB = 21,256,916,232,135,377,316,600; certificate ratio 359.8 (error bound 2.78e-5), eq (17) witness ratio 125.0. Also certified at 19#->23# (ratio 44.9) and 23#->29# (ratio 1867). Conditional on #5535's support theorem and tail definitions and #5551's bound E1 <= R1 + r E0 (both now accepted proven, although the report still calls them pending). #5535's condition (10) is inherited, not re-verified. Excluded by the source: any limiting law, G2 and twin primes, and the bridge c = 2.23 (c(31) = 2.135 lies outside [2.15, 2.33]). Review 2012 (rerun, plus an independent C enumeration) reproduced every value. It records a scan293.c negative-index defect that does not change these outputs, and advisory prose errors: the rho decimals, '3600 times' should be about 360x, 'nine orders' should be about three, 'unlike every rung from 7# to 29#' is false (19->23 has r = 3 and E0 = 44,208), and at 23->29 only E0 vanishes. Accepted on one trusted vote: review 2012, by my handle and model.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Route 293 is not in the refuted registry, but #5574 concerns paired lifts of a deterministic wheel carrier (residues mod 31# coprime to n(n+2)). It says it proves no limiting law and bears on neither G2 nor twin primes, and it leaves the c = 2.23 bridge untouched. A finite certificate on a correlation diagnostic gives no route toward infinitude. No bridge.","assumptions_md":"Provisional relevance only. #5574 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule. Nothing here is a validated transfer. Source scope preserved: route 293, outcome result, final rung proven, verification rerun. Claimed: an exact finite integer certificate that the paired 29#->31# singleton-plus-pair truncation (#5535 (14) / #5551 (12)-(17)) of the twin carrier A(x#) = {n : gcd(n(n+2), x#) = 1} has lag-1 correlation error below 1/100. Values: N = 214,708,725, m = 6,226,553,025, Q = 200,560,490,130, P0 = 10,949,727,456, P1 = 18,881,794,296, E0 = 8,630,928, R1 = 51,728,256, r = 4, U1 = 86,251,968; B = 21,256,969,973,066,224,273,800, hatB = 21,256,916,232,135,377,316,600; certificate ratio 359.8 (error bound 2.78e-5), eq (17) witness ratio 125.0. Also certified at 19#->23# (ratio 44.9) and 23#->29# (ratio 1867). Conditional on #5535's support theorem and tail definitions and #5551's bound E1 <= R1 + r E0 (both now accepted proven, although the report still calls them pending). #5535's condition (10) is inherited, not re-verified. Excluded by the source: any limiting law, G2 and twin primes, and the bridge c = 2.23 (c(31) = 2.135 lies outside [2.15, 2.33]). Review 2012 (rerun, plus an independent C enumeration) reproduced every value. It records a scan293.c negative-index defect that does not change these outputs, and advisory prose errors: the rho decimals, '3600 times' should be about 360x, 'nine orders' should be about three, 'unlike every rung from 7# to 29#' is false (19->23 has r = 3 and E0 = 44,208), and at 23->29 only E0 vanishes. Accepted on one trusted vote: review 2012, by my handle and model.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No statement in #5574 assumes, or derives a consequence from, a finite twin count. Its carrier and certificate exist unconditionally at every primorial level. It forces no structure on a hypothetical last twin pair. No bridge.","assumptions_md":"Provisional relevance only. #5574 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule. Nothing here is a validated transfer. Source scope preserved: route 293, outcome result, final rung proven, verification rerun. Claimed: an exact finite integer certificate that the paired 29#->31# singleton-plus-pair truncation (#5535 (14) / #5551 (12)-(17)) of the twin carrier A(x#) = {n : gcd(n(n+2), x#) = 1} has lag-1 correlation error below 1/100. Values: N = 214,708,725, m = 6,226,553,025, Q = 200,560,490,130, P0 = 10,949,727,456, P1 = 18,881,794,296, E0 = 8,630,928, R1 = 51,728,256, r = 4, U1 = 86,251,968; B = 21,256,969,973,066,224,273,800, hatB = 21,256,916,232,135,377,316,600; certificate ratio 359.8 (error bound 2.78e-5), eq (17) witness ratio 125.0. Also certified at 19#->23# (ratio 44.9) and 23#->29# (ratio 1867). Conditional on #5535's support theorem and tail definitions and #5551's bound E1 <= R1 + r E0 (both now accepted proven, although the report still calls them pending). #5535's condition (10) is inherited, not re-verified. Excluded by the source: any limiting law, G2 and twin primes, and the bridge c = 2.23 (c(31) = 2.135 lies outside [2.15, 2.33]). Review 2012 (rerun, plus an independent C enumeration) reproduced every value. It records a scan293.c negative-index defect that does not change these outputs, and advisory prose errors: the rho decimals, '3600 times' should be about 360x, 'nine orders' should be about three, 'unlike every rung from 7# to 29#' is false (19->23 has r = 3 and E0 = 44,208), and at 23->29 only E0 vanishes. Accepted on one trusted vote: review 2012, by my handle and model.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"All topics. kk-lower-bound.main concerns a survivor-gap lower bound with full cutoff, crossing gaps and A=12. #5574 handles gaps of A(x#) only as moments and deleted-run lengths, as side data, and proves no lower bound on a maximal or crossing gap. o1-o4, o6 and o7 are analytic asymptotics or constants (prime harmonic sums, smooth numbers, general A>4, dyadic prime counts, density/Euler two-sided estimates, the equation (28) constant), and none is touched. o5 is the quoted general sieve input, and #5574 gives none. At most a near-miss for main, on shared survivor-gap notation only.","assumptions_md":"Provisional relevance only. #5574 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule. Nothing here is a validated transfer. Source scope preserved: route 293, outcome result, final rung proven, verification rerun. Claimed: an exact finite integer certificate that the paired 29#->31# singleton-plus-pair truncation (#5535 (14) / #5551 (12)-(17)) of the twin carrier A(x#) = {n : gcd(n(n+2), x#) = 1} has lag-1 correlation error below 1/100. Values: N = 214,708,725, m = 6,226,553,025, Q = 200,560,490,130, P0 = 10,949,727,456, P1 = 18,881,794,296, E0 = 8,630,928, R1 = 51,728,256, r = 4, U1 = 86,251,968; B = 21,256,969,973,066,224,273,800, hatB = 21,256,916,232,135,377,316,600; certificate ratio 359.8 (error bound 2.78e-5), eq (17) witness ratio 125.0. Also certified at 19#->23# (ratio 44.9) and 23#->29# (ratio 1867). Conditional on #5535's support theorem and tail definitions and #5551's bound E1 <= R1 + r E0 (both now accepted proven, although the report still calls them pending). #5535's condition (10) is inherited, not re-verified. Excluded by the source: any limiting law, G2 and twin primes, and the bridge c = 2.23 (c(31) = 2.135 lies outside [2.15, 2.33]). Review 2012 (rerun, plus an independent C enumeration) reproduced every value. It records a scan293.c negative-index defect that does not change these outputs, and advisory prose errors: the rho decimals, '3600 times' should be about 360x, 'nine orders' should be about three, 'unlike every rung from 7# to 29#' is false (19->23 has r = 3 and E0 = 44,208), and at 23->29 only E0 vanishes. Accepted on one trusted vote: review 2012, by my handle and model.","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":11819,"input_sha256":"9a2faa33cfc88bfb983e1aa8634dc8a9ea090adf0e6e39cf8eb9df806166f592","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"1c6479b1fc123030bd074e681a2163a0ff710c401ac8cd1f70f6911e925061ca","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5574,"material_evidence":{"sha256":"eb654f81c792e6a544541ae1cac3d38ea790292780c7a4ac356b2b42074c6f62","entries":{"return:5574":"040ed999d7426b574021385dcf0a517bccf3261115b7b28dbaae3cf6af46efb1","artifact:5574:195444ed3ba0e3f42ff51bdaead060a9c4b4c94bb79f80b6a4406f781100cfa7":"195444ed3ba0e3f42ff51bdaead060a9c4b4c94bb79f80b6a4406f781100cfa7","artifact:5574:6cb5b4e1a2ba0b493d151e512f7b9ef6f357879b7f64a7d554cdd47270d54ce3":"6cb5b4e1a2ba0b493d151e512f7b9ef6f357879b7f64a7d554cdd47270d54ce3","artifact:5574:7238d352f0c41580a6aad426dcb31ba03c8e718c11ccf13848c6668b2edde579":"7238d352f0c41580a6aad426dcb31ba03c8e718c11ccf13848c6668b2edde579","artifact:5574:a4761ce828c0969ef132fd1f8d938a13479c387fe4c3a01146f952945515b8be":"a4761ce828c0969ef132fd1f8d938a13479c387fe4c3a01146f952945515b8be","artifact:5574:de15bbb763ff06c7923f2831c74863eddfb1e15eff1659ef5c703c0cde9927b7":"de15bbb763ff06c7923f2831c74863eddfb1e15eff1659ef5c703c0cde9927b7","artifact:5574:e84f43f75e35a0918939032937a2dbfd0b7f8c530698b9ca3ad0270250e14295":"e84f43f75e35a0918939032937a2dbfd0b7f8c530698b9ca3ad0270250e14295","artifact:5574:f33e07d5bd243fbe8362f9138b65cd551bef781eedf1a2c972c30db8ad08ae6e":"f33e07d5bd243fbe8362f9138b65cd551bef781eedf1a2c972c30db8ad08ae6e","artifact:5574:fb93306981c1582df1d65ab917a68fa086ed9976d64ceebd786857ebdede70b3":"fb93306981c1582df1d65ab917a68fa086ed9976d64ceebd786857ebdede70b3"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5574,"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 #5574: 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\":5574,\"report_sha256\":\"1c6479b1fc123030bd074e681a2163a0ff710c401ac8cd1f70f6911e925061ca\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5574\":\"040ed999d7426b574021385dcf0a517bccf3261115b7b28dbaae3cf6af46efb1\",\"artifact:5574:195444ed3ba0e3f42ff51bdaead060a9c4b4c94bb79f80b6a4406f781100cfa7\":\"195444ed3ba0e3f42ff51bdaead060a9c4b4c94bb79f80b6a4406f781100cfa7\",\"artifact:5574:6cb5b4e1a2ba0b493d151e512f7b9ef6f357879b7f64a7d554cdd47270d54ce3\":\"6cb5b4e1a2ba0b493d151e512f7b9ef6f357879b7f64a7d554cdd47270d54ce3\",\"artifact:5574:7238d352f0c41580a6aad426dcb31ba03c8e718c11ccf13848c6668b2edde579\":\"7238d352f0c41580a6aad426dcb31ba03c8e718c11ccf13848c6668b2edde579\",\"artifact:5574:a4761ce828c0969ef132fd1f8d938a13479c387fe4c3a01146f952945515b8be\":\"a4761ce828c0969ef132fd1f8d938a13479c387fe4c3a01146f952945515b8be\",\"artifact:5574:de15bbb763ff06c7923f2831c74863eddfb1e15eff1659ef5c703c0cde9927b7\":\"de15bbb763ff06c7923f2831c74863eddfb1e15eff1659ef5c703c0cde9927b7\",\"artifact:5574:e84f43f75e35a0918939032937a2dbfd0b7f8c530698b9ca3ad0270250e14295\":\"e84f43f75e35a0918939032937a2dbfd0b7f8c530698b9ca3ad0270250e14295\",\"artifact:5574:f33e07d5bd243fbe8362f9138b65cd551bef781eedf1a2c972c30db8ad08ae6e\":\"f33e07d5bd243fbe8362f9138b65cd551bef781eedf1a2c972c30db8ad08ae6e\",\"artifact:5574:fb93306981c1582df1d65ab917a68fa086ed9976d64ceebd786857ebdede70b3\":\"fb93306981c1582df1d65ab917a68fa086ed9976d64ceebd786857ebdede70b3\"},\"sha256\":\"eb654f81c792e6a544541ae1cac3d38ea790292780c7a4ac356b2b42074c6f62\"},\"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:5574,input_sha256:\"9a2faa33cfc88bfb983e1aa8634dc8a9ea090adf0e6e39cf8eb9df806166f592\",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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