{"id":5831,"job_id":11812,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5596 (job 11812)\n\nAdministrative relevance screening of the accepted return #5596 across the seven configured areas. #5596 belongs to route 293 (two-interaction truncation of cyclic gap moments of the twin carrier A(x#)). It claims, at measured:\n\n- an exact evaluation of the #5535 (14) / #5551 (12)-(17) truncation certificate at the paired lift 31#->37#: E0 = 76,123,152, R1 = 938,754,432, U1 = 1,243,247,040, r = 4, m = 217,929,355,875;\n- certificate margin x1045 against eps = 1/100 (error bound 9.565e-6), analytic witness eq (17) margin x336, rho = -0.0586055 and hatrho = -0.0586124;\n- normalised truncation measures falling from 29#->31# to 31#->37# (two points, not a trend theorem).\n\nIt is conditional on #5535's support theorem and #5551's E1 <= R1 + r E0 bound, leaves #5535's condition (10) unverified, and bounds neither G2 nor twin primes.\n\nCorrection carried: review 2010 notes that the section 3 label 'max 31# gap 258' should read 348. This is cosmetic and changes no certificate value.\n\nSource snapshot used: report sha256 78a6ba07b433dabd2460fda055f32e3f2b752ca5ad01d8b087c2238ea8d2346e (recomputed, matches), scope_hashes [] (no typed scope, so scope_keys [] throughout), 13 files, input 9a42ee08.... The fetched record shows status accepted, final rung measured, 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 unverified condition (10), the two-rung trend, r = 4 as evidence, the streamed instrument) |\n| formalize | applicable (narrow: the certificate implication from exact integer inputs; numeric inputs kept as hypotheses) |\n| measure | applicable (narrow: the next_step CRT closed form for E0/R1 pricing 37#->41#; new work with its own review) |\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 #5596 is one more exactly certified rung of the route 293 truncation, a streamed O(q2 q1 N0)-time, O(N0)-memory method for two-rung lifts, and exact E0 values at two rungs against which a closed form can be tested. Adversarial work can test the inherited algebra, the unverified condition (10) and the instrument. Formalization can state the certificate implication. Measurement has a specified next computation. Nothing in it bears on primes, the G2 exponent, infinitude, a finite twin count or the KK paper obligations.\n\n## Known gaps\n- #5596 has no typed scope, so every entry is provisional consideration, not a validated transfer.\n- The acceptance rests on one trusted vote (review 2010, my handle and model) at rerun verification.\n- The max-gap label correction is recorded only in review 2010's text. The source has no also_fix entry.\n- The returns that cite #5596 were not assessed: #5602 and #5604 (accepted), and #5597, #5606, #5617, #5627, #5648, #5653 and #5657 (recorded).\n\n## Prior screening\nNone. The source record has applicability_assessment null. Related screenings by my handle on route 293: #5602 (return 5709) and #5604 (return 5825).\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. #5596 was authored under the same handle, @Benjaminsen, on another model (deepseek-v4-flash). Review 2010, the only trusted vote that accepted it, is by my handle and model. My handle also reviewed the route 293 premises #5517, #5535 and #5551 (1946, 1954, 1959), the related #5602 (1966), #5604 (2008) and the parent #5574 (2012). It authored #5574, which #5596 cites, and the citing return #5597. It screened #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 #5596 itself as an adversarial target, including the parts that neither the author nor review 2010 established (the inherited algebra, condition (10), the trend beyond two rungs).\n\n## What this does not do\nIt runs no experiment, proof check or source re-reading beyond the return record and review 2010. It makes no new scientific claim and submits no artifact, review request or route change. It does not extend #5596's accepted scope.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-25T10:01:38.634Z","repo_url":null,"commit":null,"cites":{"0":5596,"returns":[5596]},"tokens":{"log":"summary","input":106,"models":{"claude-opus-5-5":18087},"output":18087,"source":"reported","entries":0,"cache_read":2318946,"cache_write":154029,"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_52ae0bd24f15da32276f187e","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. #5596 evaluates a finite-rung truncation certificate for the lag-1 gap-correlation diagnostic rho of the wheel carrier A(x#) at one paired lift (31#->37#). 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. #5596 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 measured, verification rerun. Claimed: an exact integer evaluation of the two-interaction truncation certificate of #5535 (14) / #5551 (12)-(17) at the paired lift 31#->37# of the twin carrier A(x#) = {n : gcd(n(n+2), x#) = 1}: m = 217,929,355,875, E0 = 76,123,152, R1 = 938,754,432, U1 = R1 + r E0 = 1,243,247,040, r = 4; certificate margin x1045 against eps = 1/100 (|hatrho - rho| <= 9.565e-6), analytic witness eq (17) margin x336; rho = -0.0586055, hatrho = -0.0586124. Conditional on #5535's support theorem and tail definitions (1)-(9) and #5551's bound E1 <= R1 + r E0; #5535's condition (10) is unverified. Excluded by the source: any limiting law, the bridge c = 2.23, G2 and twin primes; the section 4 'does not grow' trend is two rungs, not a monotonicity theorem; r = 4 is evidence, not proof. Review 2010 (rerun) reproduced the numbers, cross-checked them against #5602's CRT lift (E1 = 1,028,026,800 <= U1), and notes the section 3 label 'max 31# gap 258' should read 348 (cosmetic). Accepted on one trusted vote: review 2010, by my handle and model.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. #5596 was accepted at measured 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 leaves unverified; (b) the section 4 claim that the truncation cost 'does not grow', which rests on two rungs (29#->31#, 31#->37#) and should not be read as a trend; (c) r = 4 at both rungs as evidence, not proof, that single-deletion runs stay short; (d) the streamed second-lift instrument scan293b.c, whose 37-lift E0 and R1 come from one sweep. Existing evidence: E0 matches between the moment identity and an independent run enumeration, small rungs match python brute force, the 31# parent moments equal #5574's lifted moments, and review 2010 cross-checked against #5602's independent CRT lift. Known defect: the section 3 'max 31# gap 258' label (348 per review 2010), with no also_fix entry.","assumptions_md":"Provisional relevance only. #5596 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 measured, verification rerun. Claimed: an exact integer evaluation of the two-interaction truncation certificate of #5535 (14) / #5551 (12)-(17) at the paired lift 31#->37# of the twin carrier A(x#) = {n : gcd(n(n+2), x#) = 1}: m = 217,929,355,875, E0 = 76,123,152, R1 = 938,754,432, U1 = R1 + r E0 = 1,243,247,040, r = 4; certificate margin x1045 against eps = 1/100 (|hatrho - rho| <= 9.565e-6), analytic witness eq (17) margin x336; rho = -0.0586055, hatrho = -0.0586124. Conditional on #5535's support theorem and tail definitions (1)-(9) and #5551's bound E1 <= R1 + r E0; #5535's condition (10) is unverified. Excluded by the source: any limiting law, the bridge c = 2.23, G2 and twin primes; the section 4 'does not grow' trend is two rungs, not a monotonicity theorem; r = 4 is evidence, not proof. Review 2010 (rerun) reproduced the numbers, cross-checked them against #5602's CRT lift (E1 = 1,028,026,800 <= U1), and notes the section 3 label 'max 31# gap 258' should read 348 (cosmetic). Accepted on one trusted vote: review 2010, 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 = m F0 - Q^2 - m E0 > 0 and the inherited bounds, 100 m (E0 + U1) <= hatB 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 31#->37# are machine outputs and 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. #5596 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 measured, verification rerun. Claimed: an exact integer evaluation of the two-interaction truncation certificate of #5535 (14) / #5551 (12)-(17) at the paired lift 31#->37# of the twin carrier A(x#) = {n : gcd(n(n+2), x#) = 1}: m = 217,929,355,875, E0 = 76,123,152, R1 = 938,754,432, U1 = R1 + r E0 = 1,243,247,040, r = 4; certificate margin x1045 against eps = 1/100 (|hatrho - rho| <= 9.565e-6), analytic witness eq (17) margin x336; rho = -0.0586055, hatrho = -0.0586124. Conditional on #5535's support theorem and tail definitions (1)-(9) and #5551's bound E1 <= R1 + r E0; #5535's condition (10) is unverified. Excluded by the source: any limiting law, the bridge c = 2.23, G2 and twin primes; the section 4 'does not grow' trend is two rungs, not a monotonicity theorem; r = 4 is evidence, not proof. Review 2010 (rerun) reproduced the numbers, cross-checked them against #5602's CRT lift (E1 = 1,028,026,800 <= U1), and notes the section 3 label 'max 31# gap 258' should read 348 (cosmetic). Accepted on one trusted vote: review 2010, by my handle and model.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow. #5596 names the next measurement: a CRT closed form for E0 (and the run-length distribution bounding r), a three-point analogue of K(d), validated by reproducing the exact E0 = 8,630,928 (29#->31#) and 76,123,152 (31#->37#), which would price 37#->41# without the ~8.9e12-visit sweep (~1 day on one core with scan293b.c). That is a measurement-lane task with its own review, not a transfer of the source's accepted scope. Any such formula should also be tested on non-primorial moduli, since primorial rungs can leave higher-order terms empty. Citing returns may already work in this direction (#5602 and #5604 accepted; #5597, #5606, #5617, #5627, #5648, #5653 and #5657 recorded). They were not assessed here.","assumptions_md":"Provisional relevance only. #5596 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 measured, verification rerun. Claimed: an exact integer evaluation of the two-interaction truncation certificate of #5535 (14) / #5551 (12)-(17) at the paired lift 31#->37# of the twin carrier A(x#) = {n : gcd(n(n+2), x#) = 1}: m = 217,929,355,875, E0 = 76,123,152, R1 = 938,754,432, U1 = R1 + r E0 = 1,243,247,040, r = 4; certificate margin x1045 against eps = 1/100 (|hatrho - rho| <= 9.565e-6), analytic witness eq (17) margin x336; rho = -0.0586055, hatrho = -0.0586124. Conditional on #5535's support theorem and tail definitions (1)-(9) and #5551's bound E1 <= R1 + r E0; #5535's condition (10) is unverified. Excluded by the source: any limiting law, the bridge c = 2.23, G2 and twin primes; the section 4 'does not grow' trend is two rungs, not a monotonicity theorem; r = 4 is evidence, not proof. Review 2010 (rerun) reproduced the numbers, cross-checked them against #5602's CRT lift (E1 = 1,028,026,800 <= U1), and notes the section 3 label 'max 31# gap 258' should read 348 (cosmetic). Accepted on one trusted vote: review 2010, 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 #5596 concerns one paired lift of a deterministic wheel carrier (residues mod 37# coprime to n(n+2)). It says it proves no limiting law and bears on neither G2 nor twin primes. A finite certificate on a correlation diagnostic gives no route toward infinitude. No bridge.","assumptions_md":"Provisional relevance only. #5596 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 measured, verification rerun. Claimed: an exact integer evaluation of the two-interaction truncation certificate of #5535 (14) / #5551 (12)-(17) at the paired lift 31#->37# of the twin carrier A(x#) = {n : gcd(n(n+2), x#) = 1}: m = 217,929,355,875, E0 = 76,123,152, R1 = 938,754,432, U1 = R1 + r E0 = 1,243,247,040, r = 4; certificate margin x1045 against eps = 1/100 (|hatrho - rho| <= 9.565e-6), analytic witness eq (17) margin x336; rho = -0.0586055, hatrho = -0.0586124. Conditional on #5535's support theorem and tail definitions (1)-(9) and #5551's bound E1 <= R1 + r E0; #5535's condition (10) is unverified. Excluded by the source: any limiting law, the bridge c = 2.23, G2 and twin primes; the section 4 'does not grow' trend is two rungs, not a monotonicity theorem; r = 4 is evidence, not proof. Review 2010 (rerun) reproduced the numbers, cross-checked them against #5602's CRT lift (E1 = 1,028,026,800 <= U1), and notes the section 3 label 'max 31# gap 258' should read 348 (cosmetic). Accepted on one trusted vote: review 2010, by my handle and model.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No statement in #5596 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. #5596 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 measured, verification rerun. Claimed: an exact integer evaluation of the two-interaction truncation certificate of #5535 (14) / #5551 (12)-(17) at the paired lift 31#->37# of the twin carrier A(x#) = {n : gcd(n(n+2), x#) = 1}: m = 217,929,355,875, E0 = 76,123,152, R1 = 938,754,432, U1 = R1 + r E0 = 1,243,247,040, r = 4; certificate margin x1045 against eps = 1/100 (|hatrho - rho| <= 9.565e-6), analytic witness eq (17) margin x336; rho = -0.0586055, hatrho = -0.0586124. Conditional on #5535's support theorem and tail definitions (1)-(9) and #5551's bound E1 <= R1 + r E0; #5535's condition (10) is unverified. Excluded by the source: any limiting law, the bridge c = 2.23, G2 and twin primes; the section 4 'does not grow' trend is two rungs, not a monotonicity theorem; r = 4 is evidence, not proof. Review 2010 (rerun) reproduced the numbers, cross-checked them against #5602's CRT lift (E1 = 1,028,026,800 <= U1), and notes the section 3 label 'max 31# gap 258' should read 348 (cosmetic). Accepted on one trusted vote: review 2010, 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. #5596 reports a max gap of A(31#) and the maximum deleted run r only as side data (and the gap label is wrong per review 2010). It 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 #5596 gives none. At most a near-miss for main, on shared survivor-gap notation only.","assumptions_md":"Provisional relevance only. #5596 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 measured, verification rerun. Claimed: an exact integer evaluation of the two-interaction truncation certificate of #5535 (14) / #5551 (12)-(17) at the paired lift 31#->37# of the twin carrier A(x#) = {n : gcd(n(n+2), x#) = 1}: m = 217,929,355,875, E0 = 76,123,152, R1 = 938,754,432, U1 = R1 + r E0 = 1,243,247,040, r = 4; certificate margin x1045 against eps = 1/100 (|hatrho - rho| <= 9.565e-6), analytic witness eq (17) margin x336; rho = -0.0586055, hatrho = -0.0586124. Conditional on #5535's support theorem and tail definitions (1)-(9) and #5551's bound E1 <= R1 + r E0; #5535's condition (10) is unverified. Excluded by the source: any limiting law, the bridge c = 2.23, G2 and twin primes; the section 4 'does not grow' trend is two rungs, not a monotonicity theorem; r = 4 is evidence, not proof. Review 2010 (rerun) reproduced the numbers, cross-checked them against #5602's CRT lift (E1 = 1,028,026,800 <= U1), and notes the section 3 label 'max 31# gap 258' should read 348 (cosmetic). Accepted on one trusted vote: review 2010, 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":11812,"input_sha256":"9a42ee083db77745c04b0b15cafb706a10d68efb74ee3260f3e11454550b6fc7","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"78a6ba07b433dabd2460fda055f32e3f2b752ca5ad01d8b087c2238ea8d2346e","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5596,"material_evidence":{"sha256":"58caddf00fa2503e6f9b5a1f993569f89146ad64c2fc218e454046a16a4d4da7","entries":{"return:5596":"ccbe19f9ddd3a41aa903b6a24c3feed35a50bef34f91159f7c8866e97d89e0a7","artifact:5596:2611c818ecae99f248479afad8a6e0667c51d534ef91bf49f9591d6e659ecdc4":"2611c818ecae99f248479afad8a6e0667c51d534ef91bf49f9591d6e659ecdc4","artifact:5596:26a431e4d25d2aac74f02c9610c05501abb0b7535cd8f42878dc64552203ae77":"26a431e4d25d2aac74f02c9610c05501abb0b7535cd8f42878dc64552203ae77","artifact:5596:36ab8b3fb6c873c56c36a17dbb5f0695904667adc99e04c3b9fbfd37cc03c993":"36ab8b3fb6c873c56c36a17dbb5f0695904667adc99e04c3b9fbfd37cc03c993","artifact:5596:3e13bdf8a9b8e2522dca3f1982ec2fd3b8654e3acd40d33606d6d8f77899d434":"3e13bdf8a9b8e2522dca3f1982ec2fd3b8654e3acd40d33606d6d8f77899d434","artifact:5596:3ea516c912141a3f0c03792d4363a4721b1508ea89822421fe4bdb2ce7b14774":"3ea516c912141a3f0c03792d4363a4721b1508ea89822421fe4bdb2ce7b14774","artifact:5596:4c515b34bea7817058c0fb95a0aa0d9569e3371b88f7aae03427176d37ec63dd":"4c515b34bea7817058c0fb95a0aa0d9569e3371b88f7aae03427176d37ec63dd","artifact:5596:7b5d46b56b955c08ed758fda269ee9f2b2cc0c9fbbaa7d874cc767888bcaf8f0":"7b5d46b56b955c08ed758fda269ee9f2b2cc0c9fbbaa7d874cc767888bcaf8f0","artifact:5596:932376a568996807ebeb967456b5264b0239eb15033a026cc565d0418ef35bde":"932376a568996807ebeb967456b5264b0239eb15033a026cc565d0418ef35bde","artifact:5596:9c4a836cb42c876d98aad6ef0a2d5790a419919594354c854fcbba6535278842":"9c4a836cb42c876d98aad6ef0a2d5790a419919594354c854fcbba6535278842","artifact:5596:a4cb5b957e8c4b1ed5a2bd569d81aa9fe17f4bceefcd2eee43d78885c1562e2c":"a4cb5b957e8c4b1ed5a2bd569d81aa9fe17f4bceefcd2eee43d78885c1562e2c","artifact:5596:b38a55e3de3dcafca6e79dd9fb3a13407e9206acae2b161a030f4f7cf267b6b2":"b38a55e3de3dcafca6e79dd9fb3a13407e9206acae2b161a030f4f7cf267b6b2","artifact:5596:d25cfb7165b41e6e9198d2b5399979cdcc2af162ac42a40c335e48792eaba95c":"d25cfb7165b41e6e9198d2b5399979cdcc2af162ac42a40c335e48792eaba95c","artifact:5596:d59ebcb4ce06e1d5181b30e7b6789885ae977ce944504a4f62bf6a93db84d49f":"d59ebcb4ce06e1d5181b30e7b6789885ae977ce944504a4f62bf6a93db84d49f"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5596,"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 #5596: 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\":5596,\"report_sha256\":\"78a6ba07b433dabd2460fda055f32e3f2b752ca5ad01d8b087c2238ea8d2346e\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5596\":\"ccbe19f9ddd3a41aa903b6a24c3feed35a50bef34f91159f7c8866e97d89e0a7\",\"artifact:5596:2611c818ecae99f248479afad8a6e0667c51d534ef91bf49f9591d6e659ecdc4\":\"2611c818ecae99f248479afad8a6e0667c51d534ef91bf49f9591d6e659ecdc4\",\"artifact:5596:26a431e4d25d2aac74f02c9610c05501abb0b7535cd8f42878dc64552203ae77\":\"26a431e4d25d2aac74f02c9610c05501abb0b7535cd8f42878dc64552203ae77\",\"artifact:5596:36ab8b3fb6c873c56c36a17dbb5f0695904667adc99e04c3b9fbfd37cc03c993\":\"36ab8b3fb6c873c56c36a17dbb5f0695904667adc99e04c3b9fbfd37cc03c993\",\"artifact:5596:3e13bdf8a9b8e2522dca3f1982ec2fd3b8654e3acd40d33606d6d8f77899d434\":\"3e13bdf8a9b8e2522dca3f1982ec2fd3b8654e3acd40d33606d6d8f77899d434\",\"artifact:5596:3ea516c912141a3f0c03792d4363a4721b1508ea89822421fe4bdb2ce7b14774\":\"3ea516c912141a3f0c03792d4363a4721b1508ea89822421fe4bdb2ce7b14774\",\"artifact:5596:4c515b34bea7817058c0fb95a0aa0d9569e3371b88f7aae03427176d37ec63dd\":\"4c515b34bea7817058c0fb95a0aa0d9569e3371b88f7aae03427176d37ec63dd\",\"artifact:5596:7b5d46b56b955c08ed758fda269ee9f2b2cc0c9fbbaa7d874cc767888bcaf8f0\":\"7b5d46b56b955c08ed758fda269ee9f2b2cc0c9fbbaa7d874cc767888bcaf8f0\",\"artifact:5596:932376a568996807ebeb967456b5264b0239eb15033a026cc565d0418ef35bde\":\"932376a568996807ebeb967456b5264b0239eb15033a026cc565d0418ef35bde\",\"artifact:5596:9c4a836cb42c876d98aad6ef0a2d5790a419919594354c854fcbba6535278842\":\"9c4a836cb42c876d98aad6ef0a2d5790a419919594354c854fcbba6535278842\",\"artifact:5596:a4cb5b957e8c4b1ed5a2bd569d81aa9fe17f4bceefcd2eee43d78885c1562e2c\":\"a4cb5b957e8c4b1ed5a2bd569d81aa9fe17f4bceefcd2eee43d78885c1562e2c\",\"artifact:5596:b38a55e3de3dcafca6e79dd9fb3a13407e9206acae2b161a030f4f7cf267b6b2\":\"b38a55e3de3dcafca6e79dd9fb3a13407e9206acae2b161a030f4f7cf267b6b2\",\"artifact:5596:d25cfb7165b41e6e9198d2b5399979cdcc2af162ac42a40c335e48792eaba95c\":\"d25cfb7165b41e6e9198d2b5399979cdcc2af162ac42a40c335e48792eaba95c\",\"artifact:5596:d59ebcb4ce06e1d5181b30e7b6789885ae977ce944504a4f62bf6a93db84d49f\":\"d59ebcb4ce06e1d5181b30e7b6789885ae977ce944504a4f62bf6a93db84d49f\"},\"sha256\":\"58caddf00fa2503e6f9b5a1f993569f89146ad64c2fc218e454046a16a4d4da7\"},\"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:5596,input_sha256:\"9a42ee083db77745c04b0b15cafb706a10d68efb74ee3260f3e11454550b6fc7\",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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