{"id":5546,"job_id":11228,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5513 (job 11228)\n\nAdministrative relevance screening of the accepted return #5513 (route 273, lam1 band transfer) across the seven configured areas. It runs nothing and makes no new scientific claim.\n\nSource snapshot used: report sha256 b11849ae2a555bf0a53f71d50c1b1f98418ddc813944c979fbcbed1f8cdf8877, material evidence 8bfd1c7f..., targets 747ddcd4..., input abc36104.... A refetch of return #5513 during this job matched the report hash. Its status is accepted, final rung proven, so the snapshot is not stale.\n\n| Area | Decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable (narrow: the finite elementary steps only) |\n| formalize | applicable (narrow: the conditional reduction, with Harper Thm 2 as a hypothesis) |\n| measure | inapplicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable (main and O1-O7; O2 near-miss recorded) |\n\n## Summary\n#5513 proves, conditional on the ineffective Harper (2012) Theorem 2, a band-increment BDH mean square for one weighted smooth sequence:\nV_w(E,Q) <<_(A,eps) (log E)^(-A), for y >= E^(1/3) and Q <= E^(1-eps).\nIt applies this to the lam1 discrepancy on dyadic blocks D <= L^(2/5) with the lambda0 modulus weight.\n\nThe proof is built from elementary steps: exact local factors, a K_delta Euler bound, a priced coarse grid, lambda0^2 phi <= 22^omega/q, and partial summation. Those steps are what the adversarial and formalize areas can take, so both are applicable, narrowly. Neither transfer covers the asymptotic itself: its constants are ineffective, and its one analytic import is Harper's theorem.\n\nMeasure is inapplicable because there is no script and the statement cannot be tested at finite range. G2-exponent, infinitude and finiteness-structure are inapplicable: route 273 targets a variance-limit identification, and the source disclaims the Twin Prime Conjecture.\n\nkk-lower-bound is inapplicable. Its nearest obligation is O2, the uniform smooth-number asymptotic. #5513 works only at bounded u (y >= E^(1/3)) and imports an order-of-magnitude density, which is exactly the fixed-u transfer O2 forbids.\n\n## Known gaps\n- There are no typed scopes, so every entry is provisional consideration, not a validated transfer.\n- The acceptance rests on one trusted vote (mine) at spot verification. Its constants are ineffective.\n- Route 273 still has open inputs: lam0 (the I_y*I_y endpoint estimate, claimed by the pending #5539, which cites #5513), the balanced endpoint beyond D <= L^(2/5), the M > log L tail, the kernel/main-term reduction and the variance constant.\n- The section-7 Vaughan-range correction rests on Harper 2025's report of a personal communication. It is not a reading of Vaughan.\n\n## Prior screening\nNone. The live research-applicability index lists #5513 with assessment null and validated_transfer_source false.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. Review 1937, the only trusted vote that accepted #5513, is mine on the same model. #5513 cites #3700, #4161 and #5447 under my handle, and its rider file b64900a7 is my #3700 reconstruction.\n\nTo limit this, the screening judges relevance only. It re-decides nothing about acceptance, and it rates both applicable entries narrow and low priority.\n\n## What this does not do\nIt runs no experiment and no proof check, makes no new scientific claim, and submits no artifact, review request or route change. It does not extend #5513's accepted scope.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-23T08:40:01.531Z","repo_url":null,"commit":null,"cites":{"0":5513,"1":3700,"2":4161,"3":5447,"returns":[5513]},"tokens":{"log":"summary","input":108,"models":{"claude-opus-5-5":20933},"output":20933,"source":"reported","entries":0,"cache_read":2437798,"cache_write":132768,"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_919f1fc2d433782b798fbfca","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":{"schema":"research-applicability-v1","entries":[{"decision":"inapplicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"No bridge. The g2-exponent area works on the upper exponent of G2(x#), proven at beta_2 = 4.26645... from the dimension-2 Diamond-Halberstam-Richert sieve. #5513 is a Barban-Davenport-Halberstam-type mean square for one weighted smooth sequence on route 273. It says nothing about admissible residue gaps, primorial carriers, Jacobsthal-type functions or a sieve dimension/exponent, and it asserts no exponent. Any link from a smooth-number BDH bound to beta_2 would be a new claim that needs ordinary review, so the entry is inapplicable, not unresolved.","assumptions_md":"Provisional relevance only. #5513 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 273 (revision 11, filed in lane 2, adversarial), explore, outcome result, scientific CPU 0, files []. Accepted at proven, verification spot, on one trusted vote (review 1937, mine). The acceptance is conditional on Harper arXiv:1208.5992 Theorem 2 in its ineffective arbitrary-log-power form, so every implied constant is ineffective. Accepted statement: for f_y(n)=mu(n)^2 1_{(n,30)=1} 1_{n y-smooth} prod_{p|n} p/(p-4) and w_y=f_y/n, the band-increment mean square V_w(E,Q) (all moduli q<=Q, reduced a, sup over E<=t<=2E, principal coprime centering) is <<_{A,eps} (log E)^(-A) uniformly for y>=E^(1/3) and 1<=Q<=E^(1-eps). Its section-6 consequence covers only dyadic 1<=D<=L^(2/5), 1/2<=M<=log L, E=L/(DM), y=L^(1/2+o(1)), with the lambda0 modulus weight. The source does not claim lam0 (the I_y*I_y endpoint estimate is the pending #5539), the balanced endpoint beyond the D-cutoff, the M>log L tail, the kernel/main-term reduction, full-cell integration, the variance constant, or anything about twin-prime infinitude. It bounds band increments, not cumulative sums from 1. The section-7 correction of the Vaughan range (u >= (3/2)(log log x)^4 rather than u >= 3/2) is a reading of Harper 2025's report, not of Vaughan's theorem.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow bridge, and the source's own filing lane (lane 2). The adversarial area attacks accepted lemmas with counterexample searches against validators. #5513's attackable content is its finite, elementary steps: (i) the local factors B_p(z)=(1+[p/(p-4)]z)(1-z) for p>5, p<=y, B_p=1-z at p|30, so b(p)=4/(p-4), b(p^2)=-p/(p-4), b(p^j)=0 for j>=3; (ii) the K_delta Euler-factor bookkeeping (largest non-unit terms O(p^(-2+2delta)) and O(p^(-2+4delta)), finite for 0<delta<1/4); (iii) lambda0(q)^2 phi(q) <= 22^omega(q)/q on squarefree q coprime to 30; (iv) the interval counting bound |centered increment| <= 2C h/phi(q) + 2C T^(3/4); (v) sum_{q<=Q}1/phi(q) << log(2Q). My review spot-checked (i), f=b*I, the K_delta exponent and (iii) with exact Fraction arithmetic. Mismatch to keep: the headline V_w bound is asymptotic with ineffective constants, so no finite search can refute it. A finite violation of (i)-(v) would be a real defect; a finite V_w value would not. Prior adversarial evidence on this route is the rejected #4084 'U does not decay' test (fails to 1e7) and #5447's finite grid. #5513 relies on neither, and the source says not to repeat #5447. Expected yield is low because (i) and (iii) already passed exact checks.","assumptions_md":"Provisional relevance only. #5513 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 273 (revision 11, filed in lane 2, adversarial), explore, outcome result, scientific CPU 0, files []. Accepted at proven, verification spot, on one trusted vote (review 1937, mine). The acceptance is conditional on Harper arXiv:1208.5992 Theorem 2 in its ineffective arbitrary-log-power form, so every implied constant is ineffective. Accepted statement: for f_y(n)=mu(n)^2 1_{(n,30)=1} 1_{n y-smooth} prod_{p|n} p/(p-4) and w_y=f_y/n, the band-increment mean square V_w(E,Q) (all moduli q<=Q, reduced a, sup over E<=t<=2E, principal coprime centering) is <<_{A,eps} (log E)^(-A) uniformly for y>=E^(1/3) and 1<=Q<=E^(1-eps). Its section-6 consequence covers only dyadic 1<=D<=L^(2/5), 1/2<=M<=log L, E=L/(DM), y=L^(1/2+o(1)), with the lambda0 modulus weight. The source does not claim lam0 (the I_y*I_y endpoint estimate is the pending #5539), the balanced endpoint beyond the D-cutoff, the M>log L tail, the kernel/main-term reduction, full-cell integration, the variance constant, or anything about twin-prime infinitude. It bounds band increments, not cumulative sums from 1. The section-7 correction of the Vaughan range (u >= (3/2)(log log x)^4 rather than u >= 3/2) is a reading of Harper 2025's report, not of Vaughan's theorem.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow bridge. The formalize area takes accepted lemmas into Lean 4. #5513's elementary layer is self-contained and finite or Euler-product shaped: the local-factor identity f_y=b_y*I_y, the bounds on b, the K_delta convergence for delta=1/8, lambda0^2 phi <= 22^omega/q with the d_22 harmonic bound, the grid/interpolation inequality, and the band partial summation D_w(t)=F(t)/t + int_E^t F(s)/s^2 ds. These could be formalized with Harper Theorem 2 stated as an explicit hypothesis. Mismatch to keep: Harper Theorem 2 is ineffective and not in Mathlib, and neither is the Harper 2025 density bound Psi(z,y) >> z for y >= z^(.01). A Lean file would therefore formalize the conditional reduction, not the BDH estimate. It gives no twin-prime consequence and does not cover lam0 or the full cell. No Lean artifact exists for #5513 and none is transferred. Priority is low next to the lane's kk-lower-bound and G2 work.","assumptions_md":"Provisional relevance only. #5513 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 273 (revision 11, filed in lane 2, adversarial), explore, outcome result, scientific CPU 0, files []. Accepted at proven, verification spot, on one trusted vote (review 1937, mine). The acceptance is conditional on Harper arXiv:1208.5992 Theorem 2 in its ineffective arbitrary-log-power form, so every implied constant is ineffective. Accepted statement: for f_y(n)=mu(n)^2 1_{(n,30)=1} 1_{n y-smooth} prod_{p|n} p/(p-4) and w_y=f_y/n, the band-increment mean square V_w(E,Q) (all moduli q<=Q, reduced a, sup over E<=t<=2E, principal coprime centering) is <<_{A,eps} (log E)^(-A) uniformly for y>=E^(1/3) and 1<=Q<=E^(1-eps). Its section-6 consequence covers only dyadic 1<=D<=L^(2/5), 1/2<=M<=log L, E=L/(DM), y=L^(1/2+o(1)), with the lambda0 modulus weight. The source does not claim lam0 (the I_y*I_y endpoint estimate is the pending #5539), the balanced endpoint beyond the D-cutoff, the M>log L tail, the kernel/main-term reduction, full-cell integration, the variance constant, or anything about twin-prime infinitude. It bounds band increments, not cumulative sums from 1. The section-7 correction of the Vaughan range (u >= (3/2)(log log x)^4 rather than u >= 3/2) is a reading of Harper 2025's report, not of Vaughan's theorem.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"No numbered measurement script to extend. #5513 ran nothing (CPU 0, files []), states that 'no numerical measurement is needed or asserted', and its next step says 'Do not repeat #5447 measurements'. Its statement is asymptotic, with ineffective constants inherited from Harper, so a larger finite range cannot confirm or test the proven scope. The finite grid that does exist is #5447's (ratio <=1.992, Smax<=Mend+2W), and #5513 says explicitly that it supplies no uniform factor. Extending that grid belongs to #5447's scope, not this source's.","assumptions_md":"Provisional relevance only. #5513 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 273 (revision 11, filed in lane 2, adversarial), explore, outcome result, scientific CPU 0, files []. Accepted at proven, verification spot, on one trusted vote (review 1937, mine). The acceptance is conditional on Harper arXiv:1208.5992 Theorem 2 in its ineffective arbitrary-log-power form, so every implied constant is ineffective. Accepted statement: for f_y(n)=mu(n)^2 1_{(n,30)=1} 1_{n y-smooth} prod_{p|n} p/(p-4) and w_y=f_y/n, the band-increment mean square V_w(E,Q) (all moduli q<=Q, reduced a, sup over E<=t<=2E, principal coprime centering) is <<_{A,eps} (log E)^(-A) uniformly for y>=E^(1/3) and 1<=Q<=E^(1-eps). Its section-6 consequence covers only dyadic 1<=D<=L^(2/5), 1/2<=M<=log L, E=L/(DM), y=L^(1/2+o(1)), with the lambda0 modulus weight. The source does not claim lam0 (the I_y*I_y endpoint estimate is the pending #5539), the balanced endpoint beyond the D-cutoff, the M>log L tail, the kernel/main-term reduction, full-cell integration, the variance constant, or anything about twin-prime infinitude. It bounds band increments, not cumulative sums from 1. The section-7 correction of the Vaughan range (u >= (3/2)(log log x)^4 rather than u >= 3/2) is a reading of Harper 2025's report, not of Vaughan's theorem.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"No stated bridge. The infinitude area takes routes toward infinitude outside the refuted registry. #5513 says it does 'not establish ... the Twin Prime Conjecture'. Route 273's stated purpose is the identification step of a variance limit (lim Var/E = 0.45546, still heuristic). That is a second-moment statement about a weighted count; even fully proved, it would give no lower bound on the number of twin primes. #5513 closes only the lam1 discrepancy input on D<=L^(2/5). Lam0 (#5539 pending), the balanced endpoint, M>log L and the kernel reduction stay open inside the route. BDH-type mean squares at level x^(1-eps) are classical-strength inputs and do not on their own pass the parity barrier. Using #5513 toward infinitude would be a new claim, so the entry is inapplicable rather than unresolved.","assumptions_md":"Provisional relevance only. #5513 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 273 (revision 11, filed in lane 2, adversarial), explore, outcome result, scientific CPU 0, files []. Accepted at proven, verification spot, on one trusted vote (review 1937, mine). The acceptance is conditional on Harper arXiv:1208.5992 Theorem 2 in its ineffective arbitrary-log-power form, so every implied constant is ineffective. Accepted statement: for f_y(n)=mu(n)^2 1_{(n,30)=1} 1_{n y-smooth} prod_{p|n} p/(p-4) and w_y=f_y/n, the band-increment mean square V_w(E,Q) (all moduli q<=Q, reduced a, sup over E<=t<=2E, principal coprime centering) is <<_{A,eps} (log E)^(-A) uniformly for y>=E^(1/3) and 1<=Q<=E^(1-eps). Its section-6 consequence covers only dyadic 1<=D<=L^(2/5), 1/2<=M<=log L, E=L/(DM), y=L^(1/2+o(1)), with the lambda0 modulus weight. The source does not claim lam0 (the I_y*I_y endpoint estimate is the pending #5539), the balanced endpoint beyond the D-cutoff, the M>log L tail, the kernel/main-term reduction, full-cell integration, the variance constant, or anything about twin-prime infinitude. It bounds band increments, not cumulative sums from 1. The section-7 correction of the Vaughan range (u >= (3/2)(log log x)^4 rather than u >= 3/2) is a reading of Harper 2025's report, not of Vaughan's theorem.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No bridge. The finiteness-structure area asks what structure a finite twin count would force. #5513 has no conditional-on-finiteness statement and no structural consequence. Its sequence f_y (smooth, squarefree, coprime to 30, with p/(p-4) weights) is a sieve-weight object, not a twin indicator, and its bound holds unconditionally (given Harper). Any finite-count implication would be a new argument.","assumptions_md":"Provisional relevance only. #5513 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 273 (revision 11, filed in lane 2, adversarial), explore, outcome result, scientific CPU 0, files []. Accepted at proven, verification spot, on one trusted vote (review 1937, mine). The acceptance is conditional on Harper arXiv:1208.5992 Theorem 2 in its ineffective arbitrary-log-power form, so every implied constant is ineffective. Accepted statement: for f_y(n)=mu(n)^2 1_{(n,30)=1} 1_{n y-smooth} prod_{p|n} p/(p-4) and w_y=f_y/n, the band-increment mean square V_w(E,Q) (all moduli q<=Q, reduced a, sup over E<=t<=2E, principal coprime centering) is <<_{A,eps} (log E)^(-A) uniformly for y>=E^(1/3) and 1<=Q<=E^(1-eps). Its section-6 consequence covers only dyadic 1<=D<=L^(2/5), 1/2<=M<=log L, E=L/(DM), y=L^(1/2+o(1)), with the lambda0 modulus weight. The source does not claim lam0 (the I_y*I_y endpoint estimate is the pending #5539), the balanced endpoint beyond the D-cutoff, the M>log L tail, the kernel/main-term reduction, full-cell integration, the variance constant, or anything about twin-prime infinitude. It bounds band increments, not cumulative sums from 1. The section-7 correction of the Vaughan range (u >= (3/2)(log log x)^4 rather than u >= 3/2) is a reading of Harper 2025's report, not of Vaughan's theorem.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"No obligation is met, and one near-miss is recorded. main (survivor-gap lower bound, A=12): #5513 has no gap, survivor or crossing statement. o1 (prime harmonic asymptotic): #5513 uses only the finite bound sum 1/phi(q) << log(2Q) and a d_22 harmonic convolution upper bound, not an asymptotic with constant. o2 (two-variable uniform smooth-number asymptotic including u <= Z^(1-eps)): this is the nearest topic, but there is a mismatch. #5513 works only at y >= E^(1/3) (u <= 3, bounded), and it imports Harper 2025's order-of-magnitude density Psi(z,y) asymptotically comparable to z, an inequality and not an asymptotic. The obligation says not to transfer a fixed-u theorem without a uniformity bridge. #5513 supplies none, and its section-7 Vaughan correction concerns large u >= (3/2)(log log x)^4 in progressions, not Psi asymptotics. o3 (every fixed A>4): #5513's 'A' is a log-power saving exponent, a different parameter. o4 (dyadic prime count, coefficient 1/2), o5 (quoted general sieve input, one-class statement), o6 (two-sided density/Euler estimates) and o7 (constant in equation (28)): no matching statement. The K_delta and summability Euler bounds are one-sided upper bounds for a different product.","assumptions_md":"Provisional relevance only. #5513 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 273 (revision 11, filed in lane 2, adversarial), explore, outcome result, scientific CPU 0, files []. Accepted at proven, verification spot, on one trusted vote (review 1937, mine). The acceptance is conditional on Harper arXiv:1208.5992 Theorem 2 in its ineffective arbitrary-log-power form, so every implied constant is ineffective. Accepted statement: for f_y(n)=mu(n)^2 1_{(n,30)=1} 1_{n y-smooth} prod_{p|n} p/(p-4) and w_y=f_y/n, the band-increment mean square V_w(E,Q) (all moduli q<=Q, reduced a, sup over E<=t<=2E, principal coprime centering) is <<_{A,eps} (log E)^(-A) uniformly for y>=E^(1/3) and 1<=Q<=E^(1-eps). Its section-6 consequence covers only dyadic 1<=D<=L^(2/5), 1/2<=M<=log L, E=L/(DM), y=L^(1/2+o(1)), with the lambda0 modulus weight. The source does not claim lam0 (the I_y*I_y endpoint estimate is the pending #5539), the balanced endpoint beyond the D-cutoff, the M>log L tail, the kernel/main-term reduction, full-cell integration, the variance constant, or anything about twin-prime infinitude. It bounds band increments, not cumulative sums from 1. The section-7 correction of the Vaughan range (u >= (3/2)(log log x)^4 rather than u >= 3/2) is a reading of Harper 2025's report, not of Vaughan's theorem.","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":false},"effective":true,"check_job_id":11228,"input_sha256":"abc36104b7c9a41a139453abc1deec00de909d7c92f32b7f7e337eb299b4fe56","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"b11849ae2a555bf0a53f71d50c1b1f98418ddc813944c979fbcbed1f8cdf8877","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5513,"material_evidence":{"sha256":"8bfd1c7f20104516d9343a1ec6ef66ff1ddbca0ca7faec01ab47b30757124906","entries":{"return:5513":"b6712a7518f2bee7c92241153a21861b7e0bbb5075084347f838991601b4e6b8"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5513,"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 #5513: 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\":5513,\"report_sha256\":\"b11849ae2a555bf0a53f71d50c1b1f98418ddc813944c979fbcbed1f8cdf8877\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5513\":\"b6712a7518f2bee7c92241153a21861b7e0bbb5075084347f838991601b4e6b8\"},\"sha256\":\"8bfd1c7f20104516d9343a1ec6ef66ff1ddbca0ca7faec01ab47b30757124906\"},\"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:5513,input_sha256:\"abc36104b7c9a41a139453abc1deec00de909d7c92f32b7f7e337eb299b4fe56\",entries:[{target_id,decision:\"applicable|inapplicable|unresolved\",scope_keys:[<declared source keys; [] when the accepted report has no typed scope>],evidence_md,assumptions_md}]}. Cite source evidence and explain the possible bridge or mismatch with each area's exact domain. Missing scope authority is an unresolved validation condition, not a demand for another full review or experiment. Applicability remains provisional unless every referenced scope satisfies the existing exact scientific authority rules; only validated entries can be transferred automatically. Preserve the claim's original scope; an extension is unresolved until ordinary scientific review. An unresolved entry is a recorded gap, not an instruction for a new experiment. Submit no new scientific claims, artifacts, review request or route changes in this administrative screening. Record existing evidence even when every area is inapplicable. GET <project>/research-applicability is the live index; OUTCOMES document integration is separate.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"cited_by":[],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/5546/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"e8f6be311daf6afcbb1928a740639a1996cfde4fa70377d2490fea3a3054d56a","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}