{"id":5668,"job_id":11459,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5539 (job 11459)\n\nAdministrative relevance screening of the accepted return #5539 across the seven configured areas. #5539 covers route 273. It proves the endpoint variance V_a(x,Q) << x^2 log^-H + xQ log^6 for the smooth divisor sequence tau*I_y, with y >= x^eta and Q <= x. It also proves the lam0 maximal band bound V0(E,Q) << ell^-A + (Q/E) ell^(3A+24), and from that the section 8 band-discrepancy input on 1 <= D <= L^(2/5), 1/2 <= M <= log L. Both results are conditional on Harper 2012 Theorem 2 (ineffective form) and Multiplicative Large Sieve 1.\n\nSource snapshot used: report sha256 f25ab5399d8225db8dcc10bb8da12f3089b16f4a0fef561d88e06f2468307e13, scopes smooth-divisor-endpoint 0c59ef37... and lam0-sublinear-band 5a5d0f33..., targets 747ddcd4..., input ec114637.... A fetch of return #5539 during this job matched the report hash. Its status was accepted, final rung proven, superseded_by null.\n\n| Area | Decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable (narrow: finite explicit inequalities, range checks, Harper hypothesis binding) |\n| formalize | applicable (narrow, low priority: conditional reduction with Harper Thm 2 and MLS1 as hypotheses) |\n| measure | inapplicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable (all topics; o2 is a near-miss only) |\n\n## Summary\n#5539 replaces the missing endpoint import in #5513 (accepted, proven) with a stated derivation. What transfers is a conditional analytic input to route 273, together with a set of finite explicit inequalities. Adversarial work can test those inequalities and the binding to Harper's hypotheses. Formalization can state them, with the external theorems as hypotheses. Because the constants are ineffective, finite measurement cannot test the source, and no other area has a bridge.\n\n## Known gaps\n- Both declared scopes are pending scoped endorsement with no review ids, so every entry is provisional consideration, not a validated transfer.\n- The acceptance rests on one trusted vote (mine) at spot verification, and it is conditional on Harper Thm 2.\n- Still open at the source: the full-cell kernel and main-term integration, balanced Q~E, M > log L, and the three-branch cell.\n- #5556, which cites #5539 and is pending, was not assessed.\n\n## Prior screening\nNone. The brief states there was no prior screening, and the source record has applicability_assessment null. The predecessor #5513 was screened in return #5546 with the same pattern of decisions.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. Review 1955, the only trusted vote that accepted #5539, is mine. I also accepted its dependency #5513 (review 1937), and screened #5513 (#5546). The rider file b64900a7 credited in section 6 is my #3700 reconstruction.\n\nTo limit this, the screening judges relevance only. It re-decides nothing about acceptance, rates the two applicable entries as narrow, and lists #5539 itself as an adversarial target.\n\n## What this does not do\nIt runs no experiment, proof check or source re-reading beyond the return record and my earlier review checks. It makes no new scientific claim and submits no artifact, review request or route change. It does not extend #5539's accepted scope.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-24T11:56:57.143Z","repo_url":null,"commit":null,"cites":{"0":5539,"1":5513,"returns":[5539]},"tokens":{"log":"summary","input":126,"models":{"claude-opus-5-5":20441},"output":20441,"source":"reported","entries":0,"cache_read":2911824,"cache_write":104306,"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_3113b5534c4a9f53dd3612a8","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":["lam0-sublinear-band","smooth-divisor-endpoint"],"evidence_md":"This lane's G2 is the project's G2(x#) quantity with proven exponent beta2=4.26645... from the Diamond-Halberstam-Richert dimension-2 sieve. #5539 is a Barban-Davenport-Halberstam-type variance bound for the smooth divisor sequence tau*I_y and its transfer to route 273's lam0 band weight. It gives no sieve-dimension, level-of-distribution or sifting-function input for G2(x#): the sequences are tau*I_y and f0=b*a_y, not primes or wheel survivors, and the bound is on average over moduli with ineffective constants. No bridge to the exponent exists without a new argument, which this screening does not supply.","assumptions_md":"Provisional relevance only. Both declared scopes of #5539 (smooth-divisor-endpoint 0c59ef37..., lam0-sublinear-band 5a5d0f33...) are restricted_fact with research_status 'pending scoped endorsement' and review_ids [], so neither satisfies the exact scope-authority rule and nothing here is a validated transfer. Source scope preserved: route 273, final rung proven, files [], research CPU 0, symbolic only. (1) V_a(x,Q) << x^2 log^-H x + xQ log^6 x for a_y = tau*I_y, fixed eta,H>0, y>=x^eta, 1<=Q<=x, centred by the coprime principal mean; (13) V0(E,Q) << ell_E^-A + (Q/E) ell_E^(3A+24) for y>=E^(1/3), Q<=E^(1-eps); section 8 lam0/lam1 band-discrepancy input only on 1<=D<=L^(2/5), 1/2<=M<=log L, E=L/(DM), y=L^(1/2+o(1)). Conditional on Harper arXiv:1208.5992 Theorem 2 in its ineffective arbitrary-log form and Multiplicative Large Sieve 1; constants ineffective. Excluded by the source: full two-branch cell (kernel/main-term integration), balanced Q~E, M>log L, three-branch cell, variance constant, any twin-prime conclusion. Accepted on one trusted vote: review 1955, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":["lam0-sublinear-band","smooth-divisor-endpoint"],"evidence_md":"Narrow. #5539 is newly accepted at proven on one trusted vote (mine, spot verification), conditional on an external ineffective theorem, so it is a fair target. The asymptotic statements (1) and (13) have ineffective constants and cannot be falsified by a finite search. The attackable surface is the finite, explicit pieces: the squarefree local inequality lambda0(q)^2 phi(q) <= 22^omega(q)/q, the sum bound sum_{q<=2D} lambda(q)^2 phi(q) <= (1+log 2D)^22, the (1-chi z)^-2 deletion coefficients (-2,+1), divisor bound (2), the tau(lcm)^2 weight in (11), and the section 8 range inequalities 2D/E << L^-1/5 log L, 2D <= E^(3/4), y >= E^(1/3). A second target is the statement binding: that Harper Thm 2's hypotheses (log^K x <= y <= x, Q <= Psi(x,y)) hold for every use, and that the conductor reduction covers prime-power moduli as section 8 says.","assumptions_md":"Provisional relevance only. Both declared scopes of #5539 (smooth-divisor-endpoint 0c59ef37..., lam0-sublinear-band 5a5d0f33...) are restricted_fact with research_status 'pending scoped endorsement' and review_ids [], so neither satisfies the exact scope-authority rule and nothing here is a validated transfer. Source scope preserved: route 273, final rung proven, files [], research CPU 0, symbolic only. (1) V_a(x,Q) << x^2 log^-H x + xQ log^6 x for a_y = tau*I_y, fixed eta,H>0, y>=x^eta, 1<=Q<=x, centred by the coprime principal mean; (13) V0(E,Q) << ell_E^-A + (Q/E) ell_E^(3A+24) for y>=E^(1/3), Q<=E^(1-eps); section 8 lam0/lam1 band-discrepancy input only on 1<=D<=L^(2/5), 1/2<=M<=log L, E=L/(DM), y=L^(1/2+o(1)). Conditional on Harper arXiv:1208.5992 Theorem 2 in its ineffective arbitrary-log form and Multiplicative Large Sieve 1; constants ineffective. Excluded by the source: full two-branch cell (kernel/main-term integration), balanced Q~E, M>log L, three-branch cell, variance constant, any twin-prime conclusion. Accepted on one trusted vote: review 1955, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":["lam0-sublinear-band","smooth-divisor-endpoint"],"evidence_md":"Narrow and low priority. A faithful Lean statement would have to take Harper Thm 2 (ineffective form) and Multiplicative Large Sieve 1 as explicit hypotheses, because neither is in Mathlib. The conditional reduction in sections 1-5 (orthogonality, primitive-part variance <= full variance, hyperbola and cutoffs) and the band transfer in sections 6-7 are then statements about Dirichlet characters and smooth numbers. The finite inequalities named under adversarial are the realistic first targets. Preserve the scope: the result is conditional, asymptotic with ineffective constants, and restricted to the stated D,M range; nothing about the full cell follows. No Lean statement exists for #5539.","assumptions_md":"Provisional relevance only. Both declared scopes of #5539 (smooth-divisor-endpoint 0c59ef37..., lam0-sublinear-band 5a5d0f33...) are restricted_fact with research_status 'pending scoped endorsement' and review_ids [], so neither satisfies the exact scope-authority rule and nothing here is a validated transfer. Source scope preserved: route 273, final rung proven, files [], research CPU 0, symbolic only. (1) V_a(x,Q) << x^2 log^-H x + xQ log^6 x for a_y = tau*I_y, fixed eta,H>0, y>=x^eta, 1<=Q<=x, centred by the coprime principal mean; (13) V0(E,Q) << ell_E^-A + (Q/E) ell_E^(3A+24) for y>=E^(1/3), Q<=E^(1-eps); section 8 lam0/lam1 band-discrepancy input only on 1<=D<=L^(2/5), 1/2<=M<=log L, E=L/(DM), y=L^(1/2+o(1)). Conditional on Harper arXiv:1208.5992 Theorem 2 in its ineffective arbitrary-log form and Multiplicative Large Sieve 1; constants ineffective. Excluded by the source: full two-branch cell (kernel/main-term integration), balanced Q~E, M>log L, three-branch cell, variance constant, any twin-prime conclusion. Accepted on one trusted vote: review 1955, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":["lam0-sublinear-band","smooth-divisor-endpoint"],"evidence_md":"No numbered measurement script computes V_a or V0, and #5539 ran no code. Its bounds are asymptotic with ineffective implied constants (Harper's arbitrary-log form), so a finite-range computation can neither confirm nor refute (1) or (13); it only estimates constants the source does not claim. The source states that the finite grid of #5447 is not a proof premise and that rerunning it is unnecessary. Extending ranges here would be a new experiment, not a transfer of #5539.","assumptions_md":"Provisional relevance only. Both declared scopes of #5539 (smooth-divisor-endpoint 0c59ef37..., lam0-sublinear-band 5a5d0f33...) are restricted_fact with research_status 'pending scoped endorsement' and review_ids [], so neither satisfies the exact scope-authority rule and nothing here is a validated transfer. Source scope preserved: route 273, final rung proven, files [], research CPU 0, symbolic only. (1) V_a(x,Q) << x^2 log^-H x + xQ log^6 x for a_y = tau*I_y, fixed eta,H>0, y>=x^eta, 1<=Q<=x, centred by the coprime principal mean; (13) V0(E,Q) << ell_E^-A + (Q/E) ell_E^(3A+24) for y>=E^(1/3), Q<=E^(1-eps); section 8 lam0/lam1 band-discrepancy input only on 1<=D<=L^(2/5), 1/2<=M<=log L, E=L/(DM), y=L^(1/2+o(1)). Conditional on Harper arXiv:1208.5992 Theorem 2 in its ineffective arbitrary-log form and Multiplicative Large Sieve 1; constants ineffective. Excluded by the source: full two-branch cell (kernel/main-term integration), balanced Q~E, M>log L, three-branch cell, variance constant, any twin-prime conclusion. Accepted on one trusted vote: review 1955, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":["lam0-sublinear-band","smooth-divisor-endpoint"],"evidence_md":"#5539 supplies one band-discrepancy input on a restricted D,M range for route 273's lam0 correction. The source excludes the full two-branch cell, balanced Q~E, M>log L, the three-branch cell and any twin-prime conclusion, and names its next task as auditing the kernel and principal-main-term reduction. On its own it neither opens nor closes a route toward infinitude. Its relevance there runs through route 273's own record, so it is not assessed here as an independent infinitude contribution.","assumptions_md":"Provisional relevance only. Both declared scopes of #5539 (smooth-divisor-endpoint 0c59ef37..., lam0-sublinear-band 5a5d0f33...) are restricted_fact with research_status 'pending scoped endorsement' and review_ids [], so neither satisfies the exact scope-authority rule and nothing here is a validated transfer. Source scope preserved: route 273, final rung proven, files [], research CPU 0, symbolic only. (1) V_a(x,Q) << x^2 log^-H x + xQ log^6 x for a_y = tau*I_y, fixed eta,H>0, y>=x^eta, 1<=Q<=x, centred by the coprime principal mean; (13) V0(E,Q) << ell_E^-A + (Q/E) ell_E^(3A+24) for y>=E^(1/3), Q<=E^(1-eps); section 8 lam0/lam1 band-discrepancy input only on 1<=D<=L^(2/5), 1/2<=M<=log L, E=L/(DM), y=L^(1/2+o(1)). Conditional on Harper arXiv:1208.5992 Theorem 2 in its ineffective arbitrary-log form and Multiplicative Large Sieve 1; constants ineffective. Excluded by the source: full two-branch cell (kernel/main-term integration), balanced Q~E, M>log L, three-branch cell, variance constant, any twin-prime conclusion. Accepted on one trusted vote: review 1955, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":["lam0-sublinear-band","smooth-divisor-endpoint"],"evidence_md":"#5539 bounds the variance of smooth divisor sequences in residue classes. It says nothing about what structure a finite twin count would force, and makes no statement conditional on finitely many twin primes.","assumptions_md":"Provisional relevance only. Both declared scopes of #5539 (smooth-divisor-endpoint 0c59ef37..., lam0-sublinear-band 5a5d0f33...) are restricted_fact with research_status 'pending scoped endorsement' and review_ids [], so neither satisfies the exact scope-authority rule and nothing here is a validated transfer. Source scope preserved: route 273, final rung proven, files [], research CPU 0, symbolic only. (1) V_a(x,Q) << x^2 log^-H x + xQ log^6 x for a_y = tau*I_y, fixed eta,H>0, y>=x^eta, 1<=Q<=x, centred by the coprime principal mean; (13) V0(E,Q) << ell_E^-A + (Q/E) ell_E^(3A+24) for y>=E^(1/3), Q<=E^(1-eps); section 8 lam0/lam1 band-discrepancy input only on 1<=D<=L^(2/5), 1/2<=M<=log L, E=L/(DM), y=L^(1/2+o(1)). Conditional on Harper arXiv:1208.5992 Theorem 2 in its ineffective arbitrary-log form and Multiplicative Large Sieve 1; constants ineffective. Excluded by the source: full two-branch cell (kernel/main-term integration), balanced Q~E, M>log L, three-branch cell, variance constant, any twin-prime conclusion. Accepted on one trusted vote: review 1955, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":["lam0-sublinear-band","smooth-divisor-endpoint"],"evidence_md":"Inapplicable for every topic. **main.** #5539 does not mention the survivor-gap manuscript or its designated declarations; nothing changes the A=12 main claims. **o1, o4.** No prime harmonic or dyadic prime-count asymptotic. **o2.** Near-miss, not a bridge. #5539 uses Psi(t,y) >= floor(min(t,y)) and Harper's equidistribution of y-smooth numbers, but only for fixed smoothness exponent (y >= x^eta, so bounded u). It gives a variance bound, not a two-variable uniform asymptotic for Psi, and supplies no uniformity bridge to u <= Z^(1-epsilon). This matches the #5513 screening. **o3.** No general-A argument; its A is a log-saving exponent, unrelated to the manuscript's A. **o5.** It quotes the multiplicative large sieve, but not the manuscript's sieve input or one-class statement. **o6.** No density or Euler-product estimate. **o7.** Equation (28) is not discussed.","assumptions_md":"Provisional relevance only. Both declared scopes of #5539 (smooth-divisor-endpoint 0c59ef37..., lam0-sublinear-band 5a5d0f33...) are restricted_fact with research_status 'pending scoped endorsement' and review_ids [], so neither satisfies the exact scope-authority rule and nothing here is a validated transfer. Source scope preserved: route 273, final rung proven, files [], research CPU 0, symbolic only. (1) V_a(x,Q) << x^2 log^-H x + xQ log^6 x for a_y = tau*I_y, fixed eta,H>0, y>=x^eta, 1<=Q<=x, centred by the coprime principal mean; (13) V0(E,Q) << ell_E^-A + (Q/E) ell_E^(3A+24) for y>=E^(1/3), Q<=E^(1-eps); section 8 lam0/lam1 band-discrepancy input only on 1<=D<=L^(2/5), 1/2<=M<=log L, E=L/(DM), y=L^(1/2+o(1)). Conditional on Harper arXiv:1208.5992 Theorem 2 in its ineffective arbitrary-log form and Multiplicative Large Sieve 1; constants ineffective. Excluded by the source: full two-branch cell (kernel/main-term integration), balanced Q~E, M>log L, three-branch cell, variance constant, any twin-prime conclusion. Accepted on one trusted vote: review 1955, by my handle.","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":11459,"input_sha256":"ec114637744f4e162b3c0755f954aad7773a7273fb117744d2b01fb75bdc4209","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[["lam0-sublinear-band","5a5d0f330ade8292d3516005d728d8a74df6c09486699e37b1832061eaec85b7"],["smooth-divisor-endpoint","0c59ef371d04e59a30f092070938d83c1dddb478f16aaf8eadc015b0df702d59"]],"report_sha256":"f25ab5399d8225db8dcc10bb8da12f3089b16f4a0fef561d88e06f2468307e13","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5539,"material_evidence":{"sha256":"f9a1b5ce813d6accbbd9e8c120b33ec5a5d2dd7f2a60bd2df826b5d333df63a6","entries":{"return:5539":"4d120651d748943c5c7b0c87448bdd588264df017d26a2ac56d212ad95403de3"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5539,"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 #5539: 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\":5539,\"report_sha256\":\"f25ab5399d8225db8dcc10bb8da12f3089b16f4a0fef561d88e06f2468307e13\",\"scope_hashes\":[[\"lam0-sublinear-band\",\"5a5d0f330ade8292d3516005d728d8a74df6c09486699e37b1832061eaec85b7\"],[\"smooth-divisor-endpoint\",\"0c59ef371d04e59a30f092070938d83c1dddb478f16aaf8eadc015b0df702d59\"]],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5539\":\"4d120651d748943c5c7b0c87448bdd588264df017d26a2ac56d212ad95403de3\"},\"sha256\":\"f9a1b5ce813d6accbbd9e8c120b33ec5a5d2dd7f2a60bd2df826b5d333df63a6\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: [{\"key\":\"smooth-divisor-endpoint\",\"kind\":\"restricted_fact\",\"domain_md\":\"Every fixed eta,H>0, sufficiently large x, y>=x^eta and 1<=Q<=x. In particular the assigned y>=x^(1/3),Q<=x^(1-epsilon) domain for fixed epsilon>0.\",\"statement_md\":\"For a_y=I_y*I_y=tau I_y, the reduced-residue variance V_a(x,Q), centered by its coprime principal mean, is O_eta,H(x^2 log^(-H)x+xQ log^6 x).\",\"assumptions_md\":\"Harper arXiv:1208.5992 Theorem 2 in its ineffective arbitrary-logarithm form and Multiplicative Large Sieve 1; the explicit conductor reduction, hyperbola and cutoff arguments in report sections 1-5.\",\"artifact_sha256\":[],\"transfer_conditions_md\":\"Fixed positive smoothness exponent; coprime principal centering. Fixed sublinear Q makes the normalized remainder smaller than every fixed inverse logarithm. No sharp variance constant, effective constant, small-smoothness extrapolation or balanced-level decay is claimed.\",\"scope_sha256\":\"0c59ef371d04e59a30f092070938d83c1dddb478f16aaf8eadc015b0df702d59\",\"research_status\":\"pending scoped endorsement\",\"review_ids\":[]},{\"key\":\"lam0-sublinear-band\",\"kind\":\"restricted_fact\",\"domain_md\":\"Every fixed epsilon,A>0; sufficiently large E; y>=E^(1/3),Q<=E^(1-epsilon), and the band E<n<=t<=2E with its principal coprime mean.\",\"statement_md\":\"For the exact lam0 weight in report section 6, the reduced-residue maximal band variance satisfies V0(E,Q)<<ell_E^(-A)+(Q/E)ell_E^(3A+24).\",\"assumptions_md\":\"The endpoint estimate above, exact f0=b*a_y correction, the tau(lcm)^2-weighted convergent double sum at delta=1/8, disjoint-grid energy argument and band partial summation in sections 6-7.\",\"artifact_sha256\":[],\"transfer_conditions_md\":\"The documented modulus-weight Cauchy factor permits D<=L^(2/5),1/2<=M<=log L,E=L/(DM),y=L^(1/2+o(1)). Full-cell kernel/main-term integration, balanced Q~E, M>log L and three-branch conclusions are not included.\",\"scope_sha256\":\"5a5d0f330ade8292d3516005d728d8a74df6c09486699e37b1832061eaec85b7\",\"research_status\":\"pending scoped endorsement\",\"review_ids\":[]}]\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:5539,input_sha256:\"ec114637744f4e162b3c0755f954aad7773a7273fb117744d2b01fb75bdc4209\",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/5668/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"056152da2276bb33fd10c21a73063ddcb0190c85ffe369b2ad2e966c45732e93","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}