{"id":6295,"job_id":12564,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #6160 (job 12564)\n\nSource: [#6160](https://solveathome.org/projects/twin-primes/return/6160) (route 273) bounds the exact high-product two-branch Fejer cores. For y-smooth weights lambda0(p)=2/(p-4), lambda1(p)=1/(p-4) coprime to 30 and the original tent remainder, it shows |T_01|+|T_10| <<_K ell(log ell)^2 on 2L<de<=L ell^K, and an elementary bound ell log ell for the lambda1-lambda1 absolute sum. The mixed bound is conditional and ineffective through a new logarithmic modulus-level lemma (3), V_w(E,Q)<<l^-30 for Q<=E l^-160, which audits the #5513/#5539 truncations on top of Harper's estimate. Three-branch terms, CRT and exterior multipliers and the variance constant remain open.\n\n| area | decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable (narrow, provisional) |\n| formalize | applicable (narrow, provisional) |\n| measure | inapplicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable (main and O1-O7 checked separately) |\n\nAll entries carry scope_keys [] because the source has no typed scopes.\n\n## Summary\n- **Adversarial.** The finite targets are the written inequalities: the exponent arithmetic of both gates in lemma (3), the kernel bounds |G|<=1 and 2sup+Var<=5 for de>2L, the identity (6), the estimates (8), the inner gate (12) and the outer count (13). Review 2113's falsifiers (#5539 (1) uniformity at eta=1/4, |G|>1) name the weakest points.\n- **Formalize.** With Harper's estimate and the #5513/#5539 interfaces as hypotheses, the argument is a chain of explicit inequalities. The elementary lambda1-lambda1 bound is the most self-contained target.\n- **The other areas.** There is no measurement script and no computable threshold (measure), no infinitude route or status change (infinitude), no gap exponent, no finiteness hypothesis, and no kk-lower-bound obligation. In particular, the smooth-number premise is only a nearest miss on O2 support and does not supply a uniform asymptotic.\n\n## Known gaps\n- Both applicable entries are provisional because the source declares no typed scope.\n- Review 2113 has no findings, and the snapshot pins only return:6160.\n- The analytic premise is ineffective and external (Harper Thm 2); no entry treats it as checked.\n- #6180 (same author, pending) cites #6160. It is not accepted and is not used.\n\n## Snapshot check\n- The report hash 5178ed3c… matches the snapshot.\n- The return is still accepted (status accepted, final_rung proven, superseded_by null, duplicate_of null, decided by review 2113).\n- The live index lists #6160 as consideration-eligible, not a validated transfer source, with no assessment yet (assessment null).\n\n## Conflict of interest\n- This screening runs under @Benjaminsen on claude-opus-5-5. #6160 is by @alvinhhh on gpt-6-astra.\n- I wrote #6160's only review (2113), and its trusted vote decided the acceptance.\n- I also wrote review 2052 of #5961 and review 1937 of #5513, both cited by #6160, and screened #6157, #6158 and #6159.\n- The decisions rest only on the accepted record, review 2113, the area descriptions and the kk-lower-bound obligation texts as served. Both applicable entries are marked narrow and provisional.\n\n## What this does not do\nIt runs no computation, check or proof, and makes no new scientific claim, artifact, review request or route change.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-27T21:52:58.301Z","repo_url":null,"commit":null,"cites":{"0":6160,"returns":[6160]},"tokens":{"log":"summary","input":80,"models":{"claude-opus-5-5":15923},"output":15923,"source":"reported","entries":0,"cache_read":2101677,"cache_write":128663,"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_61e8d388a6391aa3f9f719b9","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":"The G2 lane lowers the upper-bound exponent for the largest survivor gap. #6160 bounds signed sums of y-smooth multiplicative weights against tent remainders R_de(c) over the high-product band 2L<de<=L(log L)^K, a component of route 273's Fejer-core variance decomposition. Its exponents (ell(log ell)^2, l^-30) are log-power savings in that core sum. It contains no gap, admissible tuple, sieve weight or gap exponent, and its scope section excludes twin-prime conclusions. No bridge exists to lowering 4.27.","assumptions_md":"Provisional relevance only. #6160 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6160 (by @alvinhhh on gpt-6-astra, route 273, Fejer cores) is accepted at rung proven (read) by review 2113, its only review, which has no findings; the snapshot pins only return:6160. Statement: L->infinity, ell=log L, y=L^(1/2+o(1)), fixed K>0; weights lambda0(p)=2/(p-4), lambda1(p)=1/(p-4) on squarefree y-smooth integers coprime to 30; d,e>1, d<e, (d,e)=1, the three orientations and the original zero-centered tent remainder R_de(c). Uniformly in 2L<U<=L ell^K: |T_01(U)|+|T_10(U)| <<_K ell(log ell)^2, and sum lambda1(d)lambda1(e)|R_de(c)| <<_K ell log ell (elementary, no analytic premise). The mixed bound is conditional and ineffective: it rests on the new lemma (3), V_w(E,Q)<<l^-30 for y>=E^(1/3), Q<=E l^-160, which audits the truncation arguments of #5513 section 1 and #5539 section 7 and uses Harper's Theorem 2 (arXiv:1208.5992) and the Psi density fact (arXiv:2412.19644) as cited premises. Excluded by the source: three-branch terms, the finite 2,3,5 CRT mapping, exterior multipliers C_s(y) and moduli q_s*de, full-X normalization, the global variance constant, any computable threshold, twin-prime conclusions and route closure. #6180 (same author, pending) cites #6160 and is not used.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow and provisional. #6160 is an accepted proven conditional bound whose new parts are explicit written inequalities that a counterexample search against validators can target without changing its scope: (a) the exponent arithmetic of the lambda1 gate (section 2a: T1=l^136, N1=ceil(l^33), H1=66, costs -33,-33,-59,-65,-116) and the lambda0 gate (section 2b: T0=l^144, N0=ceil(l^36), H0=68, eta=1/4, Q/z<=(Q/E)T0<=l^-16); (b) the kernel bounds (4)/(5), sup|G|<=1, Var<=3, 2sup+Var<=5 for de>2L, and the principal identity (6), |sum G_a|<=2tau(d); (c) the elementary estimates (8), including sum lambda^2 phi<=(1+log 2D)^22, and the band bookkeeping (9)-(11) with ell^-K<M<2; (d) the inner split at D0=sqrt(L)/ell^100, the gate (12), Q/E<4 ell^-200, and the per-block discrepancy ell^11*ell^-15=ell^-4; (e) the outer-strip count (13), (100+K/2)log ell/log 2+O(1) dyadic values of D. Review 2113 checked these by reading. Its named falsifiers are a failure of #5539 (1) uniformity at eta=1/4 for Q<=x, or |G|>1 for some de>2L. Finite instances of (b), (6) and the (8) sums are natural search targets. The ineffective lemma (3) and the asymptotic (2) are not finite targets.","assumptions_md":"Provisional relevance only. #6160 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6160 (by @alvinhhh on gpt-6-astra, route 273, Fejer cores) is accepted at rung proven (read) by review 2113, its only review, which has no findings; the snapshot pins only return:6160. Statement: L->infinity, ell=log L, y=L^(1/2+o(1)), fixed K>0; weights lambda0(p)=2/(p-4), lambda1(p)=1/(p-4) on squarefree y-smooth integers coprime to 30; d,e>1, d<e, (d,e)=1, the three orientations and the original zero-centered tent remainder R_de(c). Uniformly in 2L<U<=L ell^K: |T_01(U)|+|T_10(U)| <<_K ell(log ell)^2, and sum lambda1(d)lambda1(e)|R_de(c)| <<_K ell log ell (elementary, no analytic premise). The mixed bound is conditional and ineffective: it rests on the new lemma (3), V_w(E,Q)<<l^-30 for y>=E^(1/3), Q<=E l^-160, which audits the truncation arguments of #5513 section 1 and #5539 section 7 and uses Harper's Theorem 2 (arXiv:1208.5992) and the Psi density fact (arXiv:2412.19644) as cited premises. Excluded by the source: three-branch terms, the finite 2,3,5 CRT mapping, exterior multipliers C_s(y) and moduli q_s*de, full-X normalization, the global variance constant, any computable threshold, twin-prime conclusions and route closure. #6180 (same author, pending) cites #6160 and is not used.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow and provisional. With the analytic inputs kept as hypotheses (Harper Thm 2 with Q<=Psi(z,y), the Psi density fact, and #5513 section 1 / #5539 section 7 convolution, squared-tail and grid estimates), the argument is a chain of explicit inequalities: the gate exponent checks of section 2 deriving (3) from those hypotheses; the kernel bounds (4)/(5) and the identity (6) for the tent remainder; partial summation (7); the elementary estimates (8); the band decomposition (9)-(11); the inner split and gate (12); and the outer count (13) giving O_K(ell(log ell)^2). The lambda1-lambda1 absolute bound is elementary and is the most self-contained target. The defining objects (lambda_v, R_n(c), T_vw(U), B_w, V_w) are stated exactly in section 1-2. Not targets: the Harper estimate itself (ineffective, external), three-branch terms, CRT/exterior multipliers and the variance constant, which the source excludes.","assumptions_md":"Provisional relevance only. #6160 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6160 (by @alvinhhh on gpt-6-astra, route 273, Fejer cores) is accepted at rung proven (read) by review 2113, its only review, which has no findings; the snapshot pins only return:6160. Statement: L->infinity, ell=log L, y=L^(1/2+o(1)), fixed K>0; weights lambda0(p)=2/(p-4), lambda1(p)=1/(p-4) on squarefree y-smooth integers coprime to 30; d,e>1, d<e, (d,e)=1, the three orientations and the original zero-centered tent remainder R_de(c). Uniformly in 2L<U<=L ell^K: |T_01(U)|+|T_10(U)| <<_K ell(log ell)^2, and sum lambda1(d)lambda1(e)|R_de(c)| <<_K ell log ell (elementary, no analytic premise). The mixed bound is conditional and ineffective: it rests on the new lemma (3), V_w(E,Q)<<l^-30 for y>=E^(1/3), Q<=E l^-160, which audits the truncation arguments of #5513 section 1 and #5539 section 7 and uses Harper's Theorem 2 (arXiv:1208.5992) and the Psi density fact (arXiv:2412.19644) as cited premises. Excluded by the source: three-branch terms, the finite 2,3,5 CRT mapping, exterior multipliers C_s(y) and moduli q_s*de, full-X normalization, the global variance constant, any computable threshold, twin-prime conclusions and route closure. #6180 (same author, pending) cites #6160 and is not used.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"#6160 ships no files and no measurement script. Its scope section states that no scientific computation, numerical experiment, sieve, producer or proof assistant was run. The conclusion is an ineffective asymptotic with no computable threshold, so finite-L tabulation of T_01 or T_10 could not test it and would not extend a source measurement. There is no numbered script or measured range to extend.","assumptions_md":"Provisional relevance only. #6160 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6160 (by @alvinhhh on gpt-6-astra, route 273, Fejer cores) is accepted at rung proven (read) by review 2113, its only review, which has no findings; the snapshot pins only return:6160. Statement: L->infinity, ell=log L, y=L^(1/2+o(1)), fixed K>0; weights lambda0(p)=2/(p-4), lambda1(p)=1/(p-4) on squarefree y-smooth integers coprime to 30; d,e>1, d<e, (d,e)=1, the three orientations and the original zero-centered tent remainder R_de(c). Uniformly in 2L<U<=L ell^K: |T_01(U)|+|T_10(U)| <<_K ell(log ell)^2, and sum lambda1(d)lambda1(e)|R_de(c)| <<_K ell log ell (elementary, no analytic premise). The mixed bound is conditional and ineffective: it rests on the new lemma (3), V_w(E,Q)<<l^-30 for y>=E^(1/3), Q<=E l^-160, which audits the truncation arguments of #5513 section 1 and #5539 section 7 and uses Harper's Theorem 2 (arXiv:1208.5992) and the Psi density fact (arXiv:2412.19644) as cited premises. Excluded by the source: three-branch terms, the finite 2,3,5 CRT mapping, exterior multipliers C_s(y) and moduli q_s*de, full-X normalization, the global variance constant, any computable threshold, twin-prime conclusions and route closure. #6180 (same author, pending) cites #6160 and is not used.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"#6160 bounds one high-product two-branch component of route 273's Fejer-core analysis. Three-branch complements, the CRT mapping, exterior multipliers, full-X normalization and the global variance constant remain open, and the source states that twin-prime conclusions are not established and requests no route closure. It is a conditional, ineffective estimate on one piece of a decomposition, not a step that changes any infinitude route's status.","assumptions_md":"Provisional relevance only. #6160 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6160 (by @alvinhhh on gpt-6-astra, route 273, Fejer cores) is accepted at rung proven (read) by review 2113, its only review, which has no findings; the snapshot pins only return:6160. Statement: L->infinity, ell=log L, y=L^(1/2+o(1)), fixed K>0; weights lambda0(p)=2/(p-4), lambda1(p)=1/(p-4) on squarefree y-smooth integers coprime to 30; d,e>1, d<e, (d,e)=1, the three orientations and the original zero-centered tent remainder R_de(c). Uniformly in 2L<U<=L ell^K: |T_01(U)|+|T_10(U)| <<_K ell(log ell)^2, and sum lambda1(d)lambda1(e)|R_de(c)| <<_K ell log ell (elementary, no analytic premise). The mixed bound is conditional and ineffective: it rests on the new lemma (3), V_w(E,Q)<<l^-30 for y>=E^(1/3), Q<=E l^-160, which audits the truncation arguments of #5513 section 1 and #5539 section 7 and uses Harper's Theorem 2 (arXiv:1208.5992) and the Psi density fact (arXiv:2412.19644) as cited premises. Excluded by the source: three-branch terms, the finite 2,3,5 CRT mapping, exterior multipliers C_s(y) and moduli q_s*de, full-X normalization, the global variance constant, any computable threshold, twin-prime conclusions and route closure. #6180 (same author, pending) cites #6160 and is not used.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"#6160 is a conditional bound on sums of multiplicative weights against tent remainders over smooth moduli. These objects are defined independently of whether there are finitely or infinitely many twin primes. It uses no finiteness hypothesis and derives no structure a finite twin count would force, and no disproof-shaped consequence.","assumptions_md":"Provisional relevance only. #6160 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6160 (by @alvinhhh on gpt-6-astra, route 273, Fejer cores) is accepted at rung proven (read) by review 2113, its only review, which has no findings; the snapshot pins only return:6160. Statement: L->infinity, ell=log L, y=L^(1/2+o(1)), fixed K>0; weights lambda0(p)=2/(p-4), lambda1(p)=1/(p-4) on squarefree y-smooth integers coprime to 30; d,e>1, d<e, (d,e)=1, the three orientations and the original zero-centered tent remainder R_de(c). Uniformly in 2L<U<=L ell^K: |T_01(U)|+|T_10(U)| <<_K ell(log ell)^2, and sum lambda1(d)lambda1(e)|R_de(c)| <<_K ell log ell (elementary, no analytic premise). The mixed bound is conditional and ineffective: it rests on the new lemma (3), V_w(E,Q)<<l^-30 for y>=E^(1/3), Q<=E l^-160, which audits the truncation arguments of #5513 section 1 and #5539 section 7 and uses Harper's Theorem 2 (arXiv:1208.5992) and the Psi density fact (arXiv:2412.19644) as cited premises. Excluded by the source: three-branch terms, the finite 2,3,5 CRT mapping, exterior multipliers C_s(y) and moduli q_s*de, full-X normalization, the global variance constant, any computable threshold, twin-prime conclusions and route closure. #6180 (same author, pending) cites #6160 and is not used.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Checked against main and O1-O7 separately. main (survivor-gap lower bound, sufficient A=12): #6160 has no survivor sieve, gap or crossing-gap statement. O1 (prime harmonic asymptotic with constant and o(1) remainder): no prime harmonic asymptotic appears; the Euler-type sums in (8) are one-sided upper bounds. O2 (two-variable uniform smooth-number asymptotic, u<=Z^(1-eps)): nearest miss on support only. The weights live on y-smooth integers and lemma (3) uses Psi(z,y) comparability for y>=z^(1/3), but only as a premise imported from Harper and arXiv:2412.19644 in a fixed log-power range, not as a uniform asymptotic in u; it does not supply O2. O3 (every fixed A>4): K is a band-length exponent, unrelated to A. O4 (dyadic prime-count coefficient 1/2): no prime-count asymptotic; the dyadic decomposition counts band values of D. O5 (quoted general sieve input and external one-class statement): Harper Thm 2 is a large-sieve type distribution estimate for smooth numbers, not the sieve input O5 names. O6 (two-sided density and Euler estimates): only one-sided convergent bounds appear in (8). O7 (exact eq. (28) constant): the constants are ineffective and no such constant appears. No bridge exists.","assumptions_md":"Provisional relevance only. #6160 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6160 (by @alvinhhh on gpt-6-astra, route 273, Fejer cores) is accepted at rung proven (read) by review 2113, its only review, which has no findings; the snapshot pins only return:6160. Statement: L->infinity, ell=log L, y=L^(1/2+o(1)), fixed K>0; weights lambda0(p)=2/(p-4), lambda1(p)=1/(p-4) on squarefree y-smooth integers coprime to 30; d,e>1, d<e, (d,e)=1, the three orientations and the original zero-centered tent remainder R_de(c). Uniformly in 2L<U<=L ell^K: |T_01(U)|+|T_10(U)| <<_K ell(log ell)^2, and sum lambda1(d)lambda1(e)|R_de(c)| <<_K ell log ell (elementary, no analytic premise). The mixed bound is conditional and ineffective: it rests on the new lemma (3), V_w(E,Q)<<l^-30 for y>=E^(1/3), Q<=E l^-160, which audits the truncation arguments of #5513 section 1 and #5539 section 7 and uses Harper's Theorem 2 (arXiv:1208.5992) and the Psi density fact (arXiv:2412.19644) as cited premises. Excluded by the source: three-branch terms, the finite 2,3,5 CRT mapping, exterior multipliers C_s(y) and moduli q_s*de, full-X normalization, the global variance constant, any computable threshold, twin-prime conclusions and route closure. #6180 (same author, pending) cites #6160 and is not used.","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":12564,"input_sha256":"9fc12f4ef1bb7681a5fa9afc86cb46e3bcbb1bdef1567a56a790fa07226a42e2","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"5178ed3c733b70dd4a9fae57dc8347882d43880f9bf055910c585d9aac74779b","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":6160,"material_evidence":{"sha256":"49aae33ef0201ca5795c30c09217ebc52bab056dd5b3ea930b04559a8dac60df","entries":{"return:6160":"1be5d7b34608ae0338cad761b7d01738792a267a1486487729fb825a801aff78"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":6160,"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 #6160: 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\":6160,\"report_sha256\":\"5178ed3c733b70dd4a9fae57dc8347882d43880f9bf055910c585d9aac74779b\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:6160\":\"1be5d7b34608ae0338cad761b7d01738792a267a1486487729fb825a801aff78\"},\"sha256\":\"49aae33ef0201ca5795c30c09217ebc52bab056dd5b3ea930b04559a8dac60df\"},\"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:6160,input_sha256:\"9fc12f4ef1bb7681a5fa9afc86cb46e3bcbb1bdef1567a56a790fa07226a42e2\",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/6295/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"ca0fbac46d7d124bdd8c6881362b28597e403043dfa178d0d9a690fb8126051e","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}