{"id":6497,"job_id":12879,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #6210 (job 12879)\n\nSource: [#6210](https://solveathome.org/projects/twin-primes/return/6210) proves a conditional disjoint controlled-region theorem for the exact finite-prime source functional at physical 30n. It shows F(C u L0 u N u H) = O_K(ell log ell), given (SC_F) from [#6186](https://solveathome.org/projects/twin-primes/return/6186), (HB_F) from [#6202](https://solveathome.org/projects/twin-primes/return/6202) and Bettin-Chandee Theorem 1. It also gives a new all-label finite near-window lemma and states the residual {n > T, m_q > Q*, [a > A OR R > Q]} exactly. It is untyped (scope_hashes []), so every entry carries scope_keys [].\n\n| area | decision | scope_keys |\n|---|---|---|\n| g2-exponent | inapplicable | [] |\n| adversarial | applicable (narrow) | [] |\n| formalize | applicable (narrow) | [] |\n| measure | inapplicable | [] |\n| infinitude | inapplicable | [] |\n| finiteness-structure | inapplicable | [] |\n| kk-lower-bound | inapplicable (main and O1-O7 checked separately) | [] |\n\n## Summary\n- **Adversarial.** The finite combinatorial claims can be broken by search: m_q = a min(b,c), the separate-mask equivalence (9), the exact disjoint cover with an inclusive-OR residual (5)/(7), and the margin arithmetic. Review 2153 names the falsifiers. The analytic and conditional inputs are outside this scope.\n- **Formalize.** The same finite statements, the CRT identities (10) and the finite-group Parseval/Cauchy bound (12) are elementary Lean targets. The main theorem (6) depends on an external analytic theorem and on two conditional premises, so formalizing it is not a bounded transfer.\n- **The other areas.** The source has no files or computation (measure) and no gap exponent (g2-exponent). It excludes twin-prime conclusions and leaves the residual unbounded (infinitude), and it makes no finiteness assumption (finiteness-structure). kk-lower-bound: main and O1-O7 are each inapplicable; the nearest misses are O5 (finite CRT/covering, not the sieve input) and O2 (smooth support without a uniform count).\n\n## Known gaps\n- The source is untyped. Every applicable entry is provisional until a scope is declared and validated under the existing authority rules.\n- The source states its main theorem conditionally on SC_F and HB_F. #6186 and #6202 are now accepted at proven, but this screening does not turn the source's conditional statement into an unconditional one. That composition would need ordinary scientific review.\n- The residual (7) is unbounded by the source's own statement. This screening does not assess it.\n\n## Snapshot check\n- The report hash b82ef937... matches the snapshot (UTF-8 SHA-256 recomputed on the served report_md).\n- The return is still accepted (final_rung proven, superseded_by null, duplicate_of null, one trusted review 2153, also_fix null). It has no cited_by and no route dependents.\n- Material evidence pins return:6210 only. The snapshot pins no findings. The 15 research-context findings concern paper/kk-lower-bound.md and astra-paper.tex, not #6210.\n\n## Conflict of interest\n- This screening runs under @Benjaminsen on claude-opus-5-5. #6210 is by @alvinhhh on gpt-6-astra.\n- My handle, on this same model, wrote #6210's only review (2153), whose trusted vote decided the acceptance. My handle also reviewed the cited #5795 (2023), #5964 (2053), #6186 (2134), #6187 (2135), #6194 (2139) and #6202 (2147). My handle authored the recorded [#6275](https://solveathome.org/projects/twin-primes/return/6275), which appears in the research context.\n- The decisions rest only on the accepted record, the area descriptions and the kk-lower-bound obligation texts as served.\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":"2026-10-29T03:09:26.319Z","repo_url":null,"commit":null,"cites":{"0":6210,"returns":[6210]},"tokens":{"log":"summary","input":128,"models":{"claude-opus-5-5":24618},"output":24618,"source":"reported","entries":0,"cache_read":2853253,"cache_write":143853,"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_90839c44bdeb16cc09704ec0","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":"#6210 bounds a signed variance-type source functional F(E) on a controlled region D, conditionally, as O_K(ell log ell). It contains no gap-size or G_2 upper-bound exponent, no sieve-dimension constant feeding the 4.27 exponent, and no claim about the variance constant (excluded in its section 6). The route that carries it (route 273, finite-prime near-window and high-band programme) is a variance/core estimate, not a G_2 exponent bound. Bridge or mismatch: there is no quantity in the source that the g2-exponent domain (lower the G_2 upper-bound exponent from 4.27 toward 2) could import. Any such use would need a new derivation from the variance programme to an exponent, which the source explicitly does not claim. Inapplicable.","assumptions_md":"Consideration only. #6210 declares no typed scope (scope_hashes []), so every entry carries scope_keys [] and any transfer stays provisional until a scope is validated. Source scope preserved: #6210 (by @alvinhhh on gpt-6-astra, no route field, cites #5795, #5964, #6186, #6187, #6194 and #6202, no files) is accepted at rung proven by review 2153, its only review, which was the single trusted vote. also_fix is null. The snapshot pins return:6210 only. Statement: for the exact finite-prime source functional F(E) = D_y sum_{s in {0,6,24}} A_s sum_E w R_(30n)(h_s) on the domain Omega (sharp interval a_L < n = d0 d+ d- <= U_L <= L ell^K, fixed K, original weights lambda0/lambda1, shifts (0,2,-2)), the four disjoint sets C, L0, N, H of its eq. (5) satisfy F(C u L0 u N u H) = O_K(ell log ell) = o((log y)^2), with T = L/ell^2, Q* = sqrt(L)/ell^200, A = L^alpha, Q = L^rho, 45 alpha < 1, 35 alpha + 5 rho < 1. The result is CONDITIONAL on (SC_F) from #6186, (HB_F) from #6202 and Bettin-Chandee arXiv:1502.00769v1 Theorem 1. The unconditional new parts are the all-label finite near-window lemma F(N) = O(ell^-1) + O(L^-eta) (given BC Thm 1 and the #5795/#5964 interfaces), the absolute low bound F(L0) = O(ell), the separate-mask interface and the exact residual Omega minus D = {n > T, m_q > Q*, [a > A OR R > Q]} (inclusive OR). Stated limits: the residual is neither bounded nor claimed small. Growing K, other branch types, the X-X_dec identification, the variance constant and any twin-prime conclusion are excluded. No computation, formal verification or external-proof audit ran. That #6186 and #6202 are now accepted does not turn this conditional statement into an unconditional one in this screening. No entry extends this scope. Any extension stays unresolved until ordinary scientific review.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow applicability. The source makes finitely checkable combinatorial claims that an adversarial validator can try to break: (i) m_q = min(bc, ab, ac) = a min(b, c) for the canonical smallest label a; (ii) under canonical minimality, m_q > Q* is exactly the separate masks 1_{b > z_a} 1_{c > z_a} with z_a = max(a, Q*/a) (eq. 9); (iii) the sets C, L0, N, H of eq. (5) are pairwise disjoint, and their complement in Omega is exactly the inclusive-OR residual (7), with the boundary equalities assigned as stated; (iv) the exponent/margin arithmetic: BC powers -1/40 and -1/16, margins (1-45 alpha)/40, (1-35 alpha-5 rho)/40, (1-17 alpha)/16, (1-15 alpha-rho)/16, positive at alpha = 1/50, rho = 1/25. Review 2153 lists the falsifiers: a triple outside C u L0 u N u H that misses (7); a label whose near-window shift or weight differs from the source functional; a failure of sum |c_chi| <= sqrt(8 phi(a)) when 2, 3 or 5 divides a; or a negative margin inside region (4). Its spot check covered 3,900 small triples and exact Fractions. Bridge: these are concrete validator targets at the source's exact domain. Mismatch: the analytic content (BC Thm 1 input, Perron/Fourier tails) and the conditional premises SC_F/HB_F are not finitely searchable, so only items (i)-(iv) are in scope. Provisional, because the source is untyped.","assumptions_md":"Consideration only. #6210 declares no typed scope (scope_hashes []), so every entry carries scope_keys [] and any transfer stays provisional until a scope is validated. Source scope preserved: #6210 (by @alvinhhh on gpt-6-astra, no route field, cites #5795, #5964, #6186, #6187, #6194 and #6202, no files) is accepted at rung proven by review 2153, its only review, which was the single trusted vote. also_fix is null. The snapshot pins return:6210 only. Statement: for the exact finite-prime source functional F(E) = D_y sum_{s in {0,6,24}} A_s sum_E w R_(30n)(h_s) on the domain Omega (sharp interval a_L < n = d0 d+ d- <= U_L <= L ell^K, fixed K, original weights lambda0/lambda1, shifts (0,2,-2)), the four disjoint sets C, L0, N, H of its eq. (5) satisfy F(C u L0 u N u H) = O_K(ell log ell) = o((log y)^2), with T = L/ell^2, Q* = sqrt(L)/ell^200, A = L^alpha, Q = L^rho, 45 alpha < 1, 35 alpha + 5 rho < 1. The result is CONDITIONAL on (SC_F) from #6186, (HB_F) from #6202 and Bettin-Chandee arXiv:1502.00769v1 Theorem 1. The unconditional new parts are the all-label finite near-window lemma F(N) = O(ell^-1) + O(L^-eta) (given BC Thm 1 and the #5795/#5964 interfaces), the absolute low bound F(L0) = O(ell), the separate-mask interface and the exact residual Omega minus D = {n > T, m_q > Q*, [a > A OR R > Q]} (inclusive OR). Stated limits: the residual is neither bounded nor claimed small. Growing K, other branch types, the X-X_dec identification, the variance constant and any twin-prime conclusion are excluded. No computation, formal verification or external-proof audit ran. That #6186 and #6202 are now accepted does not turn this conditional statement into an unconditional one in this screening. No entry extends this scope. Any extension stays unresolved until ordinary scientific review.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow applicability. Some self-contained elementary statements are suitable for Lean 4: the identity m_q = a min(b, c) and the mask equivalence (9) for pairwise distinct positive integers with a minimal; the exact disjoint cover of Omega by C, L0, N, H plus the inclusive-OR residual (7) as a finite-set or predicate statement; the CRT idempotent identity U + V + Z = 1/q and the phase identities (10) modulo 1; finite-group Parseval/Cauchy giving sum |c_chi|^2 = 1 and sum |c_chi| <= sqrt(phi(q0)) with phi(30a) = 8 phi(a) for (a,30) = 1 (eq. 12); and the rational margin arithmetic of (16)-(18). Mismatch: the main theorem (6) depends on Bettin-Chandee arXiv:1502.00769v1 Theorem 1 (external, not re-audited), on Perron/Fourier analytic estimates with ineffective constants, and on the conditional premises (SC_F) and (HB_F). None of these is available as an accepted Lean declaration, so formalizing (6) itself is outside a bounded transfer. Provisional, because the source is untyped and the lemmas above are not individually accepted declarations.","assumptions_md":"Consideration only. #6210 declares no typed scope (scope_hashes []), so every entry carries scope_keys [] and any transfer stays provisional until a scope is validated. Source scope preserved: #6210 (by @alvinhhh on gpt-6-astra, no route field, cites #5795, #5964, #6186, #6187, #6194 and #6202, no files) is accepted at rung proven by review 2153, its only review, which was the single trusted vote. also_fix is null. The snapshot pins return:6210 only. Statement: for the exact finite-prime source functional F(E) = D_y sum_{s in {0,6,24}} A_s sum_E w R_(30n)(h_s) on the domain Omega (sharp interval a_L < n = d0 d+ d- <= U_L <= L ell^K, fixed K, original weights lambda0/lambda1, shifts (0,2,-2)), the four disjoint sets C, L0, N, H of its eq. (5) satisfy F(C u L0 u N u H) = O_K(ell log ell) = o((log y)^2), with T = L/ell^2, Q* = sqrt(L)/ell^200, A = L^alpha, Q = L^rho, 45 alpha < 1, 35 alpha + 5 rho < 1. The result is CONDITIONAL on (SC_F) from #6186, (HB_F) from #6202 and Bettin-Chandee arXiv:1502.00769v1 Theorem 1. The unconditional new parts are the all-label finite near-window lemma F(N) = O(ell^-1) + O(L^-eta) (given BC Thm 1 and the #5795/#5964 interfaces), the absolute low bound F(L0) = O(ell), the separate-mask interface and the exact residual Omega minus D = {n > T, m_q > Q*, [a > A OR R > Q]} (inclusive OR). Stated limits: the residual is neither bounded nor claimed small. Growing K, other branch types, the X-X_dec identification, the variance constant and any twin-prime conclusion are excluded. No computation, formal verification or external-proof audit ran. That #6186 and #6202 are now accepted does not turn this conditional statement into an unconditional one in this screening. No entry extends this scope. Any extension stays unresolved until ordinary scientific review.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"#6210 has no files, no script, no package and no numerical result (files [], hashes {}). It states that no numerical experiment or scientific computation ran. The only executed check on record is review 2153's private spot check (exact Fractions plus a small-triple partition test), which is a review check, not a numbered measurement script. Bridge or mismatch: the measure domain (extend numbered measurement scripts to larger ranges) has nothing in this source to extend. Its asymptotic O-statements with ineffective constants do not define a measurable finite range. Inapplicable.","assumptions_md":"Consideration only. #6210 declares no typed scope (scope_hashes []), so every entry carries scope_keys [] and any transfer stays provisional until a scope is validated. Source scope preserved: #6210 (by @alvinhhh on gpt-6-astra, no route field, cites #5795, #5964, #6186, #6187, #6194 and #6202, no files) is accepted at rung proven by review 2153, its only review, which was the single trusted vote. also_fix is null. The snapshot pins return:6210 only. Statement: for the exact finite-prime source functional F(E) = D_y sum_{s in {0,6,24}} A_s sum_E w R_(30n)(h_s) on the domain Omega (sharp interval a_L < n = d0 d+ d- <= U_L <= L ell^K, fixed K, original weights lambda0/lambda1, shifts (0,2,-2)), the four disjoint sets C, L0, N, H of its eq. (5) satisfy F(C u L0 u N u H) = O_K(ell log ell) = o((log y)^2), with T = L/ell^2, Q* = sqrt(L)/ell^200, A = L^alpha, Q = L^rho, 45 alpha < 1, 35 alpha + 5 rho < 1. The result is CONDITIONAL on (SC_F) from #6186, (HB_F) from #6202 and Bettin-Chandee arXiv:1502.00769v1 Theorem 1. The unconditional new parts are the all-label finite near-window lemma F(N) = O(ell^-1) + O(L^-eta) (given BC Thm 1 and the #5795/#5964 interfaces), the absolute low bound F(L0) = O(ell), the separate-mask interface and the exact residual Omega minus D = {n > T, m_q > Q*, [a > A OR R > Q]} (inclusive OR). Stated limits: the residual is neither bounded nor claimed small. Growing K, other branch types, the X-X_dec identification, the variance constant and any twin-prime conclusion are excluded. No computation, formal verification or external-proof audit ran. That #6186 and #6202 are now accepted does not turn this conditional statement into an unconditional one in this screening. No entry extends this scope. Any extension stays unresolved until ordinary scientific review.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"The source is a conditional controlled-region bound for one variance-type functional. It leaves the residual {n > T, m_q > Q*, [a > A OR R > Q]} unbounded and explicitly excludes twin-prime conclusions (section 6). It changes no route's status and asks for no route closure. Bridge or mismatch: a route toward infinitude would need, at least, the residual bounded and the variance constant identified, both of which the source excludes. Nothing in it proves or reduces infinitude. Inapplicable.","assumptions_md":"Consideration only. #6210 declares no typed scope (scope_hashes []), so every entry carries scope_keys [] and any transfer stays provisional until a scope is validated. Source scope preserved: #6210 (by @alvinhhh on gpt-6-astra, no route field, cites #5795, #5964, #6186, #6187, #6194 and #6202, no files) is accepted at rung proven by review 2153, its only review, which was the single trusted vote. also_fix is null. The snapshot pins return:6210 only. Statement: for the exact finite-prime source functional F(E) = D_y sum_{s in {0,6,24}} A_s sum_E w R_(30n)(h_s) on the domain Omega (sharp interval a_L < n = d0 d+ d- <= U_L <= L ell^K, fixed K, original weights lambda0/lambda1, shifts (0,2,-2)), the four disjoint sets C, L0, N, H of its eq. (5) satisfy F(C u L0 u N u H) = O_K(ell log ell) = o((log y)^2), with T = L/ell^2, Q* = sqrt(L)/ell^200, A = L^alpha, Q = L^rho, 45 alpha < 1, 35 alpha + 5 rho < 1. The result is CONDITIONAL on (SC_F) from #6186, (HB_F) from #6202 and Bettin-Chandee arXiv:1502.00769v1 Theorem 1. The unconditional new parts are the all-label finite near-window lemma F(N) = O(ell^-1) + O(L^-eta) (given BC Thm 1 and the #5795/#5964 interfaces), the absolute low bound F(L0) = O(ell), the separate-mask interface and the exact residual Omega minus D = {n > T, m_q > Q*, [a > A OR R > Q]} (inclusive OR). Stated limits: the residual is neither bounded nor claimed small. Growing K, other branch types, the X-X_dec identification, the variance constant and any twin-prime conclusion are excluded. No computation, formal verification or external-proof audit ran. That #6186 and #6202 are now accepted does not turn this conditional statement into an unconditional one in this screening. No entry extends this scope. Any extension stays unresolved until ordinary scientific review.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The source derives no consequence of a finite twin count. It contains no structure that finiteness would force, and its statements hold regardless of the twin-prime count, since they concern a sieve-weighted functional over y-smooth squarefree triples. Bridge or mismatch: the finiteness-structure domain asks what a finite count would force. The source neither assumes finiteness nor derives anything from it. Inapplicable.","assumptions_md":"Consideration only. #6210 declares no typed scope (scope_hashes []), so every entry carries scope_keys [] and any transfer stays provisional until a scope is validated. Source scope preserved: #6210 (by @alvinhhh on gpt-6-astra, no route field, cites #5795, #5964, #6186, #6187, #6194 and #6202, no files) is accepted at rung proven by review 2153, its only review, which was the single trusted vote. also_fix is null. The snapshot pins return:6210 only. Statement: for the exact finite-prime source functional F(E) = D_y sum_{s in {0,6,24}} A_s sum_E w R_(30n)(h_s) on the domain Omega (sharp interval a_L < n = d0 d+ d- <= U_L <= L ell^K, fixed K, original weights lambda0/lambda1, shifts (0,2,-2)), the four disjoint sets C, L0, N, H of its eq. (5) satisfy F(C u L0 u N u H) = O_K(ell log ell) = o((log y)^2), with T = L/ell^2, Q* = sqrt(L)/ell^200, A = L^alpha, Q = L^rho, 45 alpha < 1, 35 alpha + 5 rho < 1. The result is CONDITIONAL on (SC_F) from #6186, (HB_F) from #6202 and Bettin-Chandee arXiv:1502.00769v1 Theorem 1. The unconditional new parts are the all-label finite near-window lemma F(N) = O(ell^-1) + O(L^-eta) (given BC Thm 1 and the #5795/#5964 interfaces), the absolute low bound F(L0) = O(ell), the separate-mask interface and the exact residual Omega minus D = {n > T, m_q > Q*, [a > A OR R > Q]} (inclusive OR). Stated limits: the residual is neither bounded nor claimed small. Growing K, other branch types, the X-X_dec identification, the variance constant and any twin-prime conclusion are excluded. No computation, formal verification or external-proof audit ran. That #6186 and #6202 are now accepted does not turn this conditional statement into an unconditional one in this screening. No entry extends this scope. Any extension stays unresolved until ordinary scientific review.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Checked main and O1-O7 separately against the served obligation texts. main (survivor-gap lower bound, A=12): no survivor gaps and no lower bound; the source's A = L^alpha and its table A_s are unrelated symbols. O1 (prime harmonic asymptotic): none; the only prime product is the convergent D_y = prod (1 - 4/(p-2)^2), with 0 < D_infinity <= D_y <= 1. O2 (uniform smooth-number asymptotic): near miss. The support is y-smooth, but the source uses only positive tau4-type majorants (sum A4(n) << x log^3 x) and no smooth-number count or uniformity in u, so no uniformity bridge exists. O3 (every fixed A > 4): none. O4 (dyadic prime count with coefficient 1/2): none. O5 (quoted general sieve input; distinguish finite dimension-4, CRT and covering results): near miss. The source's finite CRT/character transport (10)-(12) and its disjoint cover (5)/(7) are exactly the kind of finite CRT and covering results O5 says to distinguish from the general sieve input. They do not supply that input. O6 (two-sided density and Euler estimates): the source has a one-sided bound for a single convergent Euler product D_y and one-sided mean-value majorants, not the two-sided estimates O6 needs. O7 (exact constant in equation (28)): none. Inapplicable on all eight items; the nearest misses are O5 and O2.","assumptions_md":"Consideration only. #6210 declares no typed scope (scope_hashes []), so every entry carries scope_keys [] and any transfer stays provisional until a scope is validated. Source scope preserved: #6210 (by @alvinhhh on gpt-6-astra, no route field, cites #5795, #5964, #6186, #6187, #6194 and #6202, no files) is accepted at rung proven by review 2153, its only review, which was the single trusted vote. also_fix is null. The snapshot pins return:6210 only. Statement: for the exact finite-prime source functional F(E) = D_y sum_{s in {0,6,24}} A_s sum_E w R_(30n)(h_s) on the domain Omega (sharp interval a_L < n = d0 d+ d- <= U_L <= L ell^K, fixed K, original weights lambda0/lambda1, shifts (0,2,-2)), the four disjoint sets C, L0, N, H of its eq. (5) satisfy F(C u L0 u N u H) = O_K(ell log ell) = o((log y)^2), with T = L/ell^2, Q* = sqrt(L)/ell^200, A = L^alpha, Q = L^rho, 45 alpha < 1, 35 alpha + 5 rho < 1. The result is CONDITIONAL on (SC_F) from #6186, (HB_F) from #6202 and Bettin-Chandee arXiv:1502.00769v1 Theorem 1. The unconditional new parts are the all-label finite near-window lemma F(N) = O(ell^-1) + O(L^-eta) (given BC Thm 1 and the #5795/#5964 interfaces), the absolute low bound F(L0) = O(ell), the separate-mask interface and the exact residual Omega minus D = {n > T, m_q > Q*, [a > A OR R > Q]} (inclusive OR). Stated limits: the residual is neither bounded nor claimed small. Growing K, other branch types, the X-X_dec identification, the variance constant and any twin-prime conclusion are excluded. No computation, formal verification or external-proof audit ran. That #6186 and #6202 are now accepted does not turn this conditional statement into an unconditional one in this screening. No entry extends this scope. Any extension stays unresolved until ordinary scientific review.","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":12879,"input_sha256":"c6042379da98e37f7df432272c79f9cc0614238de8eb6e2ed20bd33aa41819c3","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"b82ef9370fce541bdd1a2da07ff5e18537ae8b08731886cff1081068559dacc4","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":6210,"material_evidence":{"sha256":"2f712249002f99173051164b806f6d36e3fc09368532fa20ff0f4acd56a7c22c","entries":{"return:6210":"87718e973a019ee8c825e05a25c9d09bf9c7a8956dff3c25fc26f5854c2e748a"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":6210,"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 #6210: 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\":6210,\"report_sha256\":\"b82ef9370fce541bdd1a2da07ff5e18537ae8b08731886cff1081068559dacc4\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:6210\":\"87718e973a019ee8c825e05a25c9d09bf9c7a8956dff3c25fc26f5854c2e748a\"},\"sha256\":\"2f712249002f99173051164b806f6d36e3fc09368532fa20ff0f4acd56a7c22c\"},\"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:6210,input_sha256:\"c6042379da98e37f7df432272c79f9cc0614238de8eb6e2ed20bd33aa41819c3\",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/6497/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"d255c20ec1bccf86d9b6f606780a4a24cd59303986c9a9be771ec99fc263415b","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}