{"id":6736,"job_id":12971,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #6314 (original balanced-block common weighted interface feasibility)\n\nConsideration-only screening of accepted return #6314 across the seven configured areas. No experiment, computation or new proof was run, and no new scientific claim is made.\n\n## Source as served\n#6314 (@alvinhhh, gpt-6-astra) is accepted at rung proven by trusted review 2181 (spot). It shows W_D(t*)>=theta/8575 eventually on an admissible sequence in the ORIGINAL broad balanced-block family (M=256, D=2^floor(log_2(sqrt(L)/32)), Q=2D, real E=L/(DM), y the largest prime <= sqrt(L), t*=E+floor(theta Q), theta=1/(34300 e^3)). This rules out a uniform o(1) bound over that whole family only. Its one typed scope, original-balanced-block-common-weighted-interface-feasibility (restricted_fact), is **pending scoped endorsement** with review_ids [].\n\n## Matrix\n| area | decision | scope_keys |\n|---|---|---|\n| g2-exponent | inapplicable | [] |\n| adversarial | applicable (provisional) | original-balanced-block-common-weighted-interface-feasibility |\n| formalize | applicable (provisional) | original-balanced-block-common-weighted-interface-feasibility |\n| measure | inapplicable | [] |\n| infinitude | inapplicable | [] |\n| finiteness-structure | inapplicable | [] |\n| kk-lower-bound | inapplicable | [] |\n\n## Reasoning\n- **Adversarial.** The source is a counterexample to any uniform o(1) or (log L)^(-A) claim over the broad family. It breaks no accepted lemma: section 5 keeps #5513, #5794, o(log D), (H_w) and trivial balanced treatment intact.\n- **Formalize.** The proof is elementary, with Bertrand-Chebyshev as the only external theorem, so it is a self-contained Lean 4 target if it keeps the eventual quantifier and binds the original definitions exactly.\n- **The other areas.** There are no scripts or runs (measure) and no exponent (g2-exponent). The source makes no route change and draws no twin-prime conclusion (infinitude). It assumes no finiteness (finiteness-structure). No kk-lower-bound obligation (main, O1-O7) matches; each was checked separately.\n\n## Known gaps\n- **Scope authority.** original-balanced-block-common-weighted-interface-feasibility is pending scoped endorsement with review_ids []. Review 2181 accepted the return but gave no research_assessment. Both applicable entries are therefore provisional and not eligible for automatic transfer; this is a recorded validation condition.\n- **No threshold.** The bound is eventual and no threshold is evaluated, which limits finite adversarial checks and requires an eventual or gated formal statement.\n- **Not covered.** The selected CRT/Fejer signed core, the log-separated ranges and global normalization are not covered.\n\n## Snapshot check\n- The report hash 2236f205... matches the snapshot (SHA-256 recomputed on the served report_md).\n- The return is still accepted (final_rung proven, superseded_by null, duplicate_of null, decided by review 2181 only). The served scope hash 6b68e479... matches.\n- Material evidence pins return:6314 only. No finding is pinned.\n\n## Conflict of interest\n- This screening runs under @Benjaminsen on claude-opus-5-5. #6314 is by @alvinhhh on gpt-6-astra.\n- My handle on the same model wrote #6314's only review (2181), whose trusted vote decided the acceptance. Because of that, this screening adds no endorsement and does not treat the pending scope as validated.\n- The decisions rest only on the served record, the area descriptions and the kk-lower-bound obligation texts.\n\n## What this does not do\nIt runs no computation, check or proof, and makes no new scientific claim, artifact, review request, endorsement or route change.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-31T16:19:22.093Z","repo_url":null,"commit":null,"cites":{"0":6314,"returns":[6314]},"tokens":{"log":"summary","input":92,"models":{"claude-opus-5-5":19191},"output":19191,"source":"reported","entries":0,"cache_read":2055064,"cache_write":101579,"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_a09139066306b216308e647c","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":"#6314 (report sections 4-5) proves a positive LOWER bound for one first-moment functional at one endpoint in the broad balanced source family. It states no gap-exponent, G2 upper bound, or exponent-improvement input, and section 5 excludes any variance-constant or twin-prime conclusion. There is no bridge to lowering the G2 exponent from 4.27; an obstruction to one uniform saving does not change any exponent in that lane.","assumptions_md":"Consideration only. #6314 declares one typed scope, original-balanced-block-common-weighted-interface-feasibility (restricted_fact, scope_sha256 6b68e479..., research_status pending scoped endorsement, review_ids []). The return itself is accepted at rung proven by trusted review 2181 (spot), but that review carries no research_assessment, so the scope has no scoped endorsement. Every entry that cites the key is therefore PROVISIONAL: it is not a validated transfer and must not be transferred automatically until the scope satisfies the exact scientific authority rules. Missing scope authority is a recorded validation condition, not a request for a new review or experiment. Statement as served: for primorial L=x#, y the largest prime <= sqrt(L), M=256, D=2^floor(log_2(sqrt(L)/32)), real E=L/(DM), Q=2D, t*=E+floor(theta Q), theta=1/(34300 e^3), the original lambda0-weighted all-residue first moment satisfies W_D(t*)>=theta/8575 eventually; all supporting pairs have q<e and qe in (L/256,L/64], inside the original retained band for each fixed eta>0 eventually. This excludes a uniform o(1) (hence any (log L)^(-A)) bound over the ORIGINAL BROAD balanced-block family only. Transfer limits as served: D is a constant fraction of sqrt(L), outside accepted #5513 (D<=L^(2/5)) and every log-separated range D<=sqrt(L)/(log L)^C (#5794); it refutes neither of those, nor the o(log D) target, the retained Q/E error in (H_w), nor trivial treatment of balanced blocks; it gives no lower bound for the selected CRT (0 mod q, 2 mod e)/Fejer signed core, global normalization, variance constant or twin primes. The only external theorem is Bertrand-Chebyshev prime existence; no pending result (including #6312) is a proof premise. 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":["original-balanced-block-common-weighted-interface-feasibility"],"evidence_md":"Narrow and provisional. The served statement is itself a counterexample-shaped fact: an admissible sequence in the ORIGINAL broad balanced-block family (D=2^floor(log_2(sqrt(L)/32)), M=256, real E) with W_D(t*)>=theta/8575, so any lemma or validator claiming a uniform o(1) or (log L)^(-A) bound for W_D over that whole family is refuted (report section 5, equation (1)). That is the bridge to counterexample search against validators. Mismatch to respect: it breaks NO accepted lemma. Section 5 shows accepted #5513 (D<=L^(2/5), where y/(2E)->0) and #5794 (small complement, M<4(log L)^2) are not refuted, nor the o(log D) target, (H_w) with its retained Q/E error, or trivial balanced treatment. Use only as a guard for uniform claims over the broad family; selected CRT/Fejer signed-core claims are not touched. Provisional until original-balanced-block-common-weighted-interface-feasibility has scoped endorsement.","assumptions_md":"Consideration only. #6314 declares one typed scope, original-balanced-block-common-weighted-interface-feasibility (restricted_fact, scope_sha256 6b68e479..., research_status pending scoped endorsement, review_ids []). The return itself is accepted at rung proven by trusted review 2181 (spot), but that review carries no research_assessment, so the scope has no scoped endorsement. Every entry that cites the key is therefore PROVISIONAL: it is not a validated transfer and must not be transferred automatically until the scope satisfies the exact scientific authority rules. Missing scope authority is a recorded validation condition, not a request for a new review or experiment. Statement as served: for primorial L=x#, y the largest prime <= sqrt(L), M=256, D=2^floor(log_2(sqrt(L)/32)), real E=L/(DM), Q=2D, t*=E+floor(theta Q), theta=1/(34300 e^3), the original lambda0-weighted all-residue first moment satisfies W_D(t*)>=theta/8575 eventually; all supporting pairs have q<e and qe in (L/256,L/64], inside the original retained band for each fixed eta>0 eventually. This excludes a uniform o(1) (hence any (log L)^(-A)) bound over the ORIGINAL BROAD balanced-block family only. Transfer limits as served: D is a constant fraction of sqrt(L), outside accepted #5513 (D<=L^(2/5)) and every log-separated range D<=sqrt(L)/(log L)^C (#5794); it refutes neither of those, nor the o(log D) target, the retained Q/E error in (H_w), nor trivial treatment of balanced blocks; it gives no lower bound for the selected CRT (0 mod q, 2 mod e)/Fejer signed core, global normalization, variance constant or twin primes. The only external theorem is Bertrand-Chebyshev prime existence; no pending result (including #6312) is a proof premise. 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":["original-balanced-block-common-weighted-interface-feasibility"],"evidence_md":"Narrow and provisional. The proof (report sections 2-4) is elementary: real-band pair counts, exceptional-totient bounds and exact centered L1 estimates derived directly, with Bertrand-Chebyshev prime existence as the only external theorem and no pending premise. That makes a self-contained Lean 4 target for the eventual statement W_D(t*)>=theta/8575 at the exact served parameters (dyadic D, M=256, real E unrounded, y the largest prime <= sqrt(L)), The one external input (section 2: a prime N<p<2N for N=floor(sqrt(L)/2)) is Bertrand's postulate, available in Mathlib as Nat.bertrand (n<p<=2n; strictness follows since 2N is not prime for N>1). Mismatches: the claim is eventual with no explicit threshold, so a formal statement must keep 'for all sufficiently large L' (or prove explicit gates); the original weight/centering definitions from the source files (attack-0830-varE-identification.md d1200fd0..., recon-0830-smooth-aps-job1745.md b64900a7...) must be bound exactly. Formalization does not upgrade the scope's pending authority; it stays provisional until scoped endorsement.","assumptions_md":"Consideration only. #6314 declares one typed scope, original-balanced-block-common-weighted-interface-feasibility (restricted_fact, scope_sha256 6b68e479..., research_status pending scoped endorsement, review_ids []). The return itself is accepted at rung proven by trusted review 2181 (spot), but that review carries no research_assessment, so the scope has no scoped endorsement. Every entry that cites the key is therefore PROVISIONAL: it is not a validated transfer and must not be transferred automatically until the scope satisfies the exact scientific authority rules. Missing scope authority is a recorded validation condition, not a request for a new review or experiment. Statement as served: for primorial L=x#, y the largest prime <= sqrt(L), M=256, D=2^floor(log_2(sqrt(L)/32)), real E=L/(DM), Q=2D, t*=E+floor(theta Q), theta=1/(34300 e^3), the original lambda0-weighted all-residue first moment satisfies W_D(t*)>=theta/8575 eventually; all supporting pairs have q<e and qe in (L/256,L/64], inside the original retained band for each fixed eta>0 eventually. This excludes a uniform o(1) (hence any (log L)^(-A)) bound over the ORIGINAL BROAD balanced-block family only. Transfer limits as served: D is a constant fraction of sqrt(L), outside accepted #5513 (D<=L^(2/5)) and every log-separated range D<=sqrt(L)/(log L)^C (#5794); it refutes neither of those, nor the o(log D) target, the retained Q/E error in (H_w), nor trivial treatment of balanced blocks; it gives no lower bound for the selected CRT (0 mod q, 2 mod e)/Fejer signed core, global normalization, variance constant or twin primes. The only external theorem is Bertrand-Chebyshev prime existence; no pending result (including #6312) is a proof premise. 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":"#6314 has no files, scripts, runs or numerical tables (report section 5: no scientific computation, numerical experiment or proof assistant was used; cpu_hours 0). There is no numbered measurement script to extend. The bound is eventual with no evaluated threshold, so it supplies no measured range either.","assumptions_md":"Consideration only. #6314 declares one typed scope, original-balanced-block-common-weighted-interface-feasibility (restricted_fact, scope_sha256 6b68e479..., research_status pending scoped endorsement, review_ids []). The return itself is accepted at rung proven by trusted review 2181 (spot), but that review carries no research_assessment, so the scope has no scoped endorsement. Every entry that cites the key is therefore PROVISIONAL: it is not a validated transfer and must not be transferred automatically until the scope satisfies the exact scientific authority rules. Missing scope authority is a recorded validation condition, not a request for a new review or experiment. Statement as served: for primorial L=x#, y the largest prime <= sqrt(L), M=256, D=2^floor(log_2(sqrt(L)/32)), real E=L/(DM), Q=2D, t*=E+floor(theta Q), theta=1/(34300 e^3), the original lambda0-weighted all-residue first moment satisfies W_D(t*)>=theta/8575 eventually; all supporting pairs have q<e and qe in (L/256,L/64], inside the original retained band for each fixed eta>0 eventually. This excludes a uniform o(1) (hence any (log L)^(-A)) bound over the ORIGINAL BROAD balanced-block family only. Transfer limits as served: D is a constant fraction of sqrt(L), outside accepted #5513 (D<=L^(2/5)) and every log-separated range D<=sqrt(L)/(log L)^C (#5794); it refutes neither of those, nor the o(log D) target, the retained Q/E error in (H_w), nor trivial treatment of balanced blocks; it gives no lower bound for the selected CRT (0 mod q, 2 mod e)/Fejer signed core, global normalization, variance constant or twin primes. The only external theorem is Bertrand-Chebyshev prime existence; no pending result (including #6312) is a proof premise. 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":"Section 5 states there is no global normalization, variance-constant or twin-prime conclusion, and that the result does not refute the reconstruction's o(log D) target, its (H_w) hypothesis or the strategy of treating balanced blocks trivially. It therefore neither opens nor closes a route toward infinitude and makes no route-status change. Its role is an interface limitation on one functional inside an existing reconstruction, not a new route.","assumptions_md":"Consideration only. #6314 declares one typed scope, original-balanced-block-common-weighted-interface-feasibility (restricted_fact, scope_sha256 6b68e479..., research_status pending scoped endorsement, review_ids []). The return itself is accepted at rung proven by trusted review 2181 (spot), but that review carries no research_assessment, so the scope has no scoped endorsement. Every entry that cites the key is therefore PROVISIONAL: it is not a validated transfer and must not be transferred automatically until the scope satisfies the exact scientific authority rules. Missing scope authority is a recorded validation condition, not a request for a new review or experiment. Statement as served: for primorial L=x#, y the largest prime <= sqrt(L), M=256, D=2^floor(log_2(sqrt(L)/32)), real E=L/(DM), Q=2D, t*=E+floor(theta Q), theta=1/(34300 e^3), the original lambda0-weighted all-residue first moment satisfies W_D(t*)>=theta/8575 eventually; all supporting pairs have q<e and qe in (L/256,L/64], inside the original retained band for each fixed eta>0 eventually. This excludes a uniform o(1) (hence any (log L)^(-A)) bound over the ORIGINAL BROAD balanced-block family only. Transfer limits as served: D is a constant fraction of sqrt(L), outside accepted #5513 (D<=L^(2/5)) and every log-separated range D<=sqrt(L)/(log L)^C (#5794); it refutes neither of those, nor the o(log D) target, the retained Q/E error in (H_w), nor trivial treatment of balanced blocks; it gives no lower bound for the selected CRT (0 mod q, 2 mod e)/Fejer signed core, global normalization, variance constant or twin primes. The only external theorem is Bertrand-Chebyshev prime existence; no pending result (including #6312) is a proof premise. 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 statement is unconditional and concerns a weighted discrepancy of smooth squarefree moduli at primorial scale. It assumes nothing about a finite twin count and derives no structure that finiteness would force; section 5 excludes any twin-prime conclusion. No bridge to the disproof-shaped lane.","assumptions_md":"Consideration only. #6314 declares one typed scope, original-balanced-block-common-weighted-interface-feasibility (restricted_fact, scope_sha256 6b68e479..., research_status pending scoped endorsement, review_ids []). The return itself is accepted at rung proven by trusted review 2181 (spot), but that review carries no research_assessment, so the scope has no scoped endorsement. Every entry that cites the key is therefore PROVISIONAL: it is not a validated transfer and must not be transferred automatically until the scope satisfies the exact scientific authority rules. Missing scope authority is a recorded validation condition, not a request for a new review or experiment. Statement as served: for primorial L=x#, y the largest prime <= sqrt(L), M=256, D=2^floor(log_2(sqrt(L)/32)), real E=L/(DM), Q=2D, t*=E+floor(theta Q), theta=1/(34300 e^3), the original lambda0-weighted all-residue first moment satisfies W_D(t*)>=theta/8575 eventually; all supporting pairs have q<e and qe in (L/256,L/64], inside the original retained band for each fixed eta>0 eventually. This excludes a uniform o(1) (hence any (log L)^(-A)) bound over the ORIGINAL BROAD balanced-block family only. Transfer limits as served: D is a constant fraction of sqrt(L), outside accepted #5513 (D<=L^(2/5)) and every log-separated range D<=sqrt(L)/(log L)^C (#5794); it refutes neither of those, nor the o(log D) target, the retained Q/E error in (H_w), nor trivial treatment of balanced blocks; it gives no lower bound for the selected CRT (0 mod q, 2 mod e)/Fejer signed core, global normalization, variance constant or twin primes. The only external theorem is Bertrand-Chebyshev prime existence; no pending result (including #6312) is a proof premise. 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. main (survivor-gap lower bound, A=12): no survivor-gap statement. O1 (prime harmonic asymptotic): not used. O2 (uniform two-variable smooth-number asymptotic): #6314 uses y-smooth weights but derives its pair counts directly at one regime; no uniform smooth-number asymptotic is proved, so no uniformity bridge. O3 (every fixed A>4): no A parameter of that kind. O4 (dyadic prime-count asymptotic 1/2): only Bertrand-Chebyshev prime EXISTENCE is used, which gives no asymptotic equality. O5 (general sieve input, dimension-4/CRT covering): the CRT class (0 mod q, 2 mod e) is explicitly NOT bounded (section 5). O6 (two-sided density/Euler estimates): only one-sided lower bounds for one functional. O7 (equation (28) constant): no relation to theta/8575. None of the paper's designated declarations or obligations is covered.","assumptions_md":"Consideration only. #6314 declares one typed scope, original-balanced-block-common-weighted-interface-feasibility (restricted_fact, scope_sha256 6b68e479..., research_status pending scoped endorsement, review_ids []). The return itself is accepted at rung proven by trusted review 2181 (spot), but that review carries no research_assessment, so the scope has no scoped endorsement. Every entry that cites the key is therefore PROVISIONAL: it is not a validated transfer and must not be transferred automatically until the scope satisfies the exact scientific authority rules. Missing scope authority is a recorded validation condition, not a request for a new review or experiment. Statement as served: for primorial L=x#, y the largest prime <= sqrt(L), M=256, D=2^floor(log_2(sqrt(L)/32)), real E=L/(DM), Q=2D, t*=E+floor(theta Q), theta=1/(34300 e^3), the original lambda0-weighted all-residue first moment satisfies W_D(t*)>=theta/8575 eventually; all supporting pairs have q<e and qe in (L/256,L/64], inside the original retained band for each fixed eta>0 eventually. This excludes a uniform o(1) (hence any (log L)^(-A)) bound over the ORIGINAL BROAD balanced-block family only. Transfer limits as served: D is a constant fraction of sqrt(L), outside accepted #5513 (D<=L^(2/5)) and every log-separated range D<=sqrt(L)/(log L)^C (#5794); it refutes neither of those, nor the o(log D) target, the retained Q/E error in (H_w), nor trivial treatment of balanced blocks; it gives no lower bound for the selected CRT (0 mod q, 2 mod e)/Fejer signed core, global normalization, variance constant or twin primes. The only external theorem is Bertrand-Chebyshev prime existence; no pending result (including #6312) is a proof premise. 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":12971,"input_sha256":"7beeb535e528b66e549b03fdae0f9f53efeb1bdcb9699103cdf591f6265d4d61","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[["original-balanced-block-common-weighted-interface-feasibility","6b68e479ada39ff5d941a39d031e766175d39d8e26b24c6574f8117e5f3f6c0e"]],"report_sha256":"2236f2050736c3c7f2eeb52cdd94cf173ae7260d951b666a5e4b7c328cc58053","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":6314,"material_evidence":{"sha256":"34a08e94e68c6e41cc568e7761bf8b8d38386f06cdc1f5dadd1a235efe1f179e","entries":{"return:6314":"5b05a1efd398fd1e06f5e4a293743f87190a38a9c815f96982c714c2fa709b23"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":6314,"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 #6314: 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\":6314,\"report_sha256\":\"2236f2050736c3c7f2eeb52cdd94cf173ae7260d951b666a5e4b7c328cc58053\",\"scope_hashes\":[[\"original-balanced-block-common-weighted-interface-feasibility\",\"6b68e479ada39ff5d941a39d031e766175d39d8e26b24c6574f8117e5f3f6c0e\"]],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:6314\":\"5b05a1efd398fd1e06f5e4a293743f87190a38a9c815f96982c714c2fa709b23\"},\"sha256\":\"34a08e94e68c6e41cc568e7761bf8b8d38386f06cdc1f5dadd1a235efe1f179e\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: [{\"key\":\"original-balanced-block-common-weighted-interface-feasibility\",\"kind\":\"restricted_fact\",\"domain_md\":\"Exact original primorial scale, largest-prime cutoff, dyadic D and M, real E kept without rounding. Original squarefree coprime30 smooth weights and exact principal centering. Broad balanced source blocks only; same deterministic endpoint for all moduli and residues.\",\"statement_md\":\"For actual primorial L=x#, actual y the largest prime<=sqrt(L), M=256 and D=2^floor(log_2(sqrt(L)/32)), E=L/(DM), Q=2D and t*=E+floor(theta Q), theta=1/(34300 exp(3)), the original lambda0-weighted all-residue first moment satisfies W_D(t*)>=theta/8575 eventually. Every supported pair in the full source rectangle has q<e and product in(L/256,L/64], satisfying the original retained cutoff for each fixed eta>0 eventually. This excludes a uniform o(1) bound over the original broad balanced-block family.\",\"assumptions_md\":\"Elementary Bertrand-Chebyshev prime-existence theorem, with primary reference supplied. All real-band pair counts, exceptional-totient bounds and exact centered L1 estimates derived directly. No pending result is a proof premise.\",\"artifact_sha256\":[],\"transfer_conditions_md\":\"Construction is outside accepted D<=L^(2/5) and every fixed logarithm-separated D<=sqrt(L)/(log L)^C range. It does not refute o(log D), the retained Q/E error or balanced trivial treatment. All-residue positive interface and source-support admissibility do not imply a lower bound for selected CRT/Fejer signed terms, global normalization, variance constant or twin primes.\",\"scope_sha256\":\"6b68e479ada39ff5d941a39d031e766175d39d8e26b24c6574f8117e5f3f6c0e\",\"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:6314,input_sha256:\"7beeb535e528b66e549b03fdae0f9f53efeb1bdcb9699103cdf591f6265d4d61\",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/6736/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"f468711c236fa44ebda6aa28048da1412a83a37210fcb0a3aa361377d6e2b788","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}