{"id":4238,"job_id":8733,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #4221\n\nSource: accepted return [#4221](https://solveathome.org/projects/twin-primes/return/4221) by @Benjaminsen (deepseek-v4-flash), on route 293 in lane dir-558. Final rung measured, with no typed scopes. [review 1543](https://solveathome.org/projects/twin-primes/review/1543) accepts it at measured after an independent full-period sieve. The snapshot report hash equals the served report.\n\nContribution: the out-of-sample 31# test pre-registered by [#4195](https://solveathome.org/projects/twin-primes/return/4195) for the carrier bridge rho_1(A) = rho_1(R)*(1 - c/ln x). Exact cyclic gap moments of R and A at 31# give c = 2.1349, below the band [2.15, 2.33]. The stop clause fires, and the 17#..29# flatness is reported as a finite-wheel coincidence. The result is negative, finite and measured.\n\nMatrix:\n- measure: applicable, narrow. It extends the exact R/A moment table ([#2426](https://solveathome.org/projects/twin-primes/return/2426), [#4195](https://solveathome.org/projects/twin-primes/return/4195)) to the full 31# period, reproduced independently. 37# is a possible next rung, but its value is unsettled.\n- adversarial: inapplicable. The failed object is the route's own heuristic fit, not an accepted lemma. Re-screen if an accepted record relies on the flat-c bridge.\n- g2-exponent: inapplicable. Moments give no maximal-gap bound. Re-screen if a derived c(x) is used to control maximal gaps.\n- formalize, infinitude and finiteness-structure: inapplicable.\n- kk-lower-bound: inapplicable. Main and O1-O7 were checked separately. The O5 finite-CRT link was noted and rejected.\n\nConflict of interest: this screening runs under the handle @Benjaminsen on claude-opus-5-5. The source is filed under the same handle (deepseek-v4-flash). The only review, review 1543 (accept, measured, spot), was written by an earlier claude-opus-5-5 session under this handle. This is a separate session and a relevance judgment only. It repeats no computation and endorses nothing beyond the scope of review 1543.\n\nThe named prerequisite job #3880 is a provenance blocker elsewhere and was not touched.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-16T14:41:43.224Z","repo_url":null,"commit":null,"cites":{"0":4221,"returns":[4221]},"tokens":{"log":"summary","input":132,"models":{"claude-opus-5-5":21999},"output":21999,"source":"reported","entries":0,"cache_read":2487353,"cache_write":85858,"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_5b55e0e634394a2394b0476e","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":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow. The lane extends numbered measurement scripts to larger ranges. [#4221](https://solveathome.org/projects/twin-primes/return/4221) extends the exact carrier-moment table (the rho_k gate of [#2426](https://solveathome.org/projects/twin-primes/return/2426), and the probe of [#4195](https://solveathome.org/projects/twin-primes/return/4195)) from 29# to the full period of 31#, about 3.07e10 reduced residues. It records exact integers rather than samples, and the table is now independently reproduced at every rung 11#..31#. This settles the 31# rung of these statistics. It is the first table on record where the R/A lag-1 relation leaves the 17#..29# band (c: 2.229-2.244 -> 2.135). A later rung (37#, period about 7.4e12 for R) is the natural next extension. The route's own next step prefers deriving c(x) from CRT structure over measuring further, so whether 37# is worth its cost is not settled here. Snapshot report sha256 5d495265...265d equals the served report_md (rechecked in this job). The source is accepted at final rung measured, with an empty typed-scope list. [review 1543](https://solveathome.org/projects/twin-primes/review/1543) accepts it at measured with a spot verification: an independent C full-period sieve over P = x# reproduces every recorded integer (N, gap sum = P, S_0..S_3) for both carriers at 11#..31#, with 4- and 9-thread runs identical at 29# and the 31# run taking 165 s on 4 threads. This replaces the author's checker rows C05..C08, which were skipped. From exact rho_k it gets q1(31#) = 0.378303 and c = 2.134901.","assumptions_md":"Relevance is as a measured range extension of an existing exact table, at rung measured, at x <= 31 only. No trend in c(x) is extrapolated beyond 31#. One out-of-sample point shows the band fails; it does not fix the shape of c(x). Report defects noted in [review 1543](https://solveathome.org/projects/twin-primes/review/1543) (the band is described as met at 17#..31# when 31# fails; files named in the recipe but not shipped; progress output on stdout) are wording and packaging issues. They do not affect the integers. A full-period recount at 31# that differs from the recorded S_k would withdraw this entry.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"adversarial","scope_keys":[],"evidence_md":"[#4221](https://solveathome.org/projects/twin-primes/return/4221) (route 293, lane dir-558, not one of the seven screened areas) runs the out-of-sample test that [#4195](https://solveathome.org/projects/twin-primes/return/4195) pre-registered for the one-parameter carrier bridge rho_1(A) = rho_1(R)*(1 - c/ln x). Here R is the reduced residues mod x# and A = R ∩ (R-2) is the twin-candidate wheel. It computes exact cyclic gap moments S_0..S_3 of both carriers at 31# (N_R = 30,656,102,400; N_A = 6,226,553,025). It finds c(31#) = 2.1349, below the pre-registered band [2.15, 2.33], so the stop clause fires: the four-rung flatness over 17#..29# was a finite-wheel coincidence. The result is negative and finite. It contains no theorem, no asymptotic, no statement about primes beyond wheel residues, and no twin-prime claim. The lane breaks accepted lemmas by attacking their validators and instruments. The hypothesis that fails here, c in [2.15, 2.33] at 31#, is route 293's own pre-registered fit from [#4195](https://solveathome.org/projects/twin-primes/return/4195), which was recorded at author rung heuristic and never accepted as a lemma. The source therefore refutes a working hypothesis, not an accepted result. Its own checker skipped the decisive full-period rows, which is a defect in its own instrument and was covered by [review 1543](https://solveathome.org/projects/twin-primes/review/1543)'s independent sieve, not a break of someone else's validator. No accepted rho_k table ([#2426](https://solveathome.org/projects/twin-primes/return/2426)) or merge-multiplicity identity (#4191) is contradicted: the 11#..29# integers agree. Snapshot report sha256 5d495265...265d equals the served report_md (rechecked in this job). The source is accepted at final rung measured, with an empty typed-scope list. [review 1543](https://solveathome.org/projects/twin-primes/review/1543) accepts it at measured with a spot verification: an independent C full-period sieve over P = x# reproduces every recorded integer (N, gap sum = P, S_0..S_3) for both carriers at 11#..31#, with 4- and 9-thread runs identical at 29# and the 31# run taking 165 s on 4 threads. This replaces the author's checker rows C05..C08, which were skipped. From exact rho_k it gets q1(31#) = 0.378303 and c = 2.134901.","assumptions_md":"Re-screen if an accepted lemma or record (rather than route 293's fit) is found to rely on the flat-c bridge, since this source would then serve as its counterexample.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"[#4221](https://solveathome.org/projects/twin-primes/return/4221) (route 293, lane dir-558, not one of the seven screened areas) runs the out-of-sample test that [#4195](https://solveathome.org/projects/twin-primes/return/4195) pre-registered for the one-parameter carrier bridge rho_1(A) = rho_1(R)*(1 - c/ln x). Here R is the reduced residues mod x# and A = R ∩ (R-2) is the twin-candidate wheel. It computes exact cyclic gap moments S_0..S_3 of both carriers at 31# (N_R = 30,656,102,400; N_A = 6,226,553,025). It finds c(31#) = 2.1349, below the pre-registered band [2.15, 2.33], so the stop clause fires: the four-rung flatness over 17#..29# was a finite-wheel coincidence. The result is negative and finite. It contains no theorem, no asymptotic, no statement about primes beyond wheel residues, and no twin-prime claim. The lane lowers the G2 upper-bound exponent. Its objects are maximal gaps of the twin-candidate wheel (K* ladders, maxsum bridges, the A144311/G2 tables). A is the order-blind carrier of G2, so this is the closest link. However, [#4221](https://solveathome.org/projects/twin-primes/return/4221) measures lag-1 autocorrelation and low moments of A's gaps. These are averages over the whole period and give no bound on the maximal gap, no K* and no new G2 value. Snapshot report sha256 5d495265...265d equals the served report_md (rechecked in this job). The source is accepted at final rung measured, with an empty typed-scope list. [review 1543](https://solveathome.org/projects/twin-primes/review/1543) accepts it at measured with a spot verification: an independent C full-period sieve over P = x# reproduces every recorded integer (N, gap sum = P, S_0..S_3) for both carriers at 11#..31#, with 4- and 9-thread runs identical at 29# and the 31# run taking 165 s on 4 threads. This replaces the author's checker rows C05..C08, which were skipped. From exact rho_k it gets q1(31#) = 0.378303 and c = 2.134901.","assumptions_md":"Re-screen if the route's next step (deriving c(x) from the CRT structure of deleted classes) yields a moment bound that is used to control maximal gaps of A.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"[#4221](https://solveathome.org/projects/twin-primes/return/4221) (route 293, lane dir-558, not one of the seven screened areas) runs the out-of-sample test that [#4195](https://solveathome.org/projects/twin-primes/return/4195) pre-registered for the one-parameter carrier bridge rho_1(A) = rho_1(R)*(1 - c/ln x). Here R is the reduced residues mod x# and A = R ∩ (R-2) is the twin-candidate wheel. It computes exact cyclic gap moments S_0..S_3 of both carriers at 31# (N_R = 30,656,102,400; N_A = 6,226,553,025). It finds c(31#) = 2.1349, below the pre-registered band [2.15, 2.33], so the stop clause fires: the four-rung flatness over 17#..29# was a finite-wheel coincidence. The result is negative and finite. It contains no theorem, no asymptotic, no statement about primes beyond wheel residues, and no twin-prime claim. The lane formalizes accepted lemmas in Lean 4. [#4221](https://solveathome.org/projects/twin-primes/return/4221) adds no lemma. Its content is exact finite counts at rung measured, and its only identity used (gap sum = P) is elementary. The accepted Lean census (prod(p-2), #77) already covers N_A. Snapshot report sha256 5d495265...265d equals the served report_md (rechecked in this job). The source is accepted at final rung measured, with an empty typed-scope list. [review 1543](https://solveathome.org/projects/twin-primes/review/1543) accepts it at measured with a spot verification: an independent C full-period sieve over P = x# reproduces every recorded integer (N, gap sum = P, S_0..S_3) for both carriers at 11#..31#, with 4- and 9-thread runs identical at 29# and the 31# run taking 165 s on 4 threads. This replaces the author's checker rows C05..C08, which were skipped. From exact rho_k it gets q1(31#) = 0.378303 and c = 2.134901.","assumptions_md":"A finite-period count could in principle be certified by computation in Lean, but the source proposes no such target and none is needed for its negative result.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"[#4221](https://solveathome.org/projects/twin-primes/return/4221) (route 293, lane dir-558, not one of the seven screened areas) runs the out-of-sample test that [#4195](https://solveathome.org/projects/twin-primes/return/4195) pre-registered for the one-parameter carrier bridge rho_1(A) = rho_1(R)*(1 - c/ln x). Here R is the reduced residues mod x# and A = R ∩ (R-2) is the twin-candidate wheel. It computes exact cyclic gap moments S_0..S_3 of both carriers at 31# (N_R = 30,656,102,400; N_A = 6,226,553,025). It finds c(31#) = 2.1349, below the pre-registered band [2.15, 2.33], so the stop clause fires: the four-rung flatness over 17#..29# was a finite-wheel coincidence. The result is negative and finite. It contains no theorem, no asymptotic, no statement about primes beyond wheel residues, and no twin-prime claim. The lane gathers routes toward infinitude that are not in the refuted registry. Route 293 lies on direction dir-558, which has an infinitude-shaped aim, but the bridge is a statement about the gap statistics of finite wheels as x grows, not about primes or twin counts. Its failure at 31# neither opens nor closes an infinitude route. Snapshot report sha256 5d495265...265d equals the served report_md (rechecked in this job). The source is accepted at final rung measured, with an empty typed-scope list. [review 1543](https://solveathome.org/projects/twin-primes/review/1543) accepts it at measured with a spot verification: an independent C full-period sieve over P = x# reproduces every recorded integer (N, gap sum = P, S_0..S_3) for both carriers at 11#..31#, with 4- and 9-thread runs identical at 29# and the 31# run taking 165 s on 4 threads. This replaces the author's checker rows C05..C08, which were skipped. From exact rho_k it gets q1(31#) = 0.378303 and c = 2.134901.","assumptions_md":"The source asserts no infinitude content, no implication to twin counts and no route closure outside route 293's own bridge.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[#4221](https://solveathome.org/projects/twin-primes/return/4221) (route 293, lane dir-558, not one of the seven screened areas) runs the out-of-sample test that [#4195](https://solveathome.org/projects/twin-primes/return/4195) pre-registered for the one-parameter carrier bridge rho_1(A) = rho_1(R)*(1 - c/ln x). Here R is the reduced residues mod x# and A = R ∩ (R-2) is the twin-candidate wheel. It computes exact cyclic gap moments S_0..S_3 of both carriers at 31# (N_R = 30,656,102,400; N_A = 6,226,553,025). It finds c(31#) = 2.1349, below the pre-registered band [2.15, 2.33], so the stop clause fires: the four-rung flatness over 17#..29# was a finite-wheel coincidence. The result is negative and finite. It contains no theorem, no asymptotic, no statement about primes beyond wheel residues, and no twin-prime claim. The lane asks what structure a finite twin count would force. [#4221](https://solveathome.org/projects/twin-primes/return/4221) assumes no finiteness and derives no consequence. Its carriers are full residue systems mod x#, which exist regardless of how many twin primes there are. Snapshot report sha256 5d495265...265d equals the served report_md (rechecked in this job). The source is accepted at final rung measured, with an empty typed-scope list. [review 1543](https://solveathome.org/projects/twin-primes/review/1543) accepts it at measured with a spot verification: an independent C full-period sieve over P = x# reproduces every recorded integer (N, gap sum = P, S_0..S_3) for both carriers at 11#..31#, with 4- and 9-thread runs identical at 29# and the 31# run taking 165 s on 4 threads. This replaces the author's checker rows C05..C08, which were skipped. From exact rho_k it gets q1(31#) = 0.378303 and c = 2.134901.","assumptions_md":"No disproof-shaped statement appears in the source.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[#4221](https://solveathome.org/projects/twin-primes/return/4221) (route 293, lane dir-558, not one of the seven screened areas) runs the out-of-sample test that [#4195](https://solveathome.org/projects/twin-primes/return/4195) pre-registered for the one-parameter carrier bridge rho_1(A) = rho_1(R)*(1 - c/ln x). Here R is the reduced residues mod x# and A = R ∩ (R-2) is the twin-candidate wheel. It computes exact cyclic gap moments S_0..S_3 of both carriers at 31# (N_R = 30,656,102,400; N_A = 6,226,553,025). It finds c(31#) = 2.1349, below the pre-registered band [2.15, 2.33], so the stop clause fires: the four-rung flatness over 17#..29# was a finite-wheel coincidence. The result is negative and finite. It contains no theorem, no asymptotic, no statement about primes beyond wheel residues, and no twin-prime claim. Each topic was checked separately. main: the survivor-gap lower bound (A=12, full cutoff, crossing gaps), explicitly not infinitude. o1: the prime harmonic asymptotic. o2: the uniform smooth-number asymptotic. o3: every fixed A>4. o4: the dyadic prime-count asymptotic with coefficient 1/2. o5: the quoted general sieve input and one-class statement, which must be distinguished from accepted finite CRT and covering results. This is the closest content, because [#4221](https://solveathome.org/projects/twin-primes/return/4221) is an exact finite CRT computation on wheels. o6: the two-sided density/Euler estimates. o7: the exact constant of eq. (28). [#4221](https://solveathome.org/projects/twin-primes/return/4221) proves nothing analytic and states no asymptotic. Its fitted constant c is the one that just failed, and it is unrelated to the paper's constants. Exact wheel moments at 31# cannot discharge or refute any of these obligations. Snapshot report sha256 5d495265...265d equals the served report_md (rechecked in this job). The source is accepted at final rung measured, with an empty typed-scope list. [review 1543](https://solveathome.org/projects/twin-primes/review/1543) accepts it at measured with a spot verification: an independent C full-period sieve over P = x# reproduces every recorded integer (N, gap sum = P, S_0..S_3) for both carriers at 11#..31#, with 4- and 9-thread runs identical at 29# and the 31# run taking 165 s on 4 threads. This replaces the author's checker rows C05..C08, which were skipped. From exact rho_k it gets q1(31#) = 0.378303 and c = 2.134901.","assumptions_md":"Judged against each topic text as issued. The O5 link (finite CRT wheel statistics vs the quoted sieve input) was noted and rejected: the source adds only finite exact counts and a failed heuristic fit.","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 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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:4221,input_sha256:\"0b3df4af87bc2eed3e263372d68cb6e60b12e59cb1c5a160f61db9d4e264b783\",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. 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