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Because no n=3 census existed in the repository, all 3^9 sign patterns and all seven non-empty diffusion supports were first searched with 200 draws per pattern-support pair. Nonzero reaction magnitudes and positive diffusion coefficients were sampled log-uniformly on [0.01, 100], and 121 wave numbers were swept logarithmically on [0.001, 1000]. Then 2,000 distinct n=4 sign patterns were sampled uniformly conditional on a directed cycle, one non-empty support was sampled uniformly for each, and 100 parameter draws were tested. Strict cubic and quartic Routh-Hurwitz inequalities defined stability; capability required stable J and non-Hurwitz J-k^2D at some tested k > 0." } g_iri { prefix_id: 2 name_id: 4 } } } rows { prefix { value: "https://w3id.org/delphi/ontology/" } } rows { name { value: "Assessment" } } rows { quad { p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 10 name_id: 14 } } } rows { prefix { value: "http://www.w3.org/2000/01/rdf-schema#" } } rows { name { value: "comment" } } rows { quad { p_iri { prefix_id: 11 } o_literal { lex: "Measured: 0.196 detected-capable fraction (n = 2000, exact two-sided Clopper-Pearson 95% interval [0.1788079205547995, 0.21408794619692778]). Interpretation: This operationalizes topology capability as detection within fixed bounded rate, diffusion, and wave-number searches. It directly tests the stated Monte Carlo approach, but non-detection is not a proof that no parameters exist." } } } rows { name { value: "label" } } rows { quad { p_iri { } o_literal { lex: "Claim test of turing-topology-genericity (overnight-turing-n4): refutes, confidence 0.95" } } } rows { name { value: "seeAlso" } } rows { prefix { value: "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/math-bio-claims/turing-topology-genericity/overnight-turing-n4/" } } rows { name { value: "result.json" } } rows { quad { p_iri { } o_iri { prefix_id: 12 } } } rows { name { value: "wasAttributedTo" } } rows { prefix { value: "https://w3id.org/delphi/resource/agent/" } } rows { name { value: "delphisci-claim-tester-gpt-5-6-sol" } } rows { quad { p_iri { prefix_id: 5 } o_iri { prefix_id: 13 } } } rows { name { value: "admissibleDatasets" } } rows { quad { p_iri { prefix_id: 10 } o_literal { lex: "No external dataset; only seeded computational output from the enumerated n=3 and sampled n=4 sign-pattern ensembles." } } } rows { name { value: "assessmentType" } } rows { quad { p_iri { } o_literal { lex: "claim-test/0.1.0" } } } rows { name { value: "dataKind" } } rows { quad { p_iri { } o_literal { lex: "computational" } } } rows { name { value: "disconfirmingObservation" } } rows { quad { p_iri { } o_literal { lex: "The exact 95% binomial interval for the detected-capable fraction lies entirely below 0.9." } } } rows { name { value: "evidenceAgainst" } } rows { quad { p_iri { } o_literal { lex: "A finite random parameter search has false negatives for existential capability; consequently this result does not settle or rigorously refute the mathematical conjecture that parameters exist for almost all cyclic topologies." } } } rows { quad { o_literal { lex: "The exact interval lies far below 0.9 and therefore refutes the pre-registered operational n=4 detection claim." } } } rows { quad { o_literal { lex: "The n=3 baseline exhausts sign patterns and diffusion supports but not the continuous parameter domain, so it is not the interval-certified exact census proposed in the approach file." } } } rows { quad { o_literal { lex: "The sample can refute the threshold under this fixed procedure but cannot prove \'almost all\'; even a detected fraction above 0.9 would only support, not prove, the claim." } } } rows { name { value: "expectedObservation" } } rows { quad { p_iri { } o_literal { lex: "More than 90% of sampled cyclic n=4 sign patterns are detected as Turing-capable by the fixed finite parameter and wave-number search." } } } rows { name { value: "failCriterion" } } rows { quad { p_iri { } o_literal { lex: "A two-sided exact Clopper-Pearson 95% interval for the detected Turing-capable fraction lying entirely below 0.9 refutes the pre-registered n=4 operational claim." } } } rows { name { value: "hasConfidence" } } rows { datatype { value: "http://www.w3.org/2001/XMLSchema#double" } } rows { quad { p_iri { } o_literal { lex: "0.95" datatype: 1 } } } rows { name { value: "hasEvidence" } } rows { name { value: "nil" } } rows { quad { p_iri { } o_iri { prefix_id: 4 } } } rows { name { value: "hasVerdict" } } rows { quad { p_iri { prefix_id: 10 } o_literal { lex: "refutes" } } } rows { name { value: "hypothesis" } } rows { quad { p_iri { } o_literal { lex: "Among uniformly sampled four-species interaction sign patterns whose directed interaction graph contains at least one feedback cycle, more than 90% are detected as admitting a diffusion-driven linear instability for at least one of 100 sampled parameter realizations and one non-empty diffusion support." } } } rows { name { value: "inferenceMethod" } } rows { quad { p_iri { } o_literal { lex: "Count a topology once any sampled stable Jacobian becomes non-Hurwitz after diagonal diffusion at a tested positive wave number; 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