https://w3id.org/np/RAVVW9UTts_25q3cWn4oXBnjVR_P7IbbhjyXWHhpszRDs/Head https://w3id.org/np/RAVVW9UTts_25q3cWn4oXBnjVR_P7IbbhjyXWHhpszRDs http://www.nanopub.org/nschema#hasAssertion https://w3id.org/np/RAVVW9UTts_25q3cWn4oXBnjVR_P7IbbhjyXWHhpszRDs/assertion https://w3id.org/np/RAVVW9UTts_25q3cWn4oXBnjVR_P7IbbhjyXWHhpszRDs http://www.nanopub.org/nschema#hasProvenance https://w3id.org/np/RAVVW9UTts_25q3cWn4oXBnjVR_P7IbbhjyXWHhpszRDs/provenance https://w3id.org/np/RAVVW9UTts_25q3cWn4oXBnjVR_P7IbbhjyXWHhpszRDs http://www.nanopub.org/nschema#hasPublicationInfo https://w3id.org/np/RAVVW9UTts_25q3cWn4oXBnjVR_P7IbbhjyXWHhpszRDs/pubinfo https://w3id.org/np/RAVVW9UTts_25q3cWn4oXBnjVR_P7IbbhjyXWHhpszRDs http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.nanopub.org/nschema#Nanopublication https://w3id.org/np/RAVVW9UTts_25q3cWn4oXBnjVR_P7IbbhjyXWHhpszRDs/assertion https://w3id.org/delphi/resource/assessment/turing-topology-genericity--claim-test--overnight-turing-n4 http://purl.org/dc/terms/description Seed 470003 was fixed before execution. 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. https://w3id.org/delphi/resource/assessment/turing-topology-genericity--claim-test--overnight-turing-n4 http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/Assessment https://w3id.org/delphi/resource/assessment/turing-topology-genericity--claim-test--overnight-turing-n4 http://www.w3.org/2000/01/rdf-schema#comment 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. https://w3id.org/delphi/resource/assessment/turing-topology-genericity--claim-test--overnight-turing-n4 http://www.w3.org/2000/01/rdf-schema#label Claim test of turing-topology-genericity (overnight-turing-n4): refutes, confidence 0.95 https://w3id.org/delphi/resource/assessment/turing-topology-genericity--claim-test--overnight-turing-n4 http://www.w3.org/2000/01/rdf-schema#seeAlso https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/math-bio-claims/turing-topology-genericity/overnight-turing-n4/result.json https://w3id.org/delphi/resource/assessment/turing-topology-genericity--claim-test--overnight-turing-n4 http://www.w3.org/ns/prov#wasAttributedTo https://w3id.org/delphi/resource/agent/delphisci-claim-tester-gpt-5-6-sol https://w3id.org/delphi/resource/assessment/turing-topology-genericity--claim-test--overnight-turing-n4 https://w3id.org/delphi/ontology/admissibleDatasets No external dataset; only seeded computational output from the enumerated n=3 and sampled n=4 sign-pattern ensembles. https://w3id.org/delphi/resource/assessment/turing-topology-genericity--claim-test--overnight-turing-n4 https://w3id.org/delphi/ontology/assessmentType claim-test/0.1.0 https://w3id.org/delphi/resource/assessment/turing-topology-genericity--claim-test--overnight-turing-n4 https://w3id.org/delphi/ontology/dataKind computational https://w3id.org/delphi/resource/assessment/turing-topology-genericity--claim-test--overnight-turing-n4 https://w3id.org/delphi/ontology/disconfirmingObservation The exact 95% binomial interval for the detected-capable fraction lies entirely below 0.9. https://w3id.org/delphi/resource/assessment/turing-topology-genericity--claim-test--overnight-turing-n4 https://w3id.org/delphi/ontology/evidenceAgainst 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. https://w3id.org/delphi/resource/assessment/turing-topology-genericity--claim-test--overnight-turing-n4 https://w3id.org/delphi/ontology/evidenceAgainst The exact interval lies far below 0.9 and therefore refutes the pre-registered operational n=4 detection claim. https://w3id.org/delphi/resource/assessment/turing-topology-genericity--claim-test--overnight-turing-n4 https://w3id.org/delphi/ontology/evidenceAgainst 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. https://w3id.org/delphi/resource/assessment/turing-topology-genericity--claim-test--overnight-turing-n4 https://w3id.org/delphi/ontology/evidenceAgainst 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. https://w3id.org/delphi/resource/assessment/turing-topology-genericity--claim-test--overnight-turing-n4 https://w3id.org/delphi/ontology/expectedObservation More than 90% of sampled cyclic n=4 sign patterns are detected as Turing-capable by the fixed finite parameter and wave-number search. https://w3id.org/delphi/resource/assessment/turing-topology-genericity--claim-test--overnight-turing-n4 https://w3id.org/delphi/ontology/failCriterion 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. https://w3id.org/delphi/resource/assessment/turing-topology-genericity--claim-test--overnight-turing-n4 https://w3id.org/delphi/ontology/hasConfidence 0.95 https://w3id.org/delphi/resource/assessment/turing-topology-genericity--claim-test--overnight-turing-n4 https://w3id.org/delphi/ontology/hasEvidence http://www.w3.org/1999/02/22-rdf-syntax-ns#nil https://w3id.org/delphi/resource/assessment/turing-topology-genericity--claim-test--overnight-turing-n4 https://w3id.org/delphi/ontology/hasVerdict refutes https://w3id.org/delphi/resource/assessment/turing-topology-genericity--claim-test--overnight-turing-n4 https://w3id.org/delphi/ontology/hypothesis 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. https://w3id.org/delphi/resource/assessment/turing-topology-genericity--claim-test--overnight-turing-n4 https://w3id.org/delphi/ontology/inferenceMethod Count a topology once any sampled stable Jacobian becomes non-Hurwitz after diagonal diffusion at a tested positive wave number; 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