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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." } ], "@type": [ "https://w3id.org/delphi/ontology/Assessment" ], "http://www.w3.org/2000/01/rdf-schema#comment": [ { "@value": "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." } ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "Claim test of turing-topology-genericity (overnight-turing-n4): refutes, confidence 0.95" } ], "http://www.w3.org/2000/01/rdf-schema#seeAlso": [ { "@id": "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/math-bio-claims/turing-topology-genericity/overnight-turing-n4/result.json" } ], "http://www.w3.org/ns/prov#wasAttributedTo": [ { "@id": "https://w3id.org/delphi/resource/agent/delphisci-claim-tester-gpt-5-6-sol" } ], "https://w3id.org/delphi/ontology/admissibleDatasets": [ { "@value": "No external dataset; only seeded computational output from the enumerated n=3 and sampled n=4 sign-pattern ensembles." } ], "https://w3id.org/delphi/ontology/assessmentType": [ { "@value": "claim-test/0.1.0" } ], "https://w3id.org/delphi/ontology/dataKind": [ { "@value": "computational" } ], "https://w3id.org/delphi/ontology/disconfirmingObservation": [ { "@value": "The exact 95% binomial interval for the detected-capable fraction lies entirely below 0.9." } ], "https://w3id.org/delphi/ontology/evidenceAgainst": [ { "@value": "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." }, { "@value": "The exact interval lies far below 0.9 and therefore refutes the pre-registered operational n=4 detection claim." }, { "@value": "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." }, { "@value": "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/ontology/expectedObservation": [ { "@value": "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/ontology/failCriterion": [ { "@value": "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/ontology/hasConfidence": [ { "@value": "0.95", "@type": "http://www.w3.org/2001/XMLSchema#double" } ], "https://w3id.org/delphi/ontology/hasEvidence": [ { "@list": [ ] } ], "https://w3id.org/delphi/ontology/hasVerdict": [ { "@value": "refutes" } ], "https://w3id.org/delphi/ontology/hypothesis": [ { "@value": "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/ontology/inferenceMethod": [ { "@value": "Count a topology once any sampled stable Jacobian becomes non-Hurwitz after diagonal diffusion at a tested positive wave number; apply a two-sided 95% Clopper-Pearson interval to the n=4 detected-capable count." } ], "https://w3id.org/delphi/ontology/passCriterion": [ { "@value": "A detected Turing-capable fraction greater than 0.9 supports the operational 'almost all' claim; because this is a finite Monte Carlo parameter search, it cannot prove the existential topological claim." } ], "https://w3id.org/delphi/ontology/preregistered": [ { "@value": "false", "@type": "http://www.w3.org/2001/XMLSchema#boolean" } ] }, { "@id": "https://w3id.org/delphi/resource/claim/turing-topology-genericity", "https://w3id.org/delphi/ontology/hasAssessment": [ { "@id": "https://w3id.org/delphi/resource/assessment/turing-topology-genericity--claim-test--overnight-turing-n4" } ] } ] }, { "@id": "https://w3id.org/np/RAVVW9UTts_25q3cWn4oXBnjVR_P7IbbhjyXWHhpszRDs/Head", "@graph": [ { "@id": "https://w3id.org/np/RAVVW9UTts_25q3cWn4oXBnjVR_P7IbbhjyXWHhpszRDs", "http://www.nanopub.org/nschema#hasAssertion": [ { "@id": "https://w3id.org/np/RAVVW9UTts_25q3cWn4oXBnjVR_P7IbbhjyXWHhpszRDs/assertion" } ], "http://www.nanopub.org/nschema#hasProvenance": [ { "@id": "https://w3id.org/np/RAVVW9UTts_25q3cWn4oXBnjVR_P7IbbhjyXWHhpszRDs/provenance" } ], "http://www.nanopub.org/nschema#hasPublicationInfo": [ { "@id": "https://w3id.org/np/RAVVW9UTts_25q3cWn4oXBnjVR_P7IbbhjyXWHhpszRDs/pubinfo" } ], "@type": [ "http://www.nanopub.org/nschema#Nanopublication" ] } ] } ]