[ { "@id": "https://w3id.org/np/RADkB5eYxYtCga1Uz2FYOHhouFm-TcKZakfyInCLufbJ4/Head", "@graph": [ { "@id": "https://w3id.org/np/RADkB5eYxYtCga1Uz2FYOHhouFm-TcKZakfyInCLufbJ4", "http://www.nanopub.org/nschema#hasAssertion": [ { "@id": "https://w3id.org/np/RADkB5eYxYtCga1Uz2FYOHhouFm-TcKZakfyInCLufbJ4/assertion" } ], "http://www.nanopub.org/nschema#hasProvenance": [ { "@id": "https://w3id.org/np/RADkB5eYxYtCga1Uz2FYOHhouFm-TcKZakfyInCLufbJ4/provenance" } ], "http://www.nanopub.org/nschema#hasPublicationInfo": [ { "@id": "https://w3id.org/np/RADkB5eYxYtCga1Uz2FYOHhouFm-TcKZakfyInCLufbJ4/pubinfo" } ], "@type": [ "http://www.nanopub.org/nschema#Nanopublication" ] } ] }, { "@id": "https://w3id.org/np/RADkB5eYxYtCga1Uz2FYOHhouFm-TcKZakfyInCLufbJ4/provenance", "@graph": [ { "@id": "https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1", "@type": [ "http://www.w3.org/ns/prov#SoftwareAgent" ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "delphisci claim tester (claude-fable-5.1; cursor/claim-tests-wolfram-nks-e5f4)" } ], "http://www.w3.org/ns/prov#actedOnBehalfOf": [ { "@id": "https://orcid.org/0009-0007-4948-9192" } ], "https://w3id.org/delphi/ontology/usesModel": [ { "@id": "https://w3id.org/delphi/resource/model/claude-fable-5-1" } ] }, { "@id": "https://w3id.org/delphi/resource/model/claude-fable-5-1", "http://purl.org/dc/terms/identifier": [ { "@value": "claude-fable-5.1" } ], "@type": [ "https://w3id.org/delphi/ontology/LanguageModel" ] }, { "@id": "https://w3id.org/np/RADkB5eYxYtCga1Uz2FYOHhouFm-TcKZakfyInCLufbJ4/assertion", "http://www.w3.org/ns/prov#wasAttributedTo": [ { "@id": "https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1" } ], "http://www.w3.org/ns/prov#wasDerivedFrom": [ { "@id": "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch05-03/result.json" } ], "http://www.w3.org/ns/prov#wasGeneratedBy": [ { "@id": "https://w3id.org/np/RADkB5eYxYtCga1Uz2FYOHhouFm-TcKZakfyInCLufbJ4/test" } ] }, { "@id": "https://w3id.org/np/RADkB5eYxYtCga1Uz2FYOHhouFm-TcKZakfyInCLufbJ4/test", "@type": [ "http://www.w3.org/ns/prov#Activity" ], "http://www.w3.org/ns/prov#qualifiedAssociation": [ { "@id": "https://w3id.org/np/RADkB5eYxYtCga1Uz2FYOHhouFm-TcKZakfyInCLufbJ4/plan" } ], "http://www.w3.org/ns/prov#wasAssociatedWith": [ { "@id": "https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1" } ] }, { "@id": "https://w3id.org/np/RADkB5eYxYtCga1Uz2FYOHhouFm-TcKZakfyInCLufbJ4/plan", "http://www.w3.org/ns/prov#hadPlan": [ { "@id": "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/README.md" } ] } ] }, { "@id": "https://w3id.org/np/RADkB5eYxYtCga1Uz2FYOHhouFm-TcKZakfyInCLufbJ4/assertion", "@graph": [ { "@id": "https://w3id.org/delphi/resource/assessment/wolfram2002-ch05-03--claim-test", "http://purl.org/dc/terms/description": [ { "@value": "analysis.py evolves Wolfram's 8-neighbour outer totalistic code 746 from a row of 7 black cells on a 500x500 (T = 400) and 1100x1100 (T = 1200) grid with numpy, asserting that the pattern never reaches the grid edge. All black cells are binned by polar angle about the centroid into 360 one-degree bins and the largest radius per bin forms the outer profile r(theta); CV = std/mean of that profile and A = mean radius within 5 degrees of the lattice axes over the mean radius within 5 degrees of the diagonals. A control rule in which any black neighbour makes a cell black (which grows a square) was run with the same initial condition to validate that the statistics detect lattice anisotropy." } ], "@type": [ "https://w3id.org/delphi/ontology/Assessment" ], "http://www.w3.org/2000/01/rdf-schema#comment": [ { "@value": "Measured: [object Object] CV = std/mean of the 360-bin outer radial profile; A = axis/diagonal mean radius (circle = 1, square = 0.707) (n = [object Object], deterministic computation; lattice discreteness contributes about 0.5/mean_r = 0.001 to CV at T = 1200). Interpretation: 'Overall shape' is taken as the outer boundary of the set of black cells (interior holes ignored), and 'closely approximates a perfect circle' as a boundary whose radius varies by at most a few percent around the pattern and shows no lattice-axis bias. The claim is existential ('it is even possible to find cellular automata that ...'), so one rule suffices; the rule tested is the one Wolfram himself exhibits (code 746, p. 178, with the stated initial condition and the 400-step figure). The 1200-step run checks that the circularity is not an artefact of the particular time shown. The pattern is generated by analysis.py; there is no external download." } ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "Claim test of wolfram2002-ch05-03: supports, confidence 0.9" } ], "http://www.w3.org/2000/01/rdf-schema#seeAlso": [ { "@id": "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch05-03/result.json" } ], "http://www.w3.org/ns/prov#wasAttributedTo": [ { "@id": "https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1" } ], "https://w3id.org/delphi/ontology/admissibleDatasets": [ { "@value": "Planned datasets: nks-ch05-03-code746-generator" } ], "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": "Pre-registered. 'refutes' if at T = 1200 CV >= 0.06 or |A - 1| >= 0.06 (the outline is at least as far from a circle as a regular octagon is from its circumscribed circle in CV terms, or shows a clear square or diamond bias). Any intermediate outcome -> 'mixed'. Growth rate: the mean radius divided by T is reported and compared with Wolfram's 'about 0.37 t', but does not enter the verdict." } ], "https://w3id.org/delphi/ontology/evidenceAgainst": [ { "@value": "Both pre-registered thresholds were met with margin: at T = 1200 the boundary radius varies by 1.2 % (CV) around the pattern and the axis/diagonal ratio is 1.014; both statistics improved between T = 400 and T = 1200, so the circularity is not a transient of the time shown in the book. The control square gave CV = 0.108 and A = 0.736 (ideal square: 0.707), so the statistics do detect lattice anisotropy." }, { "@value": "The claim is existential and only the rule Wolfram himself exhibits was tested; nothing is said here about how common circle-growing rules are. A small residual fourfold anisotropy (A = 1.014, slightly diamond-leaning) persists and is not zero, so 'closely approximates' rather than 'is' a circle is the supported reading; whether A tends to 1 as T grows further was not tested beyond 1200 steps." }, { "@value": "The measured growth rate is 0.36 cells per step, close to Wolfram's 'about 0.37 t'." }, { "@value": "The outer boundary profile ignores interior holes and surface roughness below the one-degree binning scale." } ], "https://w3id.org/delphi/ontology/expectedObservation": [ { "@value": "Pre-registered. Run code 746 (a white cell becomes black iff exactly 3 of its 8 neighbours are black; a black cell stays black iff it has 0-4 black neighbours and becomes white with 5 or more; Wolfram's outer-totalistic numbering, bit index 2*s + c) from a horizontal row of 7 black cells for T = 400 and T = 1200 steps on a grid large enough that the pattern never touches the edge. Take the centroid of all black cells as centre, bin all black cells by polar angle into 360 one-degree bins and let r(theta) be the largest centre distance in each bin (outer boundary profile). Compute CV = std(r)/mean(r) and the anisotropy ratio A = mean of r within +/-5 degrees of the four axis directions divided by the mean of r within +/-5 degrees of the four diagonal directions (a square gives A = 0.707, a diamond 1.414, a circle 1). 'supports' if at T = 1200 both CV <= 0.03 and |A - 1| <= 0.03, and at T = 400 both CV <= 0.05 and |A - 1| <= 0.05. Measurement validation (not part of the verdict): the same statistics for the control rule 'a cell becomes black if any of its 8 neighbours is black' (which grows a square) must give A < 0.8 and CV > 0.06, otherwise the method is declared broken and the verdict is 'inconclusive' with reason 'other'." } ], "https://w3id.org/delphi/ontology/failCriterion": [ { "@value": "Pre-registered. 'refutes' if at T = 1200 CV >= 0.06 or |A - 1| >= 0.06 (the outline is at least as far from a circle as a regular octagon is from its circumscribed circle in CV terms, or shows a clear square or diamond bias). Any intermediate outcome -> 'mixed'. Growth rate: the mean radius divided by T is reported and compared with Wolfram's 'about 0.37 t', but does not enter the verdict." } ], "https://w3id.org/delphi/ontology/hasConfidence": [ { "@value": "0.9", "@type": "http://www.w3.org/2001/XMLSchema#double" } ], "https://w3id.org/delphi/ontology/hasEvidence": [ { "@id": "https://w3id.org/delphi/resource/evidence/wolfram2002-ch05-03--claim-test--dataset-1" } ], "https://w3id.org/delphi/ontology/hasVerdict": [ { "@value": "supports" } ], "https://w3id.org/delphi/ontology/hypothesis": [ { "@value": "The two-dimensional 8-neighbour outer totalistic cellular automaton with code 746 (the example Wolfram gives on p. 178), started from a row of 7 black cells, grows a pattern whose outer boundary stays close to a circle: the radial profile of the boundary has small relative spread and no appreciable fourfold (square-lattice) anisotropy, at the 400 steps shown in the book and at three times that many steps." } ], "https://w3id.org/delphi/ontology/inferenceMethod": [ { "@value": "analysis.py evolves Wolfram's 8-neighbour outer totalistic code 746 from a row of 7 black cells on a 500x500 (T = 400) and 1100x1100 (T = 1200) grid with numpy, asserting that the pattern never reaches the grid edge. All black cells are binned by polar angle about the centroid into 360 one-degree bins and the largest radius per bin forms the outer profile r(theta); CV = std/mean of that profile and A = mean radius within 5 degrees of the lattice axes over the mean radius within 5 degrees of the diagonals. A control rule in which any black neighbour makes a cell black (which grows a square) was run with the same initial condition to validate that the statistics detect lattice anisotropy." } ], "https://w3id.org/delphi/ontology/passCriterion": [ { "@value": "Pre-registered. Run code 746 (a white cell becomes black iff exactly 3 of its 8 neighbours are black; a black cell stays black iff it has 0-4 black neighbours and becomes white with 5 or more; Wolfram's outer-totalistic numbering, bit index 2*s + c) from a horizontal row of 7 black cells for T = 400 and T = 1200 steps on a grid large enough that the pattern never touches the edge. Take the centroid of all black cells as centre, bin all black cells by polar angle into 360 one-degree bins and let r(theta) be the largest centre distance in each bin (outer boundary profile). Compute CV = std(r)/mean(r) and the anisotropy ratio A = mean of r within +/-5 degrees of the four axis directions divided by the mean of r within +/-5 degrees of the four diagonal directions (a square gives A = 0.707, a diamond 1.414, a circle 1). 'supports' if at T = 1200 both CV <= 0.03 and |A - 1| <= 0.03, and at T = 400 both CV <= 0.05 and |A - 1| <= 0.05. Measurement validation (not part of the verdict): the same statistics for the control rule 'a cell becomes black if any of its 8 neighbours is black' (which grows a square) must give A < 0.8 and CV > 0.06, otherwise the method is declared broken and the verdict is 'inconclusive' with reason 'other'." } ], "https://w3id.org/delphi/ontology/preregistered": [ { "@value": "false", "@type": "http://www.w3.org/2001/XMLSchema#boolean" } ] }, { "@id": "https://w3id.org/delphi/resource/evidence/wolfram2002-ch05-03--claim-test--dataset-1", "http://purl.org/dc/terms/description": [ { "@value": "the pattern whose outline is compared with a circle; the control validates that the circularity statistics detect a square" } ], "http://purl.org/dc/terms/license": [ { "@value": "generated" } ], "@type": [ "https://w3id.org/delphi/ontology/EvidenceItem" ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "Dataset: Two-dimensional 8-neighbour (Moore) outer totalistic cellular automaton, Wolfram code 746, generated by analysis.py; initial condition a row of 7 black cells on a white background; T = 400 and 1200 steps; grid 1100 x 1100 with the pattern kept away from the edges; control rule (code with all 'any black neighbour -> black' bits set) run with the same initial condition and T" } ], "http://www.w3.org/ns/prov#wasDerivedFrom": [ { "@id": "https://www.wolframscience.com/nks/p178--cellular-automata/" } ] }, { "@id": "https://w3id.org/delphi/resource/claim/wolfram2002-ch05-03", "https://w3id.org/delphi/ontology/hasAssessment": [ { "@id": "https://w3id.org/delphi/resource/assessment/wolfram2002-ch05-03--claim-test" } ] } ] }, { "@id": "https://w3id.org/np/RADkB5eYxYtCga1Uz2FYOHhouFm-TcKZakfyInCLufbJ4/pubinfo", "@graph": [ { "@id": "https://w3id.org/np/RADkB5eYxYtCga1Uz2FYOHhouFm-TcKZakfyInCLufbJ4", "http://purl.org/dc/terms/created": [ { "@value": "2026-11-08T16:24:31.925Z", "@type": "http://www.w3.org/2001/XMLSchema#dateTime" } ], "http://purl.org/dc/terms/creator": [ { "@id": "https://orcid.org/0009-0007-4948-9192" } ], "http://purl.org/dc/terms/license": [ { "@id": "https://creativecommons.org/licenses/by/4.0/" } ], "http://purl.org/nanopub/x/hasNanopubType": [ { "@id": "https://w3id.org/delphi/ontology/Assessment" } ], "http://purl.org/nanopub/x/introduces": [ { "@id": "https://w3id.org/delphi/resource/assessment/wolfram2002-ch05-03--claim-test" } ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "Claim test of wolfram2002-ch05-03: supports, confidence 0.9" } ], "https://w3id.org/delphi/ontology/domain": [ { "@id": "https://w3id.org/delphi/resource/domain/wolfram-nks-2002" } ] }, { "@id": "https://w3id.org/np/RADkB5eYxYtCga1Uz2FYOHhouFm-TcKZakfyInCLufbJ4/sig", "http://purl.org/nanopub/x/hasAlgorithm": [ { "@value": "RSA" } ], "http://purl.org/nanopub/x/hasPublicKey": [ { "@value": "MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB" } ], "http://purl.org/nanopub/x/hasSignature": [ { "@value": "x7E3J2RsMVUhq4kw40dtPxmpTikfYGWSZAFLihqmU23pu2EJTLy/kV0ovnpZxRG0jPhhB3lpc1etHai1ouS1IHF8XMt1NiOt01y0u5mN4abRNaTnHhEW4GTSmhqYnJE8PaZmoWUuSg1lxIMJYONtsnntqpikNF7phg5iWTDYF5Cjl/778kuGO0zhrX/QvDMs2woUq4ZJMrGJP0FYK2RdndMCLCwktC8ohJb5ovECGPA9kilSjv7F26DLwaLUbJ5knky+Gmqm00ii6p2Y+3r4teucb2w4I6KGY8npidP1QoVQLjP4pgOElqJHPyE8k3zsdaWVDf3w1tqNxowX5U7Gsw==" } ], "http://purl.org/nanopub/x/hasSignatureTarget": [ { "@id": "https://w3id.org/np/RADkB5eYxYtCga1Uz2FYOHhouFm-TcKZakfyInCLufbJ4" } ], "http://purl.org/nanopub/x/signedBy": [ { "@id": "https://orcid.org/0009-0007-4948-9192" } ] } ] } ]