https://w3id.org/np/RADkB5eYxYtCga1Uz2FYOHhouFm-TcKZakfyInCLufbJ4
.trig | .trig.txt | .jelly | .jelly.txt | .jsonld | .jsonld.txt | .nq | .nq.txt | .xml | .xml.txt
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<https://w3id.org/delphi/resource/assessment/wolfram2002-ch05-03--claim-test> a <https://w3id.org/delphi/ontology/Assessment>;
dc:description "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.";
<http://www.w3.org/2000/01/rdf-schema#comment> "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> "Claim test of wolfram2002-ch05-03: supports, confidence 0.9";
<http://www.w3.org/2000/01/rdf-schema#seeAlso> <https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch05-03/result.json>;
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<https://w3id.org/delphi/ontology/admissibleDatasets> "Planned datasets: nks-ch05-03-code746-generator";
<https://w3id.org/delphi/ontology/assessmentType> "claim-test/0.1.0";
<https://w3id.org/delphi/ontology/dataKind> "computational";
<https://w3id.org/delphi/ontology/disconfirmingObservation> "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> "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.",
"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.",
"The measured growth rate is 0.36 cells per step, close to Wolfram's 'about 0.37 t'.",
"The outer boundary profile ignores interior holes and surface roughness below the one-degree binning scale.";
<https://w3id.org/delphi/ontology/expectedObservation> "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> "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> "0.9"^^xsd:double;
<https://w3id.org/delphi/ontology/hasEvidence> <https://w3id.org/delphi/resource/evidence/wolfram2002-ch05-03--claim-test--dataset-1>;
<https://w3id.org/delphi/ontology/hasVerdict> "supports";
<https://w3id.org/delphi/ontology/hypothesis> "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> "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> "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'.";
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dc:description "the pattern whose outline is compared with a circle; the control validates that the circularity statistics detect a square";
dc:license "generated";
<http://www.w3.org/2000/01/rdf-schema#label> "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";
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