https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg
.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-ch02-02--claim-test> a <https://w3id.org/delphi/ontology/Assessment>;
dc:description "analysis.py evolves rules 30, 50 and 90 from a single black cell for 4096 steps and analyses the interior window rows 2048-4095, |x| <= 1024 (2048 x 2049 cells). It computes the black fraction; the maximum fraction of cells agreeing with a space-time shifted copy of the pattern over all shifts p <= 64, |s| <= p (on rows 3072-4095, |x| <= 512); the maximum agreement of the pattern with its own 2x and 3x decimations over all offsets; and lzma (preset 9e) and bz2 (level 9) sizes of the bit-packed window divided by those of a density-matched Bernoulli pattern. Thresholds and control requirements are those pre-registered. Run time about 30 s.";
<http://www.w3.org/2000/01/rdf-schema#comment> "Measured: [object Object] fractions of cells (agreement) and compressed size relative to a density-matched Bernoulli pattern (n = 4196352, deterministic; the Bernoulli reference varies by about 0.03 % between seeds (second control 1.000 / 1.0003)). Interpretation: Wolfram contrasts rule 30 with the three kinds of simple behavior he has just shown (uniform, repetitive, nested), so 'irregular and complex with almost no overall regularity' is operationalized as the failure of a quantitative detector for each simple kind plus near-incompressibility, measured on the interior of the pattern. The interior window deliberately excludes the left and right edges, where Wolfram himself notes (p. 27) some regularity (the periodic right edge and diagonal stripes on the left); the claim is about the overall pattern, and the edges are a vanishing fraction of the light cone. Detectors are finite: A_rep only checks space-time periods up to 64 steps, A_nest only scale factors 2 and 3, and compressors only the regularities they model, so a pass is bounded non-detection, not a proof of irregularity.";
<http://www.w3.org/2000/01/rdf-schema#label> "Claim test of wolfram2002-ch02-02: supports, confidence 0.85";
<http://www.w3.org/2000/01/rdf-schema#seeAlso> <https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch02-02/result.json>;
prov:wasAttributedTo <https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-opus-5-5>;
<https://w3id.org/delphi/ontology/admissibleDatasets> "The exact rule 30 evolution from a single black cell on an unbounded (light-cone-sized) lattice, generated by committed code; control rules and random references generated by the same code with a fixed seed. No data derived from Wolfram's own figures.";
<https://w3id.org/delphi/ontology/assessmentType> "claim-test/0.1.0";
<https://w3id.org/delphi/ontology/dataKind> "computational";
<https://w3id.org/delphi/ontology/disconfirmingObservation> "A space-time shift or decimation that reproduces at least 90 % of the interior cells, or a compressor that halves the size relative to the density-matched random pattern.";
<https://w3id.org/delphi/ontology/evidenceAgainst> "All four pre-registered pass conditions hold and all validity controls hold: in the interior, rule 30 is half black (0.5005), no shift up to 64 steps reproduces more than 62.5 % of cells, 2x and 3x decimations agree with the pattern at chance level (0.50), and lzma/bz2 save only 12 % and 10 % relative to a random pattern of the same density.",
"Detectors are finite (periods <= 64, scale factors 2 and 3, two compressors on a 2048-row window); passing them is bounded non-detection of uniform, repetitive and nested structure, not a proof that rule 30 has no global regularity.",
"Rule 30 is not featureless: the best shift (p = 2, s = 2, along the left-going diagonal) agrees on 62.5 % of cells rather than 50 %, and the compressors find 10-12 % redundancy. Both reflect the diagonal stripes on the left side of the pattern, which Wolfram himself notes; they are consistent with 'almost no overall regularity' but show it is not literally none.",
"The rule 90 control window is 98.6 % white, so its high shift agreement (0.9865) is mostly background; it is used only as the nested and compressible control, for which it is unambiguous (decimation agreement 1.0, lzma ratio 0.03).";
<https://w3id.org/delphi/ontology/expectedObservation> "In the interior of rule 30's single-cell pattern, shift-agreement and decimation-agreement stay near the random value 0.5 and general-purpose compressors achieve no more than 20 % saving relative to a density-matched random pattern, while the same detectors flag rule 50 as repetitive and rule 90 as nested.";
<https://w3id.org/delphi/ontology/failCriterion> "Pre-registered. 'refutes' if black fraction in W is outside [0.2, 0.8], or A_rep >= 0.90, or A_nest >= 0.90, or either normalized compression ratio < 0.50. 'mixed' if no refuting threshold is reached but some pass condition fails (e.g. A_rep in (0.75, 0.90) or a ratio in [0.50, 0.80)). If a validity control fails, the verdict is 'inconclusive' with reason 'other'.";
<https://w3id.org/delphi/ontology/hasConfidence> "0.85"^^xsd:double;
<https://w3id.org/delphi/ontology/hasEvidence> <https://w3id.org/delphi/resource/evidence/wolfram2002-ch02-02--claim-test--dataset-1>,
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch02-02--claim-test--dataset-2>,
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch02-02--claim-test--dataset-3>;
<https://w3id.org/delphi/ontology/hasVerdict> "supports";
<https://w3id.org/delphi/ontology/hypothesis> "The space-time pattern of elementary cellular automaton rule 30 grown from a single black cell is, in its interior, neither uniform, nor repetitive (no shift-periodicity), nor nested (no self-similarity under 2x or 3x decimation), and is essentially incompressible by general-purpose compressors relative to a random pattern of the same density, whereas reference rules that are repetitive (rule 50) and nested (rule 90) are detected as such by the same measures.";
<https://w3id.org/delphi/ontology/inferenceMethod> "Black fraction, maximum shift agreement A_rep (p <= 64, |s| <= p), maximum decimation agreement A_nest (k = 2, 3), and lzma/bz2 size ratios against a density-matched Bernoulli pattern, each compared with the pre-registered thresholds; validity requires the repetitive (rule 50) and nested (rule 90) controls to be detected.";
<https://w3id.org/delphi/ontology/passCriterion> "Pre-registered. Evolve rule 30 from a single black cell for T = 4096 steps. Analysis window W: rows t in [2048, 4095], columns |x| <= 1024 (entirely inside the light cone; 2048 x 2049 cells). (0) Not uniform: black fraction in W between 0.40 and 0.60. (1) Not repetitive: on the sub-window rows [3072, 4095], |x| <= 512, the maximum over all space-time shifts (p, s) with 1 <= p <= 64 and |s| <= p of the fraction of cells with a(t, x) = a(t - p, x - s) is A_rep <= 0.75 (random pattern ~0.5; strictly periodic pattern 1.0). (2) Not nested: for decimation factors k in {2, 3} and all offsets (a, b) in {0..k-1}^2, the agreement between a(k t + a, k x + b) of the full pattern and a(t, x) of the same pattern, over t in [T/(2k), T/k), |x| <= T/(4k), has maximum A_nest <= 0.60 (rule 90 gives 1.0 for k = 2). (3) Incompressible: lzma (preset 9 extreme) and bz2 (level 9) sizes of the bit-packed window W, divided by the sizes for a Bernoulli(p) pattern of the same shape with p equal to W's black fraction (numpy PCG64, seed 20261031), are both >= 0.80. Validity controls, required for the verdict to count: rule 50 from a single cell gives A_rep >= 0.99 on its own window; rule 90 gives A_nest >= 0.99; rule 90 and rule 50 normalized lzma ratios <= 0.5; a second independent Bernoulli control gives normalized ratio within [0.97, 1.03]. Verdict 'supports' if (0)-(3) all pass and the controls hold.";
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<https://w3id.org/delphi/resource/evidence/wolfram2002-ch02-02--claim-test--dataset-1>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "the pattern under test";
dc:license "";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: Elementary CA rule 30 from a single black cell, 4096 steps on a 8193-cell lattice (generated by analysis.py)";
prov:wasDerivedFrom <https://www.wolframscience.com/nks/p27--how-do-simple-programs-behave/> .
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch02-02--claim-test--dataset-2>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "positive controls for the repetition, nesting and compression detectors";
dc:license "";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: Elementary CA rules 50 (repetitive) and 90 (nested) from a single black cell, 4096 steps (generated by analysis.py)" .
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch02-02--claim-test--dataset-3>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "density-matched random reference for compressed sizes";
dc:license "";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: Bernoulli(p) patterns of the window shape, p matched to each rule's black fraction, numpy PCG64 seed 20261031 (generated by analysis.py)" .
}
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