https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg/Head https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg http://www.nanopub.org/nschema#hasAssertion https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg/assertion https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg http://www.nanopub.org/nschema#hasProvenance https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg/provenance https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg http://www.nanopub.org/nschema#hasPublicationInfo https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg/pubinfo https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.nanopub.org/nschema#Nanopublication https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg/assertion https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-02--claim-test http://purl.org/dc/terms/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. https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-02--claim-test http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/Assessment https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-02--claim-test 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. https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-02--claim-test http://www.w3.org/2000/01/rdf-schema#label Claim test of wolfram2002-ch02-02: supports, confidence 0.85 https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-02--claim-test 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 https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-02--claim-test http://www.w3.org/ns/prov#wasAttributedTo https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-opus-5-5 https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-02--claim-test 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/resource/assessment/wolfram2002-ch02-02--claim-test https://w3id.org/delphi/ontology/assessmentType claim-test/0.1.0 https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-02--claim-test https://w3id.org/delphi/ontology/dataKind computational https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-02--claim-test 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/resource/assessment/wolfram2002-ch02-02--claim-test 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. https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-02--claim-test https://w3id.org/delphi/ontology/evidenceAgainst 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. https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-02--claim-test https://w3id.org/delphi/ontology/evidenceAgainst 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. https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-02--claim-test https://w3id.org/delphi/ontology/evidenceAgainst 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/resource/assessment/wolfram2002-ch02-02--claim-test 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/resource/assessment/wolfram2002-ch02-02--claim-test 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/resource/assessment/wolfram2002-ch02-02--claim-test https://w3id.org/delphi/ontology/hasConfidence 0.85 https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-02--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch02-02--claim-test--dataset-1 https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-02--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch02-02--claim-test--dataset-2 https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-02--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch02-02--claim-test--dataset-3 https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-02--claim-test https://w3id.org/delphi/ontology/hasVerdict supports https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-02--claim-test 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/resource/assessment/wolfram2002-ch02-02--claim-test 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/resource/assessment/wolfram2002-ch02-02--claim-test 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. https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-02--claim-test https://w3id.org/delphi/ontology/preregistered false https://w3id.org/delphi/resource/claim/wolfram2002-ch02-02 https://w3id.org/delphi/ontology/hasAssessment https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-02--claim-test https://w3id.org/delphi/resource/evidence/wolfram2002-ch02-02--claim-test--dataset-1 http://purl.org/dc/terms/description the pattern under test https://w3id.org/delphi/resource/evidence/wolfram2002-ch02-02--claim-test--dataset-1 http://purl.org/dc/terms/license https://w3id.org/delphi/resource/evidence/wolfram2002-ch02-02--claim-test--dataset-1 http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/EvidenceItem https://w3id.org/delphi/resource/evidence/wolfram2002-ch02-02--claim-test--dataset-1 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) https://w3id.org/delphi/resource/evidence/wolfram2002-ch02-02--claim-test--dataset-1 http://www.w3.org/ns/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 http://purl.org/dc/terms/description positive controls for the repetition, nesting and compression detectors https://w3id.org/delphi/resource/evidence/wolfram2002-ch02-02--claim-test--dataset-2 http://purl.org/dc/terms/license https://w3id.org/delphi/resource/evidence/wolfram2002-ch02-02--claim-test--dataset-2 http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/EvidenceItem https://w3id.org/delphi/resource/evidence/wolfram2002-ch02-02--claim-test--dataset-2 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 http://purl.org/dc/terms/description density-matched random reference for compressed sizes https://w3id.org/delphi/resource/evidence/wolfram2002-ch02-02--claim-test--dataset-3 http://purl.org/dc/terms/license https://w3id.org/delphi/resource/evidence/wolfram2002-ch02-02--claim-test--dataset-3 http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/EvidenceItem https://w3id.org/delphi/resource/evidence/wolfram2002-ch02-02--claim-test--dataset-3 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) https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg/provenance https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-opus-5-5 http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.w3.org/ns/prov#SoftwareAgent https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-opus-5-5 http://www.w3.org/2000/01/rdf-schema#label delphisci claim tester (claude-opus-5.5; cursor local subagent) https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-opus-5-5 http://www.w3.org/ns/prov#actedOnBehalfOf https://orcid.org/0009-0007-4948-9192 https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-opus-5-5 https://w3id.org/delphi/ontology/usesModel https://w3id.org/delphi/resource/model/claude-opus-5-5 https://w3id.org/delphi/resource/model/claude-opus-5-5 http://purl.org/dc/terms/identifier claude-opus-5.5 https://w3id.org/delphi/resource/model/claude-opus-5-5 http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/LanguageModel https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg/assertion http://www.w3.org/ns/prov#wasAttributedTo https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-opus-5-5 https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg/assertion http://www.w3.org/ns/prov#wasDerivedFrom https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch02-02/result.json https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg/assertion http://www.w3.org/ns/prov#wasGeneratedBy https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg/test https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg/plan http://www.w3.org/ns/prov#hadPlan https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/README.md https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg/test http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.w3.org/ns/prov#Activity https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg/test http://www.w3.org/ns/prov#qualifiedAssociation https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg/plan https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg/test http://www.w3.org/ns/prov#wasAssociatedWith https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-opus-5-5 https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg/pubinfo https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg http://purl.org/dc/terms/created 2026-11-08T16:24:31.914Z https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg http://purl.org/dc/terms/creator https://orcid.org/0009-0007-4948-9192 https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg http://purl.org/dc/terms/license https://creativecommons.org/licenses/by/4.0/ https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg http://purl.org/nanopub/x/hasNanopubType https://w3id.org/delphi/ontology/Assessment https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg http://purl.org/nanopub/x/introduces https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-02--claim-test https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg http://www.w3.org/2000/01/rdf-schema#label Claim test of wolfram2002-ch02-02: supports, confidence 0.85 https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg https://w3id.org/delphi/ontology/domain https://w3id.org/delphi/resource/domain/wolfram-nks-2002 https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg/sig http://purl.org/nanopub/x/hasAlgorithm RSA https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg/sig http://purl.org/nanopub/x/hasPublicKey MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg/sig http://purl.org/nanopub/x/hasSignature tazxe6B6NaGo80VuYsYURaL6bJ4l8JdHgnW+B3XZxS5fEscM2s/FN1rBJIenxw5uPE+kJJ93UzEitouOnNhRX4BDRIUzvSwJWpY5ypb6ilD7wJiXGm25bj2KqI/6MVgOi4oM8ZUb5hiM1KjELrKImcnu85Gw2y8gIQQd5CfZmbU+Uxk8zpIALDS7wrG1mz7EUsUEsyaZQVdFco1JwR9czfKYNQMjiJA3EMeLmlywj03C8arXDl39X6kW8/WP/xoRYes9+eAXfryWS6f+0SpZB5d1mxibMPvmSby+kD6KgXRLXGj4/SLldNfn2Fm9uwZ/kQHHjHCvocbgG3wsP7LM1g== https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg/sig http://purl.org/nanopub/x/hasSignatureTarget https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg https://w3id.org/np/RApov6k-EpCGb0i-lmaKFLeIY1MLcogOqxL7y4joqGmOg/sig http://purl.org/nanopub/x/signedBy https://orcid.org/0009-0007-4948-9192