https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius/Head https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius http://www.nanopub.org/nschema#hasAssertion https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius/assertion https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius http://www.nanopub.org/nschema#hasProvenance https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius/provenance https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius http://www.nanopub.org/nschema#hasPublicationInfo https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius/pubinfo https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.nanopub.org/nschema#Nanopublication https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius/assertion https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-05--claim-test http://purl.org/dc/terms/description analysis.py ran all 2187 three-colour totalistic codes from a single gray cell for T = 3000 steps on an array of width 2*(T+128)+1 (boundaries cannot reach the centre), then classified the central 128-column strip: time-periodic with p <= 256 over rows 2250..2999, or lzma compressibility rho over rows 1500..2999 below tau. Calibration before the census: nested references rho = 0.017..0.037 (Pascal mod 2 / mod 3, Thue-Morse and period-doubling outer products), irregular references rho = 0.099..0.136 (elementary rules 110, 124, 137, 193) and 1.11..1.12 (rules 30, 45); classes separated, tau = sqrt(0.0367 * 0.0985) = 0.0601. Result: 1706 codes periodic, 145 non-periodic but nested-compressible (rho <= 0.042), 336 irregular (rho 0.12..1.11, median 0.90; 169 with rho >= 0.9); regular fraction 1851/2187 = 0.8464, inside the pre-registered [0.80, 0.90] band. https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-05--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-ch03-05--claim-test http://www.w3.org/2000/01/rdf-schema#comment Measured: 0.8464 fraction of the 2187 codes classified regular (late-time strip periodic with p <= 256, or rho < tau) (n = 2187, deterministic given tau = 0.060; a few long-transient codes may be misclassified at T = 3000). Interpretation: 'Ultimately quite regular' is read as 'repetitive or nested at late times', operationalised as late-time periodicity of the central strip or compressibility at the level of classical nested patterns; 'the remainder' as everything compressing like random or localised-structure patterns, with elementary class-3 and class-4 rules from a different family used to fix the threshold. 'About 85 %' is given a +/- 5 percentage-point band. Long transients (Wolfram mentions code 1599 resolving only after thousands of steps) may leave a few ultimately regular codes labelled irregular at T = 3000, which biases the regular fraction downward slightly. All patterns are generated by analysis.py; there is no external download. https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-05--claim-test http://www.w3.org/2000/01/rdf-schema#label Claim test of wolfram2002-ch03-05: supports, confidence 0.75 https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-05--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-ch03-05/result.json https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-05--claim-test http://www.w3.org/ns/prov#wasAttributedTo https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-05--claim-test https://w3id.org/delphi/ontology/admissibleDatasets Planned datasets: nks-ch03-05-totalistic3-generator https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-05--claim-test https://w3id.org/delphi/ontology/assessmentType claim-test/0.1.0 https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-05--claim-test https://w3id.org/delphi/ontology/dataKind computational https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-05--claim-test https://w3id.org/delphi/ontology/disconfirmingObservation Pre-registered. 'refutes' if the regular fraction is below 0.70 or above 0.95. 'mixed' if it lies in [0.70, 0.80) or (0.90, 0.95]. 'inconclusive' with reason 'other' if the calibration fails to separate the reference classes (largest nested rho >= smallest irregular rho). The number of irregular codes that are random-looking (rho above the smallest random reference) versus structured-irregular is reported but not decisive. https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-05--claim-test https://w3id.org/delphi/ontology/evidenceAgainst 'About 85 %' is Wolfram's rounded figure; the pre-registered band [0.80, 0.90] was chosen to allow +/- 5 points of classification ambiguity. The measured 84.6 % lands within 0.4 points of the quoted figure. https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-05--claim-test https://w3id.org/delphi/ontology/evidenceAgainst Codes are classified from a single gray cell only, as in the book's figure; a black-cell start would give a different census. https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-05--claim-test https://w3id.org/delphi/ontology/evidenceAgainst Periodicity and compressibility are measured on the central 128 columns only; patterns whose irregularity is confined to the edges of the growing region (and whose centre is periodic) count as regular. https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-05--claim-test https://w3id.org/delphi/ontology/evidenceAgainst T = 3000 steps: codes with transients longer than about 750 steps in the periodicity window, or whose late-time structure first appears beyond 3000 steps (NKS mentions code 1599 at thousands of steps), may be misclassified; code 1599 is counted irregular here (rho 0.55). https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-05--claim-test https://w3id.org/delphi/ontology/evidenceAgainst The pre-registered 'random-like' sub-count (rho above the smallest 2-colour random reference, 1.11) is not comparable across alphabets and came out as 0; the post-hoc quantiles added to measured.extra show 169 of the 336 irregular codes have rho >= 0.9, i.e. compress essentially like random 3-colour data. This sub-count was pre-registered as non-decisive. https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-05--claim-test https://w3id.org/delphi/ontology/evidenceAgainst The regular/irregular split depends on tau, which is calibrated on elementary (2-colour) reference rules; the gap between the nested references (max 0.037) and the structured-irregular references (min 0.099) is wide and the census has no codes between 0.042 and 0.119, so the fraction is insensitive to the exact value of tau within that gap. https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-05--claim-test https://w3id.org/delphi/ontology/expectedObservation Pre-registered. Each code c in 0..2186 (Wolfram's convention: base-3 digit k of c is the new colour for neighbourhood sum k in 0..6; colours 0 = white, 1 = gray, 2 = black) is run for T = 3000 steps from a single gray cell on a white background with an array wide enough that boundary effects cannot reach the central 128 columns. Statistics on the central strip (columns -64..63): (i) periodic: rows 2250..2999 are time-periodic with some period p <= 256; (ii) rho = 8 * lzma_bytes / (cells * log2(3)) over rows 1500..2999. Calibration (performed before the codes are run): nested references are the same-size strips of Pascal's triangle mod 3 (3 symbols), Pascal's triangle mod 2, and the Thue-Morse and period-doubling outer-product patterns (normalised by log2 of their own alphabet size); irregular references are the strips of elementary rules 110, 124, 137, 193 (localised structures) and 30, 45 (random) run from a single black cell with the same geometry. tau = geometric mean of the largest nested-reference rho and the smallest irregular-reference rho. A code is 'regular' iff it is periodic or rho < tau. 'supports' if the regular fraction lies in [0.80, 0.90]. https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-05--claim-test https://w3id.org/delphi/ontology/failCriterion Pre-registered. 'refutes' if the regular fraction is below 0.70 or above 0.95. 'mixed' if it lies in [0.70, 0.80) or (0.90, 0.95]. 'inconclusive' with reason 'other' if the calibration fails to separate the reference classes (largest nested rho >= smallest irregular rho). The number of irregular codes that are random-looking (rho above the smallest random reference) versus structured-irregular is reported but not decisive. https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-05--claim-test https://w3id.org/delphi/ontology/hasConfidence 0.75 https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-05--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch03-05--claim-test--dataset-1 https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-05--claim-test https://w3id.org/delphi/ontology/hasVerdict supports https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-05--claim-test https://w3id.org/delphi/ontology/hypothesis When all 2187 three-colour nearest-neighbour totalistic cellular automata are run from a single gray cell for a few thousand steps, about 85 % produce patterns whose late-time central region is time-periodic or compresses like classical nested patterns, and the remaining 15 % or so compress like random or class-4 (localised-structure) patterns. https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-05--claim-test https://w3id.org/delphi/ontology/inferenceMethod analysis.py ran all 2187 three-colour totalistic codes from a single gray cell for T = 3000 steps on an array of width 2*(T+128)+1 (boundaries cannot reach the centre), then classified the central 128-column strip: time-periodic with p <= 256 over rows 2250..2999, or lzma compressibility rho over rows 1500..2999 below tau. Calibration before the census: nested references rho = 0.017..0.037 (Pascal mod 2 / mod 3, Thue-Morse and period-doubling outer products), irregular references rho = 0.099..0.136 (elementary rules 110, 124, 137, 193) and 1.11..1.12 (rules 30, 45); classes separated, tau = sqrt(0.0367 * 0.0985) = 0.0601. Result: 1706 codes periodic, 145 non-periodic but nested-compressible (rho <= 0.042), 336 irregular (rho 0.12..1.11, median 0.90; 169 with rho >= 0.9); regular fraction 1851/2187 = 0.8464, inside the pre-registered [0.80, 0.90] band. https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-05--claim-test https://w3id.org/delphi/ontology/passCriterion Pre-registered. Each code c in 0..2186 (Wolfram's convention: base-3 digit k of c is the new colour for neighbourhood sum k in 0..6; colours 0 = white, 1 = gray, 2 = black) is run for T = 3000 steps from a single gray cell on a white background with an array wide enough that boundary effects cannot reach the central 128 columns. Statistics on the central strip (columns -64..63): (i) periodic: rows 2250..2999 are time-periodic with some period p <= 256; (ii) rho = 8 * lzma_bytes / (cells * log2(3)) over rows 1500..2999. Calibration (performed before the codes are run): nested references are the same-size strips of Pascal's triangle mod 3 (3 symbols), Pascal's triangle mod 2, and the Thue-Morse and period-doubling outer-product patterns (normalised by log2 of their own alphabet size); irregular references are the strips of elementary rules 110, 124, 137, 193 (localised structures) and 30, 45 (random) run from a single black cell with the same geometry. tau = geometric mean of the largest nested-reference rho and the smallest irregular-reference rho. A code is 'regular' iff it is periodic or rho < tau. 'supports' if the regular fraction lies in [0.80, 0.90]. https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-05--claim-test https://w3id.org/delphi/ontology/preregistered false https://w3id.org/delphi/resource/claim/wolfram2002-ch03-05 https://w3id.org/delphi/ontology/hasAssessment https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-05--claim-test https://w3id.org/delphi/resource/evidence/wolfram2002-ch03-05--claim-test--dataset-1 http://purl.org/dc/terms/description the finite rule space whose regular fraction the claim reports https://w3id.org/delphi/resource/evidence/wolfram2002-ch03-05--claim-test--dataset-1 http://purl.org/dc/terms/license generated https://w3id.org/delphi/resource/evidence/wolfram2002-ch03-05--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-ch03-05--claim-test--dataset-1 http://www.w3.org/2000/01/rdf-schema#label Dataset: All 2187 three-colour nearest-neighbour totalistic cellular automata (Wolfram code numbering) from a single gray cell, 3000 steps, generated by analysis.py, plus the calibration reference patterns described in pass_criterion https://w3id.org/delphi/resource/evidence/wolfram2002-ch03-05--claim-test--dataset-1 http://www.w3.org/ns/prov#wasDerivedFrom https://www.wolframscience.com/nks/p65--more-cellular-automata/ https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius/provenance https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 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-fable-5-1 http://www.w3.org/2000/01/rdf-schema#label delphisci claim tester (claude-fable-5.1; cursor/claim-tests-wolfram-nks-e5f4) https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 http://www.w3.org/ns/prov#actedOnBehalfOf https://orcid.org/0009-0007-4948-9192 https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 https://w3id.org/delphi/ontology/usesModel https://w3id.org/delphi/resource/model/claude-fable-5-1 https://w3id.org/delphi/resource/model/claude-fable-5-1 http://purl.org/dc/terms/identifier claude-fable-5.1 https://w3id.org/delphi/resource/model/claude-fable-5-1 http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/LanguageModel https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius/assertion http://www.w3.org/ns/prov#wasAttributedTo https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius/assertion http://www.w3.org/ns/prov#wasDerivedFrom https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch03-05/result.json https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius/assertion http://www.w3.org/ns/prov#wasGeneratedBy https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius/test https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius/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/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius/test http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.w3.org/ns/prov#Activity https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius/test http://www.w3.org/ns/prov#qualifiedAssociation https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius/plan https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius/test http://www.w3.org/ns/prov#wasAssociatedWith https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius/pubinfo https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius http://purl.org/dc/terms/created 2026-11-08T16:24:31.919Z https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius http://purl.org/dc/terms/creator https://orcid.org/0009-0007-4948-9192 https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius http://purl.org/dc/terms/license https://creativecommons.org/licenses/by/4.0/ https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius http://purl.org/nanopub/x/hasNanopubType https://w3id.org/delphi/ontology/Assessment https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius http://purl.org/nanopub/x/introduces https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-05--claim-test https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius http://www.w3.org/2000/01/rdf-schema#label Claim test of wolfram2002-ch03-05: supports, confidence 0.75 https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius https://w3id.org/delphi/ontology/domain https://w3id.org/delphi/resource/domain/wolfram-nks-2002 https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius/sig http://purl.org/nanopub/x/hasAlgorithm RSA https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius/sig http://purl.org/nanopub/x/hasPublicKey MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius/sig http://purl.org/nanopub/x/hasSignature eoM3Ry3xwAX/fQE0aI7q1O1J+MepIfHHccKR2Jvw5jLD35y2WnJEDXYckjKwSdvDpryzWpMw4ojYH3Z1lNTWOYBkoZbapaixyOf6wD5QBwkvWg+9WfcYDhe7iAef7jB7pEn7Rvstn6Tac7K5u3UTFVHstbc2W/wFhBCNcBMmyfnS7QyCD+gmg4aaXtPFdGATcqY86bWUf9hibjG7rtv2hjEXs/uwzy6Rko/oflzb8kk8RB2Z9yXAKjAYk/T98Cn3GE/OuvlEtgagCNKOP8wfxaptnbmZlF7IqUBR6826GNyYrDeszpCdb52d5S4BuFv8x8FwJGWALsz1GE9+kd/IqQ== https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius/sig http://purl.org/nanopub/x/hasSignatureTarget https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius/sig http://purl.org/nanopub/x/signedBy https://orcid.org/0009-0007-4948-9192