rows { options { physical_type: PHYSICAL_STREAM_TYPE_QUADS max_name_table_size: 128 max_prefix_table_size: 16 max_datatype_table_size: 16 logical_type: LOGICAL_STREAM_TYPE_DATASETS version: 2 } } rows { prefix { value: "https://w3id.org/np/" } } rows { name { value: "RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius" } } rows { namespace { name: "this" value { prefix_id: 1 } } } rows { prefix { value: "https://w3id.org/np/RAT3SmVJ6DDLEDqlFo4i2tB-J_VHLjBDMfd9DSeG0Sius/" } } rows { name { } } rows { namespace { name: "sub" value { prefix_id: 2 } } } rows { prefix { value: "http://www.nanopub.org/nschema#" } } rows { namespace { name: "np" value { prefix_id: 3 name_id: 2 } } } rows { prefix { value: "http://www.w3.org/1999/02/22-rdf-syntax-ns#" } } rows { namespace { name: "rdf" value { prefix_id: 4 name_id: 2 } } } rows { prefix { value: "http://www.w3.org/ns/prov#" } } rows { namespace { name: "prov" value { prefix_id: 5 name_id: 2 } } } rows { prefix { value: "http://purl.org/nanopub/x/" } } rows { namespace { name: "npx" value { prefix_id: 6 name_id: 2 } } } rows { prefix { value: "http://purl.org/dc/terms/" } } rows { namespace { name: "dc" value { prefix_id: 7 name_id: 2 } } } rows { prefix { value: "http://www.w3.org/2001/XMLSchema#" } } rows { namespace { name: "xsd" value { prefix_id: 8 name_id: 2 } } } rows { name { value: "hasAssertion" } } rows { name { value: "assertion" } } rows { name { value: "Head" } } rows { quad { s_iri { prefix_id: 1 name_id: 1 } p_iri { prefix_id: 3 name_id: 3 } o_iri { prefix_id: 2 } g_iri { } } } rows { name { value: "hasProvenance" } } rows { name { value: "provenance" } } rows { quad { p_iri { prefix_id: 3 } o_iri { prefix_id: 2 } } } rows { name { value: "hasPublicationInfo" } } rows { name { value: "pubinfo" } } rows { quad { p_iri { prefix_id: 3 } o_iri { prefix_id: 2 } } } rows { name { value: "type" } } rows { name { value: "Nanopublication" } } rows { quad { p_iri { prefix_id: 4 } o_iri { prefix_id: 3 } } } rows { prefix { value: "https://w3id.org/delphi/resource/assessment/" } } rows { name { value: "wolfram2002-ch03-05--claim-test" } } rows { name { value: "description" } } rows { quad { s_iri { prefix_id: 9 } p_iri { prefix_id: 7 } o_literal { lex: "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." } g_iri { prefix_id: 2 name_id: 4 } } } rows { prefix { value: "https://w3id.org/delphi/ontology/" } } rows { name { value: "Assessment" } } rows { quad { p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 10 name_id: 14 } } } rows { prefix { value: "http://www.w3.org/2000/01/rdf-schema#" } } rows { name { value: "comment" } } rows { quad { p_iri { prefix_id: 11 } o_literal { lex: "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." } } } rows { name { value: "label" } } rows { quad { p_iri { } o_literal { lex: "Claim test of wolfram2002-ch03-05: supports, confidence 0.75" } } } rows { name { value: "seeAlso" } } rows { prefix { value: "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch03-05/" } } rows { name { value: "result.json" } } rows { quad { p_iri { } o_iri { prefix_id: 12 } } } rows { name { value: "wasAttributedTo" } } rows { prefix { value: "https://w3id.org/delphi/resource/agent/" } } rows { name { value: "delphisci-claim-tester-claude-fable-5-1" } } rows { quad { p_iri { prefix_id: 5 } o_iri { prefix_id: 13 } } } rows { name { value: "admissibleDatasets" } } rows { quad { p_iri { prefix_id: 10 } o_literal { lex: "Planned datasets: nks-ch03-05-totalistic3-generator" } } } rows { name { value: "assessmentType" } } rows { quad { p_iri { } o_literal { lex: "claim-test/0.1.0" } } } rows { name { value: "dataKind" } } rows { quad { p_iri { } o_literal { lex: "computational" } } } rows { name { value: "disconfirmingObservation" } } rows { quad { p_iri { } o_literal { lex: "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." } } } rows { name { value: "evidenceAgainst" } } rows { quad { p_iri { } o_literal { lex: "\'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." } } } rows { quad { o_literal { lex: "Codes are classified from a single gray cell only, as in the book\'s figure; a black-cell start would give a different census." } } } rows { quad { o_literal { lex: "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." } } } rows { quad { o_literal { lex: "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)." } } } rows { quad { o_literal { lex: "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." } } } rows { quad { o_literal { lex: "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." } } } rows { name { value: "expectedObservation" } } rows { quad { p_iri { } o_literal { lex: "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]." } } } rows { name { value: "failCriterion" } } rows { quad { p_iri { } o_literal { lex: "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." } } } rows { name { value: "hasConfidence" } } rows { datatype { value: "http://www.w3.org/2001/XMLSchema#double" } } rows { quad { p_iri { } o_literal { lex: "0.75" datatype: 1 } } } rows { name { value: "hasEvidence" } } rows { prefix { value: "https://w3id.org/delphi/resource/evidence/" } } rows { name { value: "wolfram2002-ch03-05--claim-test--dataset-1" } } rows { quad { p_iri { } o_iri { prefix_id: 14 } } } rows { name { value: "hasVerdict" } } rows { quad { p_iri { prefix_id: 10 } o_literal { lex: "supports" } } } rows { name { value: "hypothesis" } } rows { quad { p_iri { } o_literal { lex: "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." } } } rows { name { value: "inferenceMethod" } } rows { quad { p_iri { } o_literal { lex: "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." } } } rows { name { value: "passCriterion" } } rows { quad { p_iri { } o_literal { lex: "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]." } } } rows { name { value: "preregistered" } } rows { datatype { value: "http://www.w3.org/2001/XMLSchema#boolean" } } rows { quad { p_iri { } o_literal { lex: "false" datatype: 2 } } } rows { prefix { value: "https://w3id.org/delphi/resource/claim/" } } rows { name { value: "wolfram2002-ch03-05" } } rows { name { value: "hasAssessment" } } rows { quad { s_iri { prefix_id: 15 } p_iri { prefix_id: 10 } o_iri { prefix_id: 9 name_id: 12 } } } rows { quad { s_iri { prefix_id: 14 name_id: 30 } p_iri { prefix_id: 7 name_id: 13 } o_literal { lex: "the finite rule space whose regular fraction the claim reports" } } } rows { name { value: "license" } } rows { quad { p_iri { name_id: 38 } o_literal { lex: "generated" } } } rows { name { value: "EvidenceItem" } } rows { quad { p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 10 name_id: 39 } } } rows { quad { p_iri { prefix_id: 11 name_id: 16 } o_literal { lex: "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" } } } rows { name { value: "wasDerivedFrom" } } rows { prefix { value: "https://www.wolframscience.com/nks/p65--more-cellular-automata/" } } rows { quad { p_iri { prefix_id: 5 name_id: 40 } o_iri { prefix_id: 16 name_id: 2 } } } rows { name { value: "SoftwareAgent" } } rows { quad { s_iri { prefix_id: 13 name_id: 20 } p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 5 name_id: 41 } g_iri { prefix_id: 2 name_id: 7 } } } rows { quad { p_iri { prefix_id: 11 name_id: 16 } o_literal { lex: "delphisci claim tester (claude-fable-5.1; cursor/claim-tests-wolfram-nks-e5f4)" } } } rows { name { value: "actedOnBehalfOf" } } rows { prefix { id: 6 value: "https://orcid.org/" } } rows { name { value: "0009-0007-4948-9192" } } rows { quad { p_iri { prefix_id: 5 name_id: 42 } o_iri { prefix_id: 6 } } } rows { name { value: "usesModel" } } rows { prefix { id: 8 value: "https://w3id.org/delphi/resource/model/" } } rows { name { value: "claude-fable-5-1" } } rows { quad { p_iri { prefix_id: 10 } o_iri { prefix_id: 8 } } } rows { name { value: "identifier" } } rows { quad { s_iri { name_id: 45 } p_iri { prefix_id: 7 } o_literal { lex: "claude-fable-5.1" } } } rows { name { value: "LanguageModel" } } rows { quad { p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 10 name_id: 47 } } } rows { quad { s_iri { prefix_id: 2 name_id: 4 } p_iri { prefix_id: 5 name_id: 19 } o_iri { prefix_id: 13 } } } rows { quad { p_iri { prefix_id: 5 name_id: 40 } o_iri { prefix_id: 12 name_id: 18 } } } rows { name { value: "wasGeneratedBy" } } rows { name { value: "test" } } rows { quad { p_iri { prefix_id: 5 name_id: 48 } o_iri { prefix_id: 2 } } } rows { name { value: "plan" } } rows { name { value: "hadPlan" } } rows { prefix { id: 1 value: "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/" } } rows { name { value: "README.md" } } rows { quad { s_iri { } p_iri { prefix_id: 5 } o_iri { prefix_id: 1 } } } rows { name { value: "Activity" } } rows { quad { s_iri { prefix_id: 2 name_id: 49 } p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 5 name_id: 53 } } } rows { name { value: "qualifiedAssociation" } } rows { quad { p_iri { } o_iri { prefix_id: 2 name_id: 50 } } } rows { name { value: "wasAssociatedWith" } } rows { quad { p_iri { prefix_id: 5 name_id: 55 } o_iri { prefix_id: 13 name_id: 20 } } } rows { prefix { id: 3 value: "https://w3id.org/np/" } } rows { name { value: "created" } } rows { datatype { value: "http://www.w3.org/2001/XMLSchema#dateTime" } } rows { quad { s_iri { prefix_id: 3 name_id: 1 } p_iri { prefix_id: 7 name_id: 56 } o_literal { lex: "2026-11-08T16:24:31.919Z" datatype: 3 } g_iri { prefix_id: 2 name_id: 9 } } } rows { name { value: "creator" } } rows { quad { p_iri { prefix_id: 7 name_id: 57 } o_iri { prefix_id: 6 name_id: 43 } } } rows { prefix { id: 15 value: "https://creativecommons.org/licenses/by/4.0/" } } rows { quad { p_iri { prefix_id: 7 name_id: 38 } o_iri { prefix_id: 15 name_id: 2 } } } rows { prefix { id: 9 value: "http://purl.org/nanopub/x/" } } rows { name { value: "hasNanopubType" } } rows { quad { p_iri { prefix_id: 9 name_id: 58 } o_iri { prefix_id: 10 name_id: 14 } } } rows { name { value: "introduces" } } rows { prefix { id: 14 value: "https://w3id.org/delphi/resource/assessment/" } } rows { quad { p_iri { prefix_id: 9 name_id: 59 } o_iri { prefix_id: 14 name_id: 12 } } } rows { quad { p_iri { prefix_id: 11 name_id: 16 } o_literal { lex: "Claim test of wolfram2002-ch03-05: supports, confidence 0.75" } } } rows { name { value: "domain" } } rows { prefix { id: 16 value: "https://w3id.org/delphi/resource/domain/" } } rows { name { value: "wolfram-nks-2002" } } rows { quad { p_iri { prefix_id: 10 name_id: 60 } o_iri { prefix_id: 16 } } } rows { name { value: "sig" } } rows { name { value: "hasAlgorithm" } } rows { quad { s_iri { prefix_id: 2 } p_iri { prefix_id: 9 } o_literal { lex: "RSA" } } } rows { name { value: "hasPublicKey" } } rows { quad { p_iri { } o_literal { lex: "MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB" } } } rows { name { value: "hasSignature" } } rows { quad { p_iri { } o_literal { lex: "eoM3Ry3xwAX/fQE0aI7q1O1J+MepIfHHccKR2Jvw5jLD35y2WnJEDXYckjKwSdvDpryzWpMw4ojYH3Z1lNTWOYBkoZbapaixyOf6wD5QBwkvWg+9WfcYDhe7iAef7jB7pEn7Rvstn6Tac7K5u3UTFVHstbc2W/wFhBCNcBMmyfnS7QyCD+gmg4aaXtPFdGATcqY86bWUf9hibjG7rtv2hjEXs/uwzy6Rko/oflzb8kk8RB2Z9yXAKjAYk/T98Cn3GE/OuvlEtgagCNKOP8wfxaptnbmZlF7IqUBR6826GNyYrDeszpCdb52d5S4BuFv8x8FwJGWALsz1GE9+kd/IqQ==" } } } rows { name { value: "hasSignatureTarget" } } rows { quad { p_iri { } o_iri { prefix_id: 3 name_id: 1 } } } rows { name { value: "signedBy" } } rows { quad { p_iri { prefix_id: 9 name_id: 67 } o_iri { prefix_id: 6 name_id: 43 } } }