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: "RAg9pnroLV2vhxGng11SRTWhCRiGT2KFgCFVhOfjpH444" } } rows { namespace { name: "this" value { prefix_id: 1 } } } rows { prefix { value: "https://w3id.org/np/RAg9pnroLV2vhxGng11SRTWhCRiGT2KFgCFVhOfjpH444/" } } 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-ch06-14--claim-test" } } rows { name { value: "description" } } rows { quad { s_iri { prefix_id: 9 } p_iri { prefix_id: 7 } o_literal { lex: "analysis.py generates the rule 30 centre column for 2^20 steps from a single black cell (S1) and from a seeded random row of width 2^21+1 (S2) using big-integer bit operations, a PCG64 stream (S3) and the Thue-Morse sequence (S4), checks S1 against all 100001 terms of the OEIS A051023 b-file, and applies ten NIST SP 800-22-style tests (monobit, block frequency M=128, runs, longest run M=10000, serial m=16, approximate entropy m=10, cumulative sums, DFT, Bonferroni autocorrelation over lags 1-64, 16-bit block chi-square) plus the lzma compression ratio to each. Runtime about 5 min, dominated by the two 2^20-step evolutions." } 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: 10 randomness tests passed (p >= 0.01) by the rule 30 single-cell centre column, out of 10 (n = 1048576, at alpha = 0.01 per test a truly random sequence fails at least one of 10 tests with probability about 0.10). Interpretation: \'Random behaviour\' is read as the book itself reads it (practical randomness, pp. 261 and 1085 ff.): the sequence passes standard statistical tests and is incompressible, not algorithmic randomness, which no finite test can establish. \'No randomness in initial conditions\' is realised by the single-black-cell seed; the book\'s own comparison (p. 261) is with random initial conditions, so S2 is the matched control and S4 is a control for a deterministic but nested (non-random) sequence that the battery must reject for the test to be discriminating. Rule 22 is also mentioned in the claim\'s context but its single-cell pattern is nested; only rule 30, the book\'s example on this page, is tested." } } } rows { name { value: "label" } } rows { quad { p_iri { } o_literal { lex: "Claim test of wolfram2002-ch06-14: supports, confidence 0.9" } } } rows { name { value: "seeAlso" } } rows { prefix { value: "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch06-14/" } } 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: rule30-centre-column-generator, oeis-a051023-bfile" } } } 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. FAIL (refutes) if S1 passes 7 or fewer of the 10 tests or has lzma ratio < 0.98 (an exploitable regularity), or if S1 disagrees with OEIS A051023 (then the generator is wrong and the test is aborted as inconclusive/other). If S1 passes exactly 8, or S4 fails fewer than 4 tests (battery not discriminating), the verdict is \'mixed\'. If the OEIS file cannot be fetched the OEIS cross-check is dropped and reported, and the verdict rests on the generated sequences." } } } rows { name { value: "evidenceAgainst" } } rows { quad { p_iri { } o_literal { lex: "Only rule 30 was tested. Rule 22, also named in the claim\'s context, gives a nested pattern from a single black cell, and the book\'s example on p. 261 is rule 30." } } } rows { quad { o_literal { lex: "Passing a finite statistical battery is practical randomness, the sense the book uses; it does not establish algorithmic randomness or exclude a regularity invisible to these tests (the sequence is of course computable)." } } } rows { quad { o_literal { lex: "S1\'s smallest p-value is 0.037 (approximate entropy, m = 10); with ten tests at alpha = 0.01 a single marginal value is expected. S2 (random initial row) had its smallest p-value at 0.018 (cumulative sums). Both rule 30 columns are statistically indistinguishable from the PCG64 stream in this battery, while Thue-Morse fails 7 of 10 tests and compresses to 0.4% of its size." } } } rows { quad { o_literal { lex: "The 16-bit block chi-square test has expected count 1 per cell, so its chi-square p-value is approximate (the true null variance of the statistic is about 1.5 times the chi-square value); the same approximation is applied to all four sequences and S1 passed it with p = 0.26." } } } rows { name { value: "expectedObservation" } } rows { quad { p_iri { } o_literal { lex: "Pre-registered. Sequences of N = 2^20 bits: (S1) rule 30 centre column from a single black cell; (S2) rule 30 centre column from a random initial row (numpy seed 20261031, width 2N+1, so that the column is exactly the random-initial-condition case); (S3) numpy PCG64 bits, seed 20261031; (S4) the Thue-Morse sequence. Battery of 10 tests, each giving a p-value with pass meaning p >= 0.01: monobit frequency; block frequency (M = 128); runs; longest run of ones (M = 10000, K = 6); serial (m = 16, minimum of the two p-values); approximate entropy (m = 10); cumulative sums (minimum of forward and backward); discrete Fourier transform spectral test; autocorrelation (lags 1..64, Bonferroni-corrected normal p-value of the largest |r|); and a 16-bit non-overlapping block chi-square uniformity test. Also record the lzma compression ratio of the packed bits. PASS (supports) if S1 passes at least 9 of 10 tests and has lzma ratio >= 0.99, S2 and S3 each pass at least 9 of 10, S4 fails at least 4 tests, and the first terms of S1 agree exactly with the OEIS A051023 b-file over the whole length of the b-file." } } } rows { name { value: "failCriterion" } } rows { quad { p_iri { } o_literal { lex: "Pre-registered. FAIL (refutes) if S1 passes 7 or fewer of the 10 tests or has lzma ratio < 0.98 (an exploitable regularity), or if S1 disagrees with OEIS A051023 (then the generator is wrong and the test is aborted as inconclusive/other). If S1 passes exactly 8, or S4 fails fewer than 4 tests (battery not discriminating), the verdict is \'mixed\'. If the OEIS file cannot be fetched the OEIS cross-check is dropped and reported, and the verdict rests on the generated sequences." } } } rows { name { value: "hasConfidence" } } rows { datatype { value: "http://www.w3.org/2001/XMLSchema#double" } } rows { quad { p_iri { } o_literal { lex: "0.9" datatype: 1 } } } rows { name { value: "hasEvidence" } } rows { prefix { value: "https://w3id.org/delphi/resource/evidence/" } } rows { name { value: "wolfram2002-ch06-14--claim-test--dataset-1" } } rows { quad { p_iri { } o_iri { prefix_id: 14 } } } rows { name { value: "wolfram2002-ch06-14--claim-test--dataset-2" } } rows { quad { o_iri { } } } 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: "If the claim holds, the centre column of rule 30 started from a single black cell (an initial condition with no randomness) passes a standard battery of statistical randomness tests as well as the centre column of rule 30 started from a random initial condition and as well as a pseudo-random reference stream, whereas a nested deterministic sequence (Thue-Morse) fails the same battery." } } } rows { name { value: "inferenceMethod" } } rows { quad { p_iri { } o_literal { lex: "analysis.py generates the rule 30 centre column for 2^20 steps from a single black cell (S1) and from a seeded random row of width 2^21+1 (S2) using big-integer bit operations, a PCG64 stream (S3) and the Thue-Morse sequence (S4), checks S1 against all 100001 terms of the OEIS A051023 b-file, and applies ten NIST SP 800-22-style tests (monobit, block frequency M=128, runs, longest run M=10000, serial m=16, approximate entropy m=10, cumulative sums, DFT, Bonferroni autocorrelation over lags 1-64, 16-bit block chi-square) plus the lzma compression ratio to each. Runtime about 5 min, dominated by the two 2^20-step evolutions." } } } rows { name { value: "passCriterion" } } rows { quad { p_iri { } o_literal { lex: "Pre-registered. Sequences of N = 2^20 bits: (S1) rule 30 centre column from a single black cell; (S2) rule 30 centre column from a random initial row (numpy seed 20261031, width 2N+1, so that the column is exactly the random-initial-condition case); (S3) numpy PCG64 bits, seed 20261031; (S4) the Thue-Morse sequence. Battery of 10 tests, each giving a p-value with pass meaning p >= 0.01: monobit frequency; block frequency (M = 128); runs; longest run of ones (M = 10000, K = 6); serial (m = 16, minimum of the two p-values); approximate entropy (m = 10); cumulative sums (minimum of forward and backward); discrete Fourier transform spectral test; autocorrelation (lags 1..64, Bonferroni-corrected normal p-value of the largest |r|); and a 16-bit non-overlapping block chi-square uniformity test. Also record the lzma compression ratio of the packed bits. PASS (supports) if S1 passes at least 9 of 10 tests and has lzma ratio >= 0.99, S2 and S3 each pass at least 9 of 10, S4 fails at least 4 tests, and the first terms of S1 agree exactly with the OEIS A051023 b-file over the whole length of the b-file." } } } 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-ch06-14" } } 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 sequences whose randomness is tested" } } } rows { name { value: "license" } } rows { quad { p_iri { name_id: 39 } o_literal { lex: "generated by this test" } } } rows { name { value: "EvidenceItem" } } rows { quad { p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 10 name_id: 40 } } } rows { quad { p_iri { prefix_id: 11 name_id: 16 } o_literal { lex: "Dataset: Rule 30 centre column from a single black cell and from a random initial row, pseudo-random reference bits, and the Thue-Morse sequence, 2^20 bits each, generated by analysis.py" } } } rows { name { value: "wasDerivedFrom" } } rows { prefix { value: "https://www.wolframscience.com/nks/p261--randomness-in-class-3-systems/" } } rows { quad { p_iri { prefix_id: 5 name_id: 41 } o_iri { prefix_id: 16 name_id: 2 } } } rows { quad { s_iri { prefix_id: 14 name_id: 31 } p_iri { prefix_id: 7 name_id: 13 } o_literal { lex: "independent published copy of the centre column to validate the generator" } } } rows { quad { p_iri { name_id: 39 } o_literal { lex: "CC BY-SA 4.0 (OEIS)" } } } rows { quad { p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 10 name_id: 40 } } } rows { quad { p_iri { prefix_id: 11 name_id: 16 } o_literal { lex: "Dataset: OEIS A051023, middle column of rule 30 from a single black cell (b-file)" } } } rows { name { value: "atLocation" } } rows { prefix { id: 6 value: "https://oeis.org/A051023/" } } rows { name { value: "b051023.txt" } } rows { quad { p_iri { prefix_id: 5 name_id: 42 } o_iri { prefix_id: 6 } } } rows { prefix { id: 8 value: "https://oeis.org/" } } rows { name { value: "A051023" } } rows { quad { p_iri { prefix_id: 5 name_id: 41 } o_iri { prefix_id: 8 name_id: 44 } } } rows { name { value: "hasChecksum" } } rows { quad { p_iri { prefix_id: 10 } o_literal { lex: "sha256:4d0c4a0272bc2b0fb5c1e91281d6dffc757d67cd6ffd8aa9f7486dac4685c1a9" } } } 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: 46 } 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-9241)" } } } rows { name { value: "actedOnBehalfOf" } } rows { prefix { id: 1 value: "https://orcid.org/" } } rows { name { value: "0009-0007-4948-9192" } } rows { quad { p_iri { prefix_id: 5 name_id: 47 } o_iri { prefix_id: 1 } } } rows { name { value: "usesModel" } } rows { prefix { id: 3 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: 3 } } } rows { name { value: "identifier" } } rows { quad { s_iri { name_id: 50 } 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: 52 } } } 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: 41 } 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: 53 } o_iri { prefix_id: 2 } } } rows { name { value: "plan" } } rows { name { value: "hadPlan" } } rows { prefix { id: 15 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: 15 } } } rows { name { value: "Activity" } } rows { quad { s_iri { prefix_id: 2 name_id: 54 } p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 5 name_id: 58 } } } rows { name { value: "qualifiedAssociation" } } rows { quad { p_iri { } o_iri { prefix_id: 2 name_id: 55 } } } rows { name { value: "wasAssociatedWith" } } rows { quad { p_iri { prefix_id: 5 name_id: 60 } o_iri { prefix_id: 13 name_id: 20 } } } rows { prefix { id: 9 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: 9 name_id: 1 } p_iri { prefix_id: 7 name_id: 61 } o_literal { lex: "2026-11-08T16:24:31.927Z" datatype: 3 } g_iri { prefix_id: 2 name_id: 9 } } } rows { name { value: "creator" } } rows { quad { p_iri { prefix_id: 7 name_id: 62 } o_iri { prefix_id: 1 name_id: 48 } } } rows { prefix { id: 16 value: "https://creativecommons.org/licenses/by/4.0/" } } rows { quad { p_iri { prefix_id: 7 name_id: 39 } o_iri { prefix_id: 16 name_id: 2 } } } rows { prefix { id: 14 value: "http://purl.org/nanopub/x/" } } rows { name { value: "hasNanopubType" } } rows { quad { p_iri { prefix_id: 14 name_id: 63 } o_iri { prefix_id: 10 name_id: 14 } } } rows { name { value: "introduces" } } rows { prefix { id: 6 value: "https://w3id.org/delphi/resource/assessment/" } } rows { quad { p_iri { prefix_id: 14 name_id: 64 } o_iri { prefix_id: 6 name_id: 12 } } } rows { quad { p_iri { prefix_id: 11 name_id: 16 } o_literal { lex: "Claim test of wolfram2002-ch06-14: supports, confidence 0.9" } } } rows { name { value: "domain" } } rows { prefix { id: 8 value: "https://w3id.org/delphi/resource/domain/" } } rows { name { value: "wolfram-nks-2002" } } rows { quad { p_iri { prefix_id: 10 name_id: 65 } o_iri { prefix_id: 8 } } } rows { name { value: "sig" } } rows { name { value: "hasAlgorithm" } } rows { quad { s_iri { prefix_id: 2 } p_iri { prefix_id: 14 } 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: "AUn4czodZkhTOBzGp3i/nMM5UdarDbD4q6rIIOnX9T6kbQnxT2sx8TBnZdK69w8J10XFjyG7QNX4zE9X+hZrZ2mUGrDtVQu5fTcDr+7/knlZDF2ozxcPdltD0aLDG8KrmaAj+Lq8gDxch2WgfFM7bG7hnq772wx3AeHV9vT/2d2mKYD2monItJsujAc3yASALcaH/mzNN11mEOuAyuJhqVfYjFZZJM9/t9NmsLmF7vUDGi3nrts4YV4LPrppn3Y+BJKoZjae8rQzgIEzDj1xB+QShvOBCboBxiFYt8034+B1a+0iDcC7DCdhvVUcco+IlbR/L+rD8hO/EYP/UK0r0w==" } } } rows { name { value: "hasSignatureTarget" } } rows { quad { p_iri { } o_iri { prefix_id: 9 name_id: 1 } } } rows { name { value: "signedBy" } } rows { quad { p_iri { prefix_id: 14 name_id: 72 } o_iri { prefix_id: 1 name_id: 48 } } }