[ { "@id": "https://w3id.org/np/RAg9pnroLV2vhxGng11SRTWhCRiGT2KFgCFVhOfjpH444/assertion", "@graph": [ { "@id": "https://w3id.org/delphi/resource/assessment/wolfram2002-ch06-14--claim-test", "http://purl.org/dc/terms/description": [ { "@value": "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." } ], "@type": [ "https://w3id.org/delphi/ontology/Assessment" ], "http://www.w3.org/2000/01/rdf-schema#comment": [ { "@value": "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." } ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "Claim test of wolfram2002-ch06-14: supports, confidence 0.9" } ], "http://www.w3.org/2000/01/rdf-schema#seeAlso": [ { "@id": "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch06-14/result.json" } ], "http://www.w3.org/ns/prov#wasAttributedTo": [ { "@id": "https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1" } ], "https://w3id.org/delphi/ontology/admissibleDatasets": [ { "@value": "Planned datasets: rule30-centre-column-generator, oeis-a051023-bfile" } ], "https://w3id.org/delphi/ontology/assessmentType": [ { "@value": "claim-test/0.1.0" } ], "https://w3id.org/delphi/ontology/dataKind": [ { "@value": "computational" } ], "https://w3id.org/delphi/ontology/disconfirmingObservation": [ { "@value": "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." } ], "https://w3id.org/delphi/ontology/evidenceAgainst": [ { "@value": "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." }, { "@value": "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)." }, { "@value": "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." }, { "@value": "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." } ], "https://w3id.org/delphi/ontology/expectedObservation": [ { "@value": "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." } ], "https://w3id.org/delphi/ontology/failCriterion": [ { "@value": "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." } ], "https://w3id.org/delphi/ontology/hasConfidence": [ { "@value": "0.9", "@type": "http://www.w3.org/2001/XMLSchema#double" } ], "https://w3id.org/delphi/ontology/hasEvidence": [ { "@id": "https://w3id.org/delphi/resource/evidence/wolfram2002-ch06-14--claim-test--dataset-1" }, { "@id": "https://w3id.org/delphi/resource/evidence/wolfram2002-ch06-14--claim-test--dataset-2" } ], "https://w3id.org/delphi/ontology/hasVerdict": [ { "@value": "supports" } ], "https://w3id.org/delphi/ontology/hypothesis": [ { "@value": "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." } ], "https://w3id.org/delphi/ontology/inferenceMethod": [ { "@value": "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." } ], "https://w3id.org/delphi/ontology/passCriterion": [ { "@value": "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. 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