@prefix this: . @prefix sub: . @prefix np: . @prefix rdf: . @prefix prov: . @prefix npx: . @prefix dc: . @prefix xsd: . sub:Head { this: a np:Nanopublication; np:hasAssertion sub:assertion; np:hasProvenance sub:provenance; np:hasPublicationInfo sub:pubinfo . } sub:assertion { a ; dc:description "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."; "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."; "Claim test of wolfram2002-ch06-14: supports, confidence 0.9"; ; prov:wasAttributedTo ; "Planned datasets: rule30-centre-column-generator, oeis-a051023-bfile"; "claim-test/0.1.0"; "computational"; "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."; "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.", "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).", "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.", "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."; "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."; "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."; "0.9"^^xsd:double; , ; "supports"; "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."; "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."; "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."; "false"^^xsd:boolean . . a ; dc:description "the sequences whose randomness is tested"; dc:license "generated by this test"; "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"; prov:wasDerivedFrom . a ; dc:description "independent published copy of the centre column to validate the generator"; dc:license "CC BY-SA 4.0 (OEIS)"; "Dataset: OEIS A051023, middle column of rule 30 from a single black cell (b-file)"; prov:atLocation ; prov:wasDerivedFrom ; "sha256:4d0c4a0272bc2b0fb5c1e91281d6dffc757d67cd6ffd8aa9f7486dac4685c1a9" . } sub:provenance { a prov:SoftwareAgent; "delphisci claim tester (claude-fable-5.1; cursor/claim-tests-wolfram-nks-9241)"; prov:actedOnBehalfOf ; . a ; dc:identifier "claude-fable-5.1" . sub:assertion prov:wasAttributedTo ; prov:wasDerivedFrom ; prov:wasGeneratedBy sub:test . sub:plan prov:hadPlan . sub:test a prov:Activity; prov:qualifiedAssociation sub:plan; prov:wasAssociatedWith . } sub:pubinfo { this: dc:created "2026-11-08T16:24:31.927Z"^^xsd:dateTime; dc:creator ; dc:license ; npx:hasNanopubType ; npx:introduces ; "Claim test of wolfram2002-ch06-14: supports, confidence 0.9"; . sub:sig npx:hasAlgorithm "RSA"; npx:hasPublicKey "MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB"; npx:hasSignature "AUn4czodZkhTOBzGp3i/nMM5UdarDbD4q6rIIOnX9T6kbQnxT2sx8TBnZdK69w8J10XFjyG7QNX4zE9X+hZrZ2mUGrDtVQu5fTcDr+7/knlZDF2ozxcPdltD0aLDG8KrmaAj+Lq8gDxch2WgfFM7bG7hnq772wx3AeHV9vT/2d2mKYD2monItJsujAc3yASALcaH/mzNN11mEOuAyuJhqVfYjFZZJM9/t9NmsLmF7vUDGi3nrts4YV4LPrppn3Y+BJKoZjae8rQzgIEzDj1xB+QShvOBCboBxiFYt8034+B1a+0iDcC7DCdhvVUcco+IlbR/L+rD8hO/EYP/UK0r0w=="; npx:hasSignatureTarget this:; npx:signedBy . }