. . . . "analysis.py evolves rule 110 from one black cell and cuts out rows 80..159, columns 60..139. It fits a first-order Markov chain to within-row transitions, draws 80 rows with random.Random(20261102), and compares transition frequencies, 4-bit block entropy, and vertical agreement. A second run matched derived/measured.json byte for byte." . . "Measured: 0.7884493670886076 vertical agreement of consecutive rule-110 rows in the 80 by 80 window (n = 6320, exact window; the Markov sample is one seeded draw of 80 rows). Interpretation: The probabilistic model is a first-order Markov chain, one of the kinds the claim names. It is fit to one deterministic rule, elementary rule 110, in one window. 'Reproduce the statistics used in fitting' is the sample's transition probabilities staying within 0.05 of the fit. 'More random' is a 4-bit block entropy at least 0.03 higher. The detailed feature is vertical agreement between consecutive rows, which the cellular automaton has because each row determines the next, and which independent Markov rows are not built to keep. One rule and one model do not survey every probabilistic fit. The computation says nothing about organisms." . "Claim test of wolfram2002-ch10-13: mixed, confidence 0.73" . . . "The rule-110 window and the Markov samples generated by the checksummed script, with the locked bounds and seed 20261102. No organism record is admissible." . "claim-test/0.1.0" . "computational" . "The samples match the transitions within 0.05, and they are neither 0.03 higher in h4 nor 0.15 lower in vertical agreement." . "The sample transitions stay within 0.05 of the fit: P(1|0) is 0.14779602420051857 against 0.15256899259591652, and P(1|1) is 0.5975177304964538 against 0.6162104133118625. Vertical agreement falls from 0.7884493670886076 to 0.5977848101265822, past the locked gap of 0.15. Block entropy does not rise: sample h4 is 0.7375219947505822 and data h4 is 0.746435604101548. One gap holds and one does not." . "This is a computation about rule 110 and one probabilistic model. It says nothing about organisms." . "This is one rule, one 80 by 80 window, and an order-1 Markov chain. A higher-order model could keep more of the vertical agreement. A different rule could raise the sample entropy. The thresholds were not changed after the run." . "Samples from the Markov chain fit to the rule-110 window match both transition probabilities within 0.05, have h4 at least 0.03 above the data, and have vertical agreement at least 0.15 below the data." . "Pre-registered. Refutes if the transitions match within 0.05 and both gaps fail: sample h4 < data h4 + 0.03 and data vertical agreement < sample vertical agreement + 0.15. Mixed if the transitions match and exactly one gap fails. Inconclusive if either transition has no observations or the sample misses a fitted transition by more than 0.05." . "0.73"^^ . . . "mixed" . "A first-order Markov chain fit to rows of rule 110 reproduces its own transition probabilities, while its samples have higher 4-bit block entropy than the cellular-automaton rows and lose the rows' vertical agreement." . "Fit the transitions, redraw 80 rows, and compare transition error, h4, and vertical agreement with the locked gaps. Both gaps plus a transition match supports. A transition match with both gaps failing refutes. One gap is mixed. A missed transition is inconclusive." . "Pre-registered. Rule 110, one black cell at index 100, homogeneous white background, width 201, t = 0..160. Data: rows 80..159, columns 60..139 (80 by 80). The Markov chain uses within-row transitions only. P(1) is the bit frequency. Eighty sample rows of length 80 are drawn with random.Random(20261102). h4 is the normalized 4-bit block entropy of the concatenated rows. Vertical agreement is the fraction of cells equal to the cell above. Supports if and only if both sample transitions are within 0.05 of the fitted transitions, sample h4 >= data h4 + 0.03, and data vertical agreement >= sample vertical agreement + 0.15." . "false"^^ . . "deterministic data the Markov chain is fit to" . "" . . "Dataset: Rule 110 rows from one black cell" . "sha256:62fb3c2bab77d57ed49803b1d51d496f1e56e845e841a8c2d988ca0473f1509c" . "typical samples from the fitted model" . "" . . "Dataset: Eighty rows drawn from the fitted first-order Markov chain" . . "delphisci claim tester (Grok 4.7; cursor/claim-tests-wolfram-programs-b8d9)" . . . "Grok 4.7" . . . . . . . . . "2026-11-08T16:24:31.935Z"^^ . . . . . "Claim test of wolfram2002-ch10-13: mixed, confidence 0.73" . . "RSA" . 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