. . . . "analysis.py evolves rule 54 for 256 steps from every initial condition n = 1..65535 (binary digits of n on white; batches of 512 vectorised in numpy on a lattice wide enough that the light cone never reaches the edge), encodes every 6 x 6 space-time tile with top-left in rows 128..250 inside the light cone as a 36-bit integer and counts distinct tiles D; patterns with D <= 400 are also tested for exact temporal periodicity (period <= 16) of the light-cone core over steps 128..256. The 20 initial conditions with the largest D are re-run for 512 steps. Per-initial-condition values in derived/census.csv.xz; runtime about 3 minutes." . . "Measured: 0 number of initial conditions n <= 65536 whose rule-54 pattern has more than 1050 distinct 6x6 tiles in steps 128-256 (n = 65535, exhaustive over n = 1..65535 (n = 65536 has 17 bits and was not included)). Interpretation: The claim is a finite observational statement about the first 10^8 initial conditions; the full census is beyond a few minutes of Python, so this is a scaled census (2^16 initial conditions) with the book's informal judgement 'nothing fundamentally more complicated than repetitive or nested' frozen into a local-complexity classifier. The classifier counts distinct 6 x 6 space-time tiles in the second half of the evolution: self-similar (nested) and periodic patterns have bounded tile vocabularies, whereas class 3 patterns have thousands and class 4 patterns with interacting gliders over a thousand. The threshold was set from controls outside the rule-54 family plus the book's own eight rule-54 examples; it is admittedly coarse, and the random-seed rule 150 controls (nested, up to 1007) show that nested patterns with wide seeds approach it. A failure under this classifier would therefore need the T = 512 confirmation and visual inspection before being read as a counterexample to Wolfram's census." . "Claim test of wolfram2002-ch11-21: supports, confidence 0.6" . . . "Planned datasets: rule54-initial-condition-census" . "claim-test/0.1.0" . "computational" . "Pre-registered. The claim FAILS if at least one initial condition n <= 65536 has D > 1050 and the T = 512 re-run also gives D > 1050 (sustained local complexity comparable to the class 3/4 controls). If some exceed 1050 at T = 256 but not at T = 512 the verdict is 'mixed' (transient complexity). The census is 1/1526 of the book's 10^8 initial conditions; a pass is consistent with the claim but far from exhausting it." . "'Repetitive or nested' was frozen into a local-complexity classifier (distinct 6 x 6 space-time tiles) with a threshold set from controls outside the family (rule 90/150/22/18 nested, rules 250/108/184/62/41 repetitive, rules 110/30/45 complex) and the book's own eight rule-54 examples. The margin is large (426 observed vs. 1094 for the least complex rule-110 control) but the classifier is coarse: a class-4-like pattern with a small glider repertoire could in principle have a modest tile vocabulary, and nested patterns from wide seeds (rule 150 random 14-bit seeds reach 1007) approach the threshold." . "Finite horizon (256 steps, re-checks to 512): slowly developing complexity, e.g. structures appearing only after thousands of steps, would be missed." . "Pre-registered decision: 0 of 65,535 initial conditions exceeds the 1050-tile threshold (0 exceed even the stricter 700). The largest vocabulary is 426 tiles (n = 52843) and the twenty largest all fall back to 391 tiles at steps 256-512, the same vocabulary as the book's examples n = 787 and 803; the distribution is strongly clustered (median 68; 50,561 below 100; 214 between 400 and 500), consistent with a small repertoire of repetitive and nested forms. 17.2% of the patterns are exactly periodic in the core with period 4 over steps 128-256." . "This is a scaled census: 2^16 initial conditions rather than the 10^8 of the book, i.e. seeds of at most 16 cells, so wider seeds (where interacting structures are more likely) are untested; a pass here is consistent with Wolfram's census but does not reproduce it." . "Pre-registered. Family: initial conditions n = 1..65536 (16 bits), cell values = binary digits of n placed on an infinite white background (validated against the figure: n = 1 single cell, n = 3 two cells, n = 291 nested); rule 54 run for T = 256 steps on a lattice wide enough that the light cone never reaches the edge. Classifier (frozen before the census): the number D of distinct 6 x 6 space-time tiles whose top-left corner lies in rows 128..250 and inside the light cone (plus 2 cells) of the pattern. Calibration on controls outside the family, disclosed: repetitive and nested rules give D <= 1007 (rule 90 single cell 115, random 14-bit seeds 267-395; rule 150 single 316, random seeds 804-1007; rule 22 single 119; rule 18 random 309-602; rules 250, 108, 184, 62, 41 random 1-178), while class 3/4 controls give D >= 1094 (rule 110 random 14- and 30-bit seeds 1094-1553; rule 30 6801-7166; rule 45 6338-6401), with a few class-3 rules from narrow seeds in between (rule 106: 462 and 2912; rule 126: 130-402; rule 146: 371-413; rule 73: 64-774). The eight rule-54 patterns shown in the book's figure (n = 1, 3, 75, 259, 291, 787, 803, 56549) give D = 10, 37, 315, 315, 286, 391, 391, 370, and a batch of 256 random 14-bit seeds gave max 391. Threshold: D > 1050 (geometric midpoint of 1007 and 1094) = 'more complicated'. Also recorded per initial condition: exact temporal periodicity (period <= 16) of the pattern's core over steps 128..256 ('repetitive'). The claim PASSES if 0 of the 65536 initial conditions has D > 1050. Reported, not decisive: the distribution of D, the fraction that is exactly periodic, the number with D > 700 (a stricter threshold that still clears all rule-54 book examples), and for any initial condition above threshold a re-run with T = 512." . "Pre-registered. The claim FAILS if at least one initial condition n <= 65536 has D > 1050 and the T = 512 re-run also gives D > 1050 (sustained local complexity comparable to the class 3/4 controls). If some exceed 1050 at T = 256 but not at T = 512 the verdict is 'mixed' (transient complexity). The census is 1/1526 of the book's 10^8 initial conditions; a pass is consistent with the claim but far from exhausting it." . "0.6"^^ . . "supports" . "Rule 54, run from each of the first N initial conditions (binary digits of n on a white background, as in NKS p. 697), produces only repetitive or nested patterns: none has the local space-time complexity characteristic of class 3 or class 4 behaviour." . "analysis.py evolves rule 54 for 256 steps from every initial condition n = 1..65535 (binary digits of n on white; batches of 512 vectorised in numpy on a lattice wide enough that the light cone never reaches the edge), encodes every 6 x 6 space-time tile with top-left in rows 128..250 inside the light cone as a 36-bit integer and counts distinct tiles D; patterns with D <= 400 are also tested for exact temporal periodicity (period <= 16) of the light-cone core over steps 128..256. The 20 initial conditions with the largest D are re-run for 512 steps. Per-initial-condition values in derived/census.csv.xz; runtime about 3 minutes." . "Pre-registered. Family: initial conditions n = 1..65536 (16 bits), cell values = binary digits of n placed on an infinite white background (validated against the figure: n = 1 single cell, n = 3 two cells, n = 291 nested); rule 54 run for T = 256 steps on a lattice wide enough that the light cone never reaches the edge. Classifier (frozen before the census): the number D of distinct 6 x 6 space-time tiles whose top-left corner lies in rows 128..250 and inside the light cone (plus 2 cells) of the pattern. Calibration on controls outside the family, disclosed: repetitive and nested rules give D <= 1007 (rule 90 single cell 115, random 14-bit seeds 267-395; rule 150 single 316, random seeds 804-1007; rule 22 single 119; rule 18 random 309-602; rules 250, 108, 184, 62, 41 random 1-178), while class 3/4 controls give D >= 1094 (rule 110 random 14- and 30-bit seeds 1094-1553; rule 30 6801-7166; rule 45 6338-6401), with a few class-3 rules from narrow seeds in between (rule 106: 462 and 2912; rule 126: 130-402; rule 146: 371-413; rule 73: 64-774). The eight rule-54 patterns shown in the book's figure (n = 1, 3, 75, 259, 291, 787, 803, 56549) give D = 10, 37, 315, 315, 286, 391, 391, 370, and a batch of 256 random 14-bit seeds gave max 391. Threshold: D > 1050 (geometric midpoint of 1007 and 1094) = 'more complicated'. Also recorded per initial condition: exact temporal periodicity (period <= 16) of the pattern's core over steps 128..256 ('repetitive'). The claim PASSES if 0 of the 65536 initial conditions has D > 1050. Reported, not decisive: the distribution of D, the fraction that is exactly periodic, the number with D > 700 (a stricter threshold that still clears all rule-54 book examples), and for any initial condition above threshold a re-run with T = 512." . "false"^^ . . "program family under test" . "generated data" . . "Dataset: Rule 54 from initial conditions 1..65536 (generated by analysis.py)" . . . "delphisci claim tester (claude-fable-5.1; cursor/wolfram-nks-claim-tests-106e)" . . . "claude-fable-5.1" . . . . . . . . . "2026-11-08T16:24:31.940Z"^^ . . . . . "Claim test of wolfram2002-ch11-21: supports, confidence 0.6" . . "RSA" . 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