https://w3id.org/np/RAAkC3IEmp8I6dAG_U8yJD57WXwevdnP61-rUHBBarpW0
.trig | .trig.txt | .jelly | .jelly.txt | .jsonld | .jsonld.txt | .nq | .nq.txt | .xml | .xml.txt
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dc:description "analysis.py evaluates all 256 rules. Damage spreading: 20 seeded random initial conditions on a 1601-cell open lattice, centre cell flipped in a copy, damage width after 400 steps; propagating if width >= 100 in >= 10 trials. Price series: ring of 400 cells, seeded random initial condition, 1000 transient steps, d(t) = #black - #white for 4096 steps; exact-periodicity scan over periods <= 2048; lzma compression of the int16 first differences compared with their plug-in marginal entropy. Per-rule values in derived/rules.csv; runtime about 1 minute.";
<http://www.w3.org/2000/01/rdf-schema#comment> "Measured: 0.825 fraction of propagating rules whose black-minus-white series is significantly random (n = 40, 40 propagating rules; 33 random, 7 not). Interpretation: Wolfram's market model (p. 431-432) is a one-dimensional CA of buy/sell agents, with 'price' the running difference of black and white counts; his figure uses rule 90. 'Information will eventually propagate from one entity to all others' is read as damage spreading in the sense he uses in Chapter 6: the set of cells affected by a one-cell change grows without bound (linear growth of the damage width), which excludes pure shifts and travelling defects whose influence merely moves. 'Significant randomness' of the running totals is read as non-periodicity plus incompressibility of the increments of the black-minus-white count. 'Essentially inevitable' is read as at least 90% of the propagating rules. The claim is a universal statement over the family, so the test looks for counterexamples.";
<http://www.w3.org/2000/01/rdf-schema#label> "Claim test of wolfram2002-ch08-30: mixed, confidence 0.6";
<http://www.w3.org/2000/01/rdf-schema#seeAlso> <https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch08-30/result.json>;
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<https://w3id.org/delphi/ontology/admissibleDatasets> "Planned datasets: eca-market-model-family";
<https://w3id.org/delphi/ontology/assessmentType> "claim-test/0.1.0";
<https://w3id.org/delphi/ontology/dataKind> "computational";
<https://w3id.org/delphi/ontology/disconfirmingObservation> "Pre-registered. The claim FAILS if fewer than 75% of propagating rules are significantly random (several counterexamples to 'essentially inevitable' inside the stated family). Between 75% and 90% the verdict is 'mixed'. If fewer than 5 rules are propagating under the definition the test is underpowered (inconclusive).";
<https://w3id.org/delphi/ontology/evidenceAgainst> "Conclusions depend on the finite ring (400 cells) and horizon (4096 steps after 1000 transient); on an infinite lattice class-4 rules would keep producing gliders and the period-4 rules might not settle. 'Significant randomness' is operationalised by non-periodicity and increment incompressibility only.",
"The 7 counterexamples form two equivalence classes under mirror/complement symmetry. Rules 41, 97, 107, 121 spread damage during their long transient on the open lattice but settle on the 400-cell ring into a period-4 cycle within 1000 steps, so d(t) is exactly periodic; whether such rules count as 'information eventually propagating to all others' is a definitional question the pre-registration resolved in favour of counting them. Rules 124, 137, 193 (the symmetry partners of rule 110) are non-periodic but their increments compress to 0.37-0.40 of the marginal entropy, below the 0.5 threshold, because on a 400-cell ring few gliders survive and d(t) is nearly periodic with small fluctuations; rule 110 itself passed with ratio 1.03 from a different random seed, which shows the class-4 verdicts are seed- and size-sensitive.",
"The damage-width definition of propagation excludes shifts and single travelling defects (e.g. rules 170, 184), whose influence reaches every cell on a ring but does not spread; under a footprint definition those rules would be additional counterexamples (their d(t) is constant).",
"The measured fraction 0.825 (33/40) falls in the pre-registered 'mixed' band (0.75-0.90). The converse direction, which the claim does not assert, is clean: 0 of 216 non-propagating rules has a significantly random count series, so propagation is at least necessary for randomness in this model.";
<https://w3id.org/delphi/ontology/expectedObservation> "Pre-registered. Family: all 256 elementary CA rules (Wolfram numbering), two colours, nearest neighbours. Propagation test (per rule): 20 trials; lattice of 1601 cells (non-wrapping: cells outside are fixed to the random background and the lattice is wide enough that the perturbation cannot reach the edge in 400 steps), random initial condition with density 1/2 from a fixed seed, second copy with the centre cell flipped; after 400 steps the damage width w = (rightmost differing cell - leftmost differing cell + 1) is recorded (0 if no cell differs); a rule is 'propagating' if w >= 100 (= 0.25 x 400, i.e. the damaged region grows linearly rather than staying bounded or merely moving) in at least 10 of 20 trials. Price-series test (per rule): ring of N = 400 cells, random initial condition density 1/2 from a fixed seed, discard 1000 transient steps, record d(t) = (#black - #white) for W = 4096 further steps; d(t) is 'significantly random' if (R1) it is not exactly periodic with any period p <= W/2 within the window and (R2) the first differences D(t) = d(t+1) - d(t), stored as int16, have plug-in marginal entropy H >= 1 bit and lzma (preset 9|EXTREME) compressed size >= 0.5 x H bits per sample. Calibration on controls: i.i.d. binomial counts give ratio 1.35, an AR(1) series 1.40, a period-97 series 0.09, a noiseless sinusoid 0.47. The claim PASSES if at least 90% of propagating rules are significantly random. Reported, not decisive: the fraction of non-propagating rules that are significantly random, and the list of propagating-but-not-random rules.";
<https://w3id.org/delphi/ontology/failCriterion> "Pre-registered. The claim FAILS if fewer than 75% of propagating rules are significantly random (several counterexamples to 'essentially inevitable' inside the stated family). Between 75% and 90% the verdict is 'mixed'. If fewer than 5 rules are propagating under the definition the test is underpowered (inconclusive).";
<https://w3id.org/delphi/ontology/hasConfidence> "0.6"^^xsd:double;
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<https://w3id.org/delphi/ontology/hasVerdict> "mixed";
<https://w3id.org/delphi/ontology/hypothesis> "Among the 256 elementary cellular automata run from random initial conditions, (almost) every rule in which a single-cell perturbation spreads to an ever-growing set of cells produces a black-minus-white count series that is non-periodic and incompressible relative to its own increment distribution.";
<https://w3id.org/delphi/ontology/inferenceMethod> "analysis.py evaluates all 256 rules. Damage spreading: 20 seeded random initial conditions on a 1601-cell open lattice, centre cell flipped in a copy, damage width after 400 steps; propagating if width >= 100 in >= 10 trials. Price series: ring of 400 cells, seeded random initial condition, 1000 transient steps, d(t) = #black - #white for 4096 steps; exact-periodicity scan over periods <= 2048; lzma compression of the int16 first differences compared with their plug-in marginal entropy. Per-rule values in derived/rules.csv; runtime about 1 minute.";
<https://w3id.org/delphi/ontology/passCriterion> "Pre-registered. Family: all 256 elementary CA rules (Wolfram numbering), two colours, nearest neighbours. Propagation test (per rule): 20 trials; lattice of 1601 cells (non-wrapping: cells outside are fixed to the random background and the lattice is wide enough that the perturbation cannot reach the edge in 400 steps), random initial condition with density 1/2 from a fixed seed, second copy with the centre cell flipped; after 400 steps the damage width w = (rightmost differing cell - leftmost differing cell + 1) is recorded (0 if no cell differs); a rule is 'propagating' if w >= 100 (= 0.25 x 400, i.e. the damaged region grows linearly rather than staying bounded or merely moving) in at least 10 of 20 trials. Price-series test (per rule): ring of N = 400 cells, random initial condition density 1/2 from a fixed seed, discard 1000 transient steps, record d(t) = (#black - #white) for W = 4096 further steps; d(t) is 'significantly random' if (R1) it is not exactly periodic with any period p <= W/2 within the window and (R2) the first differences D(t) = d(t+1) - d(t), stored as int16, have plug-in marginal entropy H >= 1 bit and lzma (preset 9|EXTREME) compressed size >= 0.5 x H bits per sample. Calibration on controls: i.i.d. binomial counts give ratio 1.35, an AR(1) series 1.40, a period-97 series 0.09, a noiseless sinusoid 0.47. The claim PASSES if at least 90% of propagating rules are significantly random. Reported, not decisive: the fraction of non-propagating rules that are significantly random, and the list of propagating-but-not-random rules.";
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dc:description "program family under test; N = 400 ring for price series, 1601-cell open lattice for damage spreading";
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