@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 runs all 256 rules: 10 seeded random initial conditions on an 800-cell ring, 1000 steps, period detection up to 64 steps, then a single-cell flip of the settled configuration and 400 further steps for both copies; damage width = rightmost - leftmost differing cell + 1. Operational class 1/2 = >= 9/10 trials settled; bounded = max width <= 20; spreading = median width >= 100. The Wikipedia page is fetched for its checksum and the example rules per class are checked against the operational classification. Per-rule values in derived/rules.csv (including a post-hoc width at step 200), fetch record in derived/wikipedia.json; runtime about 50 s."; "Measured: 0.9792 fraction of operational class 1/2 rules whose settled-state perturbation stays bounded (width <= 20 after 400 steps) (n = 96, 96 operational class 1/2 rules; 94 bounded, 2 intermediate, 0 spreading). Interpretation: The claim has a conclusion (class 1 and 2 automata cannot be universal) and a stated mechanism ('never allow any transmission of information except over limited distances'). Non-universality is a statement about all possible encodings and is not testable by finite computation; the test addresses the mechanism, which is the premise of Wolfram's argument: perturbations of class 1/2 states stay localized. Wolfram's classes are phenomenological, so they are operationalised here as 'settles into a temporal cycle of period <= 64 on an 800-cell ring within 1000 steps from random initial conditions'; the damage width (not displacement) is used so that shifting class-2 rules, whose perturbation moves but does not grow, count as bounded, as the assessors noted. Perturbations are applied to the settled state because the claim concerns the asymptotic behaviour, not transients."; "Claim test of wolfram2002-ch11-19: mixed, confidence 0.7"; ; prov:wasAttributedTo ; "Planned datasets: eca-settled-state-perturbation, wikipedia-eca-class-examples"; "claim-test/0.1.0"; "computational"; "Pre-registered. The claim FAILS if any operational class 1/2 rule is 'spreading' (a settled rule that nevertheless transmits a perturbation over a linearly growing region). If some class 1/2 rules are 'intermediate' but none 'spreading', the verdict is 'mixed'. If the Wikipedia example rules are misclassified by the operational definition, that is reported as a caveat on the mapping to Wolfram's phenomenological classes but does not change the verdict."; "All 14 Wikipedia example rules are classified as expected by the operational definition (class 1 and 2 examples settle in 10/10 trials with max width <= 4; class 3 and 4 examples never settle), so the operational class maps onto Wolfram's phenomenological classes for these rules. 160 rules are not operational class 1/2; 7 of them settle in some trials, and in 5 of those (rules 14, 57, 99, 113, 143) the perturbation of the settled state spreads across the whole ring, consistent with the converse.", "Post-hoc inspection shows the two intermediate cases are static, not growing: the damage width at step 200 equals the width at step 400 (rule 37: 24:24, 21:21; rule 62: 28:27). The six class 1/2 trials whose width is larger at step 400 than at step 200 are period-2 oscillations between widths 1 and 2 in rule 62. Substantively the mechanism Wolfram states (perturbations of class 1/2 states stay localised) holds for all 96 rules; the 'mixed' verdict reflects a conservative threshold rather than a counterexample.", "Pre-registered decision: 0 of 96 operational class 1/2 rules is 'spreading', so the claim is not refuted, but 2 rules (37 and 62) are 'intermediate' (max damage width 24 and 27 in one trial each, medians 2.0 and 1.5), so the pre-registered rule gives 'mixed' rather than 'supports'. The 20-cell threshold was set before the run; with a 30-cell threshold every class 1/2 rule would be bounded.", "The test addresses the stated mechanism (bounded information transmission), not the conclusion (impossibility of universality), which concerns all encodings and is not finitely testable. Results depend on the finite ring (800 cells), horizon (1000 + 400 steps), the single-flip perturbation and one random seed; shifting class 2 rules are counted as bounded by using width rather than displacement."; "Pre-registered. Family: all 256 elementary CA rules. For each rule, 10 trials: ring of N = 800 cells, random initial condition with density 1/2 (numpy default_rng seed 20261033), evolve 1000 steps to configuration C; the trial is 'settled' if C recurs within the next 64 steps (temporal period <= 64, which includes uniform and shifted-periodic states). A rule is 'operational class 1/2' if >= 9 of 10 trials settle. In every settled trial, flip one cell of C (the cell at index 400) and evolve both copies 400 further steps on the ring (N = 800 > 2 x 400, so the damage cannot wrap); record the damage width w = rightmost - leftmost differing cell + 1 (0 if none). A rule is 'bounded' if w <= 20 in all of its settled trials, 'spreading' if the median w over settled trials >= 100 (linear growth), otherwise 'intermediate'. The claim PASSES if 100% of operational class 1/2 rules are 'bounded'. Validation (reported, not decisive): the rules Wikipedia cites as Wolfram's class 1 and 2 examples (0, 32, 160, 232; 4, 108, 218, 250) must be operational class 1/2 and the class 3 and 4 examples (22, 30, 126, 150, 182; 110, 54) must not be; and the fraction of non-settled rules that are 'spreading' is reported."; "Pre-registered. The claim FAILS if any operational class 1/2 rule is 'spreading' (a settled rule that nevertheless transmits a perturbation over a linearly growing region). If some class 1/2 rules are 'intermediate' but none 'spreading', the verdict is 'mixed'. If the Wikipedia example rules are misclassified by the operational definition, that is reported as a caveat on the mapping to Wolfram's phenomenological classes but does not change the verdict."; "0.7"^^xsd:double; , ; "mixed"; "Every elementary cellular automaton that settles into a uniform or short-period state from random initial conditions (operational class 1 or 2) transmits a single-cell perturbation of that settled state only over a bounded distance, whereas rules that do not settle spread perturbations without bound."; "analysis.py runs all 256 rules: 10 seeded random initial conditions on an 800-cell ring, 1000 steps, period detection up to 64 steps, then a single-cell flip of the settled configuration and 400 further steps for both copies; damage width = rightmost - leftmost differing cell + 1. Operational class 1/2 = >= 9/10 trials settled; bounded = max width <= 20; spreading = median width >= 100. The Wikipedia page is fetched for its checksum and the example rules per class are checked against the operational classification. Per-rule values in derived/rules.csv (including a post-hoc width at step 200), fetch record in derived/wikipedia.json; runtime about 50 s."; "Pre-registered. Family: all 256 elementary CA rules. For each rule, 10 trials: ring of N = 800 cells, random initial condition with density 1/2 (numpy default_rng seed 20261033), evolve 1000 steps to configuration C; the trial is 'settled' if C recurs within the next 64 steps (temporal period <= 64, which includes uniform and shifted-periodic states). A rule is 'operational class 1/2' if >= 9 of 10 trials settle. In every settled trial, flip one cell of C (the cell at index 400) and evolve both copies 400 further steps on the ring (N = 800 > 2 x 400, so the damage cannot wrap); record the damage width w = rightmost - leftmost differing cell + 1 (0 if none). A rule is 'bounded' if w <= 20 in all of its settled trials, 'spreading' if the median w over settled trials >= 100 (linear growth), otherwise 'intermediate'. The claim PASSES if 100% of operational class 1/2 rules are 'bounded'. Validation (reported, not decisive): the rules Wikipedia cites as Wolfram's class 1 and 2 examples (0, 32, 160, 232; 4, 108, 218, 250) must be operational class 1/2 and the class 3 and 4 examples (22, 30, 126, 150, 182; 110, 54) must not be; and the fraction of non-settled rules that are 'spreading' is reported."; "false"^^xsd:boolean . . a ; dc:description "program family under test"; dc:license "generated data"; "Dataset: 256 elementary cellular automata, settled states and single-cell perturbations (generated by analysis.py)"; prov:wasDerivedFrom . a ; dc:description "independent list of example rules per class used to validate the operational class definition"; dc:license "CC BY-SA 4.0"; "Dataset: Wikipedia, 'Elementary cellular automaton' (example rules for Wolfram's four classes)"; prov:atLocation ; prov:wasDerivedFrom ; "sha256:e56ff461b503556225f6df4778d54c436c230c444651d2ed88b9023e3135fb79" . } sub:provenance { a prov:SoftwareAgent; "delphisci claim tester (claude-fable-5.1; cursor/wolfram-nks-claim-tests-106e)"; 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 "2026-11-08T16:24:31.939Z"^^xsd:dateTime; dc:creator ; dc:license ; npx:hasNanopubType ; npx:introduces ; "Claim test of wolfram2002-ch11-19: mixed, confidence 0.7"; . sub:sig npx:hasAlgorithm "RSA"; npx:hasPublicKey "MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB"; npx:hasSignature "S6lTN/Zy027p+FEwSxElkORlXd0Z6kkvBRz8grdT33JPKu5IKdkOykX9AaYEw6RD3dwNEcuyCddpJD0dMQPnyaD3NgFdy4FnLA5CV3I3VRX5R4YdPD4329FoUmI06o2AQPHQZ11xcuW/d4PHDlyga8bpuzyk4t0Y/NNkD7trW3IzHbrdJeAewFuzaQ7bKvJd/TsziJL9AsKIUZ9gxiwH42LNb4F/BdRxUpBxUjfAO1HW/GPOiop4AXddQjIRdNiUlRL3nfYpWQ9O5Dz2Rw0TpNrNTo5LEUom5Y7hHMXShVGrfJ9HqJhJv/LsilkXC6I+j8v2BgPnOVBcSn7w5w4K6Q=="; npx:hasSignatureTarget this:; npx:signedBy . }