https://w3id.org/np/RALFAcQYwTgStBnL1QJV_ICxbpdt7BsBdhVBPRviLmMIc/Head https://w3id.org/np/RALFAcQYwTgStBnL1QJV_ICxbpdt7BsBdhVBPRviLmMIc http://www.nanopub.org/nschema#hasAssertion https://w3id.org/np/RALFAcQYwTgStBnL1QJV_ICxbpdt7BsBdhVBPRviLmMIc/assertion https://w3id.org/np/RALFAcQYwTgStBnL1QJV_ICxbpdt7BsBdhVBPRviLmMIc http://www.nanopub.org/nschema#hasProvenance https://w3id.org/np/RALFAcQYwTgStBnL1QJV_ICxbpdt7BsBdhVBPRviLmMIc/provenance https://w3id.org/np/RALFAcQYwTgStBnL1QJV_ICxbpdt7BsBdhVBPRviLmMIc http://www.nanopub.org/nschema#hasPublicationInfo https://w3id.org/np/RALFAcQYwTgStBnL1QJV_ICxbpdt7BsBdhVBPRviLmMIc/pubinfo https://w3id.org/np/RALFAcQYwTgStBnL1QJV_ICxbpdt7BsBdhVBPRviLmMIc http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.nanopub.org/nschema#Nanopublication https://w3id.org/np/RALFAcQYwTgStBnL1QJV_ICxbpdt7BsBdhVBPRviLmMIc/assertion https://w3id.org/delphi/resource/assessment/wolfram2002-ch05-06--claim-test http://purl.org/dc/terms/description analysis.py drew 36 two-color Turing machines for each of 2, 3 and 4 head states from PCG64 seed 20261102. Each situation (color, state) maps to a new color, state and cardinal direction. Each machine ran 200 steps on a 32 by 32 torus from a white tape with the head at (16, 16). Counts: {'2': {'repetitive': 25, 'nested': 0, 'complex': 11, 'simple_fraction': 0.6944444444444444, 'complex_fraction': 0.3055555555555556}, '3': {'repetitive': 18, 'nested': 0, 'complex': 18, 'simple_fraction': 0.5, 'complex_fraction': 0.5}, '4': {'repetitive': 19, 'nested': 0, 'complex': 17, 'simple_fraction': 0.5277777777777778, 'complex_fraction': 0.4722222222222222}}. https://w3id.org/delphi/resource/assessment/wolfram2002-ch05-06--claim-test http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/Assessment https://w3id.org/delphi/resource/assessment/wolfram2002-ch05-06--claim-test http://www.w3.org/2000/01/rdf-schema#comment Measured: -0.02777777777777779 complex fraction at 4 states minus complex fraction at 3 states, in a sample of 36 (n = 36, exact for this seed, grid and step bound; the sample is not a census). Interpretation: Page 184 says that two-dimensional Turing machines with two or three head states normally show only repetitive or nested behavior, and that four states make more complex behavior possible though still rare. 'Normally' is locked as a simple fraction of at least 0.75 inside this sample. The grid, the step bound and the sample size are part of the test; the result is about this sample only. It does not show that organisms behave this way. https://w3id.org/delphi/resource/assessment/wolfram2002-ch05-06--claim-test http://www.w3.org/2000/01/rdf-schema#label Claim test of wolfram2002-ch05-06: refutes, confidence 0.5 https://w3id.org/delphi/resource/assessment/wolfram2002-ch05-06--claim-test http://www.w3.org/2000/01/rdf-schema#seeAlso https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch05-06/result.json https://w3id.org/delphi/resource/assessment/wolfram2002-ch05-06--claim-test http://www.w3.org/ns/prov#wasAttributedTo https://w3id.org/delphi/resource/agent/delphisci-claim-tester-grok-4-7 https://w3id.org/delphi/resource/assessment/wolfram2002-ch05-06--claim-test https://w3id.org/delphi/ontology/admissibleDatasets Rules drawn from the finite (color, state) -> (color, state, direction) instruction set with the locked seed, grid and step bound. No other sample is consulted. https://w3id.org/delphi/resource/assessment/wolfram2002-ch05-06--claim-test https://w3id.org/delphi/ontology/assessmentType claim-test/0.1.0 https://w3id.org/delphi/resource/assessment/wolfram2002-ch05-06--claim-test https://w3id.org/delphi/ontology/dataKind computational https://w3id.org/delphi/resource/assessment/wolfram2002-ch05-06--claim-test https://w3id.org/delphi/ontology/disconfirmingObservation Fewer than half of the 2-state or 3-state sample is simple, or four states are not more often complex than three states in this sample. https://w3id.org/delphi/resource/assessment/wolfram2002-ch05-06--claim-test https://w3id.org/delphi/ontology/evidenceAgainst A configuration that has not repeated by step 200 is not a classification of the infinite run. The sample says nothing about organisms. https://w3id.org/delphi/resource/assessment/wolfram2002-ch05-06--claim-test https://w3id.org/delphi/ontology/evidenceAgainst None of the 108 machines met the nested-path bound of 60 compressed bytes, so every machine that did not repeat its configuration was called complex. In that classification the 4-state complex fraction was 0.47 and the 3-state fraction was 0.50. https://w3id.org/delphi/resource/assessment/wolfram2002-ch05-06--claim-test https://w3id.org/delphi/ontology/evidenceAgainst This is a sample of 36 machines per state count on a 32 by 32 torus for 200 steps. It does not estimate a rate of a few complex rules per million. https://w3id.org/delphi/resource/assessment/wolfram2002-ch05-06--claim-test https://w3id.org/delphi/ontology/expectedObservation At least 27 of 36 machines with 2 states, and at least 27 of 36 with 3 states, are repetitive or nested on a 32 by 32 torus in 200 steps, and the 4-state complex fraction exceeds the 3-state complex fraction by at least 0.10, with at least two complex 4-state machines. https://w3id.org/delphi/resource/assessment/wolfram2002-ch05-06--claim-test https://w3id.org/delphi/ontology/failCriterion Pre-registered. Refutes if the simple fraction for s=2 or s=3 is below 0.50, or if the complex fraction for s=4 is less than or equal to that for s=3. Mixed if neither the support thresholds nor the refute thresholds are met. The phrase 'a few rules per million' is not tested: a sample of 36 cannot resolve a rate near 10^-6. https://w3id.org/delphi/resource/assessment/wolfram2002-ch05-06--claim-test https://w3id.org/delphi/ontology/hasConfidence 0.5 https://w3id.org/delphi/resource/assessment/wolfram2002-ch05-06--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch05-06--claim-test--dataset-1 https://w3id.org/delphi/resource/assessment/wolfram2002-ch05-06--claim-test https://w3id.org/delphi/ontology/hasVerdict refutes https://w3id.org/delphi/resource/assessment/wolfram2002-ch05-06--claim-test https://w3id.org/delphi/ontology/hypothesis In a fixed sample of 36 two-dimensional two-color Turing machines at each of 2, 3 and 4 head states, run on a 32 by 32 torus for 200 steps, at least three quarters of the 2-state and 3-state machines are repetitive or nested, and the 4-state sample contains more complex machines than the 3-state sample. https://w3id.org/delphi/resource/assessment/wolfram2002-ch05-06--claim-test https://w3id.org/delphi/ontology/inferenceMethod Classify each sampled machine as repetitive (configuration repeat), nested (path lzma size <= 60 bytes) or complex. Compare simple fractions to 0.75 and 0.50, and compare complex fractions across 3 and 4 states with a gap of 0.10. https://w3id.org/delphi/resource/assessment/wolfram2002-ch05-06--claim-test https://w3id.org/delphi/ontology/passCriterion Pre-registered. This is a sample, not a census. For s head states and 2 colors, each of the 2s situations (color, state) maps to a new color in {0,1}, a new state in {0,...,s-1}, and a move in {N, E, S, W}. Draw 36 rules for s=2, then 36 for s=3, then 36 for s=4, from numpy Generator PCG64 seed 20261102, each field uniform. Grid 32 by 32, periodic boundaries, tape starts all white, head at (16, 16) in state 0. Run 200 steps. A machine is repetitive if the pair (sha256 of the tape, head x, head y, state) repeats. Otherwise pack the 200 head positions as bytes and lzma-9 compress them: nested if the compressed size is <= 60 bytes, complex otherwise. Let simple mean repetitive or nested. 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