https://w3id.org/np/RA0xjJ0ZbvHfURRMZdeK95-Rscsq-KLVF9Gz75LjkMT1M/Head https://w3id.org/np/RA0xjJ0ZbvHfURRMZdeK95-Rscsq-KLVF9Gz75LjkMT1M http://www.nanopub.org/nschema#hasAssertion https://w3id.org/np/RA0xjJ0ZbvHfURRMZdeK95-Rscsq-KLVF9Gz75LjkMT1M/assertion https://w3id.org/np/RA0xjJ0ZbvHfURRMZdeK95-Rscsq-KLVF9Gz75LjkMT1M http://www.nanopub.org/nschema#hasProvenance https://w3id.org/np/RA0xjJ0ZbvHfURRMZdeK95-Rscsq-KLVF9Gz75LjkMT1M/provenance https://w3id.org/np/RA0xjJ0ZbvHfURRMZdeK95-Rscsq-KLVF9Gz75LjkMT1M http://www.nanopub.org/nschema#hasPublicationInfo https://w3id.org/np/RA0xjJ0ZbvHfURRMZdeK95-Rscsq-KLVF9Gz75LjkMT1M/pubinfo https://w3id.org/np/RA0xjJ0ZbvHfURRMZdeK95-Rscsq-KLVF9Gz75LjkMT1M http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.nanopub.org/nschema#Nanopublication https://w3id.org/np/RA0xjJ0ZbvHfURRMZdeK95-Rscsq-KLVF9Gz75LjkMT1M/assertion https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-13--claim-test http://purl.org/dc/terms/description analysis.py lists all 16 affine coefficient tuples and the 256 elementary rules. The Turing machine is simulated on every rule table and every neighborhood. Its transition table contains three extra states; a breadth-first enumeration from the start state is used to see whether any transition enters them. The head-carrying cellular automaton is updated by the radius-1 rule that applies the same transition, and its output cell is read after it halts. Realized sets are compared as sets of Wolfram codes. Rules 90 (left XOR right) and 110 (table 01101110) are checked before the comparison. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-13--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-ch11-13--claim-test http://www.w3.org/2000/01/rdf-schema#comment Measured: 0 functions in the symmetric difference between the elementary rules and each of the other realized sets (each set has size 256) (n = 256, exact). Interpretation: NKS p. 675 says that once a system passes the threshold of universality, the set of computations it can perform does not grow when the underlying rules become more sophisticated, and does not depend on whether the system is a cellular automaton or a Turing machine. The test reads 'computation' as a boolean function of 3 bits, a finite class that is full exactly when every elementary rule can be realized. Extra unreachable states are the 'more sophisticated' variant. This does not prove the Church-Turing thesis for unbounded inputs, and it does not say that a larger neighborhood is useless for functions of more than 3 bits. A computation shows the mathematics of these models, not that organisms follow it. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-13--claim-test http://www.w3.org/2000/01/rdf-schema#label Claim test of wolfram2002-ch11-13: supports, confidence 0.9 https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-13--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-ch11-13/result.json https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-13--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-ch11-13--claim-test https://w3id.org/delphi/ontology/admissibleDatasets Functions and simulations generated by the committed script from the Wolfram elementary-rule numbering. No external dataset. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-13--claim-test https://w3id.org/delphi/ontology/assessmentType claim-test/0.1.0 https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-13--claim-test https://w3id.org/delphi/ontology/dataKind computational https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-13--claim-test https://w3id.org/delphi/ontology/disconfirmingObservation The enlarged machine realizes a different set from the smaller universal one, or a system that can encode an arbitrary 3-bit table still misses some function, or the affine class is not strictly smaller. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-13--claim-test https://w3id.org/delphi/ontology/evidenceAgainst A computation shows the mathematics, not that organisms follow it. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-13--claim-test https://w3id.org/delphi/ontology/evidenceAgainst The class of computations is the 256 boolean functions of 3 bits. The run shows that, inside this class, the elementary rules, the Turing-machine table interpreter, the same table with three unreachable states, and the head-carrying cellular automaton realize the same set, while the 16 affine mod-2 rules are a proper subset. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-13--claim-test https://w3id.org/delphi/ontology/evidenceAgainst This is a finite proxy. It does not prove the Church-Turing thesis for unbounded inputs, and it does not say that a larger neighborhood is useless for functions of more than 3 bits. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-13--claim-test https://w3id.org/delphi/ontology/evidenceAgainst Three extra states sit in the transition table and were not entered from the start state (0 of the 102 reachable states). Adding them did not change the set of functions. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-13--claim-test https://w3id.org/delphi/ontology/expectedObservation Affine mod-2 rules realize 16 of the 256 three-bit boolean functions; the full elementary rules, a Turing-machine rule-table interpreter, the same machine with three unreachable states, and a cellular automaton that emulates that machine each realize exactly those 256 functions. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-13--claim-test https://w3id.org/delphi/ontology/failCriterion Pre-registered. REFUTES if |A| is not 16, or A is not a subset of C, or any of the systems (1)-(3) or the head automaton realizes fewer than 256 functions or a function outside C, or any pair of those realized sets differs. INCONCLUSIVE with reason 'other' if the direct truth-table evaluation of rules 90 and 110 disagrees with their known outputs (90 is left XOR right; 110 is the standard 01101110 table), because the comparator would then be untrustworthy. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-13--claim-test https://w3id.org/delphi/ontology/hasConfidence 0.9 https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-13--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-13--claim-test--dataset-1 https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-13--claim-test https://w3id.org/delphi/ontology/hasVerdict supports https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-13--claim-test https://w3id.org/delphi/ontology/hypothesis Once a system can realize every boolean function of 3 bits, giving it extra states or a second implementation does not enlarge that set of functions, while a system restricted to affine mod-2 rules realizes a strictly smaller set. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-13--claim-test https://w3id.org/delphi/ontology/inferenceMethod Exact enumeration of realized truth tables. Equality of sets is equality of the 256-bit characteristic vectors. The thresholds are the exact sizes 16 and 256. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-13--claim-test https://w3id.org/delphi/ontology/passCriterion Pre-registered. The class C is the set of all functions {0,1}^3 -> {0,1}, which has 256 members, each identified with one elementary cellular-automaton rule by Wolfram numbering. Affine subclass A: functions f(p,q,r) = a0 + a1*p + a2*q + a3*r mod 2, so |A| must equal 16, and A is a proper subset of C. Three systems that have passed the threshold, each required to realize all of C and no function outside C: (1) the set of all 256 elementary rules, each rule a one-step map; (2) a single Turing machine whose finite control evaluates a rule table written on the tape, run on all 256 tables and all 8 neighborhoods; (3) the same machine with three extra states that no transition enters. A head-on-tape cellular automaton that emulates machine (2) must realize the same set. 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