https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8/Head https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8 http://www.nanopub.org/nschema#hasAssertion https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8/assertion https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8 http://www.nanopub.org/nschema#hasProvenance https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8/provenance https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8 http://www.nanopub.org/nschema#hasPublicationInfo https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8/pubinfo https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8 http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.nanopub.org/nschema#Nanopublication https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8/assertion https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-10--claim-test http://purl.org/dc/terms/description analysis.py builds, from any (k, r, rule table), an explicit finite Turing-machine transition table: states ('scan', B, j) carry the last 2r old cell values B during a left-to-right sweep, step back r cells to write each new value, finish the last r cells at the right end-marker with virtual zero reads, and return to the left marker, so one round trip is one cellular-automaton step with fixed-0 boundaries. The machine for each rule was run on W = 48 cells for 40 steps from two random initial conditions (seed 20261110) and the tape compared cell-for-cell with direct evolution after every step: all 256 elementary rules, 100 random k=3 r=1 rules, 50 random k=2 r=2 rules, 20 random k=4 r=1 rules and 10 random k=3 r=2 rules (436 rules, 1,674,240 cell comparisons). A mutation check (machine for rule 110 compared with rule 124) produced 225 mismatches in 10 steps, confirming the harness detects disagreement. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-10--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-ch11-10--claim-test http://www.w3.org/2000/01/rdf-schema#comment Measured: 0 mismatching cells between Turing-machine tape and direct cellular-automaton evolution, summed over all runs (n = 1674240, exact (deterministic comparison)). Interpretation: The claim is a logical implication (if a system type can emulate every cellular automaton and a universal cellular automaton exists, the type has universal members). The implication itself is not empirical; what can be checked computationally is its first premise for a concrete system type. We check it for Turing machines, the second family named in the claim, by implementing a uniform emulation construction (the sweeping-head scheme NKS describes for Turing machines emulating cellular automata, p. 665-666, written here from scratch rather than copied) and testing it exhaustively on the elementary rules and on random rules with more colours and larger neighbourhoods. The second premise (existence of a universal cellular automaton) is taken from the published proof that rule 110 is universal; it is not re-derived. The other families in the claim (mobile automata, substitution systems, tag and cyclic tag systems, symbolic systems, register machines) are not tested here, so a 'supports' verdict confirms the claim's structure for one family only. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-10--claim-test http://www.w3.org/2000/01/rdf-schema#label Claim test of wolfram2002-ch11-10: supports, confidence 0.7 https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-10--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-ch11-10/result.json https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-10--claim-test http://www.w3.org/ns/prov#wasAttributedTo https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-10--claim-test https://w3id.org/delphi/ontology/admissibleDatasets Planned datasets: nks-ch11-10-tm-emulation-generator https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-10--claim-test https://w3id.org/delphi/ontology/assessmentType claim-test/0.1.0 https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-10--claim-test https://w3id.org/delphi/ontology/dataKind computational https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-10--claim-test https://w3id.org/delphi/ontology/disconfirmingObservation Pre-registered. 'refutes' if any run produces a mismatch (one or more cells differing from the direct evolution) that cannot be traced to a bug in the harness rather than the construction; since the construction is uniform in (k, r, rule), a single irreparable mismatch shows the uniform construction does not emulate every cellular automaton. 'inconclusive' with reason 'other' if the harness cannot complete the runs within the time budget. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-10--claim-test https://w3id.org/delphi/ontology/evidenceAgainst Only the Turing-machine family is tested; the claim also names mobile automata, substitution systems, tag and cyclic tag systems, symbolic systems and register machines, whose emulation constructions are not checked here. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-10--claim-test https://w3id.org/delphi/ontology/evidenceAgainst The Turing machines used here have many states; they are not the small machines NKS discusses elsewhere, and nothing is claimed about minimal size. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-10--claim-test https://w3id.org/delphi/ontology/evidenceAgainst The claim is a logical implication; the computation establishes one instance of its premise, not the implication itself, which is immediate once both premises are granted. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-10--claim-test https://w3id.org/delphi/ontology/evidenceAgainst The conclusion that the resulting rule-110 machine (41 states x 3 symbols, 91 transitions) is universal rests on the published proof that rule 110 is universal (Cook 2004); that proof is not re-verified here, so the implication's second premise is assumed, not tested. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-10--claim-test https://w3id.org/delphi/ontology/evidenceAgainst The construction is tested on finite segments with fixed-0 boundaries for 40 steps; its correctness for arbitrary k and r follows from the uniform scheme rather than from exhaustive testing, and the test covers k <= 4 and r <= 2 only. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-10--claim-test https://w3id.org/delphi/ontology/expectedObservation Pre-registered. analysis.py builds, for a given (k, r, rule table), a Turing machine whose tape holds the cellular-automaton configuration on W cells between two end-marker symbols, and whose head performs one left-to-right sweep (reading each old cell value once, carrying the last 2r old values in its state, stepping back r cells to write the new value) followed by a return to the left end, so that one round trip equals one cellular-automaton step with fixed white (0) boundaries. The machine must be a genuine finite table: every (state, symbol) pair reachable in the runs has exactly one transition writing one symbol and moving one cell. Tests: (a) all 256 elementary rules (k = 2, r = 1), W = 48, 40 steps, two random initial conditions each (seed 20261110); (b) 100 random 3-colour radius-1 rules (k = 3, r = 1), same W and steps; (c) 50 random 2-colour radius-2 rules (k = 2, r = 2); (d) 20 random 4-colour radius-1 rules and 10 random 3-colour radius-2 rules. After every round trip the tape between the markers is compared cell-for-cell with the directly computed cellular-automaton configuration (fixed-0 boundary). 'supports' if the total number of mismatching cells over all runs is 0 and the rule-110 machine is produced with a finite, fully specified state table (its state count and transition count reported). https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-10--claim-test https://w3id.org/delphi/ontology/failCriterion Pre-registered. 'refutes' if any run produces a mismatch (one or more cells differing from the direct evolution) that cannot be traced to a bug in the harness rather than the construction; since the construction is uniform in (k, r, rule), a single irreparable mismatch shows the uniform construction does not emulate every cellular automaton. 'inconclusive' with reason 'other' if the harness cannot complete the runs within the time budget. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-10--claim-test https://w3id.org/delphi/ontology/hasConfidence 0.7 https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-10--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-10--claim-test--dataset-1 https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-10--claim-test https://w3id.org/delphi/ontology/hasVerdict supports https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-10--claim-test https://w3id.org/delphi/ontology/hypothesis For at least one of the system types named in the claim (Turing machines), a single uniform construction turns any one-dimensional cellular automaton rule (any number of colours k, any radius r) into a Turing machine that emulates it exactly; applied to rule 110 the construction yields an explicit Turing machine, which is then universal by the universality of rule 110 (Cook, Complex Systems 15 (2004) 1-40), so the system type contains a universal member as the claim asserts. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-10--claim-test https://w3id.org/delphi/ontology/inferenceMethod analysis.py builds, from any (k, r, rule table), an explicit finite Turing-machine transition table: states ('scan', B, j) carry the last 2r old cell values B during a left-to-right sweep, step back r cells to write each new value, finish the last r cells at the right end-marker with virtual zero reads, and return to the left marker, so one round trip is one cellular-automaton step with fixed-0 boundaries. The machine for each rule was run on W = 48 cells for 40 steps from two random initial conditions (seed 20261110) and the tape compared cell-for-cell with direct evolution after every step: all 256 elementary rules, 100 random k=3 r=1 rules, 50 random k=2 r=2 rules, 20 random k=4 r=1 rules and 10 random k=3 r=2 rules (436 rules, 1,674,240 cell comparisons). A mutation check (machine for rule 110 compared with rule 124) produced 225 mismatches in 10 steps, confirming the harness detects disagreement. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-10--claim-test https://w3id.org/delphi/ontology/passCriterion Pre-registered. analysis.py builds, for a given (k, r, rule table), a Turing machine whose tape holds the cellular-automaton configuration on W cells between two end-marker symbols, and whose head performs one left-to-right sweep (reading each old cell value once, carrying the last 2r old values in its state, stepping back r cells to write the new value) followed by a return to the left end, so that one round trip equals one cellular-automaton step with fixed white (0) boundaries. The machine must be a genuine finite table: every (state, symbol) pair reachable in the runs has exactly one transition writing one symbol and moving one cell. Tests: (a) all 256 elementary rules (k = 2, r = 1), W = 48, 40 steps, two random initial conditions each (seed 20261110); (b) 100 random 3-colour radius-1 rules (k = 3, r = 1), same W and steps; (c) 50 random 2-colour radius-2 rules (k = 2, r = 2); (d) 20 random 4-colour radius-1 rules and 10 random 3-colour radius-2 rules. After every round trip the tape between the markers is compared cell-for-cell with the directly computed cellular-automaton configuration (fixed-0 boundary). 'supports' if the total number of mismatching cells over all runs is 0 and the rule-110 machine is produced with a finite, fully specified state table (its state count and transition count reported). https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-10--claim-test https://w3id.org/delphi/ontology/preregistered false https://w3id.org/delphi/resource/claim/wolfram2002-ch11-10 https://w3id.org/delphi/ontology/hasAssessment https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-10--claim-test https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-10--claim-test--dataset-1 http://purl.org/dc/terms/description the emulation premise of the implication, for the Turing-machine family https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-10--claim-test--dataset-1 http://purl.org/dc/terms/license generated https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-10--claim-test--dataset-1 http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/EvidenceItem https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-10--claim-test--dataset-1 http://www.w3.org/2000/01/rdf-schema#label Dataset: Turing machines constructed by analysis.py from cellular-automaton rules (all 256 elementary rules; random rules with k in {2,3,4} and r in {1,2}, seed 20261110), run on W = 48 cells for 40 cellular-automaton steps and compared with direct evolution https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-10--claim-test--dataset-1 http://www.w3.org/ns/prov#wasDerivedFrom https://www.wolframscience.com/nks/p665--emulating-cellular-automata-with-other-systems/ https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8/provenance https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.w3.org/ns/prov#SoftwareAgent https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 http://www.w3.org/2000/01/rdf-schema#label delphisci claim tester (claude-fable-5.1; cursor/claim-tests-wolfram-nks-e5f4) https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 http://www.w3.org/ns/prov#actedOnBehalfOf https://orcid.org/0009-0007-4948-9192 https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 https://w3id.org/delphi/ontology/usesModel https://w3id.org/delphi/resource/model/claude-fable-5-1 https://w3id.org/delphi/resource/model/claude-fable-5-1 http://purl.org/dc/terms/identifier claude-fable-5.1 https://w3id.org/delphi/resource/model/claude-fable-5-1 http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/LanguageModel https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8/assertion http://www.w3.org/ns/prov#wasAttributedTo https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8/assertion http://www.w3.org/ns/prov#wasDerivedFrom https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch11-10/result.json https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8/assertion http://www.w3.org/ns/prov#wasGeneratedBy https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8/test https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8/plan http://www.w3.org/ns/prov#hadPlan https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/README.md https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8/test http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.w3.org/ns/prov#Activity https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8/test http://www.w3.org/ns/prov#qualifiedAssociation https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8/plan https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8/test http://www.w3.org/ns/prov#wasAssociatedWith https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8/pubinfo https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8 http://purl.org/dc/terms/created 2026-11-08T16:24:31.937Z https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8 http://purl.org/dc/terms/creator https://orcid.org/0009-0007-4948-9192 https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8 http://purl.org/dc/terms/license https://creativecommons.org/licenses/by/4.0/ https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8 http://purl.org/nanopub/x/hasNanopubType https://w3id.org/delphi/ontology/Assessment https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8 http://purl.org/nanopub/x/introduces https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-10--claim-test https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8 http://www.w3.org/2000/01/rdf-schema#label Claim test of wolfram2002-ch11-10: supports, confidence 0.7 https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8 https://w3id.org/delphi/ontology/domain https://w3id.org/delphi/resource/domain/wolfram-nks-2002 https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8/sig http://purl.org/nanopub/x/hasAlgorithm RSA https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8/sig http://purl.org/nanopub/x/hasPublicKey MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8/sig http://purl.org/nanopub/x/hasSignature euOWARpSUIxVeIrCZsRrDzNtMIwgEbkm07UQB7UZgOhoFUr4SuN2ULLSjpWDsk1QwtlCdiC8TIjWie3MH+uSDlnPRao/E0wiM7Inosk5LNsP3XWCSyshEvn0dWFR1rFpEXpJ56cnV4IW6kBvC/FbWsp53ZMKaJ8l38lMjzhhi3m/reHtpH/JuAlH9SH0r2ssfPEs8JjuewFu/0QDnUtWXPp2f+6pxL5nZYZqc/RHHvASEkS/MIdJocZePP7PJJoMfGR1qRJ1vgM4RPz6YObAjVV6Bk9c9UQxa6Rd60wKXlK72FagZQVREoCrUhRTSsjAewPZLSSDiSLdAgrE+dL5Mg== https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8/sig http://purl.org/nanopub/x/hasSignatureTarget https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8 https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8/sig http://purl.org/nanopub/x/signedBy https://orcid.org/0009-0007-4948-9192