https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8
.trig | .trig.txt | .jelly | .jelly.txt | .jsonld | .jsonld.txt | .nq | .nq.txt | .xml | .xml.txt
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@prefix sub: <https://w3id.org/np/RAEhL5SKie2VsOPiQ6YpxxJnQjBo9vAm3s73mCtHlYnm8/> .
@prefix np: <http://www.nanopub.org/nschema#> .
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@prefix dc: <http://purl.org/dc/terms/> .
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sub:Head {
this: a np:Nanopublication;
np:hasAssertion sub:assertion;
np:hasProvenance sub:provenance;
np:hasPublicationInfo sub:pubinfo .
}
sub:assertion {
<https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-10--claim-test> a <https://w3id.org/delphi/ontology/Assessment>;
dc: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.";
<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.";
<http://www.w3.org/2000/01/rdf-schema#label> "Claim test of wolfram2002-ch11-10: supports, confidence 0.7";
<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>;
prov:wasAttributedTo <https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1>;
<https://w3id.org/delphi/ontology/admissibleDatasets> "Planned datasets: nks-ch11-10-tm-emulation-generator";
<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. '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/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.",
"The Turing machines used here have many states; they are not the small machines NKS discusses elsewhere, and nothing is claimed about minimal size.",
"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.",
"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.",
"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/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/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/ontology/hasConfidence> "0.7"^^xsd:double;
<https://w3id.org/delphi/ontology/hasEvidence> <https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-10--claim-test--dataset-1>;
<https://w3id.org/delphi/ontology/hasVerdict> "supports";
<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/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/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/ontology/preregistered> "false"^^xsd:boolean .
<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>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "the emulation premise of the implication, for the Turing-machine family";
dc:license "generated";
<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";
prov:wasDerivedFrom <https://www.wolframscience.com/nks/p665--emulating-cellular-automata-with-other-systems/> .
}
sub:provenance {
<https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1> a
prov:SoftwareAgent;
<http://www.w3.org/2000/01/rdf-schema#label> "delphisci claim tester (claude-fable-5.1; cursor/claim-tests-wolfram-nks-e5f4)";
prov:actedOnBehalfOf <https://orcid.org/0009-0007-4948-9192>;
<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> a <https://w3id.org/delphi/ontology/LanguageModel>;
dc:identifier "claude-fable-5.1" .
sub:assertion prov:wasAttributedTo <https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1>;
prov:wasDerivedFrom <https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch11-10/result.json>;
prov:wasGeneratedBy sub:test .
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}
sub:pubinfo {
this: dc:created "2026-11-08T16:24:31.937Z"^^xsd:dateTime;
dc:creator <https://orcid.org/0009-0007-4948-9192>;
dc:license <https://creativecommons.org/licenses/by/4.0/>;
npx:hasNanopubType <https://w3id.org/delphi/ontology/Assessment>;
npx:introduces <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/ontology/domain> <https://w3id.org/delphi/resource/domain/wolfram-nks-2002> .
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