https://w3id.org/np/RAL2YIHcfiZJObMyO8nUwVQ_WVASS4YwSvhOZdwi0U4jM
.trig | .trig.txt | .jelly | .jelly.txt | .jsonld | .jsonld.txt | .nq | .nq.txt | .xml | .xml.txt
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sub:Head {
this: a np:Nanopublication;
np:hasAssertion sub:assertion;
np:hasProvenance sub:provenance;
np:hasPublicationInfo sub:pubinfo .
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sub:assertion {
<https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-06--claim-test> a <https://w3id.org/delphi/ontology/Assessment>;
dc:description "analysis.py fetched the NKS online note (86,136 bytes), extracted the published rule list (65 replacement rules on 5-cell neighbourhoods, arrow glyphs decoded from the HTML entity, first matching rule applies) and the block encoding, compiled the rules into a complete 19^5-entry lookup table (every neighbourhood covered), and ran the universal automaton on a cyclic array of encoded blocks. For all 256 elementary rules (16 cells, 2 random initial conditions, 8 emulated steps of 53 universal steps each) and 30 random two-colour range-2 rules (10 cells, 4 emulated steps of 285 universal steps each; 70-cell blocks), the array after each period was compared cell-for-cell with the encoding of the directly computed cyclic target configuration: 0 mismatches in 1,394,720 cells. Checks that the harness is not vacuous: encoding rule 30 but comparing against rule 110 gives 309 mismatches in 6 steps; within one 53-step period up to 208 of 320 cells differ from the resting form before the array returns to it with exactly the colour cells changed; the decoded rule-30 evolution from one black cell shows the rule-30 pattern.";
<http://www.w3.org/2000/01/rdf-schema#comment> "Measured: 0 mismatching universal-automaton cells between the evolved array and the encoding of the directly computed target configuration, summed over all checkpoints (n = 1394720, exact (deterministic comparison)). Interpretation: The claim has two parts: the fixed 19-colour rule emulates any two-colour cellular automaton of any range (the note gives the encoding with range r as a parameter), and, via the reduction of multi-colour rules to two-colour rules with larger range (NKS p. 656), any cellular automaton whatsoever. This test checks the first part directly for r = 1 (all 256 rules) and r = 2 (random rules); the colour reduction is a separate construction and is not tested here, so 'any number of colours' is covered only through the general-range mechanism, not through a run of a multi-colour target. 'Rules more complicated than its own' is read as rule tables with more entries than the universal rule's own 19^5-neighbourhood description can be said to have: range-2 two-colour rules have 32 independent entries, already outside what elementary rules can express. The cyclic arrangement of blocks is our choice for a finite run; the note does not specify boundaries.";
<http://www.w3.org/2000/01/rdf-schema#label> "Claim test of wolfram2002-ch11-06: supports, confidence 0.85";
<http://www.w3.org/2000/01/rdf-schema#seeAlso> <https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch11-06/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-notes-11-4-universal-cellular-automaton, nks-ch11-06-uca-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, with the rule list and encoding exactly as published, some target rule's evolution is not reproduced (one or more mismatching cells at a checkpoint). If mismatches occur, the first action is to re-check the transcription of the published text (lost arrows, exponent formatting); a correction that makes the parse agree with the published text is a harness fix and is disclosed in caveats; any remaining mismatch is a refutation. 'inconclusive' with reason 'data-unavailable' if the note cannot be retrieved and no verifiable copy is at hand; 'inconclusive' with reason 'other' if the cyclic-boundary set-up turns out to be incompatible with the construction in a way that cannot be resolved from the published description (for example if the construction requires a special terminator block that the note does not specify).";
<https://w3id.org/delphi/ontology/evidenceAgainst> "Blocks are arranged cyclically, so the emulated automaton has cyclic boundaries; the note does not specify how an infinite or bounded array should be terminated. The construction worked without any terminator, which supports but does not prove that it is purely local.",
"Only two-colour targets are run (range 1 exhaustively, range 2 by random sample). The claim's 'any number of colours' rests on the separate reduction of k-colour rules to two-colour rules of larger range (NKS p. 656), which is not implemented here; the encoding's range parameter r is the only mechanism tested.",
"The emulation is verified for 8 (range 1) and 4 (range 2) emulated steps per run; longer runs were not tried but the array returns exactly to the resting form after each period, so the check is effectively of the one-step transition from an arbitrary encoded state.",
"The rule list was parsed from the HTML of the online note; the page content may change, so the SHA-256 recorded refers to the page as retrieved on 2026-10-31, and the extracted rule text is kept in derived/uca_rule.txt.",
"Universality of the 19-colour automaton in the sense of emulating any cellular automaton does not by itself cover systems other than cellular automata; the claim as stated is limited to cellular automata, so this is in scope.";
<https://w3id.org/delphi/ontology/expectedObservation> "Pre-registered. analysis.py fetches the NKS online note 'Universal cellular automaton' (https://www.wolframscience.com/nks/notes-11-4--universal-cellular-automaton/), records byte size and SHA-256 of the page, and parses the published rule list (Mathematica replacement rules on 5-cell neighbourhoods, first matching rule applies; the arrow glyphs are lost in the HTML text, so each rule is read as 'pattern in braces' followed by 'output expression') and the published block encoding Flatten[{Transpose[{Join[{4, 18(1-a), 6}, Table[9, {2^(2r+1)-3}]], 10 - 3 rtab}], Table[{9, 1}, {r}], 9, 13}] with rtab in Wolfram's standard order (outcome for all-ones neighbourhood first). The universal automaton is run on a cyclic array of N blocks (N cells of the target automaton with cyclic boundaries) for S * P steps, where P = (3r+2) 2^(2r+1) + 3r^2 + 7r + 3 is the published period (53 for r = 1, 285 for r = 2). After each P steps, each block must equal the encoding of the directly computed target configuration (strict block-level check, which also verifies the decoded colours). Tests: (a) all 256 elementary rules, N = 16, S = 8, two random initial conditions each (seed 20261106); (b) 30 random two-colour range-2 rules (32-entry tables), N = 10, S = 4, one random initial condition each. 'supports' if the total number of mismatching universal-automaton cells over all checks is 0.";
<https://w3id.org/delphi/ontology/failCriterion> "Pre-registered. 'refutes' if, with the rule list and encoding exactly as published, some target rule's evolution is not reproduced (one or more mismatching cells at a checkpoint). If mismatches occur, the first action is to re-check the transcription of the published text (lost arrows, exponent formatting); a correction that makes the parse agree with the published text is a harness fix and is disclosed in caveats; any remaining mismatch is a refutation. 'inconclusive' with reason 'data-unavailable' if the note cannot be retrieved and no verifiable copy is at hand; 'inconclusive' with reason 'other' if the cyclic-boundary set-up turns out to be incompatible with the construction in a way that cannot be resolved from the published description (for example if the construction requires a special terminator block that the note does not specify).";
<https://w3id.org/delphi/ontology/hasConfidence> "0.85"^^xsd:double;
<https://w3id.org/delphi/ontology/hasEvidence> <https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-06--claim-test--dataset-1>,
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-06--claim-test--dataset-2>;
<https://w3id.org/delphi/ontology/hasVerdict> "supports";
<https://w3id.org/delphi/ontology/hypothesis> "Wolfram's fixed 19-colour range-2 rule, started from the published block encoding of a target rule table and cell colours, reproduces the target cellular automaton's evolution exactly: after the published number of steps per emulated step, every block again has the published form with its colour cell updated to the target rule's new value, for every elementary rule (range 1) and for random two-colour range-2 rules, which have more complicated rule tables than any elementary rule.";
<https://w3id.org/delphi/ontology/inferenceMethod> "analysis.py fetched the NKS online note (86,136 bytes), extracted the published rule list (65 replacement rules on 5-cell neighbourhoods, arrow glyphs decoded from the HTML entity, first matching rule applies) and the block encoding, compiled the rules into a complete 19^5-entry lookup table (every neighbourhood covered), and ran the universal automaton on a cyclic array of encoded blocks. For all 256 elementary rules (16 cells, 2 random initial conditions, 8 emulated steps of 53 universal steps each) and 30 random two-colour range-2 rules (10 cells, 4 emulated steps of 285 universal steps each; 70-cell blocks), the array after each period was compared cell-for-cell with the encoding of the directly computed cyclic target configuration: 0 mismatches in 1,394,720 cells. Checks that the harness is not vacuous: encoding rule 30 but comparing against rule 110 gives 309 mismatches in 6 steps; within one 53-step period up to 208 of 320 cells differ from the resting form before the array returns to it with exactly the colour cells changed; the decoded rule-30 evolution from one black cell shows the rule-30 pattern.";
<https://w3id.org/delphi/ontology/passCriterion> "Pre-registered. analysis.py fetches the NKS online note 'Universal cellular automaton' (https://www.wolframscience.com/nks/notes-11-4--universal-cellular-automaton/), records byte size and SHA-256 of the page, and parses the published rule list (Mathematica replacement rules on 5-cell neighbourhoods, first matching rule applies; the arrow glyphs are lost in the HTML text, so each rule is read as 'pattern in braces' followed by 'output expression') and the published block encoding Flatten[{Transpose[{Join[{4, 18(1-a), 6}, Table[9, {2^(2r+1)-3}]], 10 - 3 rtab}], Table[{9, 1}, {r}], 9, 13}] with rtab in Wolfram's standard order (outcome for all-ones neighbourhood first). The universal automaton is run on a cyclic array of N blocks (N cells of the target automaton with cyclic boundaries) for S * P steps, where P = (3r+2) 2^(2r+1) + 3r^2 + 7r + 3 is the published period (53 for r = 1, 285 for r = 2). After each P steps, each block must equal the encoding of the directly computed target configuration (strict block-level check, which also verifies the decoded colours). Tests: (a) all 256 elementary rules, N = 16, S = 8, two random initial conditions each (seed 20261106); (b) 30 random two-colour range-2 rules (32-entry tables), N = 10, S = 4, one random initial condition each. 'supports' if the total number of mismatching universal-automaton cells over all checks is 0.";
<https://w3id.org/delphi/ontology/preregistered> "false"^^xsd:boolean .
<https://w3id.org/delphi/resource/claim/wolfram2002-ch11-06> <https://w3id.org/delphi/ontology/hasAssessment>
<https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-06--claim-test> .
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-06--claim-test--dataset-1>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "the fixed rule and the encoding whose correctness the claim asserts";
dc:license "Copyright Stephen Wolfram, LLC; used for verification only, rule text reproduced in derived/ for reproducibility";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: NKS online, notes for Chapter 11 Section 4, 'Universal cellular automaton': rule list for the 19-colour range-2 universal cellular automaton and block encoding of the initial conditions";
prov:atLocation <https://www.wolframscience.com/nks/notes-11-4--universal-cellular-automaton/>;
prov:wasDerivedFrom <https://www.wolframscience.com/nks/notes-11-4--universal-cellular-automaton/>;
<https://w3id.org/delphi/ontology/hasChecksum> "sha256:2aea025fd6734b7285d1ff2e355cebc660a40b4ac18dc16ee54d6e0f5813bf3a" .
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-06--claim-test--dataset-2>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "the emulation checks";
dc:license "generated";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: Universal-automaton runs from encoded initial conditions for all 256 elementary rules and 30 random range-2 rules (seed 20261106), generated by analysis.py and compared with direct evolution";
prov:wasDerivedFrom <https://www.wolframscience.com/nks/p644--a-universal-cellular-automaton/> .
}
sub:provenance {
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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-ch11-06/result.json>;
prov:wasGeneratedBy sub:test .
sub:plan prov:hadPlan <https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/README.md> .
sub:test a prov:Activity;
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this: dc:created "2026-11-08T16:24:31.936Z"^^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-ch11-06--claim-test>;
<http://www.w3.org/2000/01/rdf-schema#label> "Claim test of wolfram2002-ch11-06: supports, confidence 0.85";
<https://w3id.org/delphi/ontology/domain> <https://w3id.org/delphi/resource/domain/wolfram-nks-2002> .
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