https://w3id.org/np/RAJRHOniF2PF4Njm3aGzSvnIInRjGyJ-Pbvt2kkwyrp0w
.trig | .trig.txt | .jelly | .jelly.txt | .jsonld | .jsonld.txt | .nq | .nq.txt | .xml | .xml.txt
@prefix this: <https://w3id.org/np/RAJRHOniF2PF4Njm3aGzSvnIInRjGyJ-Pbvt2kkwyrp0w> .
@prefix sub: <https://w3id.org/np/RAJRHOniF2PF4Njm3aGzSvnIInRjGyJ-Pbvt2kkwyrp0w/> .
@prefix np: <http://www.nanopub.org/nschema#> .
@prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
@prefix prov: <http://www.w3.org/ns/prov#> .
@prefix npx: <http://purl.org/nanopub/x/> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
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-ch06-17--claim-test> a <https://w3id.org/delphi/ontology/Assessment>;
dc:description "analysis.py treats a block of n cells repeated forever as an n-cell ring, builds the ring's transition map on all k^n states for each rule and computes the eventual period of every state's orbit from the functional graph (cycle detection by in-degree peeling). Families: all 256 ECA for n = 1..12 (2,096,640 rule-block pairs), all 2187 three-colour totalistic rules for n = 1..6 (2,388,204 pairs, bound 3^n), and 500 seeded random range-2 binary rules for n = 1..10 (1,023,000 pairs). It then checks the reduction itself: for all 256 ECA and all 32,256 blocks of n = 1..6, a line of repeated copies of the block is evolved for 2*2^n steps and its central copy compared cell by cell with the ring evolution (15,845,376 cells). Run time about 18 s.";
<http://www.w3.org/2000/01/rdf-schema#comment> "Measured: 1 fraction of (rule, block) pairs whose eventual temporal period is <= k^n (n = 5507844, exact (exhaustive within each family; the range-2 family is a seeded sample of 500 of 2^32 rules)). Interpretation: 'Initial conditions which consist just of a fixed block of cells repeated forever' is a spatially n-periodic configuration on the infinite line. 'Simple repetitive behavior' is read as eventual time-periodicity of the configuration, and the stated bound 2^n is read, following Wolfram's own reasoning and the assessors, as k^n for k colours (2^n in the two-colour case the text has in mind). 'Any cellular automaton' cannot be enumerated, so three families are tested: all 256 elementary rules exhaustively (n = 1..12), all 2187 three-colour nearest-neighbour totalistic rules (n = 1..6, bound 3^n), and a fixed-seed random sample of 500 two-colour range-2 (5-neighbour) rules out of 2^32 (n = 1..10). The reduction 'each block evolves like a finite cyclic system' is tested separately by simulating the actual repeated-block line and comparing it with the ring.";
<http://www.w3.org/2000/01/rdf-schema#label> "Claim test of wolfram2002-ch06-17: supports, confidence 0.98";
<http://www.w3.org/2000/01/rdf-schema#seeAlso> <https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch06-17/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: eca-repeated-blocks-n1-12, totalistic-3colour-repeated-blocks-n1-6, range2-binary-sample-repeated-blocks-n1-10, line-vs-ring-equivalence-sample";
<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: any (rule, block) pair whose eventual period exceeds k^n, or any pair for which the repeated-block line evolution differs from the ring evolution inside the region unaffected by the line's ends.";
<https://w3id.org/delphi/ontology/evidenceAgainst> "The bound k^n is attained only in degenerate cases (n = 1, rules that cycle through every state); for n >= 2 the overwhelming majority of periods are below k^n / 10 (see the histogram), so the bound is loose but never violated.",
"The claim quantifies over all cellular automata; three rule families (one exhaustive over all 256 elementary rules, one exhaustive over all 2187 three-colour totalistic rules, one a 500-rule sample of range-2 rules) were tested, and the general statement rests on the finite-state argument that the line-vs-ring check confirms empirically for the elementary rules.",
"Wolfram writes 2^n for two colours; the three-colour family tests the natural k^n generalisation that the assessors and the book's own argument imply.";
<https://w3id.org/delphi/ontology/expectedObservation> "Pre-registered: (1) across all (rule, block) pairs enumerated, 100% have eventual temporal period <= k^n (zero violations); (2) for every (rule, block) pair in the equivalence sample, the central block of a long line made of repeated copies of the block evolves identically to the n-cell ring for all simulated steps (zero mismatching cells).";
<https://w3id.org/delphi/ontology/failCriterion> "Pre-registered: any (rule, block) pair whose eventual period exceeds k^n, or any pair for which the repeated-block line evolution differs from the ring evolution inside the region unaffected by the line's ends.";
<https://w3id.org/delphi/ontology/hasConfidence> "0.98"^^xsd:double;
<https://w3id.org/delphi/ontology/hasEvidence> <https://w3id.org/delphi/resource/evidence/wolfram2002-ch06-17--claim-test--dataset-1>,
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch06-17--claim-test--dataset-2>,
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch06-17--claim-test--dataset-3>,
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch06-17--claim-test--dataset-4>;
<https://w3id.org/delphi/ontology/hasVerdict> "supports";
<https://w3id.org/delphi/ontology/hypothesis> "For every cellular automaton tested and every block of n cells repeated forever as the initial condition, the evolution is eventually time-periodic with period at most k^n (k = number of colours; 2^n for two colours), and the infinite repeated-block configuration evolves exactly as a cyclic ring of n cells.";
<https://w3id.org/delphi/ontology/inferenceMethod> "analysis.py treats a block of n cells repeated forever as an n-cell ring, builds the ring's transition map on all k^n states for each rule and computes the eventual period of every state's orbit from the functional graph (cycle detection by in-degree peeling). Families: all 256 ECA for n = 1..12 (2,096,640 rule-block pairs), all 2187 three-colour totalistic rules for n = 1..6 (2,388,204 pairs, bound 3^n), and 500 seeded random range-2 binary rules for n = 1..10 (1,023,000 pairs). It then checks the reduction itself: for all 256 ECA and all 32,256 blocks of n = 1..6, a line of repeated copies of the block is evolved for 2*2^n steps and its central copy compared cell by cell with the ring evolution (15,845,376 cells). Run time about 18 s.";
<https://w3id.org/delphi/ontology/passCriterion> "Pre-registered: (1) across all (rule, block) pairs enumerated, 100% have eventual temporal period <= k^n (zero violations); (2) for every (rule, block) pair in the equivalence sample, the central block of a long line made of repeated copies of the block evolves identically to the n-cell ring for all simulated steps (zero mismatching cells).";
<https://w3id.org/delphi/ontology/preregistered> "false"^^xsd:boolean .
<https://w3id.org/delphi/resource/claim/wolfram2002-ch06-17> <https://w3id.org/delphi/ontology/hasAssessment>
<https://w3id.org/delphi/resource/assessment/wolfram2002-ch06-17--claim-test> .
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch06-17--claim-test--dataset-1>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "two-colour nearest-neighbour rules, bound 2^n";
dc:license "";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: All 256 ECA x all 2^n blocks of n = 1..12 cells repeated forever (generated by analysis.py)" .
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch06-17--claim-test--dataset-2>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "three-colour rules, bound 3^n";
dc:license "";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: All 2187 three-colour nearest-neighbour totalistic rules x all 3^n blocks of n = 1..6 cells (generated by analysis.py)" .
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch06-17--claim-test--dataset-3>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "non-elementary two-colour rules, bound 2^n";
dc:license "";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: 500 random two-colour range-2 rules (5-cell neighbourhood, 2^32 rule space; numpy default_rng seed 20261031) x all 2^n blocks of n = 1..10 (generated by analysis.py)" .
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch06-17--claim-test--dataset-4>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "tests the reduction of the repeated-block line to a finite cyclic system";
dc:license "";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: All 256 ECA x all blocks of n = 1..6 cells, repeated on a long line, compared with the ring (generated by analysis.py)" .
}
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-0123)";
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-ch06-17/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;
prov:qualifiedAssociation sub:plan;
prov:wasAssociatedWith <https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1> .
}
sub:pubinfo {
this: dc:created "2026-11-08T16:24:31.928Z"^^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-ch06-17--claim-test>;
<http://www.w3.org/2000/01/rdf-schema#label> "Claim test of wolfram2002-ch06-17: supports, confidence 0.98";
<https://w3id.org/delphi/ontology/domain> <https://w3id.org/delphi/resource/domain/wolfram-nks-2002> .
sub:sig npx:hasAlgorithm "RSA";
npx:hasPublicKey "MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB";
npx:hasSignature "p2GV3/rLjTiJO0jeiybfI2/qoqoyRNk5uTdcga/EggovSYbjfjR3zTFRIx5WCpNxn3mYFSFgfawJ1lmLUOqhvvtYflQGpB5U8/+3eyaCOGCwk/ho6kPtpfai8UlrMSNN6yzdjMZW6wsUGM01HwhazBDanb3DFEONcsNRC0J4cIEDrT+Yq8YTp65KuosvKMVEcSs4fq0PMMaBnwo71TsWw9/3rwU39PqaRytEPm6SzymA00nTUYHubnyY1kv29WlblJz+fHAzRiZJR9K2xLJ8gww09HcuL09e/rVDGAU69kpMmeKAvbrwEB/PEElq3/3oga7UorHgnohmSYdvgKOWTA==";
npx:hasSignatureTarget this:;
npx:signedBy <https://orcid.org/0009-0007-4948-9192> .
}