rows { options { physical_type: PHYSICAL_STREAM_TYPE_QUADS max_name_table_size: 128 max_prefix_table_size: 16 max_datatype_table_size: 16 logical_type: LOGICAL_STREAM_TYPE_DATASETS version: 2 } } rows { prefix { value: "https://w3id.org/np/" } } rows { name { value: "RAJRHOniF2PF4Njm3aGzSvnIInRjGyJ-Pbvt2kkwyrp0w" } } rows { namespace { name: "this" value { prefix_id: 1 } } } rows { prefix { value: "https://w3id.org/np/RAJRHOniF2PF4Njm3aGzSvnIInRjGyJ-Pbvt2kkwyrp0w/" } } rows { name { } } rows { namespace { name: "sub" value { prefix_id: 2 } } } rows { prefix { value: "http://www.nanopub.org/nschema#" } } rows { namespace { name: "np" value { prefix_id: 3 name_id: 2 } } } rows { prefix { value: "http://www.w3.org/1999/02/22-rdf-syntax-ns#" } } rows { namespace { name: "rdf" value { prefix_id: 4 name_id: 2 } } } rows { prefix { value: "http://www.w3.org/ns/prov#" } } rows { namespace { name: "prov" value { prefix_id: 5 name_id: 2 } } } rows { prefix { value: "http://purl.org/nanopub/x/" } } rows { namespace { name: "npx" value { prefix_id: 6 name_id: 2 } } } rows { prefix { value: "http://purl.org/dc/terms/" } } rows { namespace { name: "dc" value { prefix_id: 7 name_id: 2 } } } rows { prefix { value: "http://www.w3.org/2001/XMLSchema#" } } rows { namespace { name: "xsd" value { prefix_id: 8 name_id: 2 } } } rows { name { value: "hasAssertion" } } rows { name { value: "assertion" } } rows { name { value: "Head" } } rows { quad { s_iri { prefix_id: 1 name_id: 1 } p_iri { prefix_id: 3 name_id: 3 } o_iri { prefix_id: 2 } g_iri { } } } rows { name { value: "hasProvenance" } } rows { name { value: "provenance" } } rows { quad { p_iri { prefix_id: 3 } o_iri { prefix_id: 2 } } } rows { name { value: "hasPublicationInfo" } } rows { name { value: "pubinfo" } } rows { quad { p_iri { prefix_id: 3 } o_iri { prefix_id: 2 } } } rows { name { value: "type" } } rows { name { value: "Nanopublication" } } rows { quad { p_iri { prefix_id: 4 } o_iri { prefix_id: 3 } } } rows { prefix { value: "https://w3id.org/delphi/resource/assessment/" } } rows { name { value: "wolfram2002-ch06-17--claim-test" } } rows { name { value: "description" } } rows { quad { s_iri { prefix_id: 9 } p_iri { prefix_id: 7 } o_literal { lex: "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." } g_iri { prefix_id: 2 name_id: 4 } } } rows { prefix { value: "https://w3id.org/delphi/ontology/" } } rows { name { value: "Assessment" } } rows { quad { p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 10 name_id: 14 } } } rows { prefix { value: "http://www.w3.org/2000/01/rdf-schema#" } } rows { name { value: "comment" } } rows { quad { p_iri { prefix_id: 11 } o_literal { lex: "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." } } } rows { name { value: "label" } } rows { quad { p_iri { } o_literal { lex: "Claim test of wolfram2002-ch06-17: supports, confidence 0.98" } } } rows { name { value: "seeAlso" } } rows { prefix { value: "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch06-17/" } } rows { name { value: "result.json" } } rows { quad { p_iri { } o_iri { prefix_id: 12 } } } rows { name { value: "wasAttributedTo" } } rows { prefix { value: "https://w3id.org/delphi/resource/agent/" } } rows { name { value: "delphisci-claim-tester-claude-fable-5-1" } } rows { quad { p_iri { prefix_id: 5 } o_iri { prefix_id: 13 } } } rows { name { value: "admissibleDatasets" } } rows { quad { p_iri { prefix_id: 10 } o_literal { lex: "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" } } } rows { name { value: "assessmentType" } } rows { quad { p_iri { } o_literal { lex: "claim-test/0.1.0" } } } rows { name { value: "dataKind" } } rows { quad { p_iri { } o_literal { lex: "computational" } } } rows { name { value: "disconfirmingObservation" } } rows { quad { p_iri { } o_literal { lex: "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." } } } rows { name { value: "evidenceAgainst" } } rows { quad { p_iri { } o_literal { lex: "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." } } } rows { quad { o_literal { lex: "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." } } } rows { quad { o_literal { lex: "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." } } } rows { name { value: "expectedObservation" } } rows { quad { p_iri { } o_literal { lex: "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)." } } } rows { name { value: "failCriterion" } } rows { quad { p_iri { } o_literal { lex: "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." } } } rows { name { value: "hasConfidence" } } rows { datatype { value: "http://www.w3.org/2001/XMLSchema#double" } } rows { quad { p_iri { } o_literal { lex: "0.98" datatype: 1 } } } rows { name { value: "hasEvidence" } } rows { prefix { value: "https://w3id.org/delphi/resource/evidence/" } } rows { name { value: "wolfram2002-ch06-17--claim-test--dataset-1" } } rows { quad { p_iri { } o_iri { prefix_id: 14 } } } rows { name { value: "wolfram2002-ch06-17--claim-test--dataset-2" } } rows { quad { o_iri { } } } rows { name { value: "wolfram2002-ch06-17--claim-test--dataset-3" } } rows { quad { o_iri { } } } rows { name { value: "wolfram2002-ch06-17--claim-test--dataset-4" } } rows { quad { o_iri { } } } rows { name { value: "hasVerdict" } } rows { quad { p_iri { prefix_id: 10 } o_literal { lex: "supports" } } } rows { name { value: "hypothesis" } } rows { quad { p_iri { } o_literal { lex: "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." } } } rows { name { value: "inferenceMethod" } } rows { quad { p_iri { } o_literal { lex: "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." } } } rows { name { value: "passCriterion" } } rows { quad { p_iri { } o_literal { lex: "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)." } } } rows { name { value: "preregistered" } } rows { datatype { value: "http://www.w3.org/2001/XMLSchema#boolean" } } rows { quad { p_iri { } o_literal { lex: "false" datatype: 2 } } } rows { prefix { value: "https://w3id.org/delphi/resource/claim/" } } rows { name { value: "wolfram2002-ch06-17" } } rows { name { value: "hasAssessment" } } rows { quad { s_iri { prefix_id: 15 } p_iri { prefix_id: 10 } o_iri { prefix_id: 9 name_id: 12 } } } rows { quad { s_iri { prefix_id: 14 name_id: 30 } p_iri { prefix_id: 7 name_id: 13 } o_literal { lex: "two-colour nearest-neighbour rules, bound 2^n" } } } rows { name { value: "license" } } rows { quad { p_iri { name_id: 41 } o_literal { } } } rows { name { value: "EvidenceItem" } } rows { quad { p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 10 name_id: 42 } } } rows { quad { p_iri { prefix_id: 11 name_id: 16 } o_literal { lex: "Dataset: All 256 ECA x all 2^n blocks of n = 1..12 cells repeated forever (generated by analysis.py)" } } } rows { quad { s_iri { prefix_id: 14 name_id: 31 } p_iri { prefix_id: 7 name_id: 13 } o_literal { lex: "three-colour rules, bound 3^n" } } } rows { quad { p_iri { name_id: 41 } o_literal { } } } rows { quad { p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 10 name_id: 42 } } } rows { quad { p_iri { prefix_id: 11 name_id: 16 } o_literal { lex: "Dataset: All 2187 three-colour nearest-neighbour totalistic rules x all 3^n blocks of n = 1..6 cells (generated by analysis.py)" } } } rows { quad { s_iri { prefix_id: 14 name_id: 32 } p_iri { prefix_id: 7 name_id: 13 } o_literal { lex: "non-elementary two-colour rules, bound 2^n" } } } rows { quad { p_iri { name_id: 41 } o_literal { } } } rows { quad { p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 10 name_id: 42 } } } rows { quad { p_iri { prefix_id: 11 name_id: 16 } o_literal { lex: "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)" } } } rows { quad { s_iri { prefix_id: 14 name_id: 33 } p_iri { prefix_id: 7 name_id: 13 } o_literal { lex: "tests the reduction of the repeated-block line to a finite cyclic system" } } } rows { quad { p_iri { name_id: 41 } o_literal { } } } rows { quad { p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 10 name_id: 42 } } } rows { quad { p_iri { prefix_id: 11 name_id: 16 } o_literal { lex: "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)" } } } rows { name { value: "SoftwareAgent" } } rows { quad { s_iri { prefix_id: 13 name_id: 20 } p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 5 name_id: 43 } g_iri { prefix_id: 2 name_id: 7 } } } rows { quad { p_iri { prefix_id: 11 name_id: 16 } o_literal { lex: "delphisci claim tester (claude-fable-5.1; cursor/claim-tests-wolfram-nks-0123)" } } } rows { name { value: "actedOnBehalfOf" } } rows { prefix { value: "https://orcid.org/" } } rows { name { value: "0009-0007-4948-9192" } } rows { quad { p_iri { prefix_id: 5 name_id: 44 } o_iri { prefix_id: 16 } } } rows { name { value: "usesModel" } } rows { prefix { id: 6 value: "https://w3id.org/delphi/resource/model/" } } rows { name { value: "claude-fable-5-1" } } rows { quad { p_iri { prefix_id: 10 } o_iri { prefix_id: 6 } } } rows { name { value: "identifier" } } rows { quad { s_iri { name_id: 47 } p_iri { prefix_id: 7 } o_literal { lex: "claude-fable-5.1" } } } rows { name { value: "LanguageModel" } } rows { quad { p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 10 name_id: 49 } } } rows { quad { s_iri { prefix_id: 2 name_id: 4 } p_iri { prefix_id: 5 name_id: 19 } o_iri { prefix_id: 13 } } } rows { name { value: "wasDerivedFrom" } } rows { quad { p_iri { prefix_id: 5 name_id: 50 } o_iri { prefix_id: 12 name_id: 18 } } } rows { name { value: "wasGeneratedBy" } } rows { name { value: "test" } } rows { quad { p_iri { prefix_id: 5 name_id: 51 } o_iri { prefix_id: 2 } } } rows { name { value: "plan" } } rows { name { value: "hadPlan" } } rows { prefix { id: 8 value: "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/" } } rows { name { value: "README.md" } } rows { quad { s_iri { } p_iri { prefix_id: 5 } o_iri { prefix_id: 8 } } } rows { name { value: "Activity" } } rows { quad { s_iri { prefix_id: 2 name_id: 52 } p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 5 name_id: 56 } } } rows { name { value: "qualifiedAssociation" } } rows { quad { p_iri { } o_iri { prefix_id: 2 name_id: 53 } } } rows { name { value: "wasAssociatedWith" } } rows { quad { p_iri { prefix_id: 5 name_id: 58 } o_iri { prefix_id: 13 name_id: 20 } } } rows { name { value: "created" } } rows { datatype { value: "http://www.w3.org/2001/XMLSchema#dateTime" } } rows { quad { s_iri { prefix_id: 1 name_id: 1 } p_iri { prefix_id: 7 name_id: 59 } o_literal { lex: "2026-11-08T16:24:31.928Z" datatype: 3 } g_iri { prefix_id: 2 name_id: 9 } } } rows { name { value: "creator" } } rows { quad { p_iri { prefix_id: 7 name_id: 60 } o_iri { prefix_id: 16 name_id: 45 } } } rows { prefix { id: 3 value: "https://creativecommons.org/licenses/by/4.0/" } } rows { quad { p_iri { prefix_id: 7 name_id: 41 } o_iri { prefix_id: 3 name_id: 2 } } } rows { prefix { id: 15 value: "http://purl.org/nanopub/x/" } } rows { name { value: "hasNanopubType" } } rows { quad { p_iri { prefix_id: 15 name_id: 61 } o_iri { prefix_id: 10 name_id: 14 } } } rows { name { value: "introduces" } } rows { quad { p_iri { prefix_id: 15 name_id: 62 } o_iri { prefix_id: 9 name_id: 12 } } } rows { quad { p_iri { prefix_id: 11 name_id: 16 } o_literal { lex: "Claim test of wolfram2002-ch06-17: supports, confidence 0.98" } } } rows { name { value: "domain" } } rows { prefix { id: 14 value: "https://w3id.org/delphi/resource/domain/" } } rows { name { value: "wolfram-nks-2002" } } rows { quad { p_iri { prefix_id: 10 name_id: 63 } o_iri { prefix_id: 14 } } } rows { name { value: "sig" } } rows { name { value: "hasAlgorithm" } } rows { quad { s_iri { prefix_id: 2 } p_iri { prefix_id: 15 } o_literal { lex: "RSA" } } } rows { name { value: "hasPublicKey" } } rows { quad { p_iri { } o_literal { lex: "MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB" } } } rows { name { value: "hasSignature" } } rows { quad { p_iri { } o_literal { lex: "p2GV3/rLjTiJO0jeiybfI2/qoqoyRNk5uTdcga/EggovSYbjfjR3zTFRIx5WCpNxn3mYFSFgfawJ1lmLUOqhvvtYflQGpB5U8/+3eyaCOGCwk/ho6kPtpfai8UlrMSNN6yzdjMZW6wsUGM01HwhazBDanb3DFEONcsNRC0J4cIEDrT+Yq8YTp65KuosvKMVEcSs4fq0PMMaBnwo71TsWw9/3rwU39PqaRytEPm6SzymA00nTUYHubnyY1kv29WlblJz+fHAzRiZJR9K2xLJ8gww09HcuL09e/rVDGAU69kpMmeKAvbrwEB/PEElq3/3oga7UorHgnohmSYdvgKOWTA==" } } } rows { name { value: "hasSignatureTarget" } } rows { quad { p_iri { } o_iri { prefix_id: 1 name_id: 1 } } } rows { name { value: "signedBy" } } rows { quad { p_iri { prefix_id: 15 name_id: 70 } o_iri { prefix_id: 16 name_id: 45 } } }