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: "RAkGmL0hGi1qXX3Rp56D6D70ZhKp3UevugXn7zplHpRn8" } } rows { namespace { name: "this" value { prefix_id: 1 } } } rows { prefix { value: "https://w3id.org/np/RAkGmL0hGi1qXX3Rp56D6D70ZhKp3UevugXn7zplHpRn8/" } } 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-ch11-09--claim-test" } } rows { name { value: "description" } } rows { quad { s_iri { prefix_id: 9 } p_iri { prefix_id: 7 } o_literal { lex: "analysis.py enumerates all 196 two-colour (blocks 1-3) and 1728 three-colour (blocks 1-2) neighbour-independent substitution rules, iterates each from a single cell of colour 1 until the word has 131072 symbols (or 60 steps), and counts distinct factors of length 1..14 with a sorted rolling-code method. It generates rule 30 from a single black cell with big-integer bit operations, taking the central 40001 cells of row 20000 and the first 65536 centre-column cells, and applies the same count. It also measures what share of the centre column\'s length-14 factors appear in any binary substitution word, and runs the one-cell-per-cell neighbour-dependent substitution systems for rules 90 and 30 against the direct CA for 1000 steps. Runtime about 19 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: 157 maximum number of distinct length-14 factors over all 1924 neighbour-independent substitution words (threshold 225) (n = 1924, exact combinatorial counts). Interpretation: \'Repetitive\' is operationalised as eventually periodic (bounded subword complexity, Morse-Hedlund), \'nested\' as a self-similar word, which for fixed points of morphisms has subword complexity O(n^2) at most (Pansiot); the threshold (n+1)^2 at n = 14 is therefore a generous upper bound for repetitive-or-nested and about a tenth of what a random-like binary sequence of this length shows. \'Cannot emulate rule 30\' is tested within the enumerated family by the complexity gap (a word with p(14) <= 225 cannot contain the rule 30 row, whose own p(14) is measured); it is not a proof over all encodings. The neighbour-dependent half is tested exactly as the book describes it (rules \'always yielding just one cell and corresponding quite directly to cellular automata\', p. 666)." } } } rows { name { value: "label" } } rows { quad { p_iri { } o_literal { lex: "Claim test of wolfram2002-ch11-09: supports, confidence 0.85" } } } rows { name { value: "seeAlso" } } rows { prefix { value: "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch11-09/" } } 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: substitution-systems-and-rule30-generator" } } } 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. FAIL (refutes) if any neighbour-independent rule in the family has p(14) >= 2000 (rule-30-like complexity), or if the neighbour-dependent construction does not reproduce rule 90 or rule 30. If some neighbour-independent rule has 225 < p(14) < 2000 the result is \'mixed\' and the rule is reported with its complexity profile." } } } rows { name { value: "evidenceAgainst" } } rows { quad { p_iri { } o_literal { lex: "The impossibility half is tested on the two complete enumerated families named in the book\'s own discussion (p. 83), not for arbitrarily long replacement blocks or alphabets; the complexity gap (at most 157 distinct length-14 factors versus 14922-16034 for rule 30) is a finite proxy for the theorem that fixed points of morphisms have polynomially bounded subword complexity." } } } rows { quad { o_literal { lex: "The length-14 factor share result (at most 0.5% of rule 30\'s centre-column factors occur in any binary substitution word) is reported as a direct check that none of the enumerated systems reproduces rule 30\'s sequence under the identity encoding; other encodings were not explored." } } } rows { quad { o_literal { lex: "The neighbour-dependent half is near-definitional: a substitution system whose single output cell depends on the cell and its two neighbours is a cellular automaton; the test confirms it reproduces rules 90 and 30 exactly for 1000 steps, which is what the book\'s figure shows." } } } rows { quad { o_literal { lex: "The subword-complexity criterion treats any word with p(14) <= 225 as repetitive-or-nested; the words with the largest complexity (e.g. 0 -> 0, 1 -> 011, p(n) = 2,4,6,9,13,...,81) are non-primitive morphic words whose complexity grows faster than linearly but far below that of rule 30, consistent with the known n log n / n^2 classes for such words." } } } rows { name { value: "expectedObservation" } } rows { quad { p_iri { } o_literal { lex: "Pre-registered. For each of the 196 two-colour rules {0 -> w0, 1 -> w1} with |w0|, |w1| in {1,2,3} and each of the 1728 three-colour rules with block lengths in {1,2}, start from a single cell of colour 1 and iterate until the word has >= L = 131072 symbols (or 60 steps if it never does), truncate to L, and compute the number p(n) of distinct length-n factors for n = 1..14. For rule 30 from a single black cell compute p(14) of (i) the central 40001 cells of the row at step 20000 and (ii) the first 65536 cells of the centre column. Build the neighbour-dependent substitution system whose rule maps each cell to one new cell given by the elementary-CA table of its (left, self, right) neighbourhood, and run it for 1000 steps from a single black cell. PASS (supports) if (a) every neighbour-independent rule has p(14) <= 225 = (14+1)^2 (eventually periodic words are those with p(14) = p(13); the rest are counted as nested), (b) both rule 30 sequences have p(14) >= 2000, and (c) the neighbour-dependent systems for rules 90 and 30 reproduce the cellular-automaton rows exactly at every one of the 1000 steps." } } } rows { name { value: "failCriterion" } } rows { quad { p_iri { } o_literal { lex: "Pre-registered. FAIL (refutes) if any neighbour-independent rule in the family has p(14) >= 2000 (rule-30-like complexity), or if the neighbour-dependent construction does not reproduce rule 90 or rule 30. If some neighbour-independent rule has 225 < p(14) < 2000 the result is \'mixed\' and the rule is reported with its complexity profile." } } } rows { name { value: "hasConfidence" } } rows { datatype { value: "http://www.w3.org/2001/XMLSchema#double" } } rows { quad { p_iri { } o_literal { lex: "0.85" datatype: 1 } } } rows { name { value: "hasEvidence" } } rows { prefix { value: "https://w3id.org/delphi/resource/evidence/" } } rows { name { value: "wolfram2002-ch11-09--claim-test--dataset-1" } } rows { quad { p_iri { } o_iri { prefix_id: 14 } } } 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: "If the claim holds, every neighbour-independent substitution system in a complete enumerated family (2 colours with replacement blocks of length 1-3; 3 colours with blocks of length 1-2) produces, from a single cell, a sequence whose subword complexity stays bounded (repetitive) or grows at most polynomially slowly (nested), far below the near-exponential subword complexity of rule 30\'s rows and centre column, so none of them can reproduce rule 30; while a neighbour-dependent substitution system (one output cell per cell, chosen from the cell and its two neighbours) reproduces rules 90 and 30 exactly." } } } rows { name { value: "inferenceMethod" } } rows { quad { p_iri { } o_literal { lex: "analysis.py enumerates all 196 two-colour (blocks 1-3) and 1728 three-colour (blocks 1-2) neighbour-independent substitution rules, iterates each from a single cell of colour 1 until the word has 131072 symbols (or 60 steps), and counts distinct factors of length 1..14 with a sorted rolling-code method. It generates rule 30 from a single black cell with big-integer bit operations, taking the central 40001 cells of row 20000 and the first 65536 centre-column cells, and applies the same count. It also measures what share of the centre column\'s length-14 factors appear in any binary substitution word, and runs the one-cell-per-cell neighbour-dependent substitution systems for rules 90 and 30 against the direct CA for 1000 steps. Runtime about 19 s." } } } rows { name { value: "passCriterion" } } rows { quad { p_iri { } o_literal { lex: "Pre-registered. For each of the 196 two-colour rules {0 -> w0, 1 -> w1} with |w0|, |w1| in {1,2,3} and each of the 1728 three-colour rules with block lengths in {1,2}, start from a single cell of colour 1 and iterate until the word has >= L = 131072 symbols (or 60 steps if it never does), truncate to L, and compute the number p(n) of distinct length-n factors for n = 1..14. For rule 30 from a single black cell compute p(14) of (i) the central 40001 cells of the row at step 20000 and (ii) the first 65536 cells of the centre column. Build the neighbour-dependent substitution system whose rule maps each cell to one new cell given by the elementary-CA table of its (left, self, right) neighbourhood, and run it for 1000 steps from a single black cell. PASS (supports) if (a) every neighbour-independent rule has p(14) <= 225 = (14+1)^2 (eventually periodic words are those with p(14) = p(13); the rest are counted as nested), (b) both rule 30 sequences have p(14) >= 2000, and (c) the neighbour-dependent systems for rules 90 and 30 reproduce the cellular-automaton rows exactly at every one of the 1000 steps." } } } 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-ch11-09" } } 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: "the computational objects the claim is about" } } } rows { name { value: "license" } } rows { quad { p_iri { name_id: 38 } o_literal { lex: "generated by this test" } } } rows { name { value: "EvidenceItem" } } rows { quad { p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 10 name_id: 39 } } } rows { quad { p_iri { prefix_id: 11 name_id: 16 } o_literal { lex: "Dataset: Enumerated neighbour-independent substitution systems (2 colours, blocks 1-3; 3 colours, blocks 1-2), rule 30 evolutions, and neighbour-dependent substitution emulations of rules 90 and 30, generated by analysis.py" } } } rows { name { value: "wasDerivedFrom" } } rows { prefix { value: "https://www.wolframscience.com/nks/p666--emulating-cellular-automata-with-other-systems/" } } rows { quad { p_iri { prefix_id: 5 name_id: 40 } o_iri { prefix_id: 16 name_id: 2 } } } 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: 41 } 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-9241)" } } } rows { name { value: "actedOnBehalfOf" } } rows { prefix { id: 6 value: "https://orcid.org/" } } rows { name { value: "0009-0007-4948-9192" } } rows { quad { p_iri { prefix_id: 5 name_id: 42 } o_iri { prefix_id: 6 } } } rows { name { value: "usesModel" } } rows { prefix { id: 8 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: 8 } } } rows { name { value: "identifier" } } rows { quad { s_iri { name_id: 45 } 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: 47 } } } rows { quad { s_iri { prefix_id: 2 name_id: 4 } p_iri { prefix_id: 5 name_id: 19 } o_iri { prefix_id: 13 } } } rows { quad { p_iri { prefix_id: 5 name_id: 40 } 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: 48 } o_iri { prefix_id: 2 } } } rows { name { value: "plan" } } rows { name { value: "hadPlan" } } rows { prefix { id: 1 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: 1 } } } rows { name { value: "Activity" } } rows { quad { s_iri { prefix_id: 2 name_id: 49 } p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 5 name_id: 53 } } } rows { name { value: "qualifiedAssociation" } } rows { quad { p_iri { } o_iri { prefix_id: 2 name_id: 50 } } } rows { name { value: "wasAssociatedWith" } } rows { quad { p_iri { prefix_id: 5 name_id: 55 } o_iri { prefix_id: 13 name_id: 20 } } } rows { prefix { id: 3 value: "https://w3id.org/np/" } } rows { name { value: "created" } } rows { datatype { value: "http://www.w3.org/2001/XMLSchema#dateTime" } } rows { quad { s_iri { prefix_id: 3 name_id: 1 } p_iri { prefix_id: 7 name_id: 56 } o_literal { lex: "2026-11-08T16:24:31.937Z" datatype: 3 } g_iri { prefix_id: 2 name_id: 9 } } } rows { name { value: "creator" } } rows { quad { p_iri { prefix_id: 7 name_id: 57 } o_iri { prefix_id: 6 name_id: 43 } } } rows { prefix { id: 15 value: "https://creativecommons.org/licenses/by/4.0/" } } rows { quad { p_iri { prefix_id: 7 name_id: 38 } o_iri { prefix_id: 15 name_id: 2 } } } rows { prefix { id: 9 value: "http://purl.org/nanopub/x/" } } rows { name { value: "hasNanopubType" } } rows { quad { p_iri { prefix_id: 9 name_id: 58 } o_iri { prefix_id: 10 name_id: 14 } } } rows { name { value: "introduces" } } rows { prefix { id: 14 value: "https://w3id.org/delphi/resource/assessment/" } } rows { quad { p_iri { prefix_id: 9 name_id: 59 } o_iri { prefix_id: 14 name_id: 12 } } } rows { quad { p_iri { prefix_id: 11 name_id: 16 } o_literal { lex: "Claim test of wolfram2002-ch11-09: supports, confidence 0.85" } } } rows { name { value: "domain" } } rows { prefix { id: 16 value: "https://w3id.org/delphi/resource/domain/" } } rows { name { value: "wolfram-nks-2002" } } rows { quad { p_iri { prefix_id: 10 name_id: 60 } o_iri { prefix_id: 16 } } } rows { name { value: "sig" } } rows { name { value: "hasAlgorithm" } } rows { quad { s_iri { prefix_id: 2 } p_iri { prefix_id: 9 } 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 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