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: "RAohAXrzytP8w7CINkKZLoog3BxIIUpggxow_mnZxeidQ" } } rows { namespace { name: "this" value { prefix_id: 1 } } } rows { prefix { value: "https://w3id.org/np/RAohAXrzytP8w7CINkKZLoog3BxIIUpggxow_mnZxeidQ/" } } 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-ch05-15--claim-test" } } rows { name { value: "description" } } rows { quad { s_iri { prefix_id: 9 } p_iri { prefix_id: 7 } o_literal { lex: "analysis.py encodes each constraint system as a bitmask of allowed length-w words. Satisfiability is decided by iterating a reachability vector over the k^(w-1) de Bruijn vertices for 4V + 1 edge steps (existence of a valid word of length 4V + w). Independently, every period word u with |u| <= V is enumerated (sum of k^p over p = 1..V candidates, each stored as the bitmask of its cyclic length-w windows) and u^infinity is accepted iff its window mask is contained in the allowed set. The two indicators are compared for all 138,856 systems (exhaustive for (k,w) = (2,2), (2,3), (2,4), (3,2), (4,2); seeded samples of 2000 and 5000 for (2,5) and (3,3)); minimal periods are tabulated. Run time about 3 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 satisfiable constraint systems that have a periodic solution with period <= k^(w-1) (n = 129939, exact for the exhaustive families; the two sampled families are 2000 and 5000 seeded draws). Interpretation: Wolfram\'s \'local set of constraints\' on a one-dimensional array of coloured cells (p. 210-211: each cell\'s neighbourhood must be one of a given set of allowed configurations) is a one-dimensional subshift of finite type: a set of allowed words of a fixed window length w over k colours. \'Can be satisfied at all\' is read as the existence of a bi-infinite arrangement all of whose windows are allowed; by compactness this is equivalent to the existence of arbitrarily long valid finite words, and operationally it is tested by the existence of a valid word of length 4V + w (any valid word longer than V must revisit a de Bruijn vertex, so this length is far beyond the threshold, and the check is done by a reachability iteration, not a cycle search). \'Simple and purely repetitive arrangement\' is read as a periodic configuration, found by brute-force enumeration of all period words u with |u| <= V = k^(w-1) and checking all cyclic windows. All constraint systems are enumerated exhaustively for (k, w) in {(2,2), (2,3), (2,4), (3,2), (4,2)} and sampled with a fixed seed for (2,5) and (3,3)." } } } rows { name { value: "label" } } rows { quad { p_iri { } o_literal { lex: "Claim test of wolfram2002-ch05-15: supports, confidence 0.97" } } } rows { name { value: "seeAlso" } } rows { prefix { value: "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch05-15/" } } 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: sft-k2-w2-all, sft-k2-w3-all, sft-k2-w4-all, sft-k3-w2-all, sft-k4-w2-all, sft-k2-w5-sample, sft-k3-w3-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: at least one constraint system admits a valid word of length 4V + w but no periodic arrangement with period <= V (this would refute the claim as stated, since the shortest possible periodic solution is bounded by V); or the two satisfiability indicators disagree in the other direction, which would indicate a broken test." } } } rows { name { value: "evidenceAgainst" } } rows { quad { p_iri { } o_literal { lex: "Satisfiability was operationalised by the existence of a valid word of length 4V + w; by compactness this is equivalent to the existence of a bi-infinite arrangement, but the equivalence itself relies on finiteness of the vertex set, so the two indicators are not logically independent even though they are computed by different algorithms." } } } rows { quad { o_literal { lex: "The claim is a theorem (a non-empty one-dimensional shift of finite type contains a periodic point, from a cycle in its de Bruijn graph); the computation confirms it exhaustively for all two-colour constraints with windows up to 4 and all four-colour constraints with window 2, and by sampling for windows 5 (two colours) and 3 (three colours). The maximal minimal period found (8 for k = 2, w = 4; exactly the two de Bruijn-cycle constraint sets) matches the bound V = k^(w-1)." } } } rows { quad { o_literal { lex: "Wolfram\'s \'simple\' is read as \'periodic\'; the observed minimal periods are small (at most V), but \'simple\' is not otherwise quantified." } } } rows { name { value: "expectedObservation" } } rows { quad { p_iri { } o_literal { lex: "Pre-registered: across all enumerated or sampled constraint systems, every system that admits a valid word of length 4V + w (the operational test of satisfiability, independent of any cycle argument) also admits a periodic arrangement u^infinity with |u| <= V whose every cyclic window of length w is allowed; and every system with no such long valid word has no periodic arrangement either. Zero violations in both directions." } } } rows { name { value: "failCriterion" } } rows { quad { p_iri { } o_literal { lex: "Pre-registered: at least one constraint system admits a valid word of length 4V + w but no periodic arrangement with period <= V (this would refute the claim as stated, since the shortest possible periodic solution is bounded by V); or the two satisfiability indicators disagree in the other direction, which would indicate a broken test." } } } rows { name { value: "hasConfidence" } } rows { datatype { value: "http://www.w3.org/2001/XMLSchema#double" } } rows { quad { p_iri { } o_literal { lex: "0.97" datatype: 1 } } } rows { name { value: "hasEvidence" } } rows { prefix { value: "https://w3id.org/delphi/resource/evidence/" } } rows { name { value: "wolfram2002-ch05-15--claim-test--dataset-1" } } rows { quad { p_iri { } o_iri { prefix_id: 14 } } } rows { name { value: "wolfram2002-ch05-15--claim-test--dataset-2" } } rows { quad { o_iri { } } } rows { name { value: "wolfram2002-ch05-15--claim-test--dataset-3" } } rows { quad { o_iri { } } } rows { name { value: "wolfram2002-ch05-15--claim-test--dataset-4" } } rows { quad { o_iri { } } } rows { name { value: "wolfram2002-ch05-15--claim-test--dataset-5" } } rows { quad { o_iri { } } } rows { name { value: "wolfram2002-ch05-15--claim-test--dataset-6" } } rows { quad { o_iri { } } } rows { name { value: "wolfram2002-ch05-15--claim-test--dataset-7" } } 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 one-dimensional local constraint system (a set of allowed length-w colour words over k colours) that admits any bi-infinite satisfying arrangement, there is a purely periodic satisfying arrangement, and its period can be taken at most V = k^(w-1)." } } } rows { name { value: "inferenceMethod" } } rows { quad { p_iri { } o_literal { lex: "analysis.py encodes each constraint system as a bitmask of allowed length-w words. Satisfiability is decided by iterating a reachability vector over the k^(w-1) de Bruijn vertices for 4V + 1 edge steps (existence of a valid word of length 4V + w). Independently, every period word u with |u| <= V is enumerated (sum of k^p over p = 1..V candidates, each stored as the bitmask of its cyclic length-w windows) and u^infinity is accepted iff its window mask is contained in the allowed set. The two indicators are compared for all 138,856 systems (exhaustive for (k,w) = (2,2), (2,3), (2,4), (3,2), (4,2); seeded samples of 2000 and 5000 for (2,5) and (3,3)); minimal periods are tabulated. Run time about 3 s." } } } rows { name { value: "passCriterion" } } rows { quad { p_iri { } o_literal { lex: "Pre-registered: across all enumerated or sampled constraint systems, every system that admits a valid word of length 4V + w (the operational test of satisfiability, independent of any cycle argument) also admits a periodic arrangement u^infinity with |u| <= V whose every cyclic window of length w is allowed; and every system with no such long valid word has no periodic arrangement either. Zero violations in both directions." } } } 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-ch05-15" } } 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: "exhaustive" } } } rows { name { value: "license" } } rows { quad { p_iri { name_id: 44 } o_literal { } } } rows { name { value: "EvidenceItem" } } rows { quad { p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 10 name_id: 45 } } } rows { quad { p_iri { prefix_id: 11 name_id: 16 } o_literal { lex: "Dataset: All 16 allowed-word sets, 2 colours, window 2 (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: "exhaustive" } } } rows { quad { p_iri { name_id: 44 } o_literal { } } } rows { quad { p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 10 name_id: 45 } } } rows { quad { p_iri { prefix_id: 11 name_id: 16 } o_literal { lex: "Dataset: All 256 allowed-word sets, 2 colours, window 3 (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: "exhaustive" } } } rows { quad { p_iri { name_id: 44 } o_literal { } } } rows { quad { p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 10 name_id: 45 } } } rows { quad { p_iri { prefix_id: 11 name_id: 16 } o_literal { lex: "Dataset: All 65536 allowed-word sets, 2 colours, window 4 (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: "exhaustive" } } } rows { quad { p_iri { name_id: 44 } o_literal { } } } rows { quad { p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 10 name_id: 45 } } } rows { quad { p_iri { prefix_id: 11 name_id: 16 } o_literal { lex: "Dataset: All 512 allowed-word sets, 3 colours, window 2 (generated by analysis.py)" } } } rows { quad { s_iri { prefix_id: 14 name_id: 34 } p_iri { prefix_id: 7 name_id: 13 } o_literal { lex: "exhaustive" } } } rows { quad { p_iri { name_id: 44 } o_literal { } } } rows { quad { p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 10 name_id: 45 } } } rows { quad { p_iri { prefix_id: 11 name_id: 16 } o_literal { lex: "Dataset: All 65536 allowed-word sets, 4 colours, window 2 (generated by analysis.py)" } } } rows { quad { s_iri { prefix_id: 14 name_id: 35 } p_iri { prefix_id: 7 name_id: 13 } o_literal { lex: "sample" } } } rows { quad { p_iri { name_id: 44 } o_literal { } } } rows { quad { p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 10 name_id: 45 } } } rows { quad { p_iri { prefix_id: 11 name_id: 16 } o_literal { lex: "Dataset: 2000 allowed-word sets sampled uniformly from the 2^32 sets, 2 colours, window 5 (numpy default_rng seed 20261031; generated by analysis.py)" } } } rows { quad { s_iri { prefix_id: 14 name_id: 36 } p_iri { prefix_id: 7 name_id: 13 } o_literal { lex: "sample" } } } rows { quad { p_iri { name_id: 44 } o_literal { } } } rows { quad { p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 10 name_id: 45 } } } rows { quad { p_iri { prefix_id: 11 name_id: 16 } o_literal { lex: "Dataset: 5000 allowed-word sets sampled uniformly from the 2^27 sets, 3 colours, window 3 (same seed; 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: 46 } 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: 47 } 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: 50 } 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: 52 } } } 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: 53 } 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: 54 } 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: 55 } p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 5 name_id: 59 } } } rows { name { value: "qualifiedAssociation" } } rows { quad { p_iri { } o_iri { prefix_id: 2 name_id: 56 } } } rows { name { value: "wasAssociatedWith" } } rows { quad { p_iri { prefix_id: 5 name_id: 61 } 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: 62 } o_literal { lex: "2026-11-08T16:24:31.926Z" datatype: 3 } g_iri { prefix_id: 2 name_id: 9 } } } rows { name { value: "creator" } } rows { quad { p_iri { prefix_id: 7 name_id: 63 } o_iri { prefix_id: 16 name_id: 48 } } } rows { prefix { id: 3 value: "https://creativecommons.org/licenses/by/4.0/" } } rows { quad { p_iri { prefix_id: 7 name_id: 44 } 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: 64 } o_iri { prefix_id: 10 name_id: 14 } } } rows { name { value: "introduces" } } rows { quad { p_iri { prefix_id: 15 name_id: 65 } 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-ch05-15: supports, confidence 0.97" } } } 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: 66 } 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: "LPykeK/KjqRcRJfXnrzY7o1kmML6e9xf9Jo651mhaMsQE9c1ocovoJsekTFC71I+hVO5LKoZ08EbdB0DsNoRXHlJKHDA1rB4Fwsc0J2LbwF0ZcEP52aNkaQV3MLtJCbxhlqfFc+LNKcUr8p26SzoHHMPpQF4MIe+PxiDbGzWjZGDwjJ+Vbl+RT8GfP4h5uqNKUSEZHn1OZetVAgiG+5J40Mdy19XrFTc4iE1vs5cMwD5QubKY9ZdhMtTf16Zdb4aEpaH8uz3J+hafzWIq/0h7s7QCJqdH0ciGyLlfrg3QHmle/HSlU0c8ZNKq8f5AlO0+GEzjyf98RtbsjneZmnM0g==" } } } 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: 73 } o_iri { prefix_id: 16 name_id: 48 } } }