https://w3id.org/np/RAohAXrzytP8w7CINkKZLoog3BxIIUpggxow_mnZxeidQ
.trig | .trig.txt | .jelly | .jelly.txt | .jsonld | .jsonld.txt | .nq | .nq.txt | .xml | .xml.txt
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sub:assertion {
<https://w3id.org/delphi/resource/assessment/wolfram2002-ch05-15--claim-test> a <https://w3id.org/delphi/ontology/Assessment>;
dc:description "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.";
<http://www.w3.org/2000/01/rdf-schema#comment> "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).";
<http://www.w3.org/2000/01/rdf-schema#label> "Claim test of wolfram2002-ch05-15: supports, confidence 0.97";
<http://www.w3.org/2000/01/rdf-schema#seeAlso> <https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch05-15/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: 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";
<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: 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.";
<https://w3id.org/delphi/ontology/evidenceAgainst> "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.",
"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).",
"Wolfram's 'simple' is read as 'periodic'; the observed minimal periods are small (at most V), but 'simple' is not otherwise quantified.";
<https://w3id.org/delphi/ontology/expectedObservation> "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.";
<https://w3id.org/delphi/ontology/failCriterion> "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.";
<https://w3id.org/delphi/ontology/hasConfidence> "0.97"^^xsd:double;
<https://w3id.org/delphi/ontology/hasEvidence> <https://w3id.org/delphi/resource/evidence/wolfram2002-ch05-15--claim-test--dataset-1>,
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch05-15--claim-test--dataset-2>,
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch05-15--claim-test--dataset-3>,
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch05-15--claim-test--dataset-4>,
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch05-15--claim-test--dataset-5>,
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch05-15--claim-test--dataset-6>,
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch05-15--claim-test--dataset-7>;
<https://w3id.org/delphi/ontology/hasVerdict> "supports";
<https://w3id.org/delphi/ontology/hypothesis> "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).";
<https://w3id.org/delphi/ontology/inferenceMethod> "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.";
<https://w3id.org/delphi/ontology/passCriterion> "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.";
<https://w3id.org/delphi/ontology/preregistered> "false"^^xsd:boolean .
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<https://w3id.org/delphi/resource/assessment/wolfram2002-ch05-15--claim-test> .
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch05-15--claim-test--dataset-1>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "exhaustive";
dc:license "";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: All 16 allowed-word sets, 2 colours, window 2 (generated by analysis.py)" .
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch05-15--claim-test--dataset-2>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "exhaustive";
dc:license "";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: All 256 allowed-word sets, 2 colours, window 3 (generated by analysis.py)" .
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch05-15--claim-test--dataset-3>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "exhaustive";
dc:license "";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: All 65536 allowed-word sets, 2 colours, window 4 (generated by analysis.py)" .
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch05-15--claim-test--dataset-4>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "exhaustive";
dc:license "";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: All 512 allowed-word sets, 3 colours, window 2 (generated by analysis.py)" .
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch05-15--claim-test--dataset-5>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "exhaustive";
dc:license "";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: All 65536 allowed-word sets, 4 colours, window 2 (generated by analysis.py)" .
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch05-15--claim-test--dataset-6>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "sample";
dc:license "";
<http://www.w3.org/2000/01/rdf-schema#label> "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)" .
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch05-15--claim-test--dataset-7>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "sample";
dc:license "";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: 5000 allowed-word sets sampled uniformly from the 2^27 sets, 3 colours, window 3 (same seed; generated by analysis.py)" .
}
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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-0123)";
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dc:identifier "claude-fable-5.1" .
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