[ { "@id": "https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/Head", "@graph": [ { "@id": "https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI", "http://www.nanopub.org/nschema#hasAssertion": [ { "@id": "https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/assertion" } ], "http://www.nanopub.org/nschema#hasProvenance": [ { "@id": "https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/provenance" } ], "http://www.nanopub.org/nschema#hasPublicationInfo": [ { "@id": "https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/pubinfo" } ], "@type": [ "http://www.nanopub.org/nschema#Nanopublication" ] } ] }, { "@id": "https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/pubinfo", "@graph": [ { "@id": "https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI", "http://purl.org/dc/terms/created": [ { "@value": "2026-11-08T16:24:31.934Z", "@type": "http://www.w3.org/2001/XMLSchema#dateTime" } ], "http://purl.org/dc/terms/creator": [ { "@id": "https://orcid.org/0009-0007-4948-9192" } ], "http://purl.org/dc/terms/license": [ { "@id": "https://creativecommons.org/licenses/by/4.0/" } ], "http://purl.org/nanopub/x/hasNanopubType": [ { "@id": "https://w3id.org/delphi/ontology/Assessment" } ], "http://purl.org/nanopub/x/introduces": [ { "@id": "https://w3id.org/delphi/resource/assessment/wolfram2002-ch09-17--claim-test" } ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "Claim test of wolfram2002-ch09-17: supports, confidence 0.93" } ], "https://w3id.org/delphi/ontology/domain": [ { "@id": "https://w3id.org/delphi/resource/domain/wolfram-nks-2002" } ] }, { "@id": "https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/sig", "http://purl.org/nanopub/x/hasAlgorithm": [ { "@value": "RSA" } ], "http://purl.org/nanopub/x/hasPublicKey": [ { "@value": "MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB" } ], "http://purl.org/nanopub/x/hasSignature": [ { "@value": "RfbSyKroBZEqR4uQMDVpy+r85P15Bdv9WxcgSqV1vJISUR6xvn+FD5+RAJfs3GXHX9IXwnhrC2qUA2NL/jJJFe1AcplvORgR6NPiZQ7uizSdlw/39TdlR9LObEgNDb/lbBgWR21mKzcrxblHOxcYytERddgSY63IXdUYcs+ktA3VZE9QmSwHa/+Kx9eJWAYT2SauYTAhB1c7w5Hv8WLSLQ+v9Eg6TeGoZpZMv9AnNmmOOuxUrC26OOIDojAzjRu7Xdwe95jOz3VOqFFseGJBTol5L3W+73zrngYCUHFHvdd7MgydZtALl1PgB6QXSTzY3dVqEf+56CGms+lWPKfMEw==" } ], "http://purl.org/nanopub/x/hasSignatureTarget": [ { "@id": "https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI" } ], "http://purl.org/nanopub/x/signedBy": [ { "@id": "https://orcid.org/0009-0007-4948-9192" } ] } ] }, { "@id": "https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/provenance", "@graph": [ { "@id": "https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1", "@type": [ "http://www.w3.org/ns/prov#SoftwareAgent" ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "delphisci claim tester (claude-fable-5.1; cursor/claim-tests-wolfram-nks-0123)" } ], "http://www.w3.org/ns/prov#actedOnBehalfOf": [ { "@id": "https://orcid.org/0009-0007-4948-9192" } ], "https://w3id.org/delphi/ontology/usesModel": [ { "@id": "https://w3id.org/delphi/resource/model/claude-fable-5-1" } ] }, { "@id": "https://w3id.org/delphi/resource/model/claude-fable-5-1", "http://purl.org/dc/terms/identifier": [ { "@value": "claude-fable-5.1" } ], "@type": [ "https://w3id.org/delphi/ontology/LanguageModel" ] }, { "@id": "https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/assertion", "http://www.w3.org/ns/prov#wasAttributedTo": [ { "@id": "https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1" } ], "http://www.w3.org/ns/prov#wasDerivedFrom": [ { "@id": "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch09-17/result.json" } ], "http://www.w3.org/ns/prov#wasGeneratedBy": [ { "@id": "https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/test" } ] }, { "@id": "https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/test", "@type": [ "http://www.w3.org/ns/prov#Activity" ], "http://www.w3.org/ns/prov#qualifiedAssociation": [ { "@id": "https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/plan" } ], "http://www.w3.org/ns/prov#wasAssociatedWith": [ { "@id": "https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1" } ] }, { "@id": "https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/plan", "http://www.w3.org/ns/prov#hadPlan": [ { "@id": "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/README.md" } ] } ] }, { "@id": "https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/assertion", "@graph": [ { "@id": "https://w3id.org/delphi/resource/assessment/wolfram2002-ch09-17--claim-test", "http://purl.org/dc/terms/description": [ { "@value": "analysis.py enumerates all 2305 one- and two-rule systems over {A,B} with lhs length 1-3 and strictly shorter rhs, classifies each syntactically as non-overlapping (37 systems; lhs sets {A}, {B}, {A,B}, {AB}, {BA}, {AAB}, {ABB}, {BAA}, {BBA}) or overlapping (2268), and for each of the 62 initial strings of length 1-5 generates every complete evolution by depth-first search over all possible replacement choices, tracking element identities so that each event is identified by (rule, consumed elements) and the causal network by its identity-labelled edges. Networks from different orders are compared first for identity and then, if they differ, up to isomorphism by brute force over event permutations. A supplementary (not pre-registered) run covers all 127 non-overlapping systems with lhs length up to 4 (which includes genuinely non-overlapping pairs such as {AAB, BBBA} and {AABB, BBAA}) from all 126 initial strings of length 1-6. Run time about 3 s." } ], "@type": [ "https://w3id.org/delphi/ontology/Assessment" ], "http://www.w3.org/2000/01/rdf-schema#comment": [ { "@value": "Measured: 1 fraction of non-overlapping (rule set, initial string) pairs with >= 2 complete evolutions whose causal networks all coincide (n = 186, exact (exhaustive within the family)). Interpretation: Wolfram's generalized substitution systems (NKS pp. 497-503) replace one occurrence of a left-hand block at a time; which occurrence, and when, is the free choice of 'order'. A causal network has one node per replacement event and an edge from event P to event E whenever E's matched block contains an element that P produced; the initial condition is represented by a node 0 that 'produces' the initial elements. Two orders give 'the same causal network' if the networks are isomorphic as node-labelled directed graphs (labels = rule applied, node 0 fixed). Non-overlap is the syntactic condition of p. 503: no non-empty proper suffix of any block equals a prefix of any block (including the block itself), and no block is a substring of another. To compare complete histories across orders, the enumeration is restricted to systems whose every rule strictly shortens the string (|rhs| < |lhs|), so every evolution terminates after finitely many events; all complete evolutions (all choices at every step) from every initial string of length <= 5 over {A, B} are generated exhaustively. Wolfram's weaker condition (no overlap among strings actually generated) is not tested." } ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "Claim test of wolfram2002-ch09-17: supports, confidence 0.93" } ], "http://www.w3.org/2000/01/rdf-schema#seeAlso": [ { "@id": "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch09-17/result.json" } ], "http://www.w3.org/ns/prov#wasAttributedTo": [ { "@id": "https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1" } ], "https://w3id.org/delphi/ontology/admissibleDatasets": [ { "@value": "Planned datasets: shrinking-substitution-systems-2-letters-exhaustive" } ], "https://w3id.org/delphi/ontology/assessmentType": [ { "@value": "claim-test/0.1.0" } ], "https://w3id.org/delphi/ontology/dataKind": [ { "@value": "computational" } ], "https://w3id.org/delphi/ontology/disconfirmingObservation": [ { "@value": "Pre-registered: at least one non-overlapping (rule set, initial string) pair whose complete evolutions produce two or more non-isomorphic causal networks." } ], "https://w3id.org/delphi/ontology/evidenceAgainst": [ { "@value": "The enumeration is restricted to terminating (strictly shrinking) systems so that complete histories can be compared; for non-terminating systems the statement concerns infinite causal networks and was not tested. Within the family the result is exhaustive: all 186 (primary) and 524 (supplementary) non-overlapping cases with a genuine choice of order gave identical, not merely isomorphic, causal networks and identical final strings, while 96.6% of overlapping rule sets showed order-dependent networks for some initial string, so the non-overlap condition is doing real work." }, { "@value": "Within the pre-registered family (lhs length <= 3) every non-overlapping rule set has a single multi-letter block or only single-letter blocks; non-overlapping pairs of multi-letter blocks appear only in the supplementary run with blocks of length 4, which was added after the primary run and is reported separately." }, { "@value": "Wolfram's weaker condition (no overlaps among the strings actually generated) and his extension to network rewriting systems were not tested; the causal-network definition (edge from the event that produced an element to the event that consumes it, with an 'init' node for the initial condition) follows pp. 497-503 but the book gives it only pictorially." } ], "https://w3id.org/delphi/ontology/expectedObservation": [ { "@value": "Pre-registered: among all enumerated (rule set, initial string) pairs whose rule set is syntactically non-overlapping and which admit at least two distinct complete evolutions, 100% have exactly one causal-network isomorphism class (and one final string) over all complete evolutions; and at least 10% of the overlapping rule sets exhibit at least two non-isomorphic causal networks for some initial string (otherwise the test has no discriminating power and the verdict is 'inconclusive', reason 'not-operationalizable')." } ], "https://w3id.org/delphi/ontology/failCriterion": [ { "@value": "Pre-registered: at least one non-overlapping (rule set, initial string) pair whose complete evolutions produce two or more non-isomorphic causal networks." } ], "https://w3id.org/delphi/ontology/hasConfidence": [ { "@value": "0.93", "@type": "http://www.w3.org/2001/XMLSchema#double" } ], "https://w3id.org/delphi/ontology/hasEvidence": [ { "@id": "https://w3id.org/delphi/resource/evidence/wolfram2002-ch09-17--claim-test--dataset-1" } ], "https://w3id.org/delphi/ontology/hasVerdict": [ { "@value": "supports" } ], "https://w3id.org/delphi/ontology/hypothesis": [ { "@value": "For every string substitution system whose left-hand-side blocks can never overlap themselves or each other, every possible order of performing replacements from a given initial string yields the same causal network (up to isomorphism), whereas systems with overlapping blocks can yield different causal networks for different orders." } ], "https://w3id.org/delphi/ontology/inferenceMethod": [ { "@value": "analysis.py enumerates all 2305 one- and two-rule systems over {A,B} with lhs length 1-3 and strictly shorter rhs, classifies each syntactically as non-overlapping (37 systems; lhs sets {A}, {B}, {A,B}, {AB}, {BA}, {AAB}, {ABB}, {BAA}, {BBA}) or overlapping (2268), and for each of the 62 initial strings of length 1-5 generates every complete evolution by depth-first search over all possible replacement choices, tracking element identities so that each event is identified by (rule, consumed elements) and the causal network by its identity-labelled edges. Networks from different orders are compared first for identity and then, if they differ, up to isomorphism by brute force over event permutations. A supplementary (not pre-registered) run covers all 127 non-overlapping systems with lhs length up to 4 (which includes genuinely non-overlapping pairs such as {AAB, BBBA} and {AABB, BBAA}) from all 126 initial strings of length 1-6. Run time about 3 s." } ], "https://w3id.org/delphi/ontology/passCriterion": [ { "@value": "Pre-registered: among all enumerated (rule set, initial string) pairs whose rule set is syntactically non-overlapping and which admit at least two distinct complete evolutions, 100% have exactly one causal-network isomorphism class (and one final string) over all complete evolutions; and at least 10% of the overlapping rule sets exhibit at least two non-isomorphic causal networks for some initial string (otherwise the test has no discriminating power and the verdict is 'inconclusive', reason 'not-operationalizable')." } ], "https://w3id.org/delphi/ontology/preregistered": [ { "@value": "false", "@type": "http://www.w3.org/2001/XMLSchema#boolean" } ] }, { "@id": "https://w3id.org/delphi/resource/evidence/wolfram2002-ch09-17--claim-test--dataset-1", "http://purl.org/dc/terms/description": [ { "@value": "exhaustive finite family; non-overlapping systems are the test set, overlapping ones the control" } ], "http://purl.org/dc/terms/license": [ { "@value": "" } ], "@type": [ "https://w3id.org/delphi/ontology/EvidenceItem" ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "Dataset: All one- and two-rule string substitution systems over {A,B} with left-hand blocks of length 1-3 and strictly shorter right-hand sides, all initial strings of length 1-5, all complete evolutions (generated by analysis.py)" } ] }, { "@id": "https://w3id.org/delphi/resource/claim/wolfram2002-ch09-17", "https://w3id.org/delphi/ontology/hasAssessment": [ { "@id": "https://w3id.org/delphi/resource/assessment/wolfram2002-ch09-17--claim-test" } ] } ] } ]