https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/Head https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI http://www.nanopub.org/nschema#hasAssertion https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/assertion https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI http://www.nanopub.org/nschema#hasProvenance https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/provenance https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI http://www.nanopub.org/nschema#hasPublicationInfo https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/pubinfo https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.nanopub.org/nschema#Nanopublication https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/assertion https://w3id.org/delphi/resource/assessment/wolfram2002-ch09-17--claim-test http://purl.org/dc/terms/description 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/resource/assessment/wolfram2002-ch09-17--claim-test http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/Assessment https://w3id.org/delphi/resource/assessment/wolfram2002-ch09-17--claim-test http://www.w3.org/2000/01/rdf-schema#comment 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. https://w3id.org/delphi/resource/assessment/wolfram2002-ch09-17--claim-test http://www.w3.org/2000/01/rdf-schema#label Claim test of wolfram2002-ch09-17: supports, confidence 0.93 https://w3id.org/delphi/resource/assessment/wolfram2002-ch09-17--claim-test http://www.w3.org/2000/01/rdf-schema#seeAlso https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch09-17/result.json https://w3id.org/delphi/resource/assessment/wolfram2002-ch09-17--claim-test http://www.w3.org/ns/prov#wasAttributedTo https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 https://w3id.org/delphi/resource/assessment/wolfram2002-ch09-17--claim-test https://w3id.org/delphi/ontology/admissibleDatasets Planned datasets: shrinking-substitution-systems-2-letters-exhaustive https://w3id.org/delphi/resource/assessment/wolfram2002-ch09-17--claim-test https://w3id.org/delphi/ontology/assessmentType claim-test/0.1.0 https://w3id.org/delphi/resource/assessment/wolfram2002-ch09-17--claim-test https://w3id.org/delphi/ontology/dataKind computational https://w3id.org/delphi/resource/assessment/wolfram2002-ch09-17--claim-test https://w3id.org/delphi/ontology/disconfirmingObservation 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/resource/assessment/wolfram2002-ch09-17--claim-test https://w3id.org/delphi/ontology/evidenceAgainst 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. https://w3id.org/delphi/resource/assessment/wolfram2002-ch09-17--claim-test https://w3id.org/delphi/ontology/evidenceAgainst 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. https://w3id.org/delphi/resource/assessment/wolfram2002-ch09-17--claim-test https://w3id.org/delphi/ontology/evidenceAgainst 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/resource/assessment/wolfram2002-ch09-17--claim-test https://w3id.org/delphi/ontology/expectedObservation 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/resource/assessment/wolfram2002-ch09-17--claim-test https://w3id.org/delphi/ontology/failCriterion 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/resource/assessment/wolfram2002-ch09-17--claim-test https://w3id.org/delphi/ontology/hasConfidence 0.93 https://w3id.org/delphi/resource/assessment/wolfram2002-ch09-17--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch09-17--claim-test--dataset-1 https://w3id.org/delphi/resource/assessment/wolfram2002-ch09-17--claim-test https://w3id.org/delphi/ontology/hasVerdict supports https://w3id.org/delphi/resource/assessment/wolfram2002-ch09-17--claim-test https://w3id.org/delphi/ontology/hypothesis 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/resource/assessment/wolfram2002-ch09-17--claim-test https://w3id.org/delphi/ontology/inferenceMethod 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/resource/assessment/wolfram2002-ch09-17--claim-test https://w3id.org/delphi/ontology/passCriterion 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/resource/assessment/wolfram2002-ch09-17--claim-test https://w3id.org/delphi/ontology/preregistered false https://w3id.org/delphi/resource/claim/wolfram2002-ch09-17 https://w3id.org/delphi/ontology/hasAssessment https://w3id.org/delphi/resource/assessment/wolfram2002-ch09-17--claim-test https://w3id.org/delphi/resource/evidence/wolfram2002-ch09-17--claim-test--dataset-1 http://purl.org/dc/terms/description exhaustive finite family; non-overlapping systems are the test set, overlapping ones the control https://w3id.org/delphi/resource/evidence/wolfram2002-ch09-17--claim-test--dataset-1 http://purl.org/dc/terms/license https://w3id.org/delphi/resource/evidence/wolfram2002-ch09-17--claim-test--dataset-1 http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/EvidenceItem https://w3id.org/delphi/resource/evidence/wolfram2002-ch09-17--claim-test--dataset-1 http://www.w3.org/2000/01/rdf-schema#label 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) https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/provenance https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.w3.org/ns/prov#SoftwareAgent https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 http://www.w3.org/2000/01/rdf-schema#label delphisci claim tester (claude-fable-5.1; cursor/claim-tests-wolfram-nks-0123) https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 http://www.w3.org/ns/prov#actedOnBehalfOf https://orcid.org/0009-0007-4948-9192 https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 https://w3id.org/delphi/ontology/usesModel https://w3id.org/delphi/resource/model/claude-fable-5-1 https://w3id.org/delphi/resource/model/claude-fable-5-1 http://purl.org/dc/terms/identifier claude-fable-5.1 https://w3id.org/delphi/resource/model/claude-fable-5-1 http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/LanguageModel https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/assertion http://www.w3.org/ns/prov#wasAttributedTo https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/assertion http://www.w3.org/ns/prov#wasDerivedFrom https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch09-17/result.json https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/assertion http://www.w3.org/ns/prov#wasGeneratedBy https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/test https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/plan http://www.w3.org/ns/prov#hadPlan https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/README.md https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/test http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.w3.org/ns/prov#Activity https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/test http://www.w3.org/ns/prov#qualifiedAssociation https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/plan https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/test http://www.w3.org/ns/prov#wasAssociatedWith https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/pubinfo https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI http://purl.org/dc/terms/created 2026-11-08T16:24:31.934Z https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI http://purl.org/dc/terms/creator https://orcid.org/0009-0007-4948-9192 https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI http://purl.org/dc/terms/license https://creativecommons.org/licenses/by/4.0/ https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI http://purl.org/nanopub/x/hasNanopubType https://w3id.org/delphi/ontology/Assessment https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI http://purl.org/nanopub/x/introduces https://w3id.org/delphi/resource/assessment/wolfram2002-ch09-17--claim-test https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI http://www.w3.org/2000/01/rdf-schema#label Claim test of wolfram2002-ch09-17: supports, confidence 0.93 https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI https://w3id.org/delphi/ontology/domain https://w3id.org/delphi/resource/domain/wolfram-nks-2002 https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/sig http://purl.org/nanopub/x/hasAlgorithm RSA https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/sig http://purl.org/nanopub/x/hasPublicKey MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/sig http://purl.org/nanopub/x/hasSignature RfbSyKroBZEqR4uQMDVpy+r85P15Bdv9WxcgSqV1vJISUR6xvn+FD5+RAJfs3GXHX9IXwnhrC2qUA2NL/jJJFe1AcplvORgR6NPiZQ7uizSdlw/39TdlR9LObEgNDb/lbBgWR21mKzcrxblHOxcYytERddgSY63IXdUYcs+ktA3VZE9QmSwHa/+Kx9eJWAYT2SauYTAhB1c7w5Hv8WLSLQ+v9Eg6TeGoZpZMv9AnNmmOOuxUrC26OOIDojAzjRu7Xdwe95jOz3VOqFFseGJBTol5L3W+73zrngYCUHFHvdd7MgydZtALl1PgB6QXSTzY3dVqEf+56CGms+lWPKfMEw== https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/sig http://purl.org/nanopub/x/hasSignatureTarget https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI https://w3id.org/np/RApmDBBdvhmqwZCWp4bWMlxy6BFnZivZP2Mr8DNZ_3srI/sig http://purl.org/nanopub/x/signedBy https://orcid.org/0009-0007-4948-9192