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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." } 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 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." } } } rows { name { value: "label" } } rows { quad { p_iri { } o_literal { lex: "Claim test of wolfram2002-ch09-17: supports, confidence 0.93" } } } rows { name { value: "seeAlso" } } rows { prefix { value: "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch09-17/" } } 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: shrinking-substitution-systems-2-letters-exhaustive" } } } 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 non-overlapping (rule set, initial string) pair whose complete evolutions produce two or more non-isomorphic causal networks." } } } rows { name { value: "evidenceAgainst" } } rows { quad { p_iri { } o_literal { lex: "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." } } } rows { quad { o_literal { lex: "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." } } } rows { quad { o_literal { lex: "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." } } } rows { name { value: "expectedObservation" } } rows { quad { p_iri { } o_literal { lex: "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\')." } } } rows { name { value: "failCriterion" } } rows { quad { p_iri { } o_literal { lex: "Pre-registered: at least one non-overlapping (rule set, initial string) pair whose complete evolutions produce two or more non-isomorphic causal networks." } } } rows { name { value: "hasConfidence" } } rows { datatype { value: "http://www.w3.org/2001/XMLSchema#double" } } rows { quad { p_iri { } o_literal { lex: "0.93" datatype: 1 } } } rows { name { value: "hasEvidence" } } rows { prefix { value: "https://w3id.org/delphi/resource/evidence/" } } rows { name { value: "wolfram2002-ch09-17--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: "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." } } } rows { name { value: "inferenceMethod" } } rows { quad { p_iri { } o_literal { lex: "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. 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