. . . . "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." . . "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." . "Claim test of wolfram2002-ch09-17: supports, confidence 0.93" . . . "Planned datasets: shrinking-substitution-systems-2-letters-exhaustive" . "claim-test/0.1.0" . "computational" . "Pre-registered: at least one non-overlapping (rule set, initial string) pair whose complete evolutions produce two or more non-isomorphic causal networks." . "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." . "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." . "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." . "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')." . "Pre-registered: at least one non-overlapping (rule set, initial string) pair whose complete evolutions produce two or more non-isomorphic causal networks." . "0.93"^^ . . "supports" . "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." . "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." . "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')." . "false"^^ . . "exhaustive finite family; non-overlapping systems are the test set, overlapping ones the control" . "" . . "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)" . . "delphisci claim tester (claude-fable-5.1; cursor/claim-tests-wolfram-nks-0123)" . . . "claude-fable-5.1" . . . . . . . . . "2026-11-08T16:24:31.934Z"^^ . . . . . "Claim test of wolfram2002-ch09-17: supports, confidence 0.93" . . "RSA" . "MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB" . "RfbSyKroBZEqR4uQMDVpy+r85P15Bdv9WxcgSqV1vJISUR6xvn+FD5+RAJfs3GXHX9IXwnhrC2qUA2NL/jJJFe1AcplvORgR6NPiZQ7uizSdlw/39TdlR9LObEgNDb/lbBgWR21mKzcrxblHOxcYytERddgSY63IXdUYcs+ktA3VZE9QmSwHa/+Kx9eJWAYT2SauYTAhB1c7w5Hv8WLSLQ+v9Eg6TeGoZpZMv9AnNmmOOuxUrC26OOIDojAzjRu7Xdwe95jOz3VOqFFseGJBTol5L3W+73zrngYCUHFHvdd7MgydZtALl1PgB6QXSTzY3dVqEf+56CGms+lWPKfMEw==" . . .