. . . . "analysis.py enumerates the 42 rules and the 903 systems. Two closures, one by a stack and one by breadth-first order, are required to agree. Completeness and consistency are decided against all 126 strings. On each complete and consistent system the breadth-first procedure is run for every string and compared with membership. The three anchor systems are classified by the same code." . . "Measured: 0 procedure errors on complete-and-consistent systems, out of 1260 string queries (10 systems times 126 strings) (n = 1260, exact). Interpretation: The claim (NKS p. 783) is the implication: if reachability of an arbitrary string is undecidable, then a multiway system with a computable negation cannot be both complete and consistent, because completeness plus consistency is itself a terminating decision procedure. The computation tests the contrapositive mechanism on a finite but exhaustive family: whenever the system is complete and consistent on the stated universe, that procedure decides reachability. Strings longer than 6, and rules with sides longer than 2, are outside the universe. Colour swap is the negation the book defines on p. 780; later pages allow any length-preserving involution, which is not the negation used here. A finite system has decidable reachability by full enumeration even when it is incomplete, so the test does not exhibit an undecidable system and does not test the gloss that equates computational irreducibility with undecidability." . "Claim test of wolfram2002-ch12-31: supports, confidence 0.9" . . . "The reachable sets are generated by the committed enumerator from the stated rules, axiom, negation and length bound. No external dataset." . "claim-test/0.1.0" . "computational" . "A complete and consistent system in which seeing the colour-swapped negation does not correctly decide that the string is unreachable, or in which the search finishes without seeing either." . "A computation shows the mathematics, not that organisms follow it." . "Negation is colour swap, the operation named on NKS p. 780. A later page allows any length-preserving involution; that wider negation was not used." . "The family is finite: strings longer than 6 and rules with a side longer than 2 are outside the universe, and a replacement that would leave the length bound does not fire. Reachability in this family is decidable by the enumeration itself, so the run does not exhibit an undecidable system." . "The identification of computational irreducibility with undecidability was not tested. Counts are not a partition: 53 systems are both incomplete and inconsistent, and 10 are complete and consistent." . "Zero procedure errors on every complete and consistent system in the 903-system family, with all three anchor systems in the classes stated in the pass criterion." . "Pre-registered. REFUTES if any complete-and-consistent system has a string whose procedure answer disagrees with membership, or for which the procedure sees both the string and its complement, or for which the procedure finishes the reachable set without seeing either. INCONCLUSIVE with reason 'underpowered' if the family has no complete-and-consistent system, or no incomplete system, or no inconsistent system. INCONCLUSIVE with reason 'other' if the two enumerations disagree. The identification of computational irreducibility with undecidability is not a pass/fail item; it is reported as untested." . "0.9"^^ . . "supports" . "On every length-bounded multiway system in the pre-registered family, with negation defined as swapping black and white, if the reachable set is both complete and consistent then the book's decision procedure — breadth-first enumeration that stops when it sees the queried string or its colour-swapped negation — terminates and answers reachability correctly for every string in the finite universe." . "Exhaustive enumeration. The verdict is supports only if the error count on complete-and-consistent systems is 0 and the three class counts and three anchors meet the pass criterion; one error refutes." . "Pre-registered. Alphabet {0,1}, black=1, white=0. Negation is colour swap (complement), the operation named on NKS p. 780. A rule is a substring replacement lhs -> rhs with lhs a nonempty string of length at most 2 and rhs a string of length at most 2 (empty rhs allowed): 6 x 7 = 42 rules. The family is every one-rule system and every unordered pair of distinct rules (903 systems). Each system starts from the axiom '1' (a single black cell, as on p. 780) and is closed under applying a rule to one occurrence of its lhs, keeping only strings of length 1 through 6 (126 strings). This length bound is part of the system, not an approximation: a replacement that would leave that range does not fire. Complete means for every string s in the universe, s or its complement is reachable. Consistent means there is no s for which both are reachable. The procedure is a BFS from '1'; its answer for s is 'reached' if s appears and 'not reached' if the complement appears first. The membership oracle is a separate fixpoint expansion of the same rules. PASS (supports) if (i) the two enumerations agree on the reachable set of every system, (ii) every complete-and-consistent system has procedure error count 0 (the procedure decides every s, exactly one of s and its complement is reachable, and the answer matches membership), (iii) the family is non-vacuous: at least one system is complete and consistent, at least one is incomplete, and at least one is inconsistent, and (iv) the three anchor systems fall in those classes: {'1'->'10','1'->'11'} is complete and consistent, {'1'->'1'} is incomplete, and {'1'->'0'} is inconsistent." . "false"^^ . . "the finite family on which the decision procedure is checked" . "" . . "Dataset: All 903 one- and two-rule multiway systems on alphabet {0,1}, axiom 1, strings of length 1..6" . . . "delphisci claim tester (grok-4.7; cursor/wolfram-nks-ch12-31-to-ch11-12-bd47)" . . . "grok-4.7" . . . . . . . . . "2026-11-08T16:24:31.943Z"^^ . . . . . "Claim test of wolfram2002-ch12-31: supports, confidence 0.9" . . "RSA" . "MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB" . "rI+zB6wYeXzD//z7iPVBbq2VJSTSdkwoAxhhHLRAnOv8O8ywjoPPaNVKhyF7THovvZWnUQ2jvsnt0IrHFUTyAu5GhPyU/vW6SEKITxNx/EZfj6t3jmQ9Q2fqsJTWMhjTjuZB7+kBqE2SkFyMbkoklB8Zb18PHypJzlOkReMwtlOWwuuGEyWSeOJHTeH9jyHXsr+9YPnZPK1D933aogSamX1p3wxJ58gVLFWk9vWlcCE1D5SiRqHYk9vsiK5FCpBSiz35E/fZ2Gk8oOWm8Z4/PDgJ1GPPJcIrU42B7ZOkCHefp94fPuBABTw4Ww2a85Z9MwIKU9MMMgMz73yWqwngKA==" . . .