. . . . "analysis.py compiles revca.c and runs the exhaustive depth-first enumeration of rule tables for (k,r) = (2,1), (2,2) and (3,1). Table entries are assigned in order of the period of their neighbourhood word; after each assignment the pair graph of the de Bruijn graph is built from definite edges (both labels assigned and equal) and the branch is cut if an off-diagonal cycle or a diagonal-to-diagonal path through off-diagonal nodes exists (both are sound: they witness two distinct configurations with the same image); the balance condition (each colour exactly k^(2r) times) also prunes. At a leaf the same test is exact. The 1800 rules found for k = 3 are then checked in Python with Wolfram's ReversibleQ (distinct successors of all cyclic configurations of length <= 9), 10000 random balanced k = 3 tables not in the list are checked to fail it, all 256 elementary rules are classified by both methods, and the k = 3 rules are grouped into symmetry families under colour permutations and reflection." . . "Measured: 1800 reversible rules among the 3^27 three-colour nearest-neighbour cellular automata (claimed 1800) (n = 7625597484987, exact (exhaustive enumeration)). Interpretation: 'Reversible' is taken as injectivity of the global map on the full shift (bi-infinite configurations), the standard notion and the one Wolfram's note tests through periodic configurations. Rule numbering is Wolfram's (table entry for neighbourhood (l,c,r) at digit position l*k^2 + c*k + r of the base-k rule number). The count is of raw rule tables, not of symmetry classes (the note gives 172 families for k = 3). The enumeration is exact, so there is no sampling uncertainty; the only risks are implementation errors, which the k = 2 (r = 1 and r = 2) checks and the independent periodic-configuration test guard against. Note: the pruning search is written in C (compiled with gcc from analysis.py) because a Python search over the pruned tree would be too slow; this is a deviation from 'python3 only' tooling and is recorded." . "Claim test of wolfram2002-ch09-02: supports, confidence 0.97" . . . "Planned datasets: reversible-ca-enumeration-generator, nks-note-numbers-of-reversible-rules" . "claim-test/0.1.0" . "computational" . "Pre-registered. 'Refutes' if the exhaustive enumeration completes and gives a count other than 6 for k = 2, r = 1 or other than 1800 for k = 3, r = 1 (with the k = 2, r = 2 check giving 62, so the method is validated). If the k = 3 enumeration cannot be completed within the compute budget (about 1 hour), the verdict is 'mixed' or 'inconclusive' (reason: other) with the k = 2 result and a lower bound on the k = 3 count reported." . "Correctness of the pair-graph criterion is checked three ways: it reproduces the known 6 elementary rules and Wolfram's 62 for k = 2, r = 2; all 256 elementary rules are classified identically by the independent periodic-configuration test; and all 1800 three-colour rules found pass that test while 10000 random balanced tables outside the list fail it. The count of 172 symmetry families also matches Wolfram's note." . "Reversibility is tested on bi-infinite configurations (the full shift). On finite cyclic lattices of a fixed size a rule can be a bijection without being reversible in this sense; the claim and Wolfram's own test use the infinite-line notion." . "The search is written in C (revca.c) and analysis.py compiles it with gcc; this is a tooling deviation from the python-only guideline, recorded in the pre-registration. The search visits 25.7 million nodes for k = 3 (about 2 minutes)." . "The total 7,625,597,484,987 = 3^27 is a count of rule tables, confirmed arithmetically; the enumeration does not visit them individually but prunes soundly, so the count 1800 is exact." . "Pre-registered. An exhaustive enumeration with an exact injectivity test (pair graph of the de Bruijn graph: a rule is injective iff the pair graph has no cycle through an off-diagonal node and no diagonal-to-diagonal path through off-diagonal nodes; used both as a sound pruning condition during depth-first assignment of the rule table and as the exact test at the leaves) yields exactly 6 reversible rules for k = 2, r = 1 and exactly 1800 for k = 3, r = 1. As a check of the method, the same program must give 62 for k = 2, r = 2 (NKS note 'Numbers of reversible rules'), and the 6 elementary rules must be {15, 51, 85, 170, 204, 240}. Also, every rule found must pass Wolfram's finite test (distinct successors for all periodic configurations of period <= 9, as his note says suffices for k = 3) and every rule not found that is sampled (10000 random balanced k = 3 rules) must fail it. 'Supports' requires the counts 6 and 1800 and the consistency checks." . "Pre-registered. 'Refutes' if the exhaustive enumeration completes and gives a count other than 6 for k = 2, r = 1 or other than 1800 for k = 3, r = 1 (with the k = 2, r = 2 check giving 62, so the method is validated). If the k = 3 enumeration cannot be completed within the compute budget (about 1 hour), the verdict is 'mixed' or 'inconclusive' (reason: other) with the k = 2 result and a lower bound on the k = 3 count reported." . "0.97"^^ . . . "supports" . "Among one-dimensional nearest-neighbour cellular automata, exactly 6 of the 256 two-colour rules and exactly 1800 of the 3^27 = 7,625,597,484,987 three-colour rules are reversible, where reversible means the global map on bi-infinite configurations is injective (equivalently bijective; equivalently, by Wolfram's note, all periodic configurations have distinct successors)." . "analysis.py compiles revca.c and runs the exhaustive depth-first enumeration of rule tables for (k,r) = (2,1), (2,2) and (3,1). Table entries are assigned in order of the period of their neighbourhood word; after each assignment the pair graph of the de Bruijn graph is built from definite edges (both labels assigned and equal) and the branch is cut if an off-diagonal cycle or a diagonal-to-diagonal path through off-diagonal nodes exists (both are sound: they witness two distinct configurations with the same image); the balance condition (each colour exactly k^(2r) times) also prunes. At a leaf the same test is exact. The 1800 rules found for k = 3 are then checked in Python with Wolfram's ReversibleQ (distinct successors of all cyclic configurations of length <= 9), 10000 random balanced k = 3 tables not in the list are checked to fail it, all 256 elementary rules are classified by both methods, and the k = 3 rules are grouped into symmetry families under colour permutations and reflection." . "Pre-registered. An exhaustive enumeration with an exact injectivity test (pair graph of the de Bruijn graph: a rule is injective iff the pair graph has no cycle through an off-diagonal node and no diagonal-to-diagonal path through off-diagonal nodes; used both as a sound pruning condition during depth-first assignment of the rule table and as the exact test at the leaves) yields exactly 6 reversible rules for k = 2, r = 1 and exactly 1800 for k = 3, r = 1. As a check of the method, the same program must give 62 for k = 2, r = 2 (NKS note 'Numbers of reversible rules'), and the 6 elementary rules must be {15, 51, 85, 170, 204, 240}. Also, every rule found must pass Wolfram's finite test (distinct successors for all periodic configurations of period <= 9, as his note says suffices for k = 3) and every rule not found that is sampled (10000 random balanced k = 3 rules) must fail it. 'Supports' requires the counts 6 and 1800 and the consistency checks." . "false"^^ . . "the enumerated program family and the list of reversible rules found (derived/)" . "CC0 (generated data)" . . "Dataset: Exhaustive enumeration of nearest-neighbour cellular automaton rules (generated by analysis.py + revca.c)" . "the reversibility test Wolfram used (ReversibleQ) and the stated counts 6, 62, 1800 used as the method check" . "copyright Stephen Wolfram LLC" . . "Dataset: NKS notes 'Numbers of reversible rules' and 'Testing for reversibility' (p. 1017)" . . . . "sha256:1af16edd18347077fb2a20db466fae3b110cf488c192824a2312ad915e2a0380" . "sha256:82e0511d9ad2fe0eef732823adc0b07abb129a9f0fd8d458147fd557d657d03b" . . "delphisci claim tester (Claude Fable 5.1 (Cursor cloud agent); cursor/claim-tests-wolfram-nks-f0e1)" . . . "Claude Fable 5.1 (Cursor cloud agent)" . . . . . . . . . "2026-11-08T16:24:31.932Z"^^ . . . . . "Claim test of wolfram2002-ch09-02: supports, confidence 0.97" . . "RSA" . "MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB" . 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