https://w3id.org/np/RAZ5GZc50OuO0Re3yh73635YuCOqtqxT7goUKou-mjBc8/Head https://w3id.org/np/RAZ5GZc50OuO0Re3yh73635YuCOqtqxT7goUKou-mjBc8 http://www.nanopub.org/nschema#hasAssertion https://w3id.org/np/RAZ5GZc50OuO0Re3yh73635YuCOqtqxT7goUKou-mjBc8/assertion https://w3id.org/np/RAZ5GZc50OuO0Re3yh73635YuCOqtqxT7goUKou-mjBc8 http://www.nanopub.org/nschema#hasProvenance https://w3id.org/np/RAZ5GZc50OuO0Re3yh73635YuCOqtqxT7goUKou-mjBc8/provenance https://w3id.org/np/RAZ5GZc50OuO0Re3yh73635YuCOqtqxT7goUKou-mjBc8 http://www.nanopub.org/nschema#hasPublicationInfo https://w3id.org/np/RAZ5GZc50OuO0Re3yh73635YuCOqtqxT7goUKou-mjBc8/pubinfo https://w3id.org/np/RAZ5GZc50OuO0Re3yh73635YuCOqtqxT7goUKou-mjBc8 http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.nanopub.org/nschema#Nanopublication https://w3id.org/np/RAZ5GZc50OuO0Re3yh73635YuCOqtqxT7goUKou-mjBc8/assertion https://w3id.org/delphi/resource/assessment/wolfram2002-ch06-19--claim-test http://purl.org/dc/terms/description analysis.py applies elementary rule 90 to every width-16 configuration, compares the even cells after two steps with one step of rule 90 on those cells, checks cell(2t, 2x) = cell(t, x) for t <= 63, and checks the simulator against the mod-2 binomial formula. The same block comparison is run for rule 30 on all 4096 width-12 states. https://w3id.org/delphi/resource/assessment/wolfram2002-ch06-19--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-ch06-19--claim-test http://www.w3.org/2000/01/rdf-schema#comment Measured: 0 mismatches of the even-cell identity among 65536 width-16 states of rule 90 (n = 65536, exact enumeration). Interpretation: A rule emulates itself when the even sublattice after two steps is the same rule on half as many cells. For rule 90 that identity is a_{t+2}(i) = a_t(i-2) XOR a_t(i+2). Nested, for the single-seed pattern, is the dyadic equality. Uniform would be a light cone of one color. Rule 30 is a control that is not this kind of self-emulation. The book's 'must' for every such rule is recorded as unproved by this check. https://w3id.org/delphi/resource/assessment/wolfram2002-ch06-19--claim-test http://www.w3.org/2000/01/rdf-schema#label Claim test of wolfram2002-ch06-19: supports, confidence 0.86 https://w3id.org/delphi/resource/assessment/wolfram2002-ch06-19--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-ch06-19/result.json https://w3id.org/delphi/resource/assessment/wolfram2002-ch06-19--claim-test http://www.w3.org/ns/prov#wasAttributedTo https://w3id.org/delphi/resource/agent/delphisci-claim-tester-grok-4-7 https://w3id.org/delphi/resource/assessment/wolfram2002-ch06-19--claim-test https://w3id.org/delphi/ontology/admissibleDatasets Exact elementary-rule iteration only, at the locked widths. Not a survey of other rules, and not evidence about organisms. https://w3id.org/delphi/resource/assessment/wolfram2002-ch06-19--claim-test https://w3id.org/delphi/ontology/assessmentType claim-test/0.1.0 https://w3id.org/delphi/resource/assessment/wolfram2002-ch06-19--claim-test https://w3id.org/delphi/ontology/dataKind computational https://w3id.org/delphi/resource/assessment/wolfram2002-ch06-19--claim-test https://w3id.org/delphi/ontology/disconfirmingObservation Any width-16 state of rule 90 whose even cells after two steps are not rule 90, with the Lucas check still matching. https://w3id.org/delphi/resource/assessment/wolfram2002-ch06-19--claim-test https://w3id.org/delphi/ontology/evidenceAgainst A match shows only that this computation behaves as claimed. It says nothing about organisms. https://w3id.org/delphi/resource/assessment/wolfram2002-ch06-19--claim-test https://w3id.org/delphi/ontology/evidenceAgainst Rule 30 fails the same identity on 4030 of 4096 width-12 states, so the identity is not true of every elementary rule. The 66 states that happen to match are not a second exemplar. https://w3id.org/delphi/resource/assessment/wolfram2002-ch06-19--claim-test https://w3id.org/delphi/ontology/evidenceAgainst The universal 'must' — every cellular automaton whose blocks evolve by the same rule is uniform or nested — is not proved by one example, and this test does not attempt that proof. https://w3id.org/delphi/resource/assessment/wolfram2002-ch06-19--claim-test https://w3id.org/delphi/ontology/evidenceAgainst This is a finite check of the exemplar. Rule 90 matches on all 65536 width-16 states and on the dyadic grid t <= 63 (8128 pairs), and the single-seed light cone has both colors (731 ones and 3494 zeros). That shows this rule is self-emulating and nested on these bounds. https://w3id.org/delphi/resource/assessment/wolfram2002-ch06-19--claim-test https://w3id.org/delphi/ontology/expectedObservation Zero mismatches of the even-cell identity on all 65536 width-16 states of rule 90, zero dyadic mismatches for t <= 63, both colors in the light cone, and at least one mismatch for rule 30 on width 12. https://w3id.org/delphi/resource/assessment/wolfram2002-ch06-19--claim-test https://w3id.org/delphi/ontology/failCriterion Pre-registered. If the Lucas check matches and rule 90 has any block mismatch, the exemplar fails and the verdict is refutes. If the Lucas check itself mismatches, the verdict is inconclusive (the simulator disagrees with the closed form). If rule 90 matches but the pattern is uniform, or rule 30 also matches on every width-12 state, the verdict is mixed. Examples do not prove the universal 'must'. https://w3id.org/delphi/resource/assessment/wolfram2002-ch06-19--claim-test https://w3id.org/delphi/ontology/hasConfidence 0.86 https://w3id.org/delphi/resource/assessment/wolfram2002-ch06-19--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch06-19--claim-test--dataset-1 https://w3id.org/delphi/resource/assessment/wolfram2002-ch06-19--claim-test https://w3id.org/delphi/ontology/hasVerdict supports https://w3id.org/delphi/resource/assessment/wolfram2002-ch06-19--claim-test https://w3id.org/delphi/ontology/hypothesis On every configuration of a width-16 ring, two steps of rule 90 restrict to one step of rule 90 on the even cells, and a single-seed evolution satisfies cell(2t, 2x) = cell(t, x) for t <= 63 and is not uniform, while rule 30 fails the same block identity. https://w3id.org/delphi/resource/assessment/wolfram2002-ch06-19--claim-test https://w3id.org/delphi/ontology/inferenceMethod Exhaustive comparison of the two-step even sublattice with one step of the same rule, plus the dyadic and Lucas checks. The universal quantifier is excluded from the verdict. https://w3id.org/delphi/resource/assessment/wolfram2002-ch06-19--claim-test https://w3id.org/delphi/ontology/passCriterion Pre-registered. Elementary rule 90, periodic ring of width 16, all 65536 configurations: the cells at even positions after two steps equal one step of rule 90 on those even cells. Separately, the infinite-line evolution from a single black cell satisfies cell(2t, 2x) = cell(t, x) for every t = 0..63 and every x = -63..63, the simulator matches the mod-2 binomial formula on every cell with t <= 64 and |x| <= t, and that light cone contains both colors. The control is elementary rule 30 on all 4096 configurations of a width-12 ring, which must produce at least one mismatch of the same even-cell identity. Supports only if rule 90 has zero block mismatches, zero dyadic mismatches, zero Lucas mismatches, both colors, and rule 30 has at least one mismatch. 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