https://w3id.org/np/RAcJTP1AFP4aqp6GSqj-lgUhCGgLTnf-CqQYzH1D3lSKw/Head https://w3id.org/np/RAcJTP1AFP4aqp6GSqj-lgUhCGgLTnf-CqQYzH1D3lSKw http://www.nanopub.org/nschema#hasAssertion https://w3id.org/np/RAcJTP1AFP4aqp6GSqj-lgUhCGgLTnf-CqQYzH1D3lSKw/assertion https://w3id.org/np/RAcJTP1AFP4aqp6GSqj-lgUhCGgLTnf-CqQYzH1D3lSKw http://www.nanopub.org/nschema#hasProvenance https://w3id.org/np/RAcJTP1AFP4aqp6GSqj-lgUhCGgLTnf-CqQYzH1D3lSKw/provenance https://w3id.org/np/RAcJTP1AFP4aqp6GSqj-lgUhCGgLTnf-CqQYzH1D3lSKw http://www.nanopub.org/nschema#hasPublicationInfo https://w3id.org/np/RAcJTP1AFP4aqp6GSqj-lgUhCGgLTnf-CqQYzH1D3lSKw/pubinfo https://w3id.org/np/RAcJTP1AFP4aqp6GSqj-lgUhCGgLTnf-CqQYzH1D3lSKw http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.nanopub.org/nschema#Nanopublication https://w3id.org/np/RAcJTP1AFP4aqp6GSqj-lgUhCGgLTnf-CqQYzH1D3lSKw/assertion https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-04--claim-test http://purl.org/dc/terms/description analysis.py computes 3^n exactly, takes the leading bit of (3^n mod 2^n)/2^n for n = 1..4096, and the leading 4096 bits of 3^4096, and computes overlapping 8-bit block entropies. The control is the 4096-bit binary representation of 2^4095. Numbers are copied from derived/measured.json. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-04--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-ch04-04--claim-test http://www.w3.org/2000/01/rdf-schema#comment Measured: 7.957383 bits of overlapping 8-bit block entropy of the leading fractional-part bits (n = 4096, plugin estimator on 4089 overlapping windows). Interpretation: The fractional part is the base-independent size Wolfram contrasts with digits. It is computed exactly as (3^n mod 2^n)/2^n, and its complexity is the block entropy of its leading binary digit, the same statistic applied to the leading bits of 3^4096. The power-of-two control is a digit sequence that is simple on purpose, so the statistic has to be able to say 'not complex'. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-04--claim-test http://www.w3.org/2000/01/rdf-schema#label Claim test of wolfram2002-ch04-04: supports, confidence 0.8 https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-04--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-ch04-04/result.json https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-04--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-ch04-04--claim-test https://w3id.org/delphi/ontology/admissibleDatasets Exact integer powers only, n through 4096, no floating point. The power-of-two string is the negative control. This is not a statement about organisms. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-04--claim-test https://w3id.org/delphi/ontology/assessmentType claim-test/0.1.0 https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-04--claim-test https://w3id.org/delphi/ontology/dataKind computational https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-04--claim-test https://w3id.org/delphi/ontology/disconfirmingObservation H8 of the fractional-part bits is below 5.0 while H8 of the digits of 3^4096 is at least 7.0. A gap larger than 0.6, or either sequence between 5.0 and 7.0, is mixed. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-04--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-ch04-04--claim-test https://w3id.org/delphi/ontology/evidenceAgainst Block entropy near 8 bits is incompressibility of 8-bit blocks, not a proof that {(3/2)^n} is equidistributed. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-04--claim-test https://w3id.org/delphi/ontology/evidenceAgainst Finite check: 4096 powers, and only the leading binary digit of each fractional part. The full fractional part could be structured in the lower bits without moving this statistic. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-04--claim-test https://w3id.org/delphi/ontology/evidenceAgainst The digit comparison is the leading 4096 bits of the single integer 3^4096 (bit length 6493), not a concatenation of every power's digits. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-04--claim-test https://w3id.org/delphi/ontology/expectedObservation H8 of the 4096 leading fractional-part bits and H8 of the leading 4096 bits of 3^4096 are both at least 7.0 and differ by at most 0.6, while H8 of the bits of 2^4095 is at most 1.5. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-04--claim-test https://w3id.org/delphi/ontology/failCriterion Pre-registered. If the control passes and H8(b) < 5.0 while H8(d) >= 7.0, the verdict is refutes: the fractional-part bits are not as complex as the digit sequence on this statistic. Every other case in which the control passes is mixed. The check is finite (4096 terms, one bit per term) and says nothing about organisms. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-04--claim-test https://w3id.org/delphi/ontology/hasConfidence 0.8 https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-04--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-04--claim-test--dataset-1 https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-04--claim-test https://w3id.org/delphi/ontology/hasVerdict supports https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-04--claim-test https://w3id.org/delphi/ontology/hypothesis The leading binary digits of the fractional parts {(3/2)^n} for n = 1..4096 have overlapping 8-bit block entropy within 0.6 bits of the leading 4096 binary digits of 3^4096, and both entropies are at least 7.0, while the 4096-bit encoding of a power of two stays at or below 1.5. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-04--claim-test https://w3id.org/delphi/ontology/inferenceMethod Shannon entropy of overlapping 8-bit blocks, with the three locked thresholds. The ones-frequency is reported and does not decide the verdict. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-04--claim-test https://w3id.org/delphi/ontology/passCriterion Pre-registered. Let b_n = 1 if 3^n mod 2^n >= 2^(n-1), else 0, for n = 1..4096. This is the leading binary digit of the exact fractional part {(3/2)^n} = (3^n mod 2^n)/2^n. Let d be the leading 4096 bits of 3^4096. Let c be the 4096-bit binary representation of 2^4095. Let H8 be the Shannon entropy of overlapping length-8 blocks. Supports if H8(b) >= 7.0, H8(d) >= 7.0, |H8(b)-H8(d)| <= 0.6, and H8(c) <= 1.5. 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