https://w3id.org/np/RAotOpvYzua1F1M_yctVtM0FonayFwO5dz0ujcYT818nQ/Head https://w3id.org/np/RAotOpvYzua1F1M_yctVtM0FonayFwO5dz0ujcYT818nQ http://www.nanopub.org/nschema#hasAssertion https://w3id.org/np/RAotOpvYzua1F1M_yctVtM0FonayFwO5dz0ujcYT818nQ/assertion https://w3id.org/np/RAotOpvYzua1F1M_yctVtM0FonayFwO5dz0ujcYT818nQ http://www.nanopub.org/nschema#hasProvenance https://w3id.org/np/RAotOpvYzua1F1M_yctVtM0FonayFwO5dz0ujcYT818nQ/provenance https://w3id.org/np/RAotOpvYzua1F1M_yctVtM0FonayFwO5dz0ujcYT818nQ http://www.nanopub.org/nschema#hasPublicationInfo https://w3id.org/np/RAotOpvYzua1F1M_yctVtM0FonayFwO5dz0ujcYT818nQ/pubinfo https://w3id.org/np/RAotOpvYzua1F1M_yctVtM0FonayFwO5dz0ujcYT818nQ http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.nanopub.org/nschema#Nanopublication https://w3id.org/np/RAotOpvYzua1F1M_yctVtM0FonayFwO5dz0ujcYT818nQ/assertion https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-09--claim-test http://purl.org/dc/terms/description analysis.py sieves the integers through 400000, takes the first 16384 gaps from the prime 3, and computes the Shannon entropy of overlapping 8-bit blocks of (gap/2) mod 2. The same entropy is computed for a constant sequence of ones and for an alternating sequence. Every number in measured is written to derived/measured.json by that script. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-09--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-ch04-09--claim-test http://www.w3.org/2000/01/rdf-schema#comment Measured: 7.788983 bits of overlapping 8-bit block entropy of half-gap parity (n = 16384, plugin estimator on 16377 overlapping windows; no sampling interval). Interpretation: Wolfram's remark that the primes obtained from the sieve look remarkably random is read as a statement about the gap sequence, not about the primes being odd (that parity is constant after 2). The raw gap parity after 2 is identically even, so it cannot witness randomness; the parity of the half-gap is the pre-registered randomness statistic. The repetitive controls are synthetic gap parities (all half-gaps odd; half-gaps alternating in parity), not other number sequences. 'Remarkably random' is operationalized only as high block entropy relative to those controls. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-09--claim-test http://www.w3.org/2000/01/rdf-schema#label Claim test of wolfram2002-ch04-09: supports, confidence 0.74 https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-09--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-ch04-09/result.json https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-09--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-ch04-09--claim-test https://w3id.org/delphi/ontology/admissibleDatasets The bit string must be generated by the sieve of Eratosthenes at the locked limit 400000, using only gaps from the prime 3 onward. No external prime table is consulted. The computation is not evidence about organisms. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-09--claim-test https://w3id.org/delphi/ontology/assessmentType claim-test/0.1.0 https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-09--claim-test https://w3id.org/delphi/ontology/dataKind computational https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-09--claim-test https://w3id.org/delphi/ontology/disconfirmingObservation The same entropy is below 5.0 bits even though the two repetitive controls sit at or below 1.01. An entropy between 5.0 and 7.2 is mixed, not a confirmation. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-09--claim-test https://w3id.org/delphi/ontology/evidenceAgainst A match shows only that this computation behaves as claimed for this statistic. It says nothing about organisms. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-09--claim-test https://w3id.org/delphi/ontology/evidenceAgainst Every gap in the sample is even (odd_gaps_in_sample = 0). Raw gap parity is therefore a constant and was not used as the randomness statistic. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-09--claim-test https://w3id.org/delphi/ontology/evidenceAgainst Finite check: 16384 gaps, the largest prime used being 180533, from a sieve limited to 400000. A different bound or a different statistic can disagree. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-09--claim-test https://w3id.org/delphi/ontology/evidenceAgainst The ones-frequency of the half-gap parity is 0.586365 (9607 of 16384), so the sequence is biased away from a fair coin. The pre-registered statistic was block entropy, which still cleared 7.2 (measured 7.788983, all 256 blocks seen). Unbiasedness was not the pass criterion. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-09--claim-test https://w3id.org/delphi/ontology/expectedObservation Overlapping 8-bit block entropy of the first 16384 half-gap parities from the prime 3 is at least 7.2 bits, while a constant control is 0 and an alternating control is at most 1.01. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-09--claim-test https://w3id.org/delphi/ontology/failCriterion Pre-registered. If both controls pass and H8 < 5.0, the verdict is refutes: the half-gap parity sequence is not remarkably random on this statistic. If both controls pass and 5.0 <= H8 < 7.2, the verdict is mixed. A match is only about this finite sieve and this statistic. It does not say that the primes are random in every respect, and it says nothing about organisms. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-09--claim-test https://w3id.org/delphi/ontology/hasConfidence 0.74 https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-09--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-09--claim-test--dataset-1 https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-09--claim-test https://w3id.org/delphi/ontology/hasVerdict supports https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-09--claim-test https://w3id.org/delphi/ontology/hypothesis The parity of successive half-gaps of the primes (gap/2 mod 2, gaps from the prime 3 onward) has overlapping 8-bit block entropy close to the 8-bit maximum, while a constant half-gap sequence and an alternating half-gap sequence stay at or below 1 bit. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-09--claim-test https://w3id.org/delphi/ontology/inferenceMethod Shannon entropy of overlapping 8-bit blocks, compared with the two locked thresholds and with the two locked repetitive controls. The frequency of ones is reported and does not decide the verdict. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-09--claim-test https://w3id.org/delphi/ontology/passCriterion Pre-registered. Sieve of Eratosthenes on the integers 0..400000. Take the first 16384 gaps whose left endpoint is a prime >= 3 (so every gap is even). Let b_i = ((p_{i+1}-p_i)/2) mod 2. Let H8 be the Shannon entropy, in bits, of the overlapping length-8 blocks of b. Supports if H8 >= 7.2 and both controls pass: the constant sequence of 16384 ones has H8 = 0, and the alternating sequence 1,0,1,0,... has H8 <= 1.01. 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