https://w3id.org/np/RAotOpvYzua1F1M_yctVtM0FonayFwO5dz0ujcYT818nQ
.trig | .trig.txt | .jelly | .jelly.txt | .jsonld | .jsonld.txt | .nq | .nq.txt | .xml | .xml.txt
@prefix this: <https://w3id.org/np/RAotOpvYzua1F1M_yctVtM0FonayFwO5dz0ujcYT818nQ> .
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@prefix dc: <http://purl.org/dc/terms/> .
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sub:Head {
this: a np:Nanopublication;
np:hasAssertion sub:assertion;
np:hasProvenance sub:provenance;
np:hasPublicationInfo sub:pubinfo .
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sub:assertion {
<https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-09--claim-test> a <https://w3id.org/delphi/ontology/Assessment>;
dc: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.";
<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.";
<http://www.w3.org/2000/01/rdf-schema#label> "Claim test of wolfram2002-ch04-09: supports, confidence 0.74";
<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>;
prov:wasAttributedTo <https://w3id.org/delphi/resource/agent/delphisci-claim-tester-grok-4-7>;
<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/ontology/assessmentType> "claim-test/0.1.0";
<https://w3id.org/delphi/ontology/dataKind> "computational";
<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/ontology/evidenceAgainst> "A match shows only that this computation behaves as claimed for this statistic. It says nothing about organisms.",
"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.",
"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.",
"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/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/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/ontology/hasConfidence> "0.74"^^xsd:double;
<https://w3id.org/delphi/ontology/hasEvidence> <https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-09--claim-test--dataset-1>;
<https://w3id.org/delphi/ontology/hasVerdict> "supports";
<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/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/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. If fewer than 16384 such gaps exist below 400000, or a control misses its bound, the verdict is inconclusive.";
<https://w3id.org/delphi/ontology/preregistered> "false"^^xsd:boolean .
<https://w3id.org/delphi/resource/claim/wolfram2002-ch04-09> <https://w3id.org/delphi/ontology/hasAssessment>
<https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-09--claim-test> .
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-09--claim-test--dataset-1>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "the prime gaps whose half-gap parity is the randomness statistic";
dc:license "generated data";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: Primes generated by the sieve of Eratosthenes up to 400000" .
}
sub:provenance {
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<http://www.w3.org/2000/01/rdf-schema#label> "delphisci claim tester (Grok 4.7; cursor/wolfram-claim-tests-b-355b)";
prov:actedOnBehalfOf <https://orcid.org/0009-0007-4948-9192>;
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dc:identifier "Grok 4.7" .
sub:assertion prov:wasAttributedTo <https://w3id.org/delphi/resource/agent/delphisci-claim-tester-grok-4-7>;
prov:wasDerivedFrom <https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch04-09/result.json>;
prov:wasGeneratedBy sub:test .
sub:plan prov:hadPlan <https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/README.md> .
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sub:pubinfo {
this: dc:created "2026-11-08T16:24:31.923Z"^^xsd:dateTime;
dc:creator <https://orcid.org/0009-0007-4948-9192>;
dc:license <https://creativecommons.org/licenses/by/4.0/>;
npx:hasNanopubType <https://w3id.org/delphi/ontology/Assessment>;
npx:introduces <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/ontology/domain> <https://w3id.org/delphi/resource/domain/wolfram-nks-2002> .
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