[ { "@id": "https://w3id.org/np/RAotOpvYzua1F1M_yctVtM0FonayFwO5dz0ujcYT818nQ/pubinfo", "@graph": [ { "@id": "https://w3id.org/np/RAotOpvYzua1F1M_yctVtM0FonayFwO5dz0ujcYT818nQ", "http://purl.org/dc/terms/created": [ { "@value": "2026-11-08T16:24:31.923Z", "@type": "http://www.w3.org/2001/XMLSchema#dateTime" } ], "http://purl.org/dc/terms/creator": [ { "@id": "https://orcid.org/0009-0007-4948-9192" } ], "http://purl.org/dc/terms/license": [ { "@id": "https://creativecommons.org/licenses/by/4.0/" } ], "http://purl.org/nanopub/x/hasNanopubType": [ { "@id": "https://w3id.org/delphi/ontology/Assessment" } ], "http://purl.org/nanopub/x/introduces": [ { "@id": "https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-09--claim-test" } ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "Claim test of wolfram2002-ch04-09: supports, confidence 0.74" } ], "https://w3id.org/delphi/ontology/domain": [ { "@id": "https://w3id.org/delphi/resource/domain/wolfram-nks-2002" } ] }, { "@id": "https://w3id.org/np/RAotOpvYzua1F1M_yctVtM0FonayFwO5dz0ujcYT818nQ/sig", "http://purl.org/nanopub/x/hasAlgorithm": [ { "@value": "RSA" } ], "http://purl.org/nanopub/x/hasPublicKey": [ { "@value": "MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB" } ], "http://purl.org/nanopub/x/hasSignature": [ { "@value": "NY1cvqapxZyXg+p/mTDg5HxwoTkkc8tszTX8dirlFJgMHVAQMQjF9dnGRFFXglSWjgQuswy4ZC41WUadoCzwpRnKnV56wPV4lfTzr/EKA4asmyPddngWMxbuI9fsorRFVenUsPLm/9DmYuVHBocU/eASVocduxbMrSXifC1pPHYZ9jiSfbZ2TrU/4Rh7HiAW7AE2QJCnBMxlP7ckWlgFqMkwPr28YscYL3rkuzR1uSbz+8uArYre3ZYtm/h1BDw+8r0+Y8whT8PDq/R5wqQ+pFoq+XFrM/lMr+iRwfMFqZwq0m5Gm4NCJq2YhRN81e5Pbc1AoHgyRPJw7+TNBvOkUA==" } ], "http://purl.org/nanopub/x/hasSignatureTarget": [ { "@id": "https://w3id.org/np/RAotOpvYzua1F1M_yctVtM0FonayFwO5dz0ujcYT818nQ" } ], "http://purl.org/nanopub/x/signedBy": [ { "@id": "https://orcid.org/0009-0007-4948-9192" } ] } ] }, { "@id": "https://w3id.org/np/RAotOpvYzua1F1M_yctVtM0FonayFwO5dz0ujcYT818nQ/assertion", "@graph": [ { "@id": "https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-09--claim-test", "http://purl.org/dc/terms/description": [ { "@value": "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." } ], "@type": [ "https://w3id.org/delphi/ontology/Assessment" ], "http://www.w3.org/2000/01/rdf-schema#comment": [ { "@value": "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": [ { "@value": "Claim test of wolfram2002-ch04-09: supports, confidence 0.74" } ], "http://www.w3.org/2000/01/rdf-schema#seeAlso": [ { "@id": "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch04-09/result.json" } ], "http://www.w3.org/ns/prov#wasAttributedTo": [ { "@id": "https://w3id.org/delphi/resource/agent/delphisci-claim-tester-grok-4-7" } ], "https://w3id.org/delphi/ontology/admissibleDatasets": [ { "@value": "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": [ { "@value": "claim-test/0.1.0" } ], "https://w3id.org/delphi/ontology/dataKind": [ { "@value": "computational" } ], "https://w3id.org/delphi/ontology/disconfirmingObservation": [ { "@value": "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": [ { "@value": "A match shows only that this computation behaves as claimed for this statistic. It says nothing about organisms." }, { "@value": "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." }, { "@value": "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." }, { "@value": "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": [ { "@value": "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": [ { "@value": "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": [ { "@value": "0.74", "@type": "http://www.w3.org/2001/XMLSchema#double" } ], "https://w3id.org/delphi/ontology/hasEvidence": [ { "@id": "https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-09--claim-test--dataset-1" } ], "https://w3id.org/delphi/ontology/hasVerdict": [ { "@value": "supports" } ], "https://w3id.org/delphi/ontology/hypothesis": [ { "@value": "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": [ { "@value": "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": [ { "@value": "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": [ { "@value": "false", "@type": "http://www.w3.org/2001/XMLSchema#boolean" } ] }, { "@id": "https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-09--claim-test--dataset-1", "http://purl.org/dc/terms/description": [ { "@value": "the prime gaps whose half-gap parity is the randomness statistic" } ], "http://purl.org/dc/terms/license": [ { "@value": "generated data" } ], "@type": [ "https://w3id.org/delphi/ontology/EvidenceItem" ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "Dataset: Primes generated by the sieve of Eratosthenes up to 400000" } ] }, { "@id": "https://w3id.org/delphi/resource/claim/wolfram2002-ch04-09", "https://w3id.org/delphi/ontology/hasAssessment": [ { "@id": "https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-09--claim-test" } ] } ] }, { "@id": "https://w3id.org/np/RAotOpvYzua1F1M_yctVtM0FonayFwO5dz0ujcYT818nQ/provenance", "@graph": [ { "@id": "https://w3id.org/delphi/resource/agent/delphisci-claim-tester-grok-4-7", "@type": [ "http://www.w3.org/ns/prov#SoftwareAgent" ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "delphisci claim tester (Grok 4.7; cursor/wolfram-claim-tests-b-355b)" } ], "http://www.w3.org/ns/prov#actedOnBehalfOf": [ { "@id": "https://orcid.org/0009-0007-4948-9192" } ], "https://w3id.org/delphi/ontology/usesModel": [ { "@id": "https://w3id.org/delphi/resource/model/grok-4-7" } ] }, { "@id": "https://w3id.org/delphi/resource/model/grok-4-7", "http://purl.org/dc/terms/identifier": [ { "@value": "Grok 4.7" } ], "@type": [ "https://w3id.org/delphi/ontology/LanguageModel" ] }, { "@id": "https://w3id.org/np/RAotOpvYzua1F1M_yctVtM0FonayFwO5dz0ujcYT818nQ/assertion", "http://www.w3.org/ns/prov#wasAttributedTo": [ { "@id": "https://w3id.org/delphi/resource/agent/delphisci-claim-tester-grok-4-7" } ], "http://www.w3.org/ns/prov#wasDerivedFrom": [ { "@id": "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch04-09/result.json" } ], "http://www.w3.org/ns/prov#wasGeneratedBy": [ { "@id": "https://w3id.org/np/RAotOpvYzua1F1M_yctVtM0FonayFwO5dz0ujcYT818nQ/test" } ] }, { "@id": "https://w3id.org/np/RAotOpvYzua1F1M_yctVtM0FonayFwO5dz0ujcYT818nQ/test", "@type": [ "http://www.w3.org/ns/prov#Activity" ], "http://www.w3.org/ns/prov#qualifiedAssociation": [ { "@id": "https://w3id.org/np/RAotOpvYzua1F1M_yctVtM0FonayFwO5dz0ujcYT818nQ/plan" } ], "http://www.w3.org/ns/prov#wasAssociatedWith": [ { "@id": "https://w3id.org/delphi/resource/agent/delphisci-claim-tester-grok-4-7" } ] }, { "@id": "https://w3id.org/np/RAotOpvYzua1F1M_yctVtM0FonayFwO5dz0ujcYT818nQ/plan", "http://www.w3.org/ns/prov#hadPlan": [ { "@id": "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/README.md" } ] } ] }, { "@id": "https://w3id.org/np/RAotOpvYzua1F1M_yctVtM0FonayFwO5dz0ujcYT818nQ/Head", "@graph": [ { "@id": "https://w3id.org/np/RAotOpvYzua1F1M_yctVtM0FonayFwO5dz0ujcYT818nQ", "http://www.nanopub.org/nschema#hasAssertion": [ { "@id": "https://w3id.org/np/RAotOpvYzua1F1M_yctVtM0FonayFwO5dz0ujcYT818nQ/assertion" } ], "http://www.nanopub.org/nschema#hasProvenance": [ { "@id": "https://w3id.org/np/RAotOpvYzua1F1M_yctVtM0FonayFwO5dz0ujcYT818nQ/provenance" } ], "http://www.nanopub.org/nschema#hasPublicationInfo": [ { "@id": "https://w3id.org/np/RAotOpvYzua1F1M_yctVtM0FonayFwO5dz0ujcYT818nQ/pubinfo" } ], "@type": [ "http://www.nanopub.org/nschema#Nanopublication" ] } ] } ]