[ { "@id": "https://w3id.org/np/RAOj3hvwtwQvXTTsQRddQuPCQygupQH2LP29_wwW5rfLc/pubinfo", "@graph": [ { "@id": "https://w3id.org/np/RAOj3hvwtwQvXTTsQRddQuPCQygupQH2LP29_wwW5rfLc", "http://purl.org/dc/terms/created": [ { "@value": "2026-11-08T16:24:31.924Z", "@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-ch04-20--claim-test" } ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "Claim test of wolfram2002-ch04-20: mixed, confidence 0.7" } ], "https://w3id.org/delphi/ontology/domain": [ { "@id": "https://w3id.org/delphi/resource/domain/wolfram-nks-2002" } ] }, { "@id": "https://w3id.org/np/RAOj3hvwtwQvXTTsQRddQuPCQygupQH2LP29_wwW5rfLc/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": "oLPH2iXBcp1LYbblmrxDd+2ZPg869YJQtPYWsRplmVGuxyykXOHPWDCVGZcyw3HJ4N5YVX8joQJc+FUadICzxRxZphCumd2dhLRkxhUVmTycU/lku93MtsynKRgly3wkpU0IFJiu518fEPtAo5BRx5c/w2qeIXkzRH5711ihldVlSsEpr5CyZDOHRrlzX0bIC4HuefKSR5/zQDH8/jynGtWoxFKD0kCavHJYqHZeCvQeIsZJ0NSFkybs2JfUDPc0GRl5MEzj5ixdBbUcmI+UVrqhwLSemxglWuKkuN6SlPE6CZvZX7y/pEcPdAYnuh4tRM2v52fDXRb/KpnyLRCMSQ==" } ], "http://purl.org/nanopub/x/hasSignatureTarget": [ { "@id": "https://w3id.org/np/RAOj3hvwtwQvXTTsQRddQuPCQygupQH2LP29_wwW5rfLc" } ], "http://purl.org/nanopub/x/signedBy": [ { "@id": "https://orcid.org/0009-0007-4948-9192" } ] } ] }, { "@id": "https://w3id.org/np/RAOj3hvwtwQvXTTsQRddQuPCQygupQH2LP29_wwW5rfLc/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/claim-tests-wolfram-programs-b8d9)" } ], "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/RAOj3hvwtwQvXTTsQRddQuPCQygupQH2LP29_wwW5rfLc/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-ch04-20/result.json" } ], "http://www.w3.org/ns/prov#wasGeneratedBy": [ { "@id": "https://w3id.org/np/RAOj3hvwtwQvXTTsQRddQuPCQygupQH2LP29_wwW5rfLc/test" } ] }, { "@id": "https://w3id.org/np/RAOj3hvwtwQvXTTsQRddQuPCQygupQH2LP29_wwW5rfLc/test", "@type": [ "http://www.w3.org/ns/prov#Activity" ], "http://www.w3.org/ns/prov#qualifiedAssociation": [ { "@id": "https://w3id.org/np/RAOj3hvwtwQvXTTsQRddQuPCQygupQH2LP29_wwW5rfLc/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/RAOj3hvwtwQvXTTsQRddQuPCQygupQH2LP29_wwW5rfLc/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/RAOj3hvwtwQvXTTsQRddQuPCQygupQH2LP29_wwW5rfLc/Head", "@graph": [ { "@id": "https://w3id.org/np/RAOj3hvwtwQvXTTsQRddQuPCQygupQH2LP29_wwW5rfLc", "http://www.nanopub.org/nschema#hasAssertion": [ { "@id": "https://w3id.org/np/RAOj3hvwtwQvXTTsQRddQuPCQygupQH2LP29_wwW5rfLc/assertion" } ], "http://www.nanopub.org/nschema#hasProvenance": [ { "@id": "https://w3id.org/np/RAOj3hvwtwQvXTTsQRddQuPCQygupQH2LP29_wwW5rfLc/provenance" } ], "http://www.nanopub.org/nschema#hasPublicationInfo": [ { "@id": "https://w3id.org/np/RAOj3hvwtwQvXTTsQRddQuPCQygupQH2LP29_wwW5rfLc/pubinfo" } ], "@type": [ "http://www.nanopub.org/nschema#Nanopublication" ] } ] }, { "@id": "https://w3id.org/np/RAOj3hvwtwQvXTTsQRddQuPCQygupQH2LP29_wwW5rfLc/assertion", "@graph": [ { "@id": "https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-20--claim-test", "http://purl.org/dc/terms/description": [ { "@value": "analysis.py iterates the fractional part of 3x/2 from 1/2 for 4096 steps with reduced integer fractions, records the half-itinerary, and computes h4, lag-1 autocorrelation, state repetition and itinerary periods through 32. The same itinerary entropy is computed for the doubling map from 1/3 and for 4096 bits from random.Random(20261102). A 16-bin chi-square is stored and is not an input to the verdict. A second run matched derived/measured.json byte for byte." } ], "@type": [ "https://w3id.org/delphi/ontology/Assessment" ], "http://www.w3.org/2000/01/rdf-schema#comment": [ { "@value": "Measured: 0.8277801256315166 normalized 4-bit block entropy h4 of the 4096-step half-itinerary of {3x/2} from 1/2 (n = 1024, exact orbit; plugin Shannon entropy on this window). Interpretation: The map named in the claim is x -> fractional part of 3x/2, and the simple seed is 1/2. 'Looks random' is read as a high 4-bit block entropy, a small lag-1 correlation, and the absence of a state cycle or an itinerary period of 32 or less inside 4096 steps. It is not read as equidistribution for Lebesgue measure: the beta transformation with multiplier 3/2 need not have a flat invariant density, so the 16-bin chi-square is recorded and does not decide the verdict. The control is the shift map, which the surrounding text says only transcribes digits, here started at the periodic seed 1/3. The computation does not say that organisms behave this way." } ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "Claim test of wolfram2002-ch04-20: mixed, confidence 0.7" } ], "http://www.w3.org/2000/01/rdf-schema#seeAlso": [ { "@id": "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch04-20/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": "Exact orbits of the two maps generated by the checksummed script, length 4096, seeds 1/2 and 1/3. No external dataset and no organism record is admissible." } ], "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": "With the doubling-map control still at h4 at most 0.25, the target itinerary has h4 at most 0.75, or lag-1 autocorrelation at least 0.40 in absolute value, or a repeated rational state, or an itinerary period of 32 or less." } ], "https://w3id.org/delphi/ontology/evidenceAgainst": [ { "@value": "Integers reached 4097 bits. A cycle longer than 4096 steps, or a longer block size, could change the appearance. The run is a finite check." }, { "@value": "Only 1328 of 4096 itinerary bits were 1. That bias, not a short cycle, is what holds h4 down. A bias-adjusted entropy was not the pre-registered statistic and is not used." }, { "@value": "The 16-bin chi-square was 602.99, so the values are not uniform on [0,1]. That number was pre-registered as not deciding the verdict." }, { "@value": "The orbit is not a short repeat: no rational state recurred in 4096 steps, no itinerary period of 32 or less appeared, and lag-1 autocorrelation was 0.105. h4 was 0.828, above the refute line 0.75 and below the support line 0.90." }, { "@value": "This is a computation about one map. It says nothing about organisms." } ], "https://w3id.org/delphi/ontology/expectedObservation": [ { "@value": "Over 4096 exact iterates, the half-itinerary of {3x/2} from 1/2 has h4 at least 0.90, lag-1 autocorrelation at most 0.15 in absolute value, and neither a repeated state nor an itinerary period of 32 or less, while the doubling map from 1/3 has h4 at most 0.25." } ], "https://w3id.org/delphi/ontology/failCriterion": [ { "@value": "Pre-registered. Refutes if h4(control) <= 0.25 and at least one of: h4(target) <= 0.75, |r| >= 0.40, a state repeats, or the itinerary has a period <= 32. Inconclusive if h4(control) > 0.25. Mixed in every other case." } ], "https://w3id.org/delphi/ontology/hasConfidence": [ { "@value": "0.7", "@type": "http://www.w3.org/2001/XMLSchema#double" } ], "https://w3id.org/delphi/ontology/hasEvidence": [ { "@id": "https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-20--claim-test--dataset-1" }, { "@id": "https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-20--claim-test--dataset-2" } ], "https://w3id.org/delphi/ontology/hasVerdict": [ { "@value": "mixed" } ], "https://w3id.org/delphi/ontology/hypothesis": [ { "@value": "The itinerary of the fractional part of 3x/2, started at 1/2, has high 4-bit block entropy and weak lag-1 correlation and does not fall into a short repeat within 4096 steps, while the shift map started at 1/3 stays repetitive." } ], "https://w3id.org/delphi/ontology/inferenceMethod": [ { "@value": "Compare h4, lag-1 autocorrelation, state repetition and itinerary period against the thresholds above. The control must stay repetitive. Chi-square against 16 equal bins is reported and is not an input to the verdict." } ], "https://w3id.org/delphi/ontology/passCriterion": [ { "@value": "Pre-registered, all required. Orbit length 4096. The target map is x -> {3x/2} with x0 = 1/2, in reduced exact rationals. The itinerary bit is 1 when x >= 1/2. h4 is the Shannon entropy of non-overlapping 4-bit blocks divided by 4. Lag-1 autocorrelation is r = sum_{i=0}^{4094} (b_i - mean)(b_{i+1} - mean) / sum_{i=0}^{4095} (b_i - mean)^2. A state repeat is any repeated reduced fraction among the 4096 states. An itinerary period p <= 32 means b_t = b_{t+p} for every admissible t. The control is x -> {2x} with x0 = 1/3 for 4096 steps. Supports if and only if h4(control) <= 0.25 and h4(target) >= 0.90 and |r| <= 0.15 and no state repeats and no itinerary period is <= 32. A 16-bin chi-square of the values x is computed and is not part of this criterion." } ], "https://w3id.org/delphi/ontology/preregistered": [ { "@value": "false", "@type": "http://www.w3.org/2001/XMLSchema#boolean" } ] }, { "@id": "https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-20--claim-test--dataset-1", "http://purl.org/dc/terms/description": [ { "@value": "the orbit claimed to look random from a simple seed" } ], "http://purl.org/dc/terms/license": [ { "@value": "" } ], "@type": [ "https://w3id.org/delphi/ontology/EvidenceItem" ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "Dataset: Exact orbit of the fractional part of 3x/2 from 1/2" } ], "https://w3id.org/delphi/ontology/hasChecksum": [ { "@value": "sha256:e5f8101d861551f586492fb2a9f1a7b9687acc718c014986729111dab6ac1c17" } ] }, { "@id": "https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-20--claim-test--dataset-2", "http://purl.org/dc/terms/description": [ { "@value": "repetitive control: a digit shift from a periodic seed" } ], "http://purl.org/dc/terms/license": [ { "@value": "" } ], "@type": [ "https://w3id.org/delphi/ontology/EvidenceItem" ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "Dataset: Exact orbit of the fractional part of 2x from 1/3" } ] }, { "@id": "https://w3id.org/delphi/resource/claim/wolfram2002-ch04-20", "https://w3id.org/delphi/ontology/hasAssessment": [ { "@id": "https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-20--claim-test" } ] } ] } ]