https://w3id.org/np/RAOj3hvwtwQvXTTsQRddQuPCQygupQH2LP29_wwW5rfLc/Head https://w3id.org/np/RAOj3hvwtwQvXTTsQRddQuPCQygupQH2LP29_wwW5rfLc http://www.nanopub.org/nschema#hasAssertion https://w3id.org/np/RAOj3hvwtwQvXTTsQRddQuPCQygupQH2LP29_wwW5rfLc/assertion https://w3id.org/np/RAOj3hvwtwQvXTTsQRddQuPCQygupQH2LP29_wwW5rfLc http://www.nanopub.org/nschema#hasProvenance https://w3id.org/np/RAOj3hvwtwQvXTTsQRddQuPCQygupQH2LP29_wwW5rfLc/provenance https://w3id.org/np/RAOj3hvwtwQvXTTsQRddQuPCQygupQH2LP29_wwW5rfLc http://www.nanopub.org/nschema#hasPublicationInfo https://w3id.org/np/RAOj3hvwtwQvXTTsQRddQuPCQygupQH2LP29_wwW5rfLc/pubinfo https://w3id.org/np/RAOj3hvwtwQvXTTsQRddQuPCQygupQH2LP29_wwW5rfLc http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.nanopub.org/nschema#Nanopublication https://w3id.org/np/RAOj3hvwtwQvXTTsQRddQuPCQygupQH2LP29_wwW5rfLc/assertion https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-20--claim-test http://purl.org/dc/terms/description 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. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-20--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-ch04-20--claim-test http://www.w3.org/2000/01/rdf-schema#comment 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. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-20--claim-test http://www.w3.org/2000/01/rdf-schema#label Claim test of wolfram2002-ch04-20: mixed, confidence 0.7 https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-20--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-ch04-20/result.json https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-20--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-ch04-20--claim-test https://w3id.org/delphi/ontology/admissibleDatasets 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/resource/assessment/wolfram2002-ch04-20--claim-test https://w3id.org/delphi/ontology/assessmentType claim-test/0.1.0 https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-20--claim-test https://w3id.org/delphi/ontology/dataKind computational https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-20--claim-test https://w3id.org/delphi/ontology/disconfirmingObservation 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/resource/assessment/wolfram2002-ch04-20--claim-test https://w3id.org/delphi/ontology/evidenceAgainst 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. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-20--claim-test https://w3id.org/delphi/ontology/evidenceAgainst 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. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-20--claim-test https://w3id.org/delphi/ontology/evidenceAgainst 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. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-20--claim-test https://w3id.org/delphi/ontology/evidenceAgainst 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. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-20--claim-test https://w3id.org/delphi/ontology/evidenceAgainst This is a computation about one map. It says nothing about organisms. https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-20--claim-test https://w3id.org/delphi/ontology/expectedObservation 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/resource/assessment/wolfram2002-ch04-20--claim-test https://w3id.org/delphi/ontology/failCriterion 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/resource/assessment/wolfram2002-ch04-20--claim-test https://w3id.org/delphi/ontology/hasConfidence 0.7 https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-20--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-20--claim-test--dataset-1 https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-20--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-20--claim-test--dataset-2 https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-20--claim-test https://w3id.org/delphi/ontology/hasVerdict mixed https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-20--claim-test https://w3id.org/delphi/ontology/hypothesis 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/resource/assessment/wolfram2002-ch04-20--claim-test https://w3id.org/delphi/ontology/inferenceMethod 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/resource/assessment/wolfram2002-ch04-20--claim-test https://w3id.org/delphi/ontology/passCriterion 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/resource/assessment/wolfram2002-ch04-20--claim-test https://w3id.org/delphi/ontology/preregistered false https://w3id.org/delphi/resource/claim/wolfram2002-ch04-20 https://w3id.org/delphi/ontology/hasAssessment https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-20--claim-test https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-20--claim-test--dataset-1 http://purl.org/dc/terms/description the orbit claimed to look random from a simple seed https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-20--claim-test--dataset-1 http://purl.org/dc/terms/license https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-20--claim-test--dataset-1 http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/EvidenceItem https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-20--claim-test--dataset-1 http://www.w3.org/2000/01/rdf-schema#label Dataset: Exact orbit of the fractional part of 3x/2 from 1/2 https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-20--claim-test--dataset-1 https://w3id.org/delphi/ontology/hasChecksum sha256:e5f8101d861551f586492fb2a9f1a7b9687acc718c014986729111dab6ac1c17 https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-20--claim-test--dataset-2 http://purl.org/dc/terms/description repetitive control: a digit shift from a periodic seed https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-20--claim-test--dataset-2 http://purl.org/dc/terms/license https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-20--claim-test--dataset-2 http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/EvidenceItem https://w3id.org/delphi/resource/evidence/wolfram2002-ch04-20--claim-test--dataset-2 http://www.w3.org/2000/01/rdf-schema#label Dataset: Exact orbit of the fractional part of 2x from 1/3 https://w3id.org/np/RAOj3hvwtwQvXTTsQRddQuPCQygupQH2LP29_wwW5rfLc/provenance https://w3id.org/delphi/resource/agent/delphisci-claim-tester-grok-4-7 http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.w3.org/ns/prov#SoftwareAgent https://w3id.org/delphi/resource/agent/delphisci-claim-tester-grok-4-7 http://www.w3.org/2000/01/rdf-schema#label delphisci claim tester (Grok 4.7; 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