@prefix this: . @prefix sub: . @prefix np: . @prefix rdf: . @prefix prov: . @prefix npx: . @prefix dc: . @prefix xsd: . sub:Head { this: a np:Nanopublication; np:hasAssertion sub:assertion; np:hasProvenance sub:provenance; np:hasPublicationInfo sub:pubinfo . } sub:assertion { a ; dc: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."; "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."; "Claim test of wolfram2002-ch04-20: mixed, confidence 0.7"; ; prov:wasAttributedTo ; "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."; "claim-test/0.1.0"; "computational"; "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."; "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.", "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.", "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.", "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.", "This is a computation about one map. It says nothing about organisms."; "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."; "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."; "0.7"^^xsd:double; , ; "mixed"; "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."; "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."; "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."; "false"^^xsd:boolean . . a ; dc:description "the orbit claimed to look random from a simple seed"; dc:license ""; "Dataset: Exact orbit of the fractional part of 3x/2 from 1/2"; "sha256:e5f8101d861551f586492fb2a9f1a7b9687acc718c014986729111dab6ac1c17" . a ; dc:description "repetitive control: a digit shift from a periodic seed"; dc:license ""; "Dataset: Exact orbit of the fractional part of 2x from 1/3" . } sub:provenance { a prov:SoftwareAgent; "delphisci claim tester (Grok 4.7; cursor/claim-tests-wolfram-programs-b8d9)"; prov:actedOnBehalfOf ; . a ; dc:identifier "Grok 4.7" . sub:assertion prov:wasAttributedTo ; prov:wasDerivedFrom ; prov:wasGeneratedBy sub:test . sub:plan prov:hadPlan . sub:test a prov:Activity; prov:qualifiedAssociation sub:plan; prov:wasAssociatedWith . } sub:pubinfo { this: dc:created "2026-11-08T16:24:31.924Z"^^xsd:dateTime; dc:creator ; dc:license ; npx:hasNanopubType ; npx:introduces ; "Claim test of wolfram2002-ch04-20: mixed, confidence 0.7"; . sub:sig npx:hasAlgorithm "RSA"; npx:hasPublicKey "MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB"; npx:hasSignature "oLPH2iXBcp1LYbblmrxDd+2ZPg869YJQtPYWsRplmVGuxyykXOHPWDCVGZcyw3HJ4N5YVX8joQJc+FUadICzxRxZphCumd2dhLRkxhUVmTycU/lku93MtsynKRgly3wkpU0IFJiu518fEPtAo5BRx5c/w2qeIXkzRH5711ihldVlSsEpr5CyZDOHRrlzX0bIC4HuefKSR5/zQDH8/jynGtWoxFKD0kCavHJYqHZeCvQeIsZJ0NSFkybs2JfUDPc0GRl5MEzj5ixdBbUcmI+UVrqhwLSemxglWuKkuN6SlPE6CZvZX7y/pEcPdAYnuh4tRM2v52fDXRb/KpnyLRCMSQ=="; npx:hasSignatureTarget this:; npx:signedBy . }