https://w3id.org/np/RAXWgdaXUHnA2ZafcwGdd9CoR1ehv_62T47DCvWAKvYR8
.trig | .trig.txt | .jelly | .jelly.txt | .jsonld | .jsonld.txt | .nq | .nq.txt | .xml | .xml.txt
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np:hasAssertion sub:assertion;
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sub:assertion {
<https://w3id.org/delphi/resource/assessment/wolfram2002-ch04-02--claim-test> a <https://w3id.org/delphi/ontology/Assessment>;
dc:description "analysis.py iterates x -> m x from 1 for 3000 steps for each of the 64 (m, b) pairs using Python integers, converts each power to base-b digits, keeps the interior 25%-75% of digit positions per row, concatenates (one byte per digit) and lzma-compresses; it also computes digit-value frequencies in the window. Per-pair results are in derived/pairs.csv. Runtime about 4 minutes.";
<http://www.w3.org/2000/01/rdf-schema#comment> "Measured: 43 pairs (m,b) with m not a power of b whose interior digit array is 'complex' by the pre-registered criteria (n = 53). Interpretation: Wolfram's 'even rather simple systems based on numbers can lead to highly complex behavior' (p. 115) is illustrated by the digit sequences of successive powers (p. 116-120: 2^t in base 2 is trivial, 3^t in base 2 looks random). 'Highly complex behavior' is read as digit arrays that a general-purpose compressor cannot reduce below 80% of their entropy bound and whose digit frequencies are uniform to within 2%, in explicit contrast to the trivial members of the same family that compress to below 10%. The claim is existential; the family is the smallest natural one containing the book's opening examples. The window excludes the leading digits (biased by Benford-type effects) and trailing digits (eventually periodic in t at fixed position, and all zero when b divides m).";
<http://www.w3.org/2000/01/rdf-schema#label> "Claim test of wolfram2002-ch04-02: supports, confidence 0.9";
<http://www.w3.org/2000/01/rdf-schema#seeAlso> <https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch04-02/result.json>;
prov:wasAttributedTo <https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1>;
<https://w3id.org/delphi/ontology/admissibleDatasets> "Planned datasets: nks-powers-digit-arrays";
<https://w3id.org/delphi/ontology/assessmentType> "claim-test/0.1.0";
<https://w3id.org/delphi/ontology/dataKind> "computational";
<https://w3id.org/delphi/ontology/disconfirmingObservation> "Pre-registered. The claim FAILS if no pair with m not a power of b is 'complex' (every such digit array compresses below 0.8 log2(b) bits per digit or has digit frequencies deviating from uniform by more than 0.02). If any trivial pair (m a power of b) is not 'simple', the measure lacks discriminating power and the verdict is inconclusive (not-operationalizable).";
<https://w3id.org/delphi/ontology/evidenceAgainst> "Incompressibility by lzma over about 3.6 million interior digits (for 3^t in base 2: 1.086 bits/digit, digit frequencies within 0.0004 of 1/2) is evidence against periodic or nested structure at these scales, not a proof of normality; the digits of 3^t in base 2 are not proven to be normal.",
"The 10 non-complex non-trivial pairs split into two explicable groups: (2,4), (2,8), (4,8), (8,4), (3,9) where m and b are powers of a common integer (the pre-registered 'm is a power of b' control missed this symmetric case; they compress to < 0.001 of the bound, i.e. are trivially regular), and the five m = 6 pairs in bases 2, 3, 4, 8, 9 where the trailing zeros of 6^t = 2^t 3^t occupy 1/log_b(6) of each row and intrude into the fixed 25%-75% window, lowering compression ratios to 0.30-0.83 and biasing digit frequencies.",
"The test covers the book's opening family (powers in positional notation) only; the claim's other illustrations in Chapter 4 (e.g. the 3n/2 system, iterated maps) were not tested.";
<https://w3id.org/delphi/ontology/expectedObservation> "Pre-registered. Family: all pairs (m, b) with multiplier m in 2..9 and base b in 2..9, iterating x_{t+1} = m x_t from x_0 = 1 for t = 1..T = 3000 (i.e. the digits of m^t). For each pair build the digit array of rows m^t written in base b; take the interior window of each row consisting of digit positions between 25% and 75% of that row's length (least significant digit = position 0), concatenate all interior digits in row order into one byte string (one digit per byte). Measure (i) bits per digit = 8 * lzma(preset 9|EXTREME) compressed size / number of digits; (ii) maximum absolute deviation of any digit-value frequency from 1/b. A pair is 'complex' if (i) >= 0.8 * log2(b) and (ii) <= 0.02; a pair is 'simple' if (i) < 0.1 * log2(b). The claim PASSES if at least one pair with m not a power of b is 'complex' AND every pair with m a power of b (m = b^j, j >= 1, e.g. (2,2), (4,2), (8,2), (9,3), (3,3), ...) is 'simple' (validity check that the measure separates trivially regular digit arrays). Reported, not decisive: how many of the 64 pairs are complex, and whether the pairs with m and b sharing all prime factors (e.g. (6,2), (4,8), (2,4)) behave differently.";
<https://w3id.org/delphi/ontology/failCriterion> "Pre-registered. The claim FAILS if no pair with m not a power of b is 'complex' (every such digit array compresses below 0.8 log2(b) bits per digit or has digit frequencies deviating from uniform by more than 0.02). If any trivial pair (m a power of b) is not 'simple', the measure lacks discriminating power and the verdict is inconclusive (not-operationalizable).";
<https://w3id.org/delphi/ontology/hasConfidence> "0.9"^^xsd:double;
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<https://w3id.org/delphi/ontology/hasVerdict> "supports";
<https://w3id.org/delphi/ontology/hypothesis> "Within the family of the simplest arithmetic iterations, repeated multiplication by a fixed small integer m viewed as a base-b digit array (Wolfram's opening example, pp. 116-120), some members produce digit arrays whose interior is incompressible with digit frequencies indistinguishable from uniform, while the trivial members (m a power of b) are detected as highly compressible.";
<https://w3id.org/delphi/ontology/inferenceMethod> "analysis.py iterates x -> m x from 1 for 3000 steps for each of the 64 (m, b) pairs using Python integers, converts each power to base-b digits, keeps the interior 25%-75% of digit positions per row, concatenates (one byte per digit) and lzma-compresses; it also computes digit-value frequencies in the window. Per-pair results are in derived/pairs.csv. Runtime about 4 minutes.";
<https://w3id.org/delphi/ontology/passCriterion> "Pre-registered. Family: all pairs (m, b) with multiplier m in 2..9 and base b in 2..9, iterating x_{t+1} = m x_t from x_0 = 1 for t = 1..T = 3000 (i.e. the digits of m^t). For each pair build the digit array of rows m^t written in base b; take the interior window of each row consisting of digit positions between 25% and 75% of that row's length (least significant digit = position 0), concatenate all interior digits in row order into one byte string (one digit per byte). Measure (i) bits per digit = 8 * lzma(preset 9|EXTREME) compressed size / number of digits; (ii) maximum absolute deviation of any digit-value frequency from 1/b. A pair is 'complex' if (i) >= 0.8 * log2(b) and (ii) <= 0.02; a pair is 'simple' if (i) < 0.1 * log2(b). The claim PASSES if at least one pair with m not a power of b is 'complex' AND every pair with m a power of b (m = b^j, j >= 1, e.g. (2,2), (4,2), (8,2), (9,3), (3,3), ...) is 'simple' (validity check that the measure separates trivially regular digit arrays). Reported, not decisive: how many of the 64 pairs are complex, and whether the pairs with m and b sharing all prime factors (e.g. (6,2), (4,8), (2,4)) behave differently.";
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dc:license <https://creativecommons.org/licenses/by/4.0/>;
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<http://www.w3.org/2000/01/rdf-schema#label> "Claim test of wolfram2002-ch04-02: supports, confidence 0.9";
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