rows { options { physical_type: PHYSICAL_STREAM_TYPE_QUADS max_name_table_size: 128 max_prefix_table_size: 16 max_datatype_table_size: 16 logical_type: LOGICAL_STREAM_TYPE_DATASETS version: 2 } } rows { prefix { value: "https://w3id.org/np/" } } rows { name { value: "RAXWgdaXUHnA2ZafcwGdd9CoR1ehv_62T47DCvWAKvYR8" } } rows { namespace { name: "this" value { prefix_id: 1 } } } rows { prefix { value: "https://w3id.org/np/RAXWgdaXUHnA2ZafcwGdd9CoR1ehv_62T47DCvWAKvYR8/" } } rows { name { } } rows { namespace { name: "sub" value { prefix_id: 2 } } } rows { prefix { value: "http://www.nanopub.org/nschema#" } } rows { namespace { name: "np" value { prefix_id: 3 name_id: 2 } } } rows { prefix { value: "http://www.w3.org/1999/02/22-rdf-syntax-ns#" } } rows { namespace { name: "rdf" value { prefix_id: 4 name_id: 2 } } } rows { prefix { value: "http://www.w3.org/ns/prov#" } } rows { namespace { name: "prov" value { prefix_id: 5 name_id: 2 } } } rows { prefix { value: "http://purl.org/nanopub/x/" } } rows { namespace { name: "npx" value { prefix_id: 6 name_id: 2 } } } rows { prefix { value: "http://purl.org/dc/terms/" } } rows { namespace { name: "dc" value { prefix_id: 7 name_id: 2 } } } rows { prefix { value: "http://www.w3.org/2001/XMLSchema#" } } rows { namespace { name: "xsd" value { prefix_id: 8 name_id: 2 } } } rows { name { value: "hasAssertion" } } rows { name { value: "assertion" } } rows { name { value: "Head" } } rows { quad { s_iri { prefix_id: 1 name_id: 1 } p_iri { prefix_id: 3 name_id: 3 } o_iri { prefix_id: 2 } g_iri { } } } rows { name { value: "hasProvenance" } } rows { name { value: "provenance" } } rows { quad { p_iri { prefix_id: 3 } o_iri { prefix_id: 2 } } } rows { name { value: "hasPublicationInfo" } } rows { name { value: "pubinfo" } } rows { quad { p_iri { prefix_id: 3 } o_iri { prefix_id: 2 } } } rows { name { value: "type" } } rows { name { value: "Nanopublication" } } rows { quad { p_iri { prefix_id: 4 } o_iri { prefix_id: 3 } } } rows { prefix { value: "https://w3id.org/delphi/resource/assessment/" } } rows { name { value: "wolfram2002-ch04-02--claim-test" } } rows { name { value: "description" } } rows { quad { s_iri { prefix_id: 9 } p_iri { prefix_id: 7 } o_literal { lex: "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." } g_iri { prefix_id: 2 name_id: 4 } } } rows { prefix { value: "https://w3id.org/delphi/ontology/" } } rows { name { value: "Assessment" } } rows { quad { p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 10 name_id: 14 } } } rows { prefix { value: "http://www.w3.org/2000/01/rdf-schema#" } } rows { name { value: "comment" } } rows { quad { p_iri { prefix_id: 11 } o_literal { lex: "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)." } } } rows { name { value: "label" } } rows { quad { p_iri { } o_literal { lex: "Claim test of wolfram2002-ch04-02: supports, confidence 0.9" } } } rows { name { value: "seeAlso" } } rows { prefix { value: "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch04-02/" } } rows { name { value: "result.json" } } rows { quad { p_iri { } o_iri { prefix_id: 12 } } } rows { name { value: "wasAttributedTo" } } rows { prefix { value: "https://w3id.org/delphi/resource/agent/" } } rows { name { value: "delphisci-claim-tester-claude-fable-5-1" } } rows { quad { p_iri { prefix_id: 5 } o_iri { prefix_id: 13 } } } rows { name { value: "admissibleDatasets" } } rows { quad { p_iri { prefix_id: 10 } o_literal { lex: "Planned datasets: nks-powers-digit-arrays" } } } rows { name { value: "assessmentType" } } rows { quad { p_iri { } o_literal { lex: "claim-test/0.1.0" } } } rows { name { value: "dataKind" } } rows { quad { p_iri { } o_literal { lex: "computational" } } } rows { name { value: "disconfirmingObservation" } } rows { quad { p_iri { } o_literal { lex: "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)." } } } rows { name { value: "evidenceAgainst" } } rows { quad { p_iri { } o_literal { lex: "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." } } } rows { quad { o_literal { lex: "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." } } } rows { quad { o_literal { lex: "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." } } } rows { name { value: "expectedObservation" } } rows { quad { p_iri { } o_literal { lex: "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." } } } rows { name { value: "failCriterion" } } rows { quad { p_iri { } o_literal { lex: "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)." } } } rows { name { value: "hasConfidence" } } rows { datatype { value: "http://www.w3.org/2001/XMLSchema#double" } } rows { quad { p_iri { } o_literal { lex: "0.9" datatype: 1 } } } rows { name { value: "hasEvidence" } } rows { prefix { value: "https://w3id.org/delphi/resource/evidence/" } } rows { name { value: "wolfram2002-ch04-02--claim-test--dataset-1" } } rows { quad { p_iri { } o_iri { prefix_id: 14 } } } rows { name { value: "hasVerdict" } } rows { quad { p_iri { prefix_id: 10 } o_literal { lex: "supports" } } } rows { name { value: "hypothesis" } } rows { quad { p_iri { } o_literal { lex: "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." } } } rows { name { value: "inferenceMethod" } } rows { quad { p_iri { } o_literal { lex: "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." } } } rows { name { value: "passCriterion" } } rows { quad { p_iri { } o_literal { lex: "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." } } } rows { name { value: "preregistered" } } rows { datatype { value: "http://www.w3.org/2001/XMLSchema#boolean" } } rows { quad { p_iri { } o_literal { lex: "false" datatype: 2 } } } rows { prefix { value: "https://w3id.org/delphi/resource/claim/" } } rows { name { value: "wolfram2002-ch04-02" } } rows { name { value: "hasAssessment" } } rows { quad { s_iri { prefix_id: 15 } p_iri { prefix_id: 10 } o_iri { prefix_id: 9 name_id: 12 } } } rows { quad { s_iri { prefix_id: 14 name_id: 30 } p_iri { prefix_id: 7 name_id: 13 } o_literal { lex: "program family under test" } } } rows { name { value: "license" } } rows { quad { p_iri { name_id: 38 } o_literal { lex: "generated data" } } } rows { name { value: "EvidenceItem" } } rows { quad { p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 10 name_id: 39 } } } rows { quad { p_iri { prefix_id: 11 name_id: 16 } o_literal { lex: "Dataset: Digit arrays of m^t in base b for m, b in 2..9, t = 1..3000 (generated by analysis.py)" } } } rows { name { value: "wasDerivedFrom" } } rows { prefix { value: "https://www.wolframscience.com/nks/p116--elementary-arithmetic/" } } rows { quad { p_iri { prefix_id: 5 name_id: 40 } o_iri { prefix_id: 16 name_id: 2 } } } rows { name { value: "SoftwareAgent" } } rows { quad { s_iri { prefix_id: 13 name_id: 20 } p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 5 name_id: 41 } g_iri { prefix_id: 2 name_id: 7 } } } rows { quad { p_iri { prefix_id: 11 name_id: 16 } o_literal { lex: "delphisci claim tester (claude-fable-5.1; cursor/wolfram-nks-claim-tests-106e)" } } } rows { name { value: "actedOnBehalfOf" } } rows { prefix { id: 6 value: "https://orcid.org/" } } rows { name { value: "0009-0007-4948-9192" } } rows { quad { p_iri { prefix_id: 5 name_id: 42 } o_iri { prefix_id: 6 } } } rows { name { value: "usesModel" } } rows { prefix { id: 8 value: "https://w3id.org/delphi/resource/model/" } } rows { name { value: "claude-fable-5-1" } } rows { quad { p_iri { prefix_id: 10 } o_iri { prefix_id: 8 } } } rows { name { value: "identifier" } } rows { quad { s_iri { name_id: 45 } p_iri { prefix_id: 7 } o_literal { lex: "claude-fable-5.1" } } } rows { name { value: "LanguageModel" } } rows { quad { p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 10 name_id: 47 } } } rows { quad { s_iri { prefix_id: 2 name_id: 4 } p_iri { prefix_id: 5 name_id: 19 } o_iri { prefix_id: 13 } } } rows { quad { p_iri { prefix_id: 5 name_id: 40 } o_iri { prefix_id: 12 name_id: 18 } } } rows { name { value: "wasGeneratedBy" } } rows { name { value: "test" } } rows { quad { p_iri { prefix_id: 5 name_id: 48 } o_iri { prefix_id: 2 } } } rows { name { value: "plan" } } rows { name { value: "hadPlan" } } rows { prefix { id: 1 value: "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/" } } rows { name { value: "README.md" } } rows { quad { s_iri { } p_iri { prefix_id: 5 } o_iri { prefix_id: 1 } } } rows { name { value: "Activity" } } rows { quad { s_iri { prefix_id: 2 name_id: 49 } p_iri { prefix_id: 4 name_id: 10 } o_iri { prefix_id: 5 name_id: 53 } } } rows { name { value: "qualifiedAssociation" } } rows { quad { p_iri { } o_iri { prefix_id: 2 name_id: 50 } } } rows { name { value: "wasAssociatedWith" } } rows { quad { p_iri { prefix_id: 5 name_id: 55 } o_iri { prefix_id: 13 name_id: 20 } } } rows { prefix { id: 3 value: "https://w3id.org/np/" } } rows { name { value: "created" } } rows { datatype { value: "http://www.w3.org/2001/XMLSchema#dateTime" } } rows { quad { s_iri { prefix_id: 3 name_id: 1 } p_iri { prefix_id: 7 name_id: 56 } o_literal { lex: "2026-11-08T16:24:31.921Z" datatype: 3 } g_iri { prefix_id: 2 name_id: 9 } } } rows { name { value: "creator" } } rows { quad { p_iri { prefix_id: 7 name_id: 57 } o_iri { prefix_id: 6 name_id: 43 } } } rows { prefix { id: 15 value: "https://creativecommons.org/licenses/by/4.0/" } } rows { quad { p_iri { prefix_id: 7 name_id: 38 } o_iri { prefix_id: 15 name_id: 2 } } } rows { prefix { id: 9 value: "http://purl.org/nanopub/x/" } } rows { name { value: "hasNanopubType" } } rows { quad { p_iri { prefix_id: 9 name_id: 58 } o_iri { prefix_id: 10 name_id: 14 } } } rows { name { value: "introduces" } } rows { prefix { id: 14 value: "https://w3id.org/delphi/resource/assessment/" } } rows { quad { p_iri { prefix_id: 9 name_id: 59 } o_iri { prefix_id: 14 name_id: 12 } } } rows { quad { p_iri { prefix_id: 11 name_id: 16 } o_literal { lex: "Claim test of wolfram2002-ch04-02: supports, confidence 0.9" } } } rows { name { value: "domain" } } rows { prefix { id: 16 value: "https://w3id.org/delphi/resource/domain/" } } rows { name { value: "wolfram-nks-2002" } } rows { quad { p_iri { prefix_id: 10 name_id: 60 } o_iri { prefix_id: 16 } } } rows { name { value: "sig" } } rows { name { value: "hasAlgorithm" } } rows { quad { s_iri { prefix_id: 2 } p_iri { prefix_id: 9 } o_literal { lex: "RSA" } } } rows { name { value: "hasPublicKey" } } rows { quad { p_iri { } o_literal { lex: "MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB" } } } rows { name { value: "hasSignature" } } rows { quad { p_iri { } o_literal { lex: "vvghdkKrT/B/AZgida2bCbGxx8E3Xcqgm4X2JC11HkWrDaUvcJ/4MywADbUYeJIg9MUQTq1wWQJmbeO5vuCv2IdgVaXkSydOhcxS+NoLQnAiANz/GyX89N99wlwxOKw+vx3Vm58CF5PfTtJUIqHjcYllTbRT3aXU3LkeGKIGESjnVxecIY5yWY0SR+YhwGFXZcAtXhoyvVG3N0v+G651fVACRwkpFIzc3tuiWcmGqcYM5CTrmSQoRj5PlA/dxRDFFsnWFhEhFwvmCGcXR+qLBIsjwSgeUqMMODeJvwYTg+U2rT+B6E+rnRbuOUTTURNHGAigJ0MKxzq/NUe/Wfd4sg==" } } } rows { name { value: "hasSignatureTarget" } } rows { quad { p_iri { } o_iri { prefix_id: 3 name_id: 1 } } } rows { name { value: "signedBy" } } rows { quad { p_iri { prefix_id: 9 name_id: 67 } o_iri { prefix_id: 6 name_id: 43 } } }