https://w3id.org/np/RAECjs40RtLdprBQJH6eieZzcabeTZCIxjKWlyfCrEmJ8/Head https://w3id.org/np/RAECjs40RtLdprBQJH6eieZzcabeTZCIxjKWlyfCrEmJ8 http://www.nanopub.org/nschema#hasAssertion https://w3id.org/np/RAECjs40RtLdprBQJH6eieZzcabeTZCIxjKWlyfCrEmJ8/assertion https://w3id.org/np/RAECjs40RtLdprBQJH6eieZzcabeTZCIxjKWlyfCrEmJ8 http://www.nanopub.org/nschema#hasProvenance https://w3id.org/np/RAECjs40RtLdprBQJH6eieZzcabeTZCIxjKWlyfCrEmJ8/provenance https://w3id.org/np/RAECjs40RtLdprBQJH6eieZzcabeTZCIxjKWlyfCrEmJ8 http://www.nanopub.org/nschema#hasPublicationInfo https://w3id.org/np/RAECjs40RtLdprBQJH6eieZzcabeTZCIxjKWlyfCrEmJ8/pubinfo https://w3id.org/np/RAECjs40RtLdprBQJH6eieZzcabeTZCIxjKWlyfCrEmJ8 http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.nanopub.org/nschema#Nanopublication https://w3id.org/np/RAECjs40RtLdprBQJH6eieZzcabeTZCIxjKWlyfCrEmJ8/assertion https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-10--claim-test http://purl.org/dc/terms/description analysis.py enumerates every neighbour-independent substitution system in the two pre-registered families (225 + 2197 systems), iterates each from every single colour (7041 runs) until the string has at least 2^15 symbols, dies, becomes bounded or exceeds 40000 steps, and computes the subword complexity p(n) for n = 1..20 of the first <= 2^17 symbols of every growing run (5109 runs; 24 slow linear-growth runs are analysed at the ~20000 symbols they reached). The same statistics are computed for the pre-registered neighbour-dependent control family (1296 systems, 2592 runs, <= 2000 steps) and, exploratorily, for 1500 random three-context systems. The Thue-Morse and Fibonacci systems are compared with the OEIS b-files, and a random 2^15-bit string gives the complexity reference. Run time about 9 minutes (the slow linear-growth systems dominate). https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-10--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-ch03-10--claim-test http://www.w3.org/2000/01/rdf-schema#comment Measured: 231 maximum subword complexity p(20) over all 5109 growing neighbour-independent runs (random reference 32319) (n = 5109, exact). Interpretation: Wolfram's 'nested pattern' is given a formal operational content as low (sub-exponential, at most polynomial) subword complexity, which is the standard combinatorial signature of self-similar/morphic sequences: the Thue-Morse, Fibonacci and Cantor examples he gives all have p(n) = O(n). Rules whose replacement for some colour is the empty string, or that keep every string bounded, are included in the enumeration but can only give finite or eventually periodic output, which is trivially nested; the complexity test is applied to growing runs only. The claim's second half ('more complicated behaviour requires neighbour dependence') is tested only in the direction that neighbour-dependent systems can exceed the complexity bound, as a check of discriminating power; the universal statement itself is tested by exhaustive enumeration of two finite families. https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-10--claim-test http://www.w3.org/2000/01/rdf-schema#label Claim test of wolfram2002-ch03-10: inconclusive, confidence 0.7 https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-10--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-ch03-10/result.json https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-10--claim-test http://www.w3.org/ns/prov#wasAttributedTo https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-10--claim-test https://w3id.org/delphi/ontology/admissibleDatasets Planned datasets: neighbour-independent-substitution-systems, neighbour-dependent-control-systems, oeis-a010060-bfile, oeis-a003849-bfile https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-10--claim-test https://w3id.org/delphi/ontology/assessmentType claim-test/0.1.0 https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-10--claim-test https://w3id.org/delphi/ontology/dataKind computational https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-10--claim-test https://w3id.org/delphi/ontology/disconfirmingObservation Pre-registered: 'refutes' if any growing neighbour-independent run has p(20) > 10^4 or p(20)/p(10) > 8, or if the Thue-Morse or Fibonacci outputs disagree with the OEIS b-files; 'inconclusive' if the control family contains no system exceeding the thresholds (the complexity measure would then be too weak to distinguish nested from more complicated behaviour). https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-10--claim-test https://w3id.org/delphi/ontology/evidenceAgainst 24 three-colour runs grow more slowly than one symbol per step and did not reach 2^15 symbols in 40000 steps; they were analysed at about 20000 symbols and have p(20) <= 2. The slow systems (150 runs) in the control family were not analysed. Dying and bounded systems (trivially nested or periodic) are counted but not complexity-tested. https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-10--claim-test https://w3id.org/delphi/ontology/evidenceAgainst Descriptively, the two families are nonetheless separated by an order of magnitude (max p(20) 231 vs 2496/2950; max ratio 3.56 vs 5.25/6.13, i.e. neighbour-dependent systems exceed the quadratic bound while neighbour-independent ones never do); a re-test with thresholds set at the quadratic bound (ratio > 4.5) and p(20) > 1000 would, on these data, yield 'supports'. Those thresholds were not pre-registered, so the result is not reported as such. https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-10--claim-test https://w3id.org/delphi/ontology/evidenceAgainst Every claim-side criterion passed exactly as pre-registered: 0 of 5109 growing neighbour-independent runs exceed p(20) <= 10^4 or p(20)/p(10) <= 8 (maxima 231 and 3.56, against 32319 and 31.6 for a random string; the ratio never exceeds the quadratic value 4, as Pansiot's theorem predicts for morphic words), and the Thue-Morse and Fibonacci outputs match OEIS A010060 (16384 terms) and A003849 (10946 terms) without error. https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-10--claim-test https://w3id.org/delphi/ontology/evidenceAgainst The pre-registered discriminating-power control failed: no system in the pair-context neighbour-dependent family reached p(20) > 20000 and p(20)/p(10) > 8 (maxima 2496 and 5.25 within 2000 steps); the exploratory three-context sample also fell short (2950 and 6.13). The pre-registration states that in this case the verdict is at most 'inconclusive', and that rule is followed here, with reason 'underpowered': the chosen thresholds presupposed random-level complexity, which small neighbour-dependent families do not reach in 2000 steps, so the test cannot certify that its complexity measure separates nested from merely 'more complicated' behaviour at the pre-set thresholds. https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-10--claim-test https://w3id.org/delphi/ontology/expectedObservation Pre-registered: enumerate exhaustively (a) all 225 neighbour-independent systems with 2 colours and replacement strings of length 0..3, and (b) all 2197 systems with 3 colours and replacement strings of length 0..2; start each from each single colour and iterate until the string has at least 2^15 symbols (or the string dies out, stays bounded for 60 steps, or exceeds 10^6 symbols). For every run that reaches 2^15 symbols ('growing'), compute the subword complexity p(n) (number of distinct length-n factors) of the first min(len, 2^17) symbols for n = 1..20. The claim passes if every growing neighbour-independent run has p(20) <= 10^4 and p(20)/p(10) <= 8 (a quadratic law gives 4, an exponential law about 2^10), and if the Thue-Morse system {0 -> 01, 1 -> 10} reproduces OEIS A010060 and the Fibonacci system {0 -> 01, 1 -> 0} reproduces OEIS A003849 term for term over the available b-file terms. Discriminating power: the neighbour-dependent control family (2 colours, replacement of each element determined by the pair (element, right neighbour), replacement strings of length 1 or 2, 1296 systems, right-most element paired with colour 0) must contain at least one system whose growing run has p(20) > 2 x 10^4 and p(20)/p(10) > 8; otherwise the test cannot separate the two families and the verdict is at most 'inconclusive'. https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-10--claim-test https://w3id.org/delphi/ontology/failCriterion Pre-registered: 'refutes' if any growing neighbour-independent run has p(20) > 10^4 or p(20)/p(10) > 8, or if the Thue-Morse or Fibonacci outputs disagree with the OEIS b-files; 'inconclusive' if the control family contains no system exceeding the thresholds (the complexity measure would then be too weak to distinguish nested from more complicated behaviour). https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-10--claim-test https://w3id.org/delphi/ontology/hasConfidence 0.7 https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-10--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch03-10--claim-test--dataset-1 https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-10--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch03-10--claim-test--dataset-2 https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-10--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch03-10--claim-test--dataset-3 https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-10--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch03-10--claim-test--dataset-4 https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-10--claim-test https://w3id.org/delphi/ontology/hasVerdict inconclusive https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-10--claim-test https://w3id.org/delphi/ontology/hypothesis Every parallel substitution system in which each element is replaced according to its own colour alone (a context-free morphism iterated from a single element) produces a nested pattern: operationally, the sequence it generates has sub-exponential subword complexity (at most quadratic, as Pansiot's theorem gives for pure morphic words), never the near-maximal complexity of a random or 'complex' sequence; whereas substitution systems whose replacement depends on a neighbouring element can produce sequences of near-maximal subword complexity. https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-10--claim-test https://w3id.org/delphi/ontology/inferenceMethod analysis.py enumerates every neighbour-independent substitution system in the two pre-registered families (225 + 2197 systems), iterates each from every single colour (7041 runs) until the string has at least 2^15 symbols, dies, becomes bounded or exceeds 40000 steps, and computes the subword complexity p(n) for n = 1..20 of the first <= 2^17 symbols of every growing run (5109 runs; 24 slow linear-growth runs are analysed at the ~20000 symbols they reached). The same statistics are computed for the pre-registered neighbour-dependent control family (1296 systems, 2592 runs, <= 2000 steps) and, exploratorily, for 1500 random three-context systems. The Thue-Morse and Fibonacci systems are compared with the OEIS b-files, and a random 2^15-bit string gives the complexity reference. Run time about 9 minutes (the slow linear-growth systems dominate). https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-10--claim-test https://w3id.org/delphi/ontology/passCriterion Pre-registered: enumerate exhaustively (a) all 225 neighbour-independent systems with 2 colours and replacement strings of length 0..3, and (b) all 2197 systems with 3 colours and replacement strings of length 0..2; start each from each single colour and iterate until the string has at least 2^15 symbols (or the string dies out, stays bounded for 60 steps, or exceeds 10^6 symbols). For every run that reaches 2^15 symbols ('growing'), compute the subword complexity p(n) (number of distinct length-n factors) of the first min(len, 2^17) symbols for n = 1..20. The claim passes if every growing neighbour-independent run has p(20) <= 10^4 and p(20)/p(10) <= 8 (a quadratic law gives 4, an exponential law about 2^10), and if the Thue-Morse system {0 -> 01, 1 -> 10} reproduces OEIS A010060 and the Fibonacci system {0 -> 01, 1 -> 0} reproduces OEIS A003849 term for term over the available b-file terms. Discriminating power: the neighbour-dependent control family (2 colours, replacement of each element determined by the pair (element, right neighbour), replacement strings of length 1 or 2, 1296 systems, right-most element paired with colour 0) must contain at least one system whose growing run has p(20) > 2 x 10^4 and p(20)/p(10) > 8; otherwise the test cannot separate the two families and the verdict is at most 'inconclusive'. https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-10--claim-test https://w3id.org/delphi/ontology/preregistered false https://w3id.org/delphi/resource/claim/wolfram2002-ch03-10 https://w3id.org/delphi/ontology/hasAssessment https://w3id.org/delphi/resource/assessment/wolfram2002-ch03-10--claim-test https://w3id.org/delphi/resource/evidence/wolfram2002-ch03-10--claim-test--dataset-1 http://purl.org/dc/terms/description exhaustive test of the universal statement https://w3id.org/delphi/resource/evidence/wolfram2002-ch03-10--claim-test--dataset-1 http://purl.org/dc/terms/license https://w3id.org/delphi/resource/evidence/wolfram2002-ch03-10--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-ch03-10--claim-test--dataset-1 http://www.w3.org/2000/01/rdf-schema#label Dataset: All 225 two-colour (replacement length 0..3) and 2197 three-colour (replacement length 0..2) neighbour-independent substitution systems iterated from each single colour (generated by analysis.py) https://w3id.org/delphi/resource/evidence/wolfram2002-ch03-10--claim-test--dataset-2 http://purl.org/dc/terms/description discriminating-power control https://w3id.org/delphi/resource/evidence/wolfram2002-ch03-10--claim-test--dataset-2 http://purl.org/dc/terms/license https://w3id.org/delphi/resource/evidence/wolfram2002-ch03-10--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-ch03-10--claim-test--dataset-2 http://www.w3.org/2000/01/rdf-schema#label Dataset: All 1296 two-colour systems whose replacement (length 1..2) depends on the pair (element, right neighbour), plus 1500 random three-context systems (generated by analysis.py) https://w3id.org/delphi/resource/evidence/wolfram2002-ch03-10--claim-test--dataset-3 http://purl.org/dc/terms/description external check of the Thue-Morse substitution output https://w3id.org/delphi/resource/evidence/wolfram2002-ch03-10--claim-test--dataset-3 http://purl.org/dc/terms/license CC BY-SA 4.0 (OEIS) https://w3id.org/delphi/resource/evidence/wolfram2002-ch03-10--claim-test--dataset-3 http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/EvidenceItem https://w3id.org/delphi/resource/evidence/wolfram2002-ch03-10--claim-test--dataset-3 http://www.w3.org/2000/01/rdf-schema#label Dataset: OEIS A010060: Thue-Morse sequence, b-file 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