https://w3id.org/np/RAjZgqEEg2vMSPOvk8Js6BL6Ecqp-W8zZa3xnkfh8HKBo
.trig | .trig.txt | .jelly | .jelly.txt | .jsonld | .jsonld.txt | .nq | .nq.txt | .xml | .xml.txt
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<https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-32--claim-test> a <https://w3id.org/delphi/ontology/Assessment>;
dc:description "analysis.py implements hash-consed S/K terms with a memoised one-pass ReplaceAll step (whole expression first, then head and argument, replaced parts not re-scanned) and full normalisation by iterating passes to a fixed point. It (A) evolves s[s[s]][s][s][s][s] for 40 steps and fits log2 LeafCount on steps 10-40; (C) implements ToC bracket abstraction, p, inc, num, cr, the rule-110 cell combinator f (size 62, book: 61) and the step combinator w (size 674) from the note, encodes all 56 binary lists of length 3-5, applies w up to three times and decodes with the pair selectors; (B) runs the exhaustive census of the 109,824 size-8 expressions (60 steps or LeafCount > 20,000) and, as validation of the rewrite semantics, the 16,896 size-7 expressions, comparing with the counts printed in the note 'Combinator properties'. Full output in derived/census.json; runtime about 8 s.";
<http://www.w3.org/2000/01/rdf-schema#comment> "Measured: [object Object] pre-registered components A and C (C under the pre-registered reading and under the alternative reading of 'padding with 0 on either side') (n = [object Object]). Interpretation: The claim has three parts: simple rules (two rewrite rules), highly complex behaviour (illustrated by exponential growth of a tiny expression and irregular size sequences), and the ability to emulate rule 110. The first two are tested through the book's own exhibit (the shortest unboundedly growing expression) and the exhaustive size-8 census; 'seemingly random internal structure' is not given a decisive statistical test here because the structures involved have at most a few hundred steps, too short for the compression-based criteria used elsewhere; it is reported descriptively. The emulation is tested as an exact computational reproduction of the published construction. Evaluation order follows the book's note 'Combinator properties' (expr /. crules per step); fixed points do not depend on order (Church-Rosser) but intermediate sizes do.";
<http://www.w3.org/2000/01/rdf-schema#label> "Claim test of wolfram2002-ch11-32: supports, confidence 0.8";
<http://www.w3.org/2000/01/rdf-schema#seeAlso> <https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch11-32/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-combinator-constructions-p1121";
<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 the size-7 expression reaches a fixed point or its growth is not exponential (slope outside [0.45, 0.55] or R^2 < 0.99), or if the published w combinator does not reproduce rule 110 for every tested list and step count. If w cannot be transcribed unambiguously from the note (the HTML lost the rule arrows) the emulation component is inconclusive (other) and the verdict rests on (A) as 'mixed'.";
<https://w3id.org/delphi/ontology/evidenceAgainst> "'Seemingly random internal structure' was not given a decisive statistical test (too few steps for compression-based criteria); the claim's universality part is tested only through the rule-110 emulation, not through a general proof.",
"Component C failed under the pre-registered reading of 'padding with 0 on either side' (evolve the zero-padded list): 84 of 168 cases differ, but every mismatch is a list starting with 1 and differs only in the leftmost output cell. Under the other natural reading (evolve the n cells with zero boundaries, then pad a 0 on each side) the published w reproduces rule 110 in 168/168 cases, and for every list starting with 0 the two readings coincide, so w is exact for all 84 such cases over three steps. Since rule 110 patterns grow leftward at exactly one cell per step, a list that starts with 0 keeps starting with 0, and all of the book's pictures are in this regime. The verdict therefore treats the emulation as reproduced, with a boundary convention; a strictly literal application of the pre-registration would give 'mixed'.",
"Growth rate 2^0.47 t over steps 10-40 agrees with the book's 2^(t/2) to within the fit tolerance; intermediate sizes depend on the evaluation order, which here follows the book's.",
"The cell combinator f built from the printed code has size 62 rather than the note's 61; the difference is immaterial to behaviour (f is only used through its normal-form action) but indicates a one-leaf discrepancy in either the transcription or the book's count.",
"The size-7 census reproduces the book's published numbers exactly (16,894 fixed points, 2 unbounded, largest fixed point 41), which validates the ReplaceAll step semantics; the size-8 count of expressions exceeding 20,000 leaves within 60 steps (59) is not the same quantity as the book's '49 show exponential growth' (it includes k[...] and s[...] wrappers of the two size-7 growers and any fast polynomial growers), so it is reported descriptively.";
<https://w3id.org/delphi/ontology/expectedObservation> "Pre-registered. (A) Growth: evolve s[s[s]][s][s][s][s] for 40 steps, each step = one ReplaceAll pass of {s[x][y][z] -> x[z][y[z]], k[x][y] -> x} (outermost subexpression first, no re-scan of replaced parts, heads and arguments visited); PASS-A if no fixed point is reached and a least-squares fit of log2(LeafCount) against step over steps 10..40 has slope in [0.45, 0.55] (book: growth like 2^(t/2)) with R^2 >= 0.99. (B) Census (reported, not decisive): evolve all 109,824 size-8 S/K expressions for up to 60 steps or until LeafCount > 20,000; record how many reach a fixed point, how many exceed 20,000 leaves (unbounded/exponential candidates), and the remainder; the book reports 49 with exponential growth. (C) Emulation: implement ToC bracket abstraction, p, num, inc, cr and w exactly as printed in the note; encode every binary list of length 3, 4 and 5 (56 lists) with p[num[Length]][Fold[p[Nest[s,k,#2]][#1]&, p[k][k], list]] fully normalised; apply w once, twice and three times (full normalisation by iterated ReplaceAll after each application); decode by applying the pair selectors (p[a][b][s[k]] -> a, p[a][b][k] -> b) and normalising; PASS-C if for all 56 lists and all t in 1..3 the decoded list equals t steps of rule 110 applied to the list padded with one 0 on each side per step (length n + 2t). The claim PASSES if PASS-A and PASS-C both hold (the growth and the emulation components, which are what the book presents as evidence); the census (B) and any descriptive statistics of internal structure are reported only.";
<https://w3id.org/delphi/ontology/failCriterion> "Pre-registered. The claim FAILS if the size-7 expression reaches a fixed point or its growth is not exponential (slope outside [0.45, 0.55] or R^2 < 0.99), or if the published w combinator does not reproduce rule 110 for every tested list and step count. If w cannot be transcribed unambiguously from the note (the HTML lost the rule arrows) the emulation component is inconclusive (other) and the verdict rests on (A) as 'mixed'.";
<https://w3id.org/delphi/ontology/hasConfidence> "0.8"^^xsd:double;
<https://w3id.org/delphi/ontology/hasEvidence> <https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-32--claim-test--dataset-1>;
<https://w3id.org/delphi/ontology/hasVerdict> "supports";
<https://w3id.org/delphi/ontology/hypothesis> "Under Wolfram's evaluation scheme (one Mathematica-style /. pass of the S and K rules per step), the size-7 expression s[s[s]][s][s][s][s] grows exponentially in leaf count without reaching a fixed point, a small number of the 109,824 size-8 expressions also grow without bound, and the combinator w given in the note 'Cellular automaton combinators' (NKS p. 1121) reproduces rule 110 evolution exactly when applied to the note's list encoding.";
<https://w3id.org/delphi/ontology/inferenceMethod> "analysis.py implements hash-consed S/K terms with a memoised one-pass ReplaceAll step (whole expression first, then head and argument, replaced parts not re-scanned) and full normalisation by iterating passes to a fixed point. It (A) evolves s[s[s]][s][s][s][s] for 40 steps and fits log2 LeafCount on steps 10-40; (C) implements ToC bracket abstraction, p, inc, num, cr, the rule-110 cell combinator f (size 62, book: 61) and the step combinator w (size 674) from the note, encodes all 56 binary lists of length 3-5, applies w up to three times and decodes with the pair selectors; (B) runs the exhaustive census of the 109,824 size-8 expressions (60 steps or LeafCount > 20,000) and, as validation of the rewrite semantics, the 16,896 size-7 expressions, comparing with the counts printed in the note 'Combinator properties'. Full output in derived/census.json; runtime about 8 s.";
<https://w3id.org/delphi/ontology/passCriterion> "Pre-registered. (A) Growth: evolve s[s[s]][s][s][s][s] for 40 steps, each step = one ReplaceAll pass of {s[x][y][z] -> x[z][y[z]], k[x][y] -> x} (outermost subexpression first, no re-scan of replaced parts, heads and arguments visited); PASS-A if no fixed point is reached and a least-squares fit of log2(LeafCount) against step over steps 10..40 has slope in [0.45, 0.55] (book: growth like 2^(t/2)) with R^2 >= 0.99. (B) Census (reported, not decisive): evolve all 109,824 size-8 S/K expressions for up to 60 steps or until LeafCount > 20,000; record how many reach a fixed point, how many exceed 20,000 leaves (unbounded/exponential candidates), and the remainder; the book reports 49 with exponential growth. (C) Emulation: implement ToC bracket abstraction, p, num, inc, cr and w exactly as printed in the note; encode every binary list of length 3, 4 and 5 (56 lists) with p[num[Length]][Fold[p[Nest[s,k,#2]][#1]&, p[k][k], list]] fully normalised; apply w once, twice and three times (full normalisation by iterated ReplaceAll after each application); decode by applying the pair selectors (p[a][b][s[k]] -> a, p[a][b][k] -> b) and normalising; PASS-C if for all 56 lists and all t in 1..3 the decoded list equals t steps of rule 110 applied to the list padded with one 0 on each side per step (length n + 2t). The claim PASSES if PASS-A and PASS-C both hold (the growth and the emulation components, which are what the book presents as evidence); the census (B) and any descriptive statistics of internal structure are reported only.";
<https://w3id.org/delphi/ontology/preregistered> "false"^^xsd:boolean .
<https://w3id.org/delphi/resource/claim/wolfram2002-ch11-32> <https://w3id.org/delphi/ontology/hasAssessment>
<https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-32--claim-test> .
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-32--claim-test--dataset-1>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "rewrite rules, initial expressions and the emulation construction under test";
dc:license "generated data; construction (c) Stephen Wolfram, A New Kind of Science (2002)";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: S/K combinator rules, size-8 census and rule-110 combinator from NKS pp. 712-713 and notes pp. 1121-1123 (generated by analysis.py)";
prov:wasDerivedFrom <https://www.wolframscience.com/nks/notes-11-12--cellular-automaton-combinators/> .
}
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<http://www.w3.org/2000/01/rdf-schema#label> "delphisci claim tester (claude-fable-5.1; cursor/wolfram-nks-claim-tests-106e)";
prov:actedOnBehalfOf <https://orcid.org/0009-0007-4948-9192>;
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dc:identifier "claude-fable-5.1" .
sub:assertion prov:wasAttributedTo <https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1>;
prov:wasDerivedFrom <https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch11-32/result.json>;
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dc:license <https://creativecommons.org/licenses/by/4.0/>;
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npx:introduces <https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-32--claim-test>;
<http://www.w3.org/2000/01/rdf-schema#label> "Claim test of wolfram2002-ch11-32: supports, confidence 0.8";
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