https://w3id.org/np/RAXy0blqw9rPPIrH82x1PKBrkIWFOv5v_JZBbQhoI3Q3A
.trig | .trig.txt | .jelly | .jelly.txt | .jsonld | .jsonld.txt | .nq | .nq.txt | .xml | .xml.txt
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sub:assertion {
<https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-13--claim-test--pr-130>
a <https://w3id.org/delphi/ontology/Assessment>;
dc:description "analysis.py evolves all 256 elementary rules from 64 six-bit programs and four input pairs for 16 steps and reads the cell at position -1. It runs one radius-4 multiplexer, whose new center is the program bit indexed by the two input bits, and a Turing machine that walks from the input bits to that same program bit and writes it on the output cell. A function is realized when one program makes all four inputs match it. Criteria were frozen in commit 093ca8002a77b774b469b965ff599d123fdaefbb before this run.";
<http://www.w3.org/2000/01/rdf-schema#comment> "Measured: 0 boolean functions of two bits realized by one ceiling system and not the other (n = 16, exact). Interpretation: The claim (NKS p. 675) says that as rules grow more capable they pass a threshold of universality, after which the set of computations they can perform is the same, so a more sophisticated rule and a different kind of system gain nothing further about what they can compute. Universality over all partial recursive functions is not a finite enumeration. The computation uses a finite universe that can actually be saturated: all 16 boolean functions of two bits. The radius-4 rule and the Turing machine are different constructions aimed at that ceiling; the elementary rules, including rule 0, are the progressive family underneath. Capability is the set of functions, not the encoding, so the comparison across kinds is extensional. A computation shows these sets are equal as mathematics, not that organisms compute.";
<http://www.w3.org/2000/01/rdf-schema#label> "Claim test of wolfram2002-ch11-13 (pr-130): supports, confidence 0.84";
<http://www.w3.org/2000/01/rdf-schema#seeAlso> <https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch11-13/pr-130/result.json>;
prov:wasAttributedTo <https://w3id.org/delphi/resource/agent/delphisci-claim-tester-grok-4-7>;
<https://w3id.org/delphi/ontology/admissibleDatasets> "Only configurations evolved by analysis.py from the pre-registered encodings. Elementary rules use Wolfram numbers 0..255. The radius-4 rule is the boolean multiplexer stated in the pass criterion, not a Wolfram code number. No external dataset.";
<https://w3id.org/delphi/ontology/assessmentType> "claim-test/0.1.0";
<https://w3id.org/delphi/ontology/dataKind> "computational";
<https://w3id.org/delphi/ontology/disconfirmingObservation> "Rule 0 realizes all 16 functions under the elementary encoding, or some elementary rule realizes more than 16 functions.";
<https://w3id.org/delphi/ontology/evidenceAgainst> "The computation shows that these programs realize the same set of two-bit boolean functions once they can realize all 16, and that rule 0 realizes fewer. It does not show that organisms compute, and it does not prove Turing universality.",
"The largest elementary capability under this encoding is 16 functions, at rule 22. Some elementary rule reaches the same set of 16.",
"The universe of computations is the 16 functions of two bits. Past that ceiling there is no further function of two bits to gain. A richer universe, such as all partial recursive functions, was not enumerated.";
<https://w3id.org/delphi/ontology/expectedObservation> "The radius-4 cellular automaton and the lookup Turing machine each realize all 16 boolean functions of two bits and those two sets are equal, rule 0 realizes at most 4 of them, and no elementary rule realizes more than those 16.";
<https://w3id.org/delphi/ontology/failCriterion> "Pre-registered. REFUTES if |Cap(rule 0)| >= 16 (the null rule already performs every computation in U, so this encoding does not measure a threshold) or if any elementary rule has |Cap| > 16. INCONCLUSIVE with reason 'underpowered' if |Cap(radius-4)| < 16 or |Cap(TM)| < 16 (a system built to sit at the ceiling did not reach it, so equality past the ceiling was not tested). MIXED if both ceiling systems equal U and |Cap(rule 0)| <= 4, but some elementary rule has |Cap| = 16 whose set of functions is a proper subset of U (impossible if cardinality is 16, retained so a counting bug cannot be scored as support) or if the two ceiling sets are both size 16 and unequal. Two size-16 subsets of a 16-element set are equal, so a reported inequality at size 16 is a counting error and is MIXED rather than a refutation of the book. Confidence: mixed 0.70, refutes 0.80, inconclusive 0.50.";
<https://w3id.org/delphi/ontology/hasConfidence> "0.84"^^xsd:double;
<https://w3id.org/delphi/ontology/hasEvidence> <https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-13--claim-test--pr-130--dataset-1>;
<https://w3id.org/delphi/ontology/hasVerdict> "supports";
<https://w3id.org/delphi/ontology/hypothesis> "Once a system can realize every boolean function of two bits, a structurally richer system that can also realize every such function realizes exactly the same set, while a system with no information flow realizes a strictly smaller set.";
<https://w3id.org/delphi/ontology/inferenceMethod> "Compare the sets of realized truth tables. Supports when both ceiling systems equal the full 16 and rule 0 is at most 4. Inconclusive (underpowered) when a ceiling system misses the full set. Refutes when rule 0 is already at the ceiling or a cardinality exceeds 16. Confidence: supports 0.84, mixed 0.70, refutes 0.80, inconclusive 0.50.";
<https://w3id.org/delphi/ontology/passCriterion> "Pre-registered. The universe U is the 16 functions from {0,1}^2 to {0,1}, truth tables ordered by inputs (b0,b1) = (0,0), (0,1), (1,0), (1,1). Three systems. (1) Elementary cellular automata, Wolfram numbers 0..255, fixed-0 boundaries. Encoding: output cell at position -1 starts at 0; input bits at positions 0 and 1; a program of 6 bits at positions 2..7 (64 programs); all other cells 0; evolve t = 1..16 steps on the tape from -17 to 23 inclusive. A function f is realized if some program and some t make cell -1 equal f(b0,b1) for all four inputs. (2) One radius-4 binary cellular automaton, one step. Neighborhood positions relative to the center, from -4 to +4. Input b0 is at +1, b1 at +2. Program bits p00, p01, p10, p11 sit at -4, -3, -2, -1 and the 16 programs are exactly the 16 truth tables in the input order above. The local rule sets the new center to the program bit indexed by b0 + 2*b1, ignoring every other neighbor. Initial center is 0. Read the center after 1 step. (3) A 2-symbol Turing machine on the tape [output=0, b0, b1, p00, p01, p10, p11]. From a head start on b0 it stores b0, moves right, stores b1, moves to p00, steps right b0+2*b1 cells, reads that bit, returns to the output cell, writes it, and halts. The same 16 truth-table programs are used. Let Cap(S) be the set of functions realized. SUPPORTS if Cap(radius-4) = Cap(TM) = U, |Cap(rule 0)| <= 4, every elementary rule has |Cap| <= 16, and every elementary rule with |Cap| = 16 has Cap equal to U. Confidence if supports: 0.84.";
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a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "the systems whose sets of two-bit boolean functions are compared";
dc:license "";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: Boolean-function capabilities of elementary rules 0..255, one radius-4 multiplexer, and one lookup Turing machine, generated by analysis.py";
prov:wasDerivedFrom <https://www.wolframscience.com/nks/p675--the-rule-110-cellular-automaton/> .
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dc:identifier "Grok 4.7" .
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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-ch11-13--claim-test--pr-130>;
<http://www.w3.org/2000/01/rdf-schema#label> "Claim test of wolfram2002-ch11-13 (pr-130): supports, confidence 0.84";
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