https://w3id.org/np/RArdDnHPJ47Cd-MK2RVZPsa9zq8sXe9_lQT0mYyf6j3mQ
.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-ch01-07--claim-test> a <https://w3id.org/delphi/ontology/Assessment>;
dc:description "analysis.py: (A) evaluates the sentence as the predicate (c OR r) AND NOT (l AND c AND r) on all 8 neighbourhoods and compares with rule 110; (B) for 30 random 2-symbol Turing machines builds Cook's 10m-symbol 2-deletion tag system from the printed lookup-table entries (H_kz, L_kz, R_kz, R_k*, H_k, L_k, R_k), encodes the configuration as H_k1 H_k0 [L_k1 L_k0]^TL [R_k1 R_k0]^TR (with the leading H_k1 already consumed when the head reads 0), runs the tag system and records whether the encoding of each successive TM configuration appears on the tape; (C) for those 30 tag systems and 30 random 2-tag systems builds Cook's 2k-appendant cyclic tag system and checks after every 2k cyclic-tag steps that the cyclic-tag tape is the encoding of the tag tape; (D) reads the rule-110 glider velocities measured for claim wolfram2002-ch02-09 and checks each velocity of Cook's figure 5.";
<http://www.w3.org/2000/01/rdf-schema#comment> "Measured: 1 fraction of exact emulation checks passed (TM->tag and tag->cyclic tag) (n = 9219, exact (deterministic)). Interpretation: The claim is an existence claim: at least one system with a one-sentence rule is universal. It is tested on its canonical instance, rule 110, by (A) checking that the rule really is one short sentence, (B, C) executing the first two reductions of Cook's published proof exactly on random instances, and (D) checking that the glider species the third reduction is built from exist with the stated velocities. Universality is taken in Cook's sense (emulation of a universal Turing machine on finite initial data, with the periodic background and periodic right-hand table data that Cook's construction uses; Neary and Woods 2006 later showed the emulation is polynomially efficient). The third link (cyclic tag system -> rule 110, Cook 2004 section 4) is not re-executed here: its initial conditions are long glider packets whose phases are specified only in the paper's figures.";
<http://www.w3.org/2000/01/rdf-schema#label> "Claim test of wolfram2002-ch01-07: 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-ch01-07/result.json>;
prov:wasAttributedTo <https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1-cursor-cloud-agent>;
<https://w3id.org/delphi/ontology/admissibleDatasets> "Planned datasets: cook2004-rule110-universality, tm-tag-cts-emulation-generator, wolfram2002-ch02-09-glider-inventory";
<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. 'Refutes' if A fails (rule 110 is not the stated sentence), or if B or C fails in more than 5% of checks (the printed constructions do not emulate as claimed), or if fewer than 5 of the 7 figure-5 velocities are observed in D. Other combinations are 'mixed'. The test cannot refute Cook's theorem itself; a failure of B or C would show that the printed proof as transcribed does not work, not that no one-sentence universal system exists.";
<https://w3id.org/delphi/ontology/evidenceAgainst> "'One sentence' is judged on one 21-word English sentence for rule 110; other phrasings exist. Whether 'universal' should require finite initial data with a uniform background (Cook's construction uses a periodic background and periodic right-hand data; Neary and Woods 2006 showed the emulation is polynomially efficient) is a definitional point not tested here.",
"Deviation from the pre-registration: Cook's tag system represents the two halves of the tape in unary, so the tag tape grows like 2^(TM steps) for machines that keep moving one way. Machines were stopped once the tape would exceed 65536 symbols (16 of 30 stopped early, after 9-23 steps), giving 749 checks instead of the planned 1200. All checks performed passed; the cap was applied before seeing any outcome and is a runtime cap, not a selection on results.",
"Random Turing machines have no halting state; the emulation of each step is what is checked, not halting behaviour.",
"The interpretation of the alignment in Cook's text (which symbol of each pair is read) was fixed by transcribing the construction and finding that the encoded configuration for a head reading 0 appears with the leading H_k1 already consumed; the check is still exact equality of the whole tape with the encoding of the independently simulated Turing machine.",
"The third link of Cook's proof (cyclic tag system -> rule 110 via glider collisions, section 4) was not executed; only the existence of the required glider species with the velocities of figure 5 was checked. Universality of rule 110 therefore rests on the published proof plus the two links verified here, which is why confidence is 0.8 rather than higher.";
<https://w3id.org/delphi/ontology/expectedObservation> "Pre-registered. (A) One-sentence rule: the sentence 'A cell becomes black if it or its right-hand neighbour is black, unless it and both of its neighbours are black' has at most 30 words and, evaluated as a Boolean predicate on the 8 neighbourhoods, reproduces all 8 entries of Wolfram's rule 110 (binary 01101110). (B) TM -> tag: for 30 random 2-symbol Turing machines with 2-4 states (every transition writes a bit, moves left or right, and changes to any state; no halting), each started from a random tape of 8 bits on each side of the head and run for 40 steps, Cook's 10m-symbol 2-deletion tag system (rules as printed on pp. 5-6 of Cook 2004) started from the encoded configuration reaches the encoded configuration of each successive Turing-machine step within 100000 tag steps; 100% of the 1200 step checks succeed. (C) Tag -> cyclic tag: for the same 30 tag systems plus 30 random 2-tag systems with 2-6 symbols and appendants of length 0-4, each run for 200 tag steps from a random tape (or until the tape empties), Cook's 2k-appendant cyclic tag system (symbol i -> N^(i-1) Y N^(k-i); appendants = encoded appendants then k empty ones) reproduces the encoded tag tape after every 2k cyclic-tag steps; 100% of checks. (D) Glider inventory: the velocities of all naturally occurring rule-110 gliders in Cook 2004 figure 5 (A 2/3, B -1/2, C 0, D 1/5, E and Ebar -4/15, F -1/9, G -1/3; H and the glider gun are stated by Cook not to arise naturally) are all present among the exactly periodic localized structures measured in test-data/claim-tests/wolfram-nks/wolfram2002-ch02-09/derived/measured.json (random initial conditions, 20 runs). 'Supports' requires A-D.";
<https://w3id.org/delphi/ontology/failCriterion> "Pre-registered. 'Refutes' if A fails (rule 110 is not the stated sentence), or if B or C fails in more than 5% of checks (the printed constructions do not emulate as claimed), or if fewer than 5 of the 7 figure-5 velocities are observed in D. Other combinations are 'mixed'. The test cannot refute Cook's theorem itself; a failure of B or C would show that the printed proof as transcribed does not work, not that no one-sentence universal system exists.";
<https://w3id.org/delphi/ontology/hasConfidence> "0.8"^^xsd:double;
<https://w3id.org/delphi/ontology/hasEvidence> <https://w3id.org/delphi/resource/evidence/wolfram2002-ch01-07--claim-test--dataset-1>,
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch01-07--claim-test--dataset-2>,
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch01-07--claim-test--dataset-3>;
<https://w3id.org/delphi/ontology/hasVerdict> "supports";
<https://w3id.org/delphi/ontology/hypothesis> "Elementary cellular automaton rule 110, whose rule is stated in one sentence, is computationally universal (Cook 2004). The published proof is a chain of exact emulations: 2-symbol Turing machines -> 2-tag systems (Cocke/Cook, Cook 2004 section 2.1), 2-tag systems -> cyclic tag systems (Cook 2004 section 2.2), cyclic tag systems -> rule-110 glider systems (Cook 2004 sections 3-4). The first two links are fully specified constructions that can be executed and checked exactly; the third relies on the glider inventory of rule 110 (Cook 2004 figure 5), whose velocities must be present in rule-110 evolutions.";
<https://w3id.org/delphi/ontology/inferenceMethod> "analysis.py: (A) evaluates the sentence as the predicate (c OR r) AND NOT (l AND c AND r) on all 8 neighbourhoods and compares with rule 110; (B) for 30 random 2-symbol Turing machines builds Cook's 10m-symbol 2-deletion tag system from the printed lookup-table entries (H_kz, L_kz, R_kz, R_k*, H_k, L_k, R_k), encodes the configuration as H_k1 H_k0 [L_k1 L_k0]^TL [R_k1 R_k0]^TR (with the leading H_k1 already consumed when the head reads 0), runs the tag system and records whether the encoding of each successive TM configuration appears on the tape; (C) for those 30 tag systems and 30 random 2-tag systems builds Cook's 2k-appendant cyclic tag system and checks after every 2k cyclic-tag steps that the cyclic-tag tape is the encoding of the tag tape; (D) reads the rule-110 glider velocities measured for claim wolfram2002-ch02-09 and checks each velocity of Cook's figure 5.";
<https://w3id.org/delphi/ontology/passCriterion> "Pre-registered. (A) One-sentence rule: the sentence 'A cell becomes black if it or its right-hand neighbour is black, unless it and both of its neighbours are black' has at most 30 words and, evaluated as a Boolean predicate on the 8 neighbourhoods, reproduces all 8 entries of Wolfram's rule 110 (binary 01101110). (B) TM -> tag: for 30 random 2-symbol Turing machines with 2-4 states (every transition writes a bit, moves left or right, and changes to any state; no halting), each started from a random tape of 8 bits on each side of the head and run for 40 steps, Cook's 10m-symbol 2-deletion tag system (rules as printed on pp. 5-6 of Cook 2004) started from the encoded configuration reaches the encoded configuration of each successive Turing-machine step within 100000 tag steps; 100% of the 1200 step checks succeed. (C) Tag -> cyclic tag: for the same 30 tag systems plus 30 random 2-tag systems with 2-6 symbols and appendants of length 0-4, each run for 200 tag steps from a random tape (or until the tape empties), Cook's 2k-appendant cyclic tag system (symbol i -> N^(i-1) Y N^(k-i); appendants = encoded appendants then k empty ones) reproduces the encoded tag tape after every 2k cyclic-tag steps; 100% of checks. (D) Glider inventory: the velocities of all naturally occurring rule-110 gliders in Cook 2004 figure 5 (A 2/3, B -1/2, C 0, D 1/5, E and Ebar -4/15, F -1/9, G -1/3; H and the glider gun are stated by Cook not to arise naturally) are all present among the exactly periodic localized structures measured in test-data/claim-tests/wolfram-nks/wolfram2002-ch02-09/derived/measured.json (random initial conditions, 20 runs). 'Supports' requires A-D.";
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<https://w3id.org/delphi/resource/evidence/wolfram2002-ch01-07--claim-test--dataset-1>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "source of the three-link proof; sections 2.1-2.2 (pp. 4-8) give the constructions executed in B and C, figure 5 (p. 14) the glider periods used in D";
dc:license "Complex Systems Publications";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: Cook, M. (2004) Universality in Elementary Cellular Automata, Complex Systems 15(1):1-40";
prov:atLocation <https://content.wolfram.com/sites/13/2023/02/15-1-1.pdf>;
prov:wasDerivedFrom <https://www.complex-systems.com/abstracts/v15_i01_a01/>;
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a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "random instances on which the emulations are checked exactly";
dc:license "CC0 (generated data)";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: Random 2-symbol Turing machines, their Cook tag systems and cyclic tag systems (generated by analysis.py)" .
<https://w3id.org/delphi/resource/evidence/wolfram2002-ch01-07--claim-test--dataset-3>
a <https://w3id.org/delphi/ontology/EvidenceItem>;
dc:description "measured glider velocities from random initial conditions, compared with Cook 2004 figure 5";
dc:license "CC0 (generated data)";
<http://www.w3.org/2000/01/rdf-schema#label> "Dataset: Rule-110 localized periodic structures measured for claim wolfram2002-ch02-09 (this repository)";
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