[ { "@id": "https://w3id.org/np/RAoSVYqYIhlW5UMb181Jym_tEk9DLIdrdq3b7P4LAc6Ck/Head", "@graph": [ { "@id": "https://w3id.org/np/RAoSVYqYIhlW5UMb181Jym_tEk9DLIdrdq3b7P4LAc6Ck", "http://www.nanopub.org/nschema#hasAssertion": [ { "@id": "https://w3id.org/np/RAoSVYqYIhlW5UMb181Jym_tEk9DLIdrdq3b7P4LAc6Ck/assertion" } ], "http://www.nanopub.org/nschema#hasProvenance": [ { "@id": "https://w3id.org/np/RAoSVYqYIhlW5UMb181Jym_tEk9DLIdrdq3b7P4LAc6Ck/provenance" } ], "http://www.nanopub.org/nschema#hasPublicationInfo": [ { "@id": "https://w3id.org/np/RAoSVYqYIhlW5UMb181Jym_tEk9DLIdrdq3b7P4LAc6Ck/pubinfo" } ], "@type": [ "http://www.nanopub.org/nschema#Nanopublication" ] } ] }, { "@id": "https://w3id.org/np/RAoSVYqYIhlW5UMb181Jym_tEk9DLIdrdq3b7P4LAc6Ck/assertion", "@graph": [ { "@id": "https://w3id.org/delphi/resource/assessment/wolfram2002-ch01-02--claim-test", "http://purl.org/dc/terms/description": [ { "@value": "analysis.py evolves elementary rules 0..31 from one black cell through t = 120 on a width-241 window and computes 4-bit block entropy on rows 40..119, columns 80..160. The control is a period-2 string of the same 6480 bits. A second run matched derived/measured.json byte for byte." } ], "@type": [ "https://w3id.org/delphi/ontology/Assessment" ], "http://www.w3.org/2000/01/rdf-schema#comment": [ { "@value": "Measured: 5 rules among 0..31 whose center-window h4 exceeds the period-2 control by at least 0.40 (n = 32, exact on this window). Interpretation: 'Very simple programs' are the first 32 elementary rules in Wolfram's numbering, run from one black cell. 'Behave complexly' is a 4-bit block entropy at least 0.40 above a period-2 string in the center of the pattern after the early rows. 'Often' is at least 3 of those 32. Nested and random-looking patterns both count as complex under this entropy comparison. The computation says nothing about organisms." } ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "Claim test of wolfram2002-ch01-02: supports, confidence 0.74" } ], "http://www.w3.org/2000/01/rdf-schema#seeAlso": [ { "@id": "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch01-02/result.json" } ], "http://www.w3.org/ns/prov#wasAttributedTo": [ { "@id": "https://w3id.org/delphi/resource/agent/delphisci-claim-tester-grok-4-7" } ], "https://w3id.org/delphi/ontology/admissibleDatasets": [ { "@value": "Elementary rules 0..31 generated by the checksummed script from one black cell, width 241, through t = 120. No organism record is admissible." } ], "https://w3id.org/delphi/ontology/assessmentType": [ { "@value": "claim-test/0.1.0" } ], "https://w3id.org/delphi/ontology/dataKind": [ { "@value": "computational" } ], "https://w3id.org/delphi/ontology/disconfirmingObservation": [ { "@value": "The control has h4 at most 0.25 and every one of the 32 rules is within 0.40 of it." } ], "https://w3id.org/delphi/ontology/evidenceAgainst": [ { "@value": "Five rules clear the gap of 0.40: 5, 13, 25, 28 and 30. The period-2 control has h4 0. Rule 30 has h4 0.9984787283141286. Rules 13, 28 and 30 are above 0.45; rules 5 and 25 are just above 0.40." }, { "@value": "Nested rules 18 and 22 have h4 0.23232159476160025 and 0.23651925604806326, below the gap, because a nested pattern is regular at the scale of 4-bit blocks. The locked statistic counts entropy, not visual nesting." }, { "@value": "This is a computation about elementary rules. It says nothing about organisms." }, { "@value": "k = 32 is a prefix of the numbering, the seed is one cell, and the window stops at t = 119. A different k would change the count." } ], "https://w3id.org/delphi/ontology/expectedObservation": [ { "@value": "At least three of rules 0..31 have center-window h4 at least 0.40 above the period-2 control, and the control itself has h4 at most 0.25." } ], "https://w3id.org/delphi/ontology/failCriterion": [ { "@value": "Pre-registered. Refutes if the control has h4 <= 0.25 and no rule is complex. Mixed if the control passes and exactly 1 or 2 rules are complex. Inconclusive if the control has h4 > 0.25." } ], "https://w3id.org/delphi/ontology/hasConfidence": [ { "@value": "0.74", "@type": "http://www.w3.org/2001/XMLSchema#double" } ], "https://w3id.org/delphi/ontology/hasEvidence": [ { "@id": "https://w3id.org/delphi/resource/evidence/wolfram2002-ch01-02--claim-test--dataset-1" } ], "https://w3id.org/delphi/ontology/hasVerdict": [ { "@value": "supports" } ], "https://w3id.org/delphi/ontology/hypothesis": [ { "@value": "Among the first 32 elementary rules, at least three have higher 4-bit block entropy, in a fixed late center window, than a period-2 control of the same length." } ], "https://w3id.org/delphi/ontology/inferenceMethod": [ { "@value": "Compare each rule's window h4 with the period-2 control. Three or more rules clearing a gap of 0.40 supports. One or two is mixed. Zero refutes. A control above 0.25 makes the test inconclusive." } ], "https://w3id.org/delphi/ontology/passCriterion": [ { "@value": "Pre-registered. k = 32, rules 0 through 31. One black cell at index 120 on a homogeneous white background. Width 241, t = 0..120, background outside the array evolving homogeneously. Window: rows 40..119 and columns 80..160 (80 by 81). h4 is the Shannon entropy of non-overlapping 4-bit blocks of that window read row by row, divided by 4. The repetitive control is the string 010101... of the same length, 6480 bits, and it must have h4 <= 0.25. A rule is complex when its h4 is at least the control h4 plus 0.40. 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