@prefix this: . @prefix sub: . @prefix np: . @prefix rdf: . @prefix prov: . @prefix npx: . @prefix dc: . @prefix xsd: . sub:Head { this: a np:Nanopublication; np:hasAssertion sub:assertion; np:hasProvenance sub:provenance; np:hasPublicationInfo sub:pubinfo . } sub:assertion { a ; dc:description "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."; "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."; "Claim test of wolfram2002-ch01-02: supports, confidence 0.74"; ; prov:wasAttributedTo ; "Elementary rules 0..31 generated by the checksummed script from one black cell, width 241, through t = 120. No organism record is admissible."; "claim-test/0.1.0"; "computational"; "The control has h4 at most 0.25 and every one of the 32 rules is within 0.40 of it."; "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.", "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.", "This is a computation about elementary rules. It says nothing about organisms.", "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."; "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."; "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."; "0.74"^^xsd:double; ; "supports"; "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."; "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."; "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. Supports if and only if at least 3 rules are complex and the control check passes."; "false"^^xsd:boolean . . a ; dc:description "the first 32 elementary evolutions"; dc:license ""; "Dataset: Single-cell evolutions of elementary rules 0 through 31"; "sha256:578309bd456622b6737981befa9fa4ae19b989f5ea552e73688e5ba0665c5eaa" . } sub:provenance { a prov:SoftwareAgent; "delphisci claim tester (Grok 4.7; cursor/claim-tests-wolfram-programs-b8d9)"; prov:actedOnBehalfOf ; . a ; dc:identifier "Grok 4.7" . sub:assertion prov:wasAttributedTo ; prov:wasDerivedFrom ; prov:wasGeneratedBy sub:test . sub:plan prov:hadPlan . sub:test a prov:Activity; prov:qualifiedAssociation sub:plan; prov:wasAssociatedWith . } sub:pubinfo { this: dc:created "2026-11-08T16:24:31.913Z"^^xsd:dateTime; dc:creator ; dc:license ; npx:hasNanopubType ; npx:introduces ; "Claim test of wolfram2002-ch01-02: supports, confidence 0.74"; . sub:sig npx:hasAlgorithm "RSA"; npx:hasPublicKey "MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB"; npx:hasSignature "m6ywCaP0Bi5RraygkHmsZCo+3wIkkm0yRTfvYnMgKJGEIsJ06iLflJuweGCpTeeVEcwO3lvisfoI0hyBQyyaXcv2mdlIx7Oxv1Fnd5Y+L7sIA82pfO+lagqsvpSck4Is++0y/NLnM2cq8PZHig58MU41OuaOTMKqsXtFmeuP0l9VlPgf8gii1PDhXg8oiOxK73lyAmhMXctFuF6HAe1QvU5gu1ox4/WNa7hhVJiyxiGod2y9BJ+uvRqU5jwNWHaJCShiouSRwJmF6Dke308uEbY7Vd1+EUdUAGc/2XCAKhz7jwVC0rLzasUYjj/il0KjuwaoTe+FBZMRJY6Ax1MPjA=="; npx:hasSignatureTarget this:; npx:signedBy . }