@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 runs the second-order map for rules 37, 0, 90 and 122 from the simple seed and from the block seed, checks a 30-step round trip, and writes each 3-block entropy trajectory. The verdict uses only rule 37R and rule 0R on the simple seed, compared with the locked thresholds."; "Measured: 1.121928 bits, late range of the 3-block entropy of rule 37R on the simple seed (n = 401, exact on this finite ring; plugin entropy of 40 overlapping blocks). Interpretation: Rule 37R is elementary rule 37 in the second-order reversible construction (new color inverted when the cell was black two steps back). 'No systematic entropy increase' and 'fluctuates between ordered and disordered' are read as a large late range, many distinct 3-block entropy values, and repeated drops of the smoothed trajectory, on one locked finite ring. Rule 0R is the simple closed-system control. Coarse graining is the 3-cell block entropy of the current row, not a thermodynamic entropy of a gas."; "Claim test of wolfram2002-ch09-05: mixed, confidence 0.6"; ; prov:wasAttributedTo ; "The trajectory is generated by the locked second-order map on a width-40 ring for 400 steps. No external simulation is loaded. This is not evidence about organisms or about laboratory thermodynamics."; "claim-test/0.1.0"; "computational"; "Rule 37R is as rigid as rule 0R (at most 4 distinct values) or it rises by at least 0.5 bits and then stays within a late range of 0.20 with fewer than 5 drops."; "A 3-block entropy on 40 cells is a coarse grain. Round trips of 30 steps succeeded for all four rules. This says nothing about organisms or about laboratory thermodynamics.", "Finite ring of width 40 and 400 steps. The book's illustrated 37R run has a period of hundreds of millions of steps; this test does not reproduce that run.", "On the deciding simple seed the pair state repeats within the first 81 steps, and the entropy takes only 6 distinct values (0, 0.503184, 0.783805, 0.833805, 1.060303, 1.121928). The late range is 1.121928 and the smoothed series drops 19 times, so the orbit is not monotone, but it missed the locked bars of 15 distinct values and no short repeat. The mean moves from 0.727726 to 0.689533, which is not a systematic rise.", "Rule 0R takes 2 distinct values, so the control is simple. Rule 90R on this ring is not entropy-flat (21 distinct values); it was not the control.", "The block seed was pre-registered as a report, not as the verdict. On that seed, rule 37R takes 279 distinct values, drops 44 times, and the mean rises from 2.072965 to 2.628999."; "On the simple seed, rule 37R has late entropy range at least 0.35, at least 15 distinct values, and at least 5 smoothed drops of 0.05, while rule 0R has at most 4 distinct values and every locked round trip returns to its start."; "Pre-registered. Refutes if the controls pass and rule 37R on the simple seed either takes at most 4 distinct entropy values, or rises systematically: fewer than 5 smoothed drops, late range below 0.20, and mean of the last 100 values exceeds the mean of the first 50 by at least 0.5. Any other controlled outcome is mixed. A failed round trip, a short repeat of 37R, or rule 0R taking more than 4 distinct values makes the verdict inconclusive. This is a finite ring and 400 steps, not the book's multi-hundred-million-step example, and it says nothing about organisms."; "0.6"^^xsd:double; ; "mixed"; "On a periodic ring of width 40, second-order rule 37R started from a single black cell fluctuates in 3-block entropy over 400 steps, while rule 0R on the same ring takes at most four distinct entropy values."; "Compare the locked summaries of the simple-seed 37R trajectory with the locked thresholds, after the round-trip and the 0R distinct-value control. The full trajectory is stored."; "Pre-registered. Second-order step, from the NKS note on page 1017: (previous, current) -> (current, previous XOR elementary(rule, current)), periodic boundary, width 40, 400 steps. Entropy h_t is the Shannon entropy, in bits, of the 40 overlapping 3-cell blocks of the current row, recorded at t = 0..400 and rounded to 6 decimals. The verdict uses the simple initial condition only: previous all white, current a single black cell at the center. Supports if the late range max(h[200:]) - min(h[200:]) is at least 0.35, the 10-step moving average drops by at least 0.05 at least 5 times, the trajectory takes at least 15 distinct values, the pair state does not repeat within the first 81 states, round-trip of 30 forward and 30 backward steps restores the simple, block, and fixed third initial conditions for rules 37, 0, 90 and 122, and rule 0R on the simple seed takes at most 4 distinct entropy values. The block seed (center bits 101100111000) and rules 90R and 122R are reported and do not decide the verdict."; "false"^^xsd:boolean . . a ; dc:description "entropy trajectories; the full series is derived/measured.json"; dc:license "generated data"; "Dataset: Second-order rules 37R, 0R, 90R and 122R on a width-40 ring"; prov:wasDerivedFrom . } sub:provenance { a prov:SoftwareAgent; "delphisci claim tester (Grok 4.7; cursor/wolfram-claim-tests-b-355b)"; 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 "2026-11-08T16:24:31.933Z"^^xsd:dateTime; dc:creator ; dc:license ; npx:hasNanopubType ; npx:introduces ; "Claim test of wolfram2002-ch09-05: mixed, confidence 0.6"; . sub:sig npx:hasAlgorithm "RSA"; npx:hasPublicKey "MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB"; npx:hasSignature "ST7fytFIm7DWhYQLZLRTpg+vxlIDwBQcqCm27Hh6RKFIxt4ktCauFCMCNtzyLWd8HfWAjCdrio0UJyHLGkto9vRjMJUFjr4dZq7d4lLt2kmscod9F8voe5ziX9DIau76gKsCh6/j64MvnYAuCI1yCvWXStPfgbO0u4xFcHB+3w9CJQFGjuaGMwL2idDOA2emkXhoVZA5FFcM2YyjlwrsOFcYMrOvpH0b2Yv+dxlg1lfaR5O4qrR7L27gK4VMtUgfJIWdHyBZGw98onHvUH+H16BZcXVbPvfpfhy4GHA5yP9aiZ0P5GLO4QAYF9cs/gcWiZ1a75/b/zxcvm5ZTRl3Fw=="; npx:hasSignatureTarget this:; npx:signedBy . }