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'Complex and seemingly random' is high digram entropy of the size-difference signs, not a stabilized or purely monotone size. The collapsing rule is the control that must look simple." } ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "Claim test of wolfram2002-ch03-17: mixed, confidence 0.58" } ], "http://www.w3.org/2000/01/rdf-schema#seeAlso": [ { "@id": "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch03-17/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": "Only this rule, this initial condition, and the locked cap. No other symbolic rule is run except the collapsing control. Not evidence about organisms." } ], "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 same rule reaches a fixed point with at most 50 leaves. Monotone or low-entropy growth is mixed, not a confirmation of randomness." } ], "https://w3id.org/delphi/ontology/evidenceAgainst": [ { "@value": "One rule, one initial condition, one scan order. The other five rules drawn on the page were not run. A match or a miss here says nothing about organisms." }, { "@value": "The rule does not stabilize: leaf count goes from 6 to 8031 in 117 steps and hits the cap. The collapsing control goes from 6 leaves to 2 and is then fixed." }, { "@value": "The size-difference signs are 113 plus, 0 minus and 4 zero, so H2 is 0.431017, below the locked randomness bar of 2. Growth on this scan is nearly monotone. That does not confirm 'seemingly random', and it does not show a simple fixed point either." } ], "https://w3id.org/delphi/ontology/expectedObservation": [ { "@value": "The orbit is still changing when it stops, has more than 50 leaves, at least 20 size-difference signs, and H2 of those signs is at least 2, while the collapsing control is fixed within 10 steps." } ], "https://w3id.org/delphi/ontology/failCriterion": [ { "@value": "Pre-registered. If the control stabilizes in 10 steps and the subject reaches a fixed point with maximum leaf count at most 50, the verdict is refutes for this rule on this bound. Any other controlled outcome that is not a support is mixed, including growth whose sign sequence has H2 < 2. If the control does not stabilize within 10 steps, or there are fewer than 20 signs and no fixed point, the verdict is inconclusive. One rule is not a survey. This says nothing about organisms." } ], "https://w3id.org/delphi/ontology/hasConfidence": [ { "@value": "0.58", "@type": "http://www.w3.org/2001/XMLSchema#double" } ], "https://w3id.org/delphi/ontology/hasEvidence": [ { "@id": "https://w3id.org/delphi/resource/evidence/wolfram2002-ch03-17--claim-test--dataset-1" } ], "https://w3id.org/delphi/ontology/hasVerdict": [ { "@value": "mixed" } ], "https://w3id.org/delphi/ontology/hypothesis": [ { "@value": "The page-104 rule e[x_][y_] -> x[y[x]], started from e[e[e][e]][e][e], does not reach a fixed point within 200 steps or 8000 leaves, and the signs of its leaf-count differences have digram entropy at least 2." } ], "https://w3id.org/delphi/ontology/inferenceMethod": [ { "@value": "Digram entropy of the sign sequence of leaf counts, with the locked thresholds, after the control has stabilized." } ], "https://w3id.org/delphi/ontology/passCriterion": [ { "@value": "Pre-registered. Expressions are binary application trees. The atom is e. A node (e[x])[y] matches and is replaced by x[y[x]]; a match is not scanned inside during that step, and non-matches are scanned function-first then argument. Leaf count is the number of e atoms in the written term. Run at most 200 steps or until the leaf count exceeds 8000. Let s_t be the sign of the successive leaf-count difference, in {-1, 0, +1}. H2 is the Shannon entropy of overlapping pairs of signs. Supports if the run does not hit a fixed point, the maximum leaf count exceeds 50, there are at least 20 signs, H2 >= 2, and the control rule e[x_][y_] -> e from the same initial condition reaches a fixed point in at most 10 steps. 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