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The test uses four of those rules as the stated set and the two the book calls simple as controls. 'Random' here is high block entropy of the space-time, not a statistical test suite. 'Localized' is the component bound above, not a glider catalog." } ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "Claim test of wolfram2002-ch09-03: mixed, confidence 0.63" } ], "http://www.w3.org/2000/01/rdf-schema#seeAlso": [ { "@id": "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch09-03/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 the locked rules, width, steps and seeds. No survey outside the set. 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": "No finite observation in this set refutes the existential claim. A single phenomenon is mixed. Neither phenomenon, or a control that looks as random as the subjects, is inconclusive." } ], "https://w3id.org/delphi/ontology/evidenceAgainst": [ { "@value": "Components do not wrap around the ring, so a structure crossing the edge is split. A match says nothing about organisms." }, { "@value": "Controls stayed simple: 0R at 0.528502 and 0.920883, 90R at 2.587075 and 2.326024, all under 5. Every 20-step round trip returned to its start." }, { "@value": "Finite set and finite bound: four rules, width 64, 128 steps, two seeds. Absence of a high-entropy run here does not show that no reversible rule looks random." }, { "@value": "Localized structures did appear: rule 73R on the block seed has 6 components inside the locked box. The highest subject entropy is that same run, H8 = 6.236165, which misses the locked randomness bar of 6.5. No subject run cleared 6.5." } ], "https://w3id.org/delphi/ontology/expectedObservation": [ { "@value": "Some run among 26R, 37R, 73R, 122R and the two seeds has H8 >= 6.5, some run has a localized component, and both seeds of 0R and 90R have H8 < 5." } ], "https://w3id.org/delphi/ontology/failCriterion": [ { "@value": "Pre-registered. There is no refutation from this finite set: if the controls and round trips pass but only one of the two phenomena appears, the verdict is mixed; if neither appears, the verdict is inconclusive with reason underpowered. If a control has H8 >= 5 or a round trip fails, the verdict is inconclusive because the statistic or the implementation did not separate the book's simple rules. This says nothing about organisms." } ], "https://w3id.org/delphi/ontology/hasConfidence": [ { "@value": "0.63", "@type": "http://www.w3.org/2001/XMLSchema#double" } ], "https://w3id.org/delphi/ontology/hasEvidence": [ { "@id": "https://w3id.org/delphi/resource/evidence/wolfram2002-ch09-03--claim-test--dataset-1" } ], "https://w3id.org/delphi/ontology/hasVerdict": [ { "@value": "mixed" } ], "https://w3id.org/delphi/ontology/hypothesis": [ { "@value": "At least one of the second-order rules 26R, 37R, 73R and 122R, on a width-64 ring for 128 steps, has overlapping 8-bit block entropy at least 6.5 and at least one of them forms a localized structure, while rules 0R and 90R stay below entropy 5." } ], "https://w3id.org/delphi/ontology/inferenceMethod": [ { "@value": "H8 of concatenated rows against 6.5 and 5.0, plus a count of 4-connected components inside the locked size box, after the round-trip check." } ], "https://w3id.org/delphi/ontology/passCriterion": [ { "@value": "Pre-registered. The set is exactly 26R, 37R, 73R, 122R. Controls are 0R and 90R. Second-order step (previous, current) -> (current, previous XOR elementary(rule, current)), periodic, width 64, 128 steps. Seeds: a single black cell at the center, and center bits 1110111 with previous all white. H8 is the Shannon entropy of overlapping 8-bit blocks of the current rows concatenated in time. A localized structure is a 4-connected component of black cells in that space-time, size 8..80, bounding width at most 12, duration at least 10; component edges do not wrap. Supports if some subject run has H8 >= 6.5 and some subject run (possibly another) has at least one localized structure, every control run has H8 < 5, and a 20-step round trip restores both seeds for every rule. The claim is existential, so a miss is not a refutation." } ], "https://w3id.org/delphi/ontology/preregistered": [ { "@value": "false", "@type": "http://www.w3.org/2001/XMLSchema#boolean" } ] }, { "@id": "https://w3id.org/delphi/resource/evidence/wolfram2002-ch09-03--claim-test--dataset-1", "http://purl.org/dc/terms/description": [ { "@value": "the stated reversible set and the two simple controls" } ], "http://purl.org/dc/terms/license": [ { "@value": "generated data" } ], "@type": [ "https://w3id.org/delphi/ontology/EvidenceItem" ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "Dataset: Second-order rules 26R, 37R, 73R, 122R with controls 0R and 90R" } ], "http://www.w3.org/ns/prov#wasDerivedFrom": [ { "@id": "https://www.wolframscience.com/nks/notes-9-2--second-order-cellular-automata/" } ] }, { "@id": "https://w3id.org/delphi/resource/claim/wolfram2002-ch09-03", "https://w3id.org/delphi/ontology/hasAssessment": [ { "@id": "https://w3id.org/delphi/resource/assessment/wolfram2002-ch09-03--claim-test" } ] } ] }, { "@id": "https://w3id.org/np/RALYJCqSWt-21HisXQ3NxU0MG_q_e4u4zFRxe6CAbPgAU/pubinfo", "@graph": [ { "@id": "https://w3id.org/np/RALYJCqSWt-21HisXQ3NxU0MG_q_e4u4zFRxe6CAbPgAU", "http://purl.org/dc/terms/created": [ { "@value": "2026-11-08T16:24:31.933Z", "@type": "http://www.w3.org/2001/XMLSchema#dateTime" } ], "http://purl.org/dc/terms/creator": [ { "@id": "https://orcid.org/0009-0007-4948-9192" } ], "http://purl.org/dc/terms/license": [ { "@id": "https://creativecommons.org/licenses/by/4.0/" } ], "http://purl.org/nanopub/x/hasNanopubType": [ { "@id": "https://w3id.org/delphi/ontology/Assessment" } ], "http://purl.org/nanopub/x/introduces": [ { "@id": "https://w3id.org/delphi/resource/assessment/wolfram2002-ch09-03--claim-test" } ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "Claim test of wolfram2002-ch09-03: mixed, confidence 0.63" } ], "https://w3id.org/delphi/ontology/domain": [ { "@id": "https://w3id.org/delphi/resource/domain/wolfram-nks-2002" } ] }, { "@id": "https://w3id.org/np/RALYJCqSWt-21HisXQ3NxU0MG_q_e4u4zFRxe6CAbPgAU/sig", "http://purl.org/nanopub/x/hasAlgorithm": [ { "@value": "RSA" } ], "http://purl.org/nanopub/x/hasPublicKey": [ { "@value": "MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB" } ], "http://purl.org/nanopub/x/hasSignature": [ { "@value": "FJrQyVbm6qC5EPtWLFUFum7YpYkchZJNQ4TpdQX3WOeJkGajZ4AM2jo4IogRqZR1gI2OKR3qmXjEFoiuHhtzWdp/UouWK6/FWshArEtdsEQRQbSCAzBPya+v1FKyu/dfiJTvXsCjmD4pff9Gh4lRI956BIVLQV9+fSNXwW09B/qRnUSuYMFYJXUsMk6M7brXg2LV8ApvhitK7FkvGUpuMbpDEog2Ua2oWNRwlrPnQEcndVa26IM41Ocs7SO1AqKnVTNjoOOW05q2ww/QXHysjedbCd4wb6mJuGBGyj4BSYNxMR/eQ1fS5JUdq2kxwuI9Zzrh0ZxHCqu5bwiCLOnZfQ==" } ], "http://purl.org/nanopub/x/hasSignatureTarget": [ { "@id": "https://w3id.org/np/RALYJCqSWt-21HisXQ3NxU0MG_q_e4u4zFRxe6CAbPgAU" } ], "http://purl.org/nanopub/x/signedBy": [ { "@id": "https://orcid.org/0009-0007-4948-9192" } ] } ] }, { "@id": "https://w3id.org/np/RALYJCqSWt-21HisXQ3NxU0MG_q_e4u4zFRxe6CAbPgAU/Head", "@graph": [ { "@id": "https://w3id.org/np/RALYJCqSWt-21HisXQ3NxU0MG_q_e4u4zFRxe6CAbPgAU", "http://www.nanopub.org/nschema#hasAssertion": [ { "@id": "https://w3id.org/np/RALYJCqSWt-21HisXQ3NxU0MG_q_e4u4zFRxe6CAbPgAU/assertion" } ], "http://www.nanopub.org/nschema#hasProvenance": [ { "@id": "https://w3id.org/np/RALYJCqSWt-21HisXQ3NxU0MG_q_e4u4zFRxe6CAbPgAU/provenance" } ], "http://www.nanopub.org/nschema#hasPublicationInfo": [ { "@id": "https://w3id.org/np/RALYJCqSWt-21HisXQ3NxU0MG_q_e4u4zFRxe6CAbPgAU/pubinfo" } ], "@type": [ "http://www.nanopub.org/nschema#Nanopublication" ] } ] }, { "@id": "https://w3id.org/np/RALYJCqSWt-21HisXQ3NxU0MG_q_e4u4zFRxe6CAbPgAU/provenance", "@graph": [ { "@id": "https://w3id.org/delphi/resource/agent/delphisci-claim-tester-grok-4-7", "@type": [ "http://www.w3.org/ns/prov#SoftwareAgent" ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "delphisci claim tester (Grok 4.7; 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