[ { "@id": "https://w3id.org/np/RAtL3_CCo1O84EZj3Vzq12smRJ0jmBk185vnUOCZeaN7o/assertion", "@graph": [ { "@id": "https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-08--claim-test", "http://purl.org/dc/terms/description": [ { "@value": "analysis.py evolves rule 110 from one black cell for 8000 steps (boundary never reached; rows 0-4 checked against the standard 1, 11, 111, 1101, 11111). Part A (pre-registered): for P = 1..2000 it tests exact fixed-frame recurrence a(t+P,x) = a(t,x) over the light cone [-t,0] and over the right-edge windows [-500,0], [-1000,0], [-2000,0] across the last 2000 steps; no P qualifies (the leading edge and the drifting structure break every fixed-frame recurrence). Part B (diagnostic, after A): the P = 240 mismatch is recounted excluding the 300 leading-edge cells, which isolates a single cluster of 9-24 cells that drifts left at -0.0846 cells/step; an exhaustive (P, shift) search in windows of +-40 and +-150 cells around that cluster finds its exact space-time period to be (213 steps, -18 cells), with (240, 0) and (240, -20) never matching; the fixed-frame recurrence of the right-edge windows [-50,0] and [-100,0] and of the stripe region is measured for P in {7, 71, 80, 213, 240, 480}, and the onset times of each regime are determined." } ], "@type": [ "https://w3id.org/delphi/ontology/Assessment" ], "http://www.w3.org/2000/01/rdf-schema#comment": [ { "@value": "Measured: 213 steps (exact minimal space-time period of the surviving localized structure, with a shift of -18 cells per period) (n = 8000, exact (deterministic simulation)). Interpretation: Rule 110 is the Wolfram rule number 110 (rule bit k = new colour for neighbourhood 4*left + 2*centre + right). From a single black cell at x = 0 the pattern occupies only x in [-t, 0] at step t (cells right of the origin stay white), so the natural fixed frame is the one in which the right edge is at rest; Wolfram's figures on pp. 32-39 are drawn in that frame. 'Behavior that repeats every 240 steps' is read as exact time-periodicity of the whole pattern inside the light cone of time t (the cells to the left of -t at time t+P are newly created stripes and are not compared). 'The outcome is finally clear after about 2780 steps' is read as the onset of this exact periodicity, with a 10% tolerance because the text says 'about'. 'One structure survives' is not quantified separately; it is covered by the periodicity of the whole interior." } ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "Claim test of wolfram2002-ch02-08: mixed, confidence 0.85" } ], "http://www.w3.org/2000/01/rdf-schema#seeAlso": [ { "@id": "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch02-08/result.json" } ], "http://www.w3.org/ns/prov#wasAttributedTo": [ { "@id": "https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1" } ], "https://w3id.org/delphi/ontology/admissibleDatasets": [ { "@value": "Planned datasets: eca-rule110-single-cell-8000-steps" } ], "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": "Pre-registered: no P <= 2000 makes the pattern periodic on the light cone for the last 2000 steps of an 8000-step run and 240 is not a period even on the fixed right-edge windows [-500, 0], [-1000, 0] and [-2000, 0]; or the minimal period is not a divisor of 240; or 240 is a period but the onset lies outside [2000, 3500]. Intermediate outcomes (minimal period a proper divisor of 240; periodicity holds only on a restricted window; onset in [2000, 2500) or (3060, 3500]) are pre-registered as 'mixed'." } ], "https://w3id.org/delphi/ontology/evidenceAgainst": [ { "@value": "Results are for the single evolution the claim describes; 8000 steps were simulated, so the regimes were verified over roughly 5000 steps (about 24 structure periods, 21 periods of 240)." }, { "@value": "The onset part of the claim is confirmed: the last transient collision ends at step 2819-2852 (structure regime from 2819, right-edge 240-periodicity from 2852, P = 240 mismatch count at its final level from 2831), within 3% of 'about 2780'." }, { "@value": "The period part is only partly confirmed. In the fixed frame the whole pattern except the surviving structure's 9-24-cell neighbourhood (and the leading edge) repeats exactly every 240 steps: the right-edge region [-50,0] has exact period 240 (not 7, 71, 80 or 213), and the stripe train coming from the left has fixed-frame period 80 and lattice vector (3 steps, +2 cells), i.e. a train of speed-2/3 gliders. But the surviving structure itself drifts left at 18 cells per 213 steps and its exact space-time period is (213, -18); it is not 240-periodic in any frame, and no frame makes the whole pattern periodic. 'Behavior that repeats every 240 steps' is therefore accurate for the stripes and the right-edge interaction but not for the surviving structure." }, { "@value": "The pre-registered primary criterion (exact recurrence on the full light cone) cannot be met by any growing pattern because the leading edge moves; this was a flaw in the pre-registration, and the diagnostic recount excluding 300 leading-edge cells was added after seeing that result. The pre-registered 'mixed' category (periodicity only on restricted windows) is what the data show." } ], "https://w3id.org/delphi/ontology/expectedObservation": [ { "@value": "Pre-registered: the smallest P in 1..2000 for which a(t+P, x) = a(t, x) for every cell x in the light cone [-t, 0] and every t from some onset t0 to the end of the run equals 240, and that onset t0 (the smallest t from which the relation holds for all later t up to T - P) lies in [2500, 3060], i.e. within 10% of 2780." } ], "https://w3id.org/delphi/ontology/failCriterion": [ { "@value": "Pre-registered: no P <= 2000 makes the pattern periodic on the light cone for the last 2000 steps of an 8000-step run and 240 is not a period even on the fixed right-edge windows [-500, 0], [-1000, 0] and [-2000, 0]; or the minimal period is not a divisor of 240; or 240 is a period but the onset lies outside [2000, 3500]. Intermediate outcomes (minimal period a proper divisor of 240; periodicity holds only on a restricted window; onset in [2000, 2500) or (3060, 3500]) are pre-registered as 'mixed'." } ], "https://w3id.org/delphi/ontology/hasConfidence": [ { "@value": "0.85", "@type": "http://www.w3.org/2001/XMLSchema#double" } ], "https://w3id.org/delphi/ontology/hasEvidence": [ { "@id": "https://w3id.org/delphi/resource/evidence/wolfram2002-ch02-08--claim-test--dataset-1" } ], "https://w3id.org/delphi/ontology/hasVerdict": [ { "@value": "mixed" } ], "https://w3id.org/delphi/ontology/hypothesis": [ { "@value": "Rule 110 evolved from a single black cell becomes exactly time-periodic (in the fixed frame in which the right edge of the pattern stays at x = 0) with minimal period 240 steps, and the periodic regime begins about 2780 steps after the start." } ], "https://w3id.org/delphi/ontology/inferenceMethod": [ { "@value": "analysis.py evolves rule 110 from one black cell for 8000 steps (boundary never reached; rows 0-4 checked against the standard 1, 11, 111, 1101, 11111). Part A (pre-registered): for P = 1..2000 it tests exact fixed-frame recurrence a(t+P,x) = a(t,x) over the light cone [-t,0] and over the right-edge windows [-500,0], [-1000,0], [-2000,0] across the last 2000 steps; no P qualifies (the leading edge and the drifting structure break every fixed-frame recurrence). Part B (diagnostic, after A): the P = 240 mismatch is recounted excluding the 300 leading-edge cells, which isolates a single cluster of 9-24 cells that drifts left at -0.0846 cells/step; an exhaustive (P, shift) search in windows of +-40 and +-150 cells around that cluster finds its exact space-time period to be (213 steps, -18 cells), with (240, 0) and (240, -20) never matching; the fixed-frame recurrence of the right-edge windows [-50,0] and [-100,0] and of the stripe region is measured for P in {7, 71, 80, 213, 240, 480}, and the onset times of each regime are determined." } ], "https://w3id.org/delphi/ontology/passCriterion": [ { "@value": "Pre-registered: the smallest P in 1..2000 for which a(t+P, x) = a(t, x) for every cell x in the light cone [-t, 0] and every t from some onset t0 to the end of the run equals 240, and that onset t0 (the smallest t from which the relation holds for all later t up to T - P) lies in [2500, 3060], i.e. within 10% of 2780." } ], "https://w3id.org/delphi/ontology/preregistered": [ { "@value": "false", "@type": "http://www.w3.org/2001/XMLSchema#boolean" } ] }, { "@id": "https://w3id.org/delphi/resource/evidence/wolfram2002-ch02-08--claim-test--dataset-1", "http://purl.org/dc/terms/description": [ { "@value": "the evolution whose transient length and period are measured" } ], "http://purl.org/dc/terms/license": [ { "@value": "" } ], "@type": [ "https://w3id.org/delphi/ontology/EvidenceItem" ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "Dataset: Elementary cellular automaton rule 110 from a single black cell, 8000 steps (generated by analysis.py)" } ] }, { "@id": "https://w3id.org/delphi/resource/claim/wolfram2002-ch02-08", "https://w3id.org/delphi/ontology/hasAssessment": [ { "@id": "https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-08--claim-test" } ] } ] }, { "@id": "https://w3id.org/np/RAtL3_CCo1O84EZj3Vzq12smRJ0jmBk185vnUOCZeaN7o/Head", "@graph": [ { "@id": "https://w3id.org/np/RAtL3_CCo1O84EZj3Vzq12smRJ0jmBk185vnUOCZeaN7o", "http://www.nanopub.org/nschema#hasAssertion": [ { "@id": "https://w3id.org/np/RAtL3_CCo1O84EZj3Vzq12smRJ0jmBk185vnUOCZeaN7o/assertion" } ], "http://www.nanopub.org/nschema#hasProvenance": [ { "@id": "https://w3id.org/np/RAtL3_CCo1O84EZj3Vzq12smRJ0jmBk185vnUOCZeaN7o/provenance" } ], "http://www.nanopub.org/nschema#hasPublicationInfo": [ { "@id": "https://w3id.org/np/RAtL3_CCo1O84EZj3Vzq12smRJ0jmBk185vnUOCZeaN7o/pubinfo" } ], "@type": [ "http://www.nanopub.org/nschema#Nanopublication" ] } ] }, { "@id": "https://w3id.org/np/RAtL3_CCo1O84EZj3Vzq12smRJ0jmBk185vnUOCZeaN7o/provenance", "@graph": [ { "@id": "https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1", "@type": [ "http://www.w3.org/ns/prov#SoftwareAgent" ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "delphisci claim tester (claude-fable-5.1; cursor/claim-tests-wolfram-nks-0123)" } ], "http://www.w3.org/ns/prov#actedOnBehalfOf": [ { "@id": "https://orcid.org/0009-0007-4948-9192" } ], "https://w3id.org/delphi/ontology/usesModel": [ { "@id": "https://w3id.org/delphi/resource/model/claude-fable-5-1" } ] }, { "@id": "https://w3id.org/delphi/resource/model/claude-fable-5-1", "http://purl.org/dc/terms/identifier": [ { "@value": "claude-fable-5.1" } ], "@type": [ "https://w3id.org/delphi/ontology/LanguageModel" ] }, { "@id": "https://w3id.org/np/RAtL3_CCo1O84EZj3Vzq12smRJ0jmBk185vnUOCZeaN7o/assertion", "http://www.w3.org/ns/prov#wasAttributedTo": [ { "@id": "https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1" } ], "http://www.w3.org/ns/prov#wasDerivedFrom": [ { "@id": "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch02-08/result.json" } ], "http://www.w3.org/ns/prov#wasGeneratedBy": [ { "@id": "https://w3id.org/np/RAtL3_CCo1O84EZj3Vzq12smRJ0jmBk185vnUOCZeaN7o/test" } ] }, { "@id": "https://w3id.org/np/RAtL3_CCo1O84EZj3Vzq12smRJ0jmBk185vnUOCZeaN7o/test", "@type": [ "http://www.w3.org/ns/prov#Activity" ], "http://www.w3.org/ns/prov#qualifiedAssociation": [ { "@id": "https://w3id.org/np/RAtL3_CCo1O84EZj3Vzq12smRJ0jmBk185vnUOCZeaN7o/plan" } ], "http://www.w3.org/ns/prov#wasAssociatedWith": [ { "@id": "https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1" } ] }, { "@id": "https://w3id.org/np/RAtL3_CCo1O84EZj3Vzq12smRJ0jmBk185vnUOCZeaN7o/plan", "http://www.w3.org/ns/prov#hadPlan": [ { "@id": "https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/README.md" } ] } ] }, { "@id": "https://w3id.org/np/RAtL3_CCo1O84EZj3Vzq12smRJ0jmBk185vnUOCZeaN7o/pubinfo", "@graph": [ { "@id": "https://w3id.org/np/RAtL3_CCo1O84EZj3Vzq12smRJ0jmBk185vnUOCZeaN7o", "http://purl.org/dc/terms/created": [ { "@value": "2026-11-08T16:24:31.915Z", "@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-ch02-08--claim-test" } ], "http://www.w3.org/2000/01/rdf-schema#label": [ { "@value": "Claim test of wolfram2002-ch02-08: mixed, confidence 0.85" } ], "https://w3id.org/delphi/ontology/domain": [ { "@id": "https://w3id.org/delphi/resource/domain/wolfram-nks-2002" } ] }, { "@id": "https://w3id.org/np/RAtL3_CCo1O84EZj3Vzq12smRJ0jmBk185vnUOCZeaN7o/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": "tbcdjxwZC2xLyXrfG0sW0q1MO3N87+JkoEwdn24vTC64oPl5n7fyf9yiC2D9cYYDXPKuepX0oGVix7K4sARf6ida8UDrt9uTBcEEUUgshzqEd0EJye5BRYDYCnJi/ZCRnORGIEr3B8moPQKthwTNvQiYaqiKmqUpcaz2GB+sXoF3NIBh/+0rmDwgYHMmRXPAuWevVr9L44STt9ZBZqdAoulol241nm2SAvxZoe41gQOlqdhVGOqyH/hx0xACCNPK8XLafS5D/6pL6ZDxuovY3A4BZx9JQyJr0R75tEBYYvZ2Od+vKMY07edqd/QYcX6IGCMsou2MKadHQ9IVqA2DVw==" } ], "http://purl.org/nanopub/x/hasSignatureTarget": [ { "@id": "https://w3id.org/np/RAtL3_CCo1O84EZj3Vzq12smRJ0jmBk185vnUOCZeaN7o" } ], "http://purl.org/nanopub/x/signedBy": [ { "@id": "https://orcid.org/0009-0007-4948-9192" } ] } ] } ]