https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE/Head https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE http://www.nanopub.org/nschema#hasAssertion https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE/assertion https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE http://www.nanopub.org/nschema#hasProvenance https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE/provenance https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE http://www.nanopub.org/nschema#hasPublicationInfo https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE/pubinfo https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.nanopub.org/nschema#Nanopublication https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE/assertion https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-09--claim-test http://purl.org/dc/terms/description analysis.py enumerates all 16384 configurations of a 14-cell ring under rule 110 and finds those that return to a rotation of themselves after 7 steps; the only non-uniform orbit (14 rotations of 00010011011111, shift 0 after 7 steps, basin 51.5% of ring states) is the ether. Twenty random initial conditions on a 700-cell ring are run for 3000 steps; a cell is 'background' when its 14-cell window equals one of the ether's window codes. Non-background cells are clustered (gap <= 3), clusters are linked across steps (centre moves <= 6 cells), and each track of >= 300 steps is tested for exact periodicity (window at t equals window at t+p shifted by s for 5 consecutive periods, p <= 60). Distinct rational velocities s/p differing by > 0.05 are counted. https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-09--claim-test http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/Assessment https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-09--claim-test http://www.w3.org/2000/01/rdf-schema#comment Measured: 7 distinct localized-structure velocities (cells/step) (n = 143, exact (deterministic computation); background fraction range over runs 0.619-0.886). Interpretation: Wolfram's statement is read as an existence claim about rule 110 (his stated example): the same cell rule, applied to different local configurations, yields (i) a regular periodic background and (ii) several distinct localized structures. 'Regular background' is operationalized as a spatially and temporally periodic configuration; 'localized structure' as a bounded cluster of non-background cells that persists and is exactly periodic up to a shift, so that its velocity s/p is a rational number. Distinct velocities are taken as evidence of 'different kinds of behavior'. No reinterpretation beyond this is needed; the test is computational and the 'dataset' is generated by analysis.py. https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-09--claim-test http://www.w3.org/2000/01/rdf-schema#label Claim test of wolfram2002-ch02-09: supports, confidence 0.97 https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-09--claim-test http://www.w3.org/2000/01/rdf-schema#seeAlso https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch02-09/result.json https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-09--claim-test http://www.w3.org/ns/prov#wasAttributedTo https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1-cursor-cloud-agent https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-09--claim-test https://w3id.org/delphi/ontology/admissibleDatasets Planned datasets: eca-rule110-random-ic-generator https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-09--claim-test https://w3id.org/delphi/ontology/assessmentType claim-test/0.1.0 https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-09--claim-test https://w3id.org/delphi/ontology/dataKind computational https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-09--claim-test https://w3id.org/delphi/ontology/disconfirmingObservation Pre-registered. 'Refutes' if no 7-step periodic 14-cell background exists or the mean background fraction is below 0.25, or if fewer than 2 distinct exactly periodic localized-structure velocities are found across all runs. Anything between (background fraction 0.25-0.50, or exactly 2 velocities) is 'mixed'. https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-09--claim-test https://w3id.org/delphi/ontology/evidenceAgainst Background matching uses a 14-cell window, so cells within 13 cells of a structure are flagged as non-background; the 0.80 background fraction is therefore a lower bound. https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-09--claim-test https://w3id.org/delphi/ontology/evidenceAgainst The test covers rule 110 (Wolfram's stated example); the claim's general wording about cellular automata is supported only by this witness. https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-09--claim-test https://w3id.org/delphi/ontology/evidenceAgainst Tracks that collide or split are cut, so the 143 periodic tracks are a sample, not a census, of structures; the velocities found (2/3, -1/2, 0, 1/5, -4/15, -1/3, -1/9) coincide with Cook's gliders A, B, C, D, E, G, F but that catalogue was not used in the detection. https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-09--claim-test https://w3id.org/delphi/ontology/expectedObservation Pre-registered. (A) Background: there is a configuration on a 14-cell ring that rule 110 maps, after 7 steps, onto a rotation of itself (a spatially 14-periodic, temporally 7-periodic background), and in 20 independent random-initial-condition runs (density 0.5, cyclic lattice of 700 cells, 3000 steps) the mean fraction of cells whose 14-cell neighbourhood matches that background (any phase) over steps 1000-3000 is at least 0.50. (B) Structures: across the same runs, tracks of non-background cells that persist for at least 300 steps and are exactly periodic (the window around the track at time t equals the window at time t+p shifted by s cells, for 5 consecutive periods) exist with at least 3 distinct velocities s/p (pairwise differing by more than 0.05 cells/step). Both (A) and (B) must hold for 'supports'. https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-09--claim-test https://w3id.org/delphi/ontology/failCriterion Pre-registered. 'Refutes' if no 7-step periodic 14-cell background exists or the mean background fraction is below 0.25, or if fewer than 2 distinct exactly periodic localized-structure velocities are found across all runs. Anything between (background fraction 0.25-0.50, or exactly 2 velocities) is 'mixed'. https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-09--claim-test https://w3id.org/delphi/ontology/hasConfidence 0.97 https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-09--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch02-09--claim-test--dataset-1 https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-09--claim-test https://w3id.org/delphi/ontology/hasVerdict supports https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-09--claim-test https://w3id.org/delphi/ontology/hypothesis Under the single local rule of elementary cellular automaton rule 110, random initial configurations settle into one dominant periodic background (the 'ether') while other finite configurations embedded in it evolve as persistent localized structures with several distinct, exactly periodic signatures (different velocities), so one rule produces qualitatively different kinds of collective behavior. https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-09--claim-test https://w3id.org/delphi/ontology/inferenceMethod analysis.py enumerates all 16384 configurations of a 14-cell ring under rule 110 and finds those that return to a rotation of themselves after 7 steps; the only non-uniform orbit (14 rotations of 00010011011111, shift 0 after 7 steps, basin 51.5% of ring states) is the ether. Twenty random initial conditions on a 700-cell ring are run for 3000 steps; a cell is 'background' when its 14-cell window equals one of the ether's window codes. Non-background cells are clustered (gap <= 3), clusters are linked across steps (centre moves <= 6 cells), and each track of >= 300 steps is tested for exact periodicity (window at t equals window at t+p shifted by s for 5 consecutive periods, p <= 60). Distinct rational velocities s/p differing by > 0.05 are counted. https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-09--claim-test https://w3id.org/delphi/ontology/passCriterion Pre-registered. (A) Background: there is a configuration on a 14-cell ring that rule 110 maps, after 7 steps, onto a rotation of itself (a spatially 14-periodic, temporally 7-periodic background), and in 20 independent random-initial-condition runs (density 0.5, cyclic lattice of 700 cells, 3000 steps) the mean fraction of cells whose 14-cell neighbourhood matches that background (any phase) over steps 1000-3000 is at least 0.50. (B) Structures: across the same runs, tracks of non-background cells that persist for at least 300 steps and are exactly periodic (the window around the track at time t equals the window at time t+p shifted by s cells, for 5 consecutive periods) exist with at least 3 distinct velocities s/p (pairwise differing by more than 0.05 cells/step). Both (A) and (B) must hold for 'supports'. https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-09--claim-test https://w3id.org/delphi/ontology/preregistered false https://w3id.org/delphi/resource/claim/wolfram2002-ch02-09 https://w3id.org/delphi/ontology/hasAssessment https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-09--claim-test https://w3id.org/delphi/resource/evidence/wolfram2002-ch02-09--claim-test--dataset-1 http://purl.org/dc/terms/description spacetime patterns in which background and localized structures are detected https://w3id.org/delphi/resource/evidence/wolfram2002-ch02-09--claim-test--dataset-1 http://purl.org/dc/terms/license CC0 (generated data) https://w3id.org/delphi/resource/evidence/wolfram2002-ch02-09--claim-test--dataset-1 http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/EvidenceItem https://w3id.org/delphi/resource/evidence/wolfram2002-ch02-09--claim-test--dataset-1 http://www.w3.org/2000/01/rdf-schema#label Dataset: Elementary cellular automaton rule 110, random initial conditions (generated by analysis.py) https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE/provenance https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1-cursor-cloud-agent http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.w3.org/ns/prov#SoftwareAgent https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1-cursor-cloud-agent http://www.w3.org/2000/01/rdf-schema#label delphisci claim tester (Claude Fable 5.1 (Cursor cloud agent); cursor/claim-tests-wolfram-nks-f0e1) https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1-cursor-cloud-agent http://www.w3.org/ns/prov#actedOnBehalfOf https://orcid.org/0009-0007-4948-9192 https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1-cursor-cloud-agent https://w3id.org/delphi/ontology/usesModel https://w3id.org/delphi/resource/model/claude-fable-5-1-cursor-cloud-agent https://w3id.org/delphi/resource/model/claude-fable-5-1-cursor-cloud-agent http://purl.org/dc/terms/identifier Claude Fable 5.1 (Cursor cloud agent) https://w3id.org/delphi/resource/model/claude-fable-5-1-cursor-cloud-agent http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/LanguageModel https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE/assertion http://www.w3.org/ns/prov#wasAttributedTo https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1-cursor-cloud-agent https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE/assertion http://www.w3.org/ns/prov#wasDerivedFrom https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/wolfram-nks/wolfram2002-ch02-09/result.json https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE/assertion http://www.w3.org/ns/prov#wasGeneratedBy https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE/test https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE/plan http://www.w3.org/ns/prov#hadPlan https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/README.md https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE/test http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.w3.org/ns/prov#Activity https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE/test http://www.w3.org/ns/prov#qualifiedAssociation https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE/plan https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE/test http://www.w3.org/ns/prov#wasAssociatedWith https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1-cursor-cloud-agent https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE/pubinfo https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE http://purl.org/dc/terms/created 2026-11-08T16:24:31.915Z https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE http://purl.org/dc/terms/creator https://orcid.org/0009-0007-4948-9192 https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE http://purl.org/dc/terms/license https://creativecommons.org/licenses/by/4.0/ https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE http://purl.org/nanopub/x/hasNanopubType https://w3id.org/delphi/ontology/Assessment https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE http://purl.org/nanopub/x/introduces https://w3id.org/delphi/resource/assessment/wolfram2002-ch02-09--claim-test https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE http://www.w3.org/2000/01/rdf-schema#label Claim test of wolfram2002-ch02-09: supports, confidence 0.97 https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE https://w3id.org/delphi/ontology/domain https://w3id.org/delphi/resource/domain/wolfram-nks-2002 https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE/sig http://purl.org/nanopub/x/hasAlgorithm RSA https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE/sig http://purl.org/nanopub/x/hasPublicKey MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE/sig http://purl.org/nanopub/x/hasSignature jUAhFlldi5kH87fkY0zHSV66ZL8UUpsmNZ/XZnlYSgZrLRs31MWDn8RUxSpzIvD2sG6aVoIYyUUxuHpfkFYKdSli6/qDOciZ1unkU89Ptjd5MuBG/JEiTBB9T2CRSzaHE9FZmn1CU+0nBa7/5/k/9j0/PaRiSNngiUQLKvFiSf5jjn2BRhccoGoHjorWXtsyznmUsBMhL4HiIwuFH622wDpDsh855ZLwDgmLOsS9xG+sAa5V/ptYOmIIprq6kU2kfxUPBOeEtbQTLvbGUvVUG3+M2yNPCA5kLaIJw+DL2g6mfsOwePd71zuml0dkNh4DxgdCgFV6pXyk3dlrDyWOMA== https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE/sig http://purl.org/nanopub/x/hasSignatureTarget https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE https://w3id.org/np/RAfXZzzFzmaK5x8kvA5OMDKsogo4nyGFpuhTB6NY-TIRE/sig http://purl.org/nanopub/x/signedBy https://orcid.org/0009-0007-4948-9192