https://w3id.org/np/RAEnZE2Tel-HtO-Mh9XTkXD95Fo2ttQ0_U_vR4X3_YQiM/Head https://w3id.org/np/RAEnZE2Tel-HtO-Mh9XTkXD95Fo2ttQ0_U_vR4X3_YQiM http://www.nanopub.org/nschema#hasAssertion https://w3id.org/np/RAEnZE2Tel-HtO-Mh9XTkXD95Fo2ttQ0_U_vR4X3_YQiM/assertion https://w3id.org/np/RAEnZE2Tel-HtO-Mh9XTkXD95Fo2ttQ0_U_vR4X3_YQiM http://www.nanopub.org/nschema#hasProvenance https://w3id.org/np/RAEnZE2Tel-HtO-Mh9XTkXD95Fo2ttQ0_U_vR4X3_YQiM/provenance https://w3id.org/np/RAEnZE2Tel-HtO-Mh9XTkXD95Fo2ttQ0_U_vR4X3_YQiM http://www.nanopub.org/nschema#hasPublicationInfo https://w3id.org/np/RAEnZE2Tel-HtO-Mh9XTkXD95Fo2ttQ0_U_vR4X3_YQiM/pubinfo https://w3id.org/np/RAEnZE2Tel-HtO-Mh9XTkXD95Fo2ttQ0_U_vR4X3_YQiM http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.nanopub.org/nschema#Nanopublication https://w3id.org/np/RAEnZE2Tel-HtO-Mh9XTkXD95Fo2ttQ0_U_vR4X3_YQiM/assertion https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-27--claim-test http://purl.org/dc/terms/description The 10 rule icons of the p. 707 figure were transcribed by grey level and arrow geometry (derived/tm25-rule.json). analysis.py simulates the machine on a tape of colour-1 cells, a 0, the rule-110 list encoded as 4*list, and 0's, with the head on the first 0 right of the data in state 1 (as in the figure), records the tape each time the head reaches a new rightmost position, decodes colour 4 as black, and compares snapshot k with rule-110 iterate k of the list (time offset and spatial shift fixed once from the single-cell run: both 0). This is done for the single-cell list and 40 random lists of length 10-60, 200 snapshots each. The pre-registration's guessed start (head on the prepended 0) is also run and reported. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-27--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-ch11-27--claim-test http://www.w3.org/2000/01/rdf-schema#comment Measured: 1 fraction of tape snapshots equal to the corresponding rule-110 step (n = 8159, exact (deterministic)). Interpretation: The claim has two parts: (i) the 2-state 5-colour machine emulates rule 110 one step per complete sweep, which is tested directly by simulation; (ii) universality follows from (i) and the universality of rule 110 (Cook 2004, Complex Systems 15(1), doi:10.25088/ComplexSystems.15.1.1), which is taken as a published premise and not re-proved here. 'Complete sweep' is operationalized as the moment the head reaches a position further right than ever before (the convention of Wolfram's compressed picture). The rule table is only published as a picture; it was transcribed from the figure's grey levels and arrow orientations (white=0, lightest grey=1, ..., darkest grey=4; the head arrow pointing down is state 1 because that is the state in which the published initial condition yields rule 110, pointing up is state 2). The number of states and colours in the table (2 and 5) is also checked. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-27--claim-test http://www.w3.org/2000/01/rdf-schema#label Claim test of wolfram2002-ch11-27: supports, confidence 0.9 https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-27--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-ch11-27/result.json https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-27--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-ch11-27--claim-test https://w3id.org/delphi/ontology/admissibleDatasets Planned datasets: nks-p707-fig-a-tm25-rule, nks-note-rule110-turing-machines, cook2004-rule110-universality https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-27--claim-test https://w3id.org/delphi/ontology/assessmentType claim-test/0.1.0 https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-27--claim-test https://w3id.org/delphi/ontology/dataKind computational https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-27--claim-test https://w3id.org/delphi/ontology/disconfirmingObservation Pre-registered. 'Refutes' if for any initial list some snapshot differs from the corresponding rule-110 iterate, or if no fixed offset makes the single-cell run match; 'inconclusive / not-operationalizable' if the rule table cannot be read unambiguously from the published figure. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-27--claim-test https://w3id.org/delphi/ontology/evidenceAgainst Deviation from the pre-registration: the head's start position was guessed as 'the first tape element' before reading the figure; with that start the machine emulates rule 110 only from a single black cell (and only in the down-arrow state). The figure on p. 707 shows the head starting on the first white cell right of the data, and with that start the emulation is exact for every list tested; the pre-registered pass criterion (100% snapshot matches with a fixed offset) is met for this figure-consistent start and the comparison itself was not changed. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-27--claim-test https://w3id.org/delphi/ontology/evidenceAgainst The rule table exists only as a picture; the transcription (grey levels 255/204/153/102/51 -> colours 0-4; up/down arrow -> states 1/2) is recorded in derived/tm25-rule.json. All 10 cases are exercised thousands of times in every run, so a transcription error would almost certainly have broken the exact agreement. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-27--claim-test https://w3id.org/delphi/ontology/evidenceAgainst The snapshots compared are the 'new rightmost head position' moments of Wolfram's compressed picture; snapshots 0 and 1 (initial tape and first excursion) also match but were excluded by the script's K_MIN = 2. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-27--claim-test https://w3id.org/delphi/ontology/evidenceAgainst Universality itself is inherited from Cook's (2004) proof for rule 110 and is not re-derived; what is verified computationally is the reduction (one rule-110 step per complete sweep). 'Simpler than the 7-state 4-color machine' is read as 2*5 = 10 < 7*4 = 28 rule cases. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-27--claim-test https://w3id.org/delphi/ontology/expectedObservation Pre-registered. Using the rule table transcribed from the p. 707 figure (10 cases; the transcription is recorded in derived/tm25-rule.json), for the single-cell initial list and for 40 random binary lists of length 10-60 (numpy default_rng seeds 0..39), with a fixed integer offset c determined once from the single-cell run and then held fixed, the k-th new-rightmost snapshot decoded as above equals rule-110 iterate k-c of the initial list for every k from c to c+199, on every cell of the window spanning the full rule-110 pattern (100% of 41 x 200 snapshot comparisons). 'Supports' if this holds. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-27--claim-test https://w3id.org/delphi/ontology/failCriterion Pre-registered. 'Refutes' if for any initial list some snapshot differs from the corresponding rule-110 iterate, or if no fixed offset makes the single-cell run match; 'inconclusive / not-operationalizable' if the rule table cannot be read unambiguously from the published figure. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-27--claim-test https://w3id.org/delphi/ontology/hasConfidence 0.9 https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-27--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-27--claim-test--dataset-1 https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-27--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-27--claim-test--dataset-2 https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-27--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-27--claim-test--dataset-3 https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-27--claim-test https://w3id.org/delphi/ontology/hasVerdict supports https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-27--claim-test https://w3id.org/delphi/ontology/hypothesis The 2-state, 5-colour Turing machine whose rule is drawn on NKS p. 707, started as described in the note 'Rule 110 Turing machines' (p. 1119: tape = Prepend[4 list, 0] with colour 1 to the left and colour 0 to the right, head on the first tape element in state 1), emulates rule 110: successive 'new rightmost head position' snapshots of the tape, decoded as colour 4 -> black and all other colours -> white, are successive steps of rule 110 applied to the initial list on a white background. Given Cook's published proof that rule 110 is universal, the machine is universal. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-27--claim-test https://w3id.org/delphi/ontology/inferenceMethod The 10 rule icons of the p. 707 figure were transcribed by grey level and arrow geometry (derived/tm25-rule.json). analysis.py simulates the machine on a tape of colour-1 cells, a 0, the rule-110 list encoded as 4*list, and 0's, with the head on the first 0 right of the data in state 1 (as in the figure), records the tape each time the head reaches a new rightmost position, decodes colour 4 as black, and compares snapshot k with rule-110 iterate k of the list (time offset and spatial shift fixed once from the single-cell run: both 0). This is done for the single-cell list and 40 random lists of length 10-60, 200 snapshots each. The pre-registration's guessed start (head on the prepended 0) is also run and reported. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-27--claim-test https://w3id.org/delphi/ontology/passCriterion Pre-registered. Using the rule table transcribed from the p. 707 figure (10 cases; the transcription is recorded in derived/tm25-rule.json), for the single-cell initial list and for 40 random binary lists of length 10-60 (numpy default_rng seeds 0..39), with a fixed integer offset c determined once from the single-cell run and then held fixed, the k-th new-rightmost snapshot decoded as above equals rule-110 iterate k-c of the initial list for every k from c to c+199, on every cell of the window spanning the full rule-110 pattern (100% of 41 x 200 snapshot comparisons). 'Supports' if this holds. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-27--claim-test https://w3id.org/delphi/ontology/preregistered false https://w3id.org/delphi/resource/claim/wolfram2002-ch11-27 https://w3id.org/delphi/ontology/hasAssessment https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-27--claim-test https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-27--claim-test--dataset-1 http://purl.org/dc/terms/description the rule table (transcribed in derived/tm25-rule.json) and the compressed-evolution figure that fixes the head's start position https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-27--claim-test--dataset-1 http://purl.org/dc/terms/license copyright Stephen Wolfram LLC; used for verification only https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-27--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-ch11-27--claim-test--dataset-1 http://www.w3.org/2000/01/rdf-schema#label Dataset: NKS p. 707, figure: rule icons of the 2-state 5-colour Turing machine https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-27--claim-test--dataset-1 http://www.w3.org/ns/prov#atLocation https://www.wolframscience.com/nks/p707--universality-in-turing-machines-and-other-systems/ https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-27--claim-test--dataset-1 http://www.w3.org/ns/prov#atLocation https://www.wolframscience.com/nks/p708--universality-in-turing-machines-and-other-systems/ https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-27--claim-test--dataset-1 http://www.w3.org/ns/prov#atLocation https://www.wolframscience.com/nks/pages/p707--universality-in-turing-machines-and-other-systems/fig-a.png https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-27--claim-test--dataset-1 http://www.w3.org/ns/prov#wasDerivedFrom https://www.wolframscience.com/nks/p707--universality-in-turing-machines-and-other-systems/ https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-27--claim-test--dataset-1 https://w3id.org/delphi/ontology/hasChecksum sha256:bb608ff09b0759e64d7f5fb39cbf5f7381bbb8a2ed4b9bee6cf7117360f4b212 https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-27--claim-test--dataset-1 https://w3id.org/delphi/ontology/hasChecksum sha256:c06ecd6a440f6364ec32b36cb015afb5b91c1ccae3feb4f152d744f5846762d9 https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-27--claim-test--dataset-1 https://w3id.org/delphi/ontology/hasChecksum sha256:f488996361cd0dd93c2c1878147764bbf54091cb447645be6d67478d831ecc54 https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-27--claim-test--dataset-2 http://purl.org/dc/terms/description tape encoding of a rule-110 initial condition: Prepend[4 list, 0], 1's to the left, 0's to the right https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-27--claim-test--dataset-2 http://purl.org/dc/terms/license copyright Stephen Wolfram LLC https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-27--claim-test--dataset-2 http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/EvidenceItem https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-27--claim-test--dataset-2 http://www.w3.org/2000/01/rdf-schema#label Dataset: NKS note 'Rule 110 Turing machines' (p. 1119) https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-27--claim-test--dataset-2 http://www.w3.org/ns/prov#atLocation https://www.wolframscience.com/nks/notes-11-12--rule-110-turing-machines/ https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-27--claim-test--dataset-2 http://www.w3.org/ns/prov#wasDerivedFrom https://www.wolframscience.com/nks/notes-11-12--rule-110-turing-machines/ https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-27--claim-test--dataset-2 https://w3id.org/delphi/ontology/hasChecksum sha256:560963ac448c1dc920703019cf004dee864f256fea752193fbda759f5c2e6a2f https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-27--claim-test--dataset-3 http://purl.org/dc/terms/description published proof that rule 110 is universal; premise for the universality conclusion, not re-verified here https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-27--claim-test--dataset-3 http://purl.org/dc/terms/license Complex Systems Publications https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-27--claim-test--dataset-3 http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/EvidenceItem https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-27--claim-test--dataset-3 http://www.w3.org/2000/01/rdf-schema#label Dataset: Cook, M. (2004) Universality in Elementary Cellular Automata, Complex Systems 15(1):1-40 https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-27--claim-test--dataset-3 http://www.w3.org/ns/prov#atLocation https://content.wolfram.com/sites/13/2023/02/15-1-1.pdf https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-27--claim-test--dataset-3 http://www.w3.org/ns/prov#wasDerivedFrom https://www.complex-systems.com/abstracts/v15_i01_a01/ https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-27--claim-test--dataset-3 https://w3id.org/delphi/ontology/hasChecksum sha256:c9a2885248ae2811c5825c5bcbaa52ca167a7d5300ba88f87ee832b93b293c03 https://w3id.org/np/RAEnZE2Tel-HtO-Mh9XTkXD95Fo2ttQ0_U_vR4X3_YQiM/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); 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