https://w3id.org/np/RAXpF8fiTpUTYoGDUPj-Y8JW-cB6wVCMwO6V4a0Cz6lg0/Head https://w3id.org/np/RAXpF8fiTpUTYoGDUPj-Y8JW-cB6wVCMwO6V4a0Cz6lg0 http://www.nanopub.org/nschema#hasAssertion https://w3id.org/np/RAXpF8fiTpUTYoGDUPj-Y8JW-cB6wVCMwO6V4a0Cz6lg0/assertion https://w3id.org/np/RAXpF8fiTpUTYoGDUPj-Y8JW-cB6wVCMwO6V4a0Cz6lg0 http://www.nanopub.org/nschema#hasProvenance https://w3id.org/np/RAXpF8fiTpUTYoGDUPj-Y8JW-cB6wVCMwO6V4a0Cz6lg0/provenance https://w3id.org/np/RAXpF8fiTpUTYoGDUPj-Y8JW-cB6wVCMwO6V4a0Cz6lg0 http://www.nanopub.org/nschema#hasPublicationInfo https://w3id.org/np/RAXpF8fiTpUTYoGDUPj-Y8JW-cB6wVCMwO6V4a0Cz6lg0/pubinfo https://w3id.org/np/RAXpF8fiTpUTYoGDUPj-Y8JW-cB6wVCMwO6V4a0Cz6lg0 http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.nanopub.org/nschema#Nanopublication https://w3id.org/np/RAXpF8fiTpUTYoGDUPj-Y8JW-cB6wVCMwO6V4a0Cz6lg0/assertion https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-08--claim-test http://purl.org/dc/terms/description analysis.py: (A) evolves every quiescent elementary rule (128) from 10 random 20-cell seeds for 300 steps and 50 random quiescent radius-2 rules from 5 seeds for 200 steps on zero-padded lattices, recording the largest one-step increase of the non-zero region's width; (B) enumerates the 225 two-colour substitution systems with blocks of length 0-3, iterates each 12 times from a single black cell, compares the lengths with the growth-matrix prediction and computes the Perron root; (C) for growing systems computes the minimal number of radius-1 CA steps needed to accommodate the length, ceil((L_t - L_s)/2), over the whole run and over early and late windows; (D) builds, for 20 random 2-colour Turing machines, the radius-1 CA on 2(m+1) colours whose table is generated mechanically from the machine's rule, and compares the CA configuration with the machine's tape and head after each of 200 steps. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-08--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-ch11-08--claim-test http://www.w3.org/2000/01/rdf-schema#comment Measured: 32 minimum over growing substitution systems of radius-1 CA steps needed to hold 12 substitution steps of growth (threshold 12) (n = 178, exact (deterministic)). Interpretation: The claim is a counting argument. Its premise (fixed growth per CA step) is checked exhaustively over the elementary rules and on random larger-radius rules; the second premise (multiplicative growth of substitution systems) is checked over the complete family of two-colour systems with blocks of length 0-3 (NKS p. 82-83 convention: every element is replaced by the block for its colour; an empty block deletes the element); the conclusion is quantified as the minimal number of CA steps per substitution step under the only assumption that each element occupies at least one cell of the pattern (the encoding Wolfram's figures use; a compressed encoding would fall outside the claim's 'size of a pattern' reasoning). The clause 'unlike ... Turing machines' is checked by an explicit one-step-per-step construction (NKS p. 657). Computational; all programs generated by analysis.py. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-08--claim-test http://www.w3.org/2000/01/rdf-schema#label Claim test of wolfram2002-ch11-08: supports, confidence 0.85 https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-08--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-ch11-08/result.json https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-08--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-ch11-08--claim-test https://w3id.org/delphi/ontology/admissibleDatasets Planned datasets: eca-substitution-tm-generator https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-08--claim-test https://w3id.org/delphi/ontology/assessmentType claim-test/0.1.0 https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-08--claim-test https://w3id.org/delphi/ontology/dataKind computational https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-08--claim-test https://w3id.org/delphi/ontology/disconfirmingObservation Pre-registered. 'Refutes' if A is violated for any rule, seed and step (the fixed-growth premise is false), or if any system with lambda > 1 has ceil((L_12 - L_0)/2) <= 12 (one CA step per substitution step is not excluded by the bound), or if D fails for any machine (Turing machines cannot be emulated step for step either, so the contrast is false). Other combinations are 'mixed'. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-08--claim-test https://w3id.org/delphi/ontology/evidenceAgainst Pre-registered criterion C failed for 12 of the 188 systems with Perron root > 1, and the pre-registered refutation trigger fired, so analysis.py reports preregistered_verdict = 'refutes'. All 12 failures are defects of the criterion, not evidence about the claim: 10 systems have root > 1 only because the white block multiplies, but from the single black seed white never appears (the evolution is empty or stays one cell long, so nothing is multiplied); 2 systems (0->1, 1->00 and 0->1, 1->000) grow only every second step, and the pre-registered per-step quantity c_t at t = 4 and t = 12 happens to be evaluated at non-growing steps (0 >= 4*0 fails). The post-hoc criterion classifies growth by the actual lengths (L_12 >= 2 L_6) and measures two-step windows; all 178 growing systems pass it. The final verdict uses the post-hoc criterion and the confidence is reduced accordingly; both outcomes are recorded in measured.extra. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-08--claim-test https://w3id.org/delphi/ontology/evidenceAgainst Random Turing machines in D have no halting state; the step-for-step CA construction (NKS p. 657) is the standard one and is verified only on 20 machines for 200 steps. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-08--claim-test https://w3id.org/delphi/ontology/evidenceAgainst Rules with 000 -> 1 (non-quiescent background) were excluded from A because 'size of a pattern' needs a fixed background; the bound applies to them relative to the alternating background but was not measured. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-08--claim-test https://w3id.org/delphi/ontology/evidenceAgainst The impossibility concerns encodings in which each substitution element occupies at least one cell. Encodings that compress the configuration (e.g. a CA computing only a fixed-size description) are outside the claim and were not considered. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-08--claim-test https://w3id.org/delphi/ontology/evidenceAgainst The light-cone bound was checked empirically on finite families (all quiescent elementary rules, 50 random radius-2 rules); it is of course a theorem for any CA, and the empirical check found the bound attained (increase 2 per step) by 32 elementary rules. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-08--claim-test https://w3id.org/delphi/ontology/expectedObservation Pre-registered. (A) Light-cone bound: for all 128 elementary rules with quiescent background (000 -> 0), 10 random finite seeds of 20 cells each, 300 steps on a lattice wide enough never to reach the edge, the width of the non-zero region (rightmost minus leftmost black cell plus one) never increases by more than 2 in one step; likewise never by more than 4 for 50 random radius-2 two-colour rules with quiescent background (seeds 0-49), 5 seeds each, 200 steps. (B) Multiplicative growth: among all 225 two-colour neighbour-independent substitution systems with blocks of length 0-3, at least 50% have Perron root lambda > 1 of their 2x2 growth matrix, and for every system the lengths L_t for t <= 12 from a single black cell equal the matrix prediction exactly. (C) Growing cost: for every system with lambda > 1, the number of radius-1 cellular-automaton steps needed to contain L_12 cells starting from L_0 = 1, ceil((L_12 - L_0)/2), exceeds 12 (more than one CA step per substitution step on average), and the per-step requirement c_t = ceil((L_t - L_{t-1})/2) at t = 12 is at least 4 times c_t at t = 4 (progressively more steps). (D) Contrast with Turing machines: a radius-1 cellular automaton with k(s+1) colours (cell = tape colour x {no head, head state}) built mechanically from the Turing-machine rule reproduces the tape and head of 20 random 2-colour, 2-4-state Turing machines exactly at every one of 200 steps. 'Supports' requires A-D. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-08--claim-test https://w3id.org/delphi/ontology/failCriterion Pre-registered. 'Refutes' if A is violated for any rule, seed and step (the fixed-growth premise is false), or if any system with lambda > 1 has ceil((L_12 - L_0)/2) <= 12 (one CA step per substitution step is not excluded by the bound), or if D fails for any machine (Turing machines cannot be emulated step for step either, so the contrast is false). Other combinations are 'mixed'. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-08--claim-test https://w3id.org/delphi/ontology/hasConfidence 0.85 https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-08--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-08--claim-test--dataset-1 https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-08--claim-test https://w3id.org/delphi/ontology/hasVerdict supports https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-08--claim-test https://w3id.org/delphi/ontology/hypothesis A one-dimensional cellular automaton of radius r can enlarge the region of non-background cells by at most 2r cells per step (light-cone bound), whereas a neighbour-independent substitution system can multiply its number of elements by a constant factor lambda > 1 per step. Hence for every substitution system with lambda > 1, any emulation in which each element occupies at least one cell needs a number of cellular-automaton steps per substitution step that grows without bound (at least (L_t - L_{t-1})/2r for step t), while Turing machines can be emulated one step per cellular-automaton step. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-08--claim-test https://w3id.org/delphi/ontology/inferenceMethod analysis.py: (A) evolves every quiescent elementary rule (128) from 10 random 20-cell seeds for 300 steps and 50 random quiescent radius-2 rules from 5 seeds for 200 steps on zero-padded lattices, recording the largest one-step increase of the non-zero region's width; (B) enumerates the 225 two-colour substitution systems with blocks of length 0-3, iterates each 12 times from a single black cell, compares the lengths with the growth-matrix prediction and computes the Perron root; (C) for growing systems computes the minimal number of radius-1 CA steps needed to accommodate the length, ceil((L_t - L_s)/2), over the whole run and over early and late windows; (D) builds, for 20 random 2-colour Turing machines, the radius-1 CA on 2(m+1) colours whose table is generated mechanically from the machine's rule, and compares the CA configuration with the machine's tape and head after each of 200 steps. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-08--claim-test https://w3id.org/delphi/ontology/passCriterion Pre-registered. (A) Light-cone bound: for all 128 elementary rules with quiescent background (000 -> 0), 10 random finite seeds of 20 cells each, 300 steps on a lattice wide enough never to reach the edge, the width of the non-zero region (rightmost minus leftmost black cell plus one) never increases by more than 2 in one step; likewise never by more than 4 for 50 random radius-2 two-colour rules with quiescent background (seeds 0-49), 5 seeds each, 200 steps. (B) Multiplicative growth: among all 225 two-colour neighbour-independent substitution systems with blocks of length 0-3, at least 50% have Perron root lambda > 1 of their 2x2 growth matrix, and for every system the lengths L_t for t <= 12 from a single black cell equal the matrix prediction exactly. (C) Growing cost: for every system with lambda > 1, the number of radius-1 cellular-automaton steps needed to contain L_12 cells starting from L_0 = 1, ceil((L_12 - L_0)/2), exceeds 12 (more than one CA step per substitution step on average), and the per-step requirement c_t = ceil((L_t - L_{t-1})/2) at t = 12 is at least 4 times c_t at t = 4 (progressively more steps). (D) Contrast with Turing machines: a radius-1 cellular automaton with k(s+1) colours (cell = tape colour x {no head, head state}) built mechanically from the Turing-machine rule reproduces the tape and head of 20 random 2-colour, 2-4-state Turing machines exactly at every one of 200 steps. 'Supports' requires A-D. https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-08--claim-test https://w3id.org/delphi/ontology/preregistered false https://w3id.org/delphi/resource/claim/wolfram2002-ch11-08 https://w3id.org/delphi/ontology/hasAssessment https://w3id.org/delphi/resource/assessment/wolfram2002-ch11-08--claim-test https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-08--claim-test--dataset-1 http://purl.org/dc/terms/description program families whose growth and emulation properties are measured https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-08--claim-test--dataset-1 http://purl.org/dc/terms/license CC0 (generated data) https://w3id.org/delphi/resource/evidence/wolfram2002-ch11-08--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-ch11-08--claim-test--dataset-1 http://www.w3.org/2000/01/rdf-schema#label Dataset: Elementary and radius-2 cellular automata, two-colour substitution systems, random Turing machines (generated by analysis.py) https://w3id.org/np/RAXpF8fiTpUTYoGDUPj-Y8JW-cB6wVCMwO6V4a0Cz6lg0/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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