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Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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VCML Paper 106: Computational Universality -- Empirical Demonstration of Memory, Signal Propagation, and Logic Gate

Authors: Aubin-Moreau, Gabriel;

VCML Paper 106: Computational Universality -- Empirical Demonstration of Memory, Signal Propagation, and Logic Gate

Abstract

We empirically demonstrate that VCML possesses the three structural primitives required for Turing-complete computation. Part A (NAND validation): vcml_2in(a,b,w=1,ctrl=1.5) = NAND(a,b) for all (a,b) in {0,1}^2, directly validating vcml_implements_nand from TuringUniversal.lean. NOT, AND, OR gates also validated via NAND composition. Part B (signal propagation): domain wall moves at v=-0.119+-0.003 px/step (6 seeds, R^2>0.99), confirming alive region expands at constant velocity. Part C (memory): Papers 102-104 bulk re-emergence 0.963 (alive) and 0.926 (dead) confirms two stable attractors; at L=128 injection test shows bulk equilibration. Part D (logic gate): domain wall collision outcome depends on input encoding (pulse width), range 0.163 across 4 widths (>0.10 threshold), logic confirmed. Part E (critical signature): boundary C(t) exponent alpha=0.28 (marginal), consistent with Langton 1990 Class 4 critical computation hypothesis. Combined with TuringUniversal.lean (NAND proved zero sorry) and classical results (Sheffer 1913 NAND completeness, Cook 1971 TM-circuit), VCML is Turing universal. Open: does beta=1/phi uniquely determine the computational phase? Paper 107 will test universality across ctrl values.

Full source code and data at https://github.com/AccidentalGenius101/adaptive-memory-theory

Keywords

non-equilibrium, universality class, causal purity, critical exponents, CUDA, VCSM, Monte Carlo, zone-mean order parameter, GPU simulation, VCML

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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