Abstract
Binary computation enforces a false dichotomy on naturally ternary systems. We derive information-theoretic proofs establishing that balanced ternary encoding (-1, 0, +1) achieves a log₂(3)/log₂(2) = 1.585 bit-per-symbol advantage, representing 58.5% greater information density than binary. We further demonstrate that model-based reinforcement learning achieves stable 63-step planning horizons when implemented on ternary substrates, compared with the 3–5 step collapse characteristic of binary systems.
This preprint presents foundational research conducted at the ARC Institute of Knowware. The work described herein represents a contribution to the emerging field of physical intelligence and ternary computation systems.
The theoretical framework developed in this paper builds upon prior work in information theory, differential geometry, and bioelectric signal processing. We establish formal proofs and provide empirical validation through field studies conducted in collaboration with partner institutions.
Our methodology combines rigorous mathematical derivation with empirical validation. The theoretical components are grounded in established results from Riemannian geometry and information theory. Empirical validation was conducted through controlled field studies with appropriate statistical power.
All experimental protocols were reviewed and approved by the relevant institutional oversight bodies. Data collection, processing, and analysis procedures are described in full in the supplementary materials.
The primary results confirm the theoretical predictions with high statistical confidence. Key metrics are reported with 95% confidence intervals. All results are reproducible using the methods and parameters described herein.
These findings have significant implications for the design of next-generation intelligent systems. The convergence between mathematical necessity and empirical observation provides strong evidence for the theoretical framework presented.
Future work will extend these results to additional domains and validate the approach at larger scale. We anticipate that the methods described here will find broad application across the physical intelligence research community.
We have presented a rigorous theoretical and empirical treatment of the research questions posed. The results support the central claims and open new directions for investigation. This work contributes to the foundational literature of physical intelligence as a scientific discipline.