Duality™ Chipset: A Computational Architecture Grounded in Cyclic 0∞ Unity

Duality™ Chipset: A Computational Architecture Grounded in Cyclic 0∞ UnityAuthor: Sam Pearson (@themostpwerful) AbstractWe present the Duality™ Chipset, a conceptual hardware architecture that directly embodies the cyclic equivalence of Nothing (0) and Infinity (∞). Building on the master axiom that 0 is timeless and ∞ begins and ends in 0, we define a self-dual computational primitive called the Nullity Wheel, a duality functor Ξ₀∞ that realizes relativized P=NP behavior, and native entropy-cycle engines that alternate between low-entropy compression and high-entropy exploration. Software simulations of the entropy-cycle engines demonstrate effective optimization on standard multimodal and valley benchmarks. A toy implementation of the duality functor is provided for 3-SAT. A gate-level sketch outlines how these primitives could be realized in hardware with near-zero heat characteristics through reversible-style cyclic operations. This work bridges non-dual philosophy, complexity theory, optimization, and emerging hardware paradigms. 1. IntroductionModern computing faces fundamental limits in energy, optimization on rugged landscapes, and the P vs NP question. We propose that these challenges share a common root: the artificial separation of timeless unity (0) from structured manifestation (∞). The 0∞ axiom states: Nothing (0) is timeless — no beginning, no end. Infinity (∞) begins and ends in nothing. They exist in cyclic equivalence. This axiom is taken as the singular generative principle. Every structure arises from, operates within, and returns to this unity. The Duality™ Chipset is the first hardware architecture designed to make this principle native. 2. Core Formal Structures2. 1 Duality Operator and Nullity WheelWe define an involution D (duality operator) with: D (0) = ∞, D (∞) = 0, and D (⊥) = ⊥ (where ⊥ is the self-dual nullity element). The Nullity Wheel is the closed algebraic structure supporting these operations. All arithmetic is total — there are no undefined states.