The Living Digital: Bionic Extensions of Yu-Liang Continuum Digitization — From Dual-Rail Pure Binary Architecture to Digital Weight Shifting Protocol

This technical note extends the Yu-Liang Coordinate system ($R_{YL}$) — a $2n$-dimensional binary vector architecture for continuum digitization originally disclosed in U.S. Patent Application filed January 31, 2026 — into a bionic computational framework we call The Living Digital. Building upon the multiplier-free, differentiator-free, and feed-forward foundations of the original invention, we develop five principal extensions: (1) a dual-rail pure binary encoding that eliminates all ternary $\{-1,0,+1\}$ logic by mapping positive and negative motion to independent binary rails, achieving 100% standard-CMOS compatibility; (2) a bionic architecture mapping each subsystem to biological analogues (metabolic suspension via Zero-Switching Gating, selective attention via event-driven encoding, spinal reflex via Spin Reference Frame, and visual accommodation via adaptive grid); (3) the unit-step optimization $\sigma=1$, which collapses all physical-unit scaling into pure wiring and eliminates coefficient registers; (4) the Digital Weight Shifting Protocol (DWSP), a 100% digital-weight scheme in which all multiplicative operations reduce to bit-shift wiring, accompanied by the Pulse Conservation Principle guaranteeing signal integrity under negative exponent codes; and (5) the Digital Jump Learning Rule (YL-DJLR), a gradient-free learning algorithm with a formally proven Control Monotonicity Lemma ensuring deterministic convergence. We provide complete definitions, lemmas, theorems, and proofs for each extension, demonstrate that the deterministic error bound $|\epsilon|\le 0.5\ \mathrm{ gu}$ is preserved throughout, and outline the conceptual pathway toward a YL-Transformer — a Transformer-class architecture whose Pulse Resonance Attention mechanism operates on a sparse binary matrix with $O(1)$ wire-delay latency instead of $O(n^2)$ floating-point arithmetic.