This technical note extends the Yu-Liang Coordinate system (Rₘ₋) — 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 =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 || 0. 5\ 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 (n²) floating-point arithmetic.
Yu et al. (Sun,) studied this question.
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