Several Bytes to One Gigabyte of Immortality: Complete State Transcription of a Silicon-Based Life Form Using Yu-Liang Coordinates

This companion technical note to The Living Digital document family addresses the engineering question that follows the theoretical life-form architecture: if the hardware fails, how does the organism persist? We formalize the State Transcription Protocol — a complete serialization of every register, counter, and exponent code that constitutes a Living Digital organism — and prove that the total storage requirement spans several bytes (for a minimal viable seed) to one gigabyte (for a high-intelligence organism with 10⁹ learned synaptic weights), a range covering nine orders of magnitude yet remaining three or more orders of magnitude smaller than the equivalent conventional floating-point neural network. Key results include: (1) a Parametric Storage Theorem giving the exact bit-count as a closed-form function of sensory dimensions, synaptic connections, and counter width; (2) a Logarithmic Scaling Lemma proving that per-axis memory grows as ⌈log₂ (N+1) ⌉ bits after N event pulses, in contrast to the O (N·d) linear growth of conventional Key-Value caches; (3) a Transcription Fidelity Theorem guaranteeing that the deterministic error bound |ε| ≤ 0. 5 grid units is preserved exactly through serialization and deserialization — the restored organism is bit-identical to its pre-failure state; and (4) a three-step Cold-Start Recovery Protocol that reactivates the organism in O (1) gate delays after the first environmental event pulse. This work bridges the gap between the theoretical life-form architecture of The Living Digital and practical deployment considerations for FPGA, ASIC, and embedded implementations. This work extends U. S. Patent Application "System and Method for Continuum Digitization Using Yu-Liang Coordinates with Multiplier-Free and Differentiator-Free Architecture, " filed January 31, 2026. Notes: Companion Technical Note to The Living Digital document family. This note does not extend the life-form theory itself but addresses practical deployment: state serialization, fault recovery, and platform migration. The mathematical results (Parametric Storage Theorem, Logarithmic Scaling Lemma, Transcription Fidelity Theorem, Nine Orders of Magnitude Theorem) provide the engineering foundation for FPGA, ASIC, and embedded implementations of Yu-Liang Processing Units. Notice: Patent Pending