The Universe BIOS Protocol: An Arithmetic Derivation of 26 Physical Constants via 24-Dimensional Discrete Electromagnetic Logic

[Errata & Version Statement] Certain precise derivations of physical constants in this V1.0 preprint (e.g., Gravitational constant $G$, Proton-to-electron mass ratio $\mu$) have been identified in subsequent research as containing phenomenological approximations aimed at aligning with macro-observations. The root cause of these derivation misalignments lies in the mismatch between macroscopic metrology and microscopic logical truth. To maintain the absolute purity of the theory, this stage of discourse will exclusively include derivations solely dependent on the six fundamental LCR invariants ($D, \Phi, \pi, R, L, C$) . The remaining issues of precise geometric matching and macro-rendering overheads are hereby presented as open problems, to be rigorously reconstructed under the "Measure Residual Calculus (MRC)" framework currently under development by the author. xuezhi cheng 2026.3.15 Modern physics identifies fundamental constants as arbitrary, independent laws of nature. This paper introduces The Primordial Logic of LCR, a framework that redefines the universe not as a smooth space-time continuum, but as a discrete 24-dimensional electromagnetic logic system. we identify six invariants. This research demonstrates that 26 traditional physical constants—including the speed of light (c), Planck’s constant (h), the fine-structure constant (\alpha), and the Higgs mass (M_H)—are not independent laws, but rather arithmetic residues or "system patches". These constants arise from: The "Entropy Tax" (R): Generated by the precision truncation of \pi across massive exponential spans. Topological Projection: The compression of 24-dimensional logic onto our observed 3D space.