1.1 Multiplier Sequence and Coding Orbit

Abstract

Starting from the three Structure Constant Theorems (, , ) and the prime factor budget, this paper derives the multiplier sequence on the Coding Orbit. The multiplier sequence is uniquely determined by the Budget-Genotype double-layer structure and Benign Mutual Conjugate Locking. The Coding Base State , and after six-layer recurrence arrives at the terminal . This paper provides the formal definition of the Budget-Genotype double-layer structure, a purely recursive proof of the Recycling Baseline Invariance Theorem, a complete proof of the seven-candidate exclusion for , a full derivation of , the exponent sequence and phase decomposition of the four stages of triality, the parameterized mechanism of mutual conjugate locking, and the step-by-step prime factor decomposition of the complete Coding Orbit.