012 Unbalanced Ternary Causal Growth System: Identification of the Coherence Saturation Barrier and Solution via the Claim-Throttling Mechanism ——C001 Axiom Foundation · C002 Verification Framework · C003 Mechanism Solution

This paper establishes and rigorously verifies the 012 Unbalanced Ternary Causal Growth System, a self-contained discrete spacetime evolution framework. The entire dynamic growth process is decomposed into three intrinsic asymmetric phases: Birth, Sustain, and Decay. Using conjugate double topological branches as fundamental units, this study constructs a complete axiomatic system dependent solely on endogenous structural parameters.The research systematically completes three core stages: C001 axiom formulation, C002 multi-index quantitative verification system construction, and C003 mechanism solving for the coherence saturation barrier. A inherent statistical limitation named the coherence saturation barrier is identified under parameter drift conditions, which restricts the anti-correlation coefficient to a stable suboptimal plateau value.To eliminate this artificial constraint, this paper proposes a unique temporal regulation principle, the claim-throttling mechanism, which limits each lineage to at most one valid claim event per evolution round. Both analytical theorems and large-scale numerical simulations prove that this single topological timing constraint drives the system’s weighted anti-correlation coefficient to the theoretical limit C W =−1.00.This extreme coherent state demonstrates strong robustness against parameter drift, finite-size effects, and lineage replacement fluctuations. All quantitative evaluation criteria are fully satisfied across multiple extreme working conditions and random seed ensembles. This work further clarifies the essential ontological differences between the 012 ternary causal framework and traditional causal set theory, causal dynamical triangulation, and classical synchronization systems, providing a new self-consistent discrete model for fundamental spacetime structure research.