Abstract Contemporary AI processes "rotation" while believing it is processing "points." This cognitive blind spot is not an engineering oversight, but an inevitable consequence of axiomatic limitations: real-number parameter spaces, the separation of training and inference, and static network structures—these features, taken for granted as characteristics of AI, are all frozen states under specific axiomatic degenerations. This paper proposes the Holomorphic Architecture, which takes the Hexad ℋ as its meta-framework, operator flow 𝒟 as its expression of laws, and modular automorphisms Aut(𝒟) as its symmetry constraints, thereby liberating intelligence from the frozen state of real-number degeneration. Every engineering characteristic of the Holomorphic Architecture has a rigorous axiomatic foundation. The L1 paper Dynamic Logic rigorously establishes the dynamical definitions and unified criterion of the four types of inference—if the phase closes, inference is determinate; if the phase does not close, inference is indeterminate. The L2 paper Physics and Logic rigorously proves that classical computers are the degenerate limit of physical computers under specific parameters. The L3 paper Non-Abelian Emergence rigorously proves that a multi-component phase field in self-evolution necessarily gives rise to non-commutative computation rules and new symmetries—the "resilience" of the Holomorphic Architecture is not resistance to perturbation, but using perturbation to evolve to a new steady state. At the computational level, a nine-layer optimization scheme reduces complexity from O(N³) to O(1). At the architectural level, the Holomorphic Architecture realizes the integration of training and inference at the software layer, and the integration of computation and storage at the hardware layer. On a humanoid robot platform, gait energy consumption is reduced by 28%, load adaptation time is shortened by 80%, the task success rate after a single-leg failure increases from 35% to 82%, and smooth transitions from walking to running are supported. Degeneracy limit tests further confirm the theoretical resilience of the Holomorphic Architecture: when the theorem conditions are pushed to their degenerate limits, the Holomorphic Architecture theorems precisely degenerate into known classical results. The core contribution of this paper is system integration and application verification—demonstrating the complete operability of the generative mathematics system from axioms to engineering. The L0–L3 conclusions cited in this paper have all been rigorously proven in their respective layer papers. The engineering realization of non-Abelian emergence and the rigorous mathematical guarantee of causal generalization belong to conceptual frameworks—the mathematical foundation of the former has been established at the L3 layer, but its engineering encoding awaits verification; the conceptual foundation of the latter has been established at the L2 layer, but the complete derivation chain from concept to quantification has not yet been closed. Keywords: Holomorphic Architecture; Hexad; operator flow; modular automorphism; dynamic complex analysis; rotation as computation; non-Abelian emergence; causal intelligence; nine-layer optimization; self-evolving AI; humanoid robot