Information-Theoretic Calculus of Sovereign Decision within Information-Axiomatic Systems and Hilbert Space: An Aesthetics of Existence

Building upon the establishment of the meta-metaphysical axiomatic system in [Treatise I] and the critique of socio-political totalitarianism in [Treatise II], this study presents an engineering existentialism that dissects the microscopic existence of individual subjects through information theory, thermodynamics, quantum state spaces, and complex systems dynamics. Initiating with a critique of the ruins of existence wrought by modern materialistic determinism and Nietzschean nihilism, this treatise redefines the human mind and personality not as fixed materialistic imprints, but as complex weight distributions (c_i) and projection operator filters within a Hilbert space. Furthermore, extending the concept of the informational negentropic evolution of life, depression and lethargy are anatomized as "mental discharge (thermal death) due to the maximization of von Neumann entropy," while cognitive bias is dissected as "an computational attractor for energy conservation." Ultimately, this study elucidates the phase transition mechanism whereby a subject shatters existing biases within a Bayesian rendering feedback loop and spontaneously declares a new orthogonal basis, thereby establishing the computational equation y=f(x,C,ε) that determines all outputs of life. This research conclusively proves that existence is not a passive product of the environment, but a sovereign declaration by the subject enacted upon the primary axiom of the first layer: "absolute affirmation (Agape)."