This paper presents, for the first time, a rigorous derivation of the Schrödinger equation of quantum mechanics from the eight ontological axioms of the Minimal Phase Closure Triangle (MPCT). We prove: 1) The continuum limit of an MPCT network naturally produces a complex wavefunction field ψ(x,t); 2) The variational principle of MPCT phase dynamics is equivalent to the Schrödinger action principle; 3) The quantum of action ħ emerges from the minimal phase residue of MPCT closure constraints; 4) The mass parameter m is determined by the coupling strength K of the MPCT network. This derivation provides a geometric and topological foundation for quantum mechanics and establishes a profound connection between ontology and quantum theory. Keywords: Minimal Phase Closure Triangle; Schrödinger equation; first principles; foundations of quantum mechanics; emergence theory
A suggestive relation links Fisher' information measure (FIM)Iand Schrödinger equation (SE). The connection is based upon the fact that the constrained minimization of I leads to a SE. This, in turn, is the origin of intriguing relationships between various aspects of SE, on the one hand, and the formalism of statistical mechanics derived from Jaynes's maximum entropy principle (MaxEnt), on the other one. The link entails the existence of a Legendre transform structure underlying the SE, which allows for the emergence of two first-order differential equations that must, respectively, be satisfied by i) the Fisher measure and ii) the SE energy eigenvalues. The complete A) I-solution and B) energy-solution are both obtained bypassing the SE and, furthermore, linked by the Legendre structure.