A theorem concerning the positive metric

Jochen Dittmann

Alon E. Faraggi, Marco Matone

We consider the two main theorems in the derivation of the Quantum Hamilton--Jacobi Equation from the Equivalence Postulate (EP) of quantum mechanics. The first one concerns a basic cocycle condition, which holds in any dimension with Euclidean or Minkowski metrics and implies a global conformal symmetry underlying the Quantum Hamilton--Jacobi Equation. In one dimension such a condition fixes the Schwarzian equation. The second theorem concerns energy quantization which follows rigorously from consistency of the equivalence postulate.

Rashmi Mehrotra, S. H. Patil

Dany D. Ruiz

This article addresses the physical, ontological, and computational implications of metric position determination in R³, building on the theoretical results established in "Minimal Configurations for Generic Position Determination in R³: Tetrahedron vs. Orthogonal Ambiguity" (Ruiz, 2026). We posit that spacetime is not an absolute Cartesian container of pre-existing coordinates, but a dynamic relational structure that emerges from the distance signatures among physical observers. 1. We analyze the collapse from the bimodal ambiguity of Theorem 3.1 to the unique solution of Theorem 3.3, characterizing this phenomenon as a discrete topological jump, a macroscopic analogue of wavefunction collapse. 2. We expose the epistemological bias of contemporary computational simulation engines, which assume a global Cartesian grid of divine origin (false absolute space). 3. We propose a new standard for relational, panperceptual simulation where physical positions are co-constructed and resolved strictly through the metric interactions of the network.

Arkadiusz Jadczyk

Wataru Kumagai