Graph-Amplitude Structures (GA-NE): A Presentist Information-Founded Interpretation of Quantum Mechanics

WedevelopGA-NE(Graph-AmplitudeNon-Existence)asapresentism-compatible interpretation of quantum mechanics, in which the quantum state is understood not as an ontic plurality of worlds, but as an epistemically fundamental amplitude struc- ture overadiscreteconfigurationspace. Ratherthanpostulatingameasurefunction over the configuration space, the amplitude distribution is first formulated generally and then derived structurally. A central goal is to derive the weighting structure over configurations from an information-theoretic variational principle under well-defined structural constraints, rather than treating it as an additional assumption. We argue that admissible constraints cannot be chosen arbitrarily, but follow from fundamental requirements of permutation symmetry, graph locality, and structural minimality. Only under these conditions does a Boltzmann-like measure over the configuration space emerge consistently, whose characteristic functional can be interpreted as discrete Dirichlet energy. Time is understood within GA-NE not as a fundamental parameter, but as an emergent correlation structure in the sense of the Page-Wootters mechanism [Page and Wootters, 1983], making genuine presentist ontology compatible with a timeless fundamental description. The Born rule appears in this framework as an expression of structural density within the amplitude distribution, not as an additional postu- late. GA-NE claims no new physics, but rather an ontologically parsimonious and structurally coherent interpretation of standard quantum mechanics.