From Possibility to Actualization: A Minimal Ontological Interpretation of Quantum Mechanics A Contribution to the Philosophy of Physics

We propose the Quantum Reality Framework (QRF) as a minimal ontological interpretation of quantum mechanics -- not a replacement theory. QRF inherits the full predictive apparatus of standard QM and reinterprets its ontological ground. The fundamental primitive is a signed amplitude function A: MxM -> R, from which the compatibility probability k = A^2/Z is derived as a formal quantity. This amplitude/compatibility distinction resolves the tension between an ontologically positive k and the sign-changing structure required for quantum interference. A compatibility structure constrained to the oscillatory Gaussian-cosine kernel A_GC, proven positive definite via Bochner's theorem, provides a concrete, parameter-specified, falsifiable physical model. The associated RKHS H_A supplies the mathematical home for a Gleason-type uniqueness theorem -- identified as the primary open problem. QRF's key move: categorical separation of pre-actual (global, A-structured, no spacetime coordinates) from actual (local, Minkowski-governed, irreversible). Entangled systems are pre-actual; Minkowski structure is motivated from locality plus an invariance postulate. QRF is positioned against six major interpretations and occupies a distinct position: realist, presentist, observer-free, non-local only at the pre-actual level. Primary falsifiable prediction: bimodal Fourier spectrum of A. Born rule: P(a_i,b_j) = A(a_i,b_j)^2 / Z, proven within A_GC, conjectured generally.