This is Not an Ellipse: A Topological Contradiction in Coherence-Based Duality Models

Abstract: This paper demonstrates that the commonly accepted duality ellipse in quantum interference models fails under dynamic conditions of access and coherence. Within the PQF (Projected Quantifier Filtration) framework, coherence is treated not as an intrinsic or static property, but as a recursive function of access: \gamma = \gamma[\delta^*(\mathfrak{f}(t))]. Using differential analysis, topological counterexamples, and homological intuition, we show that the ellipse is not a global invariant but a projection of deeper filtration dynamics. In this view, visibility and predictability are not ontological properties but sectional residues of a higher-order recursive field. The geometry collapses; recursion remains. This result invites a reorientation of quantum theory from state-based formalism to topological access-structures — where representation is no longer a valid epistemic operator. The ellipse, as argued here, is not a structure: it is a shadow cast by filtered recursion. Keywords: PQF, coherence, duality, quantum interference, topological filtration, recursion, access dynamics, δ*, non-representational theory, bifurcation, homology, decoherence, Arkady Plotnitsky, reality without realism