Filtration Geometry and Informational Curvature: PQF Development Notes

Abstract This document redefines perception not as representation or stimulus-response, but as a stratified diagram of recursive tension within a geometry of informational filtration. Grounded in the Possibilistic–Quasi–Filtration (PQF) framework, it introduces and computes the curvature tensor R(\delta^*), derived not from metric space but from recursive accessibility deformation. A scalar potential \Phi_{\text{PQF}} is constructed from this tensor, quantifying the reorganizational cost of access. The local minima of this potential identify perceptual haecceities — stabilized differences that mark the fixation points of topological torsion. These are not “objects” but local singularities of irreducible filtration structure. A formal theorem is proven: if the curvature tensor is nonzero and admits stable minima of the filtration potential, then the domain is globally non-flattenable and perception must be understood as a form of torsional resistance to reconfiguration. This makes perception an asymptotic topological attractor in the space of reorganizable access — not a product of signal processing, but of recursive stabilization. The result integrates tensor calculus, accessibility topology, and philosophical insights from Fechner’s psychophysics, Ruyer’s internal form, and Deleuze’s haecceity, constructing a model where perception is a consequence of non-metric geometry. Keywords: PQF geometry, filtration, tensor curvature, perception, recursive deformation, haecceity, scalar potential, informational topology, Ruyer, Deleuze, Fechner