PQF Twistor–Kähler Geometry: Local Holomorphic Accessibility Sheaf and Threshold Filtration Geometry

This work introduces two original and fully operational constructions within the Possest–PQF Twistor–Kähler framework: the Holomorphic Accessibility Sheaf and the Threshold Filtration Geometry (TFG). Unlike conventional geometric models that depend on external metrics or temporal baselines, the PQF formalism defines accessibility entirely within an immanent field generated by the torsion potential \Phi_{\mathrm{PQF}}. Here, both time and space are derivative effects of this field, not primitive variables. Novelty is defined with mathematical precision as a change in the topological type of a holomorphic accessibility fibre \mathscr{A}{\mathrm{hol},x} under a minimal deformation of the recursive operator \delta^*. The threshold function \theta{\mathrm{PQF}} quantifies this limit and is a geometric–topological invariant that can be computed, mapped, and compared across heterogeneous systems. This definition enables the localisation of “pre-factual” reorganisation zones — structural thresholds where qualitative change is possible but not yet actualised. The formalism applies without modification across domains: from Morse–theoretic geometry and condensed matter physics, to machine learning vulnerability mapping, nonlinear dynamics control, and evolutionary landscape analysis. The novelty and value of this work lie in its ability to merge the highest level of conceptual abstraction with an exact computational operator, translating philosophical notions of immanence, metastability, and novelty into a transdisciplinary instrument for early detection of structural transformation. PQF geometry; Twistor–Kähler structures; Holomorphic Accessibility Sheaf; Threshold Filtration Geometry; novelty detection; geometric–topological invariants; metastability; immanence; bifurcation thresholds; transdisciplinary modelling.