PQF Empirical Validation: Operatorial Tests of Filtration and Recursio Intensitatis

This companion paper provides the empirical validation of the Possest–PQF framework introduced in: Schimmelpfennig, Y. (2025). Possest–PQF: An Operatorial Theory of Filtration, Intensity, and Topological Complexity. Zenodo. https://doi.org/10.5281/zenodo.17230263 While the theoretical work established an operatorial ontology of accessibility and defined Recursio Intensitatis as a non-commutative interaction of the filtration operator $\Delta_{\mathbb F}$ and the recursion operator $\delta^*$, the present paper demonstrates that this framework is testable, measurable, and reproducible. Through synthetic accessibility fields, persistent homology, bottleneck distance, topological entropy, Betti curves, and a minimal AI experiment, we show that operator order produces robustly distinguishable signatures. Results from both Python/Colab simulations and Wolfram Mathematica computations converge: Topological novelty: Order A ($( \delta^*)^k \circ \Delta_{\mathbb F}$) sustains long-lived cycles, while Order B collapses them. Statistical confirmation: Bottleneck distance exceeds null thresholds (95%). Entropy shifts: $S_{\mathrm{top}}$ reveals directed concentration in Order A. Algorithmic impact: A toy SGD experiment confirms lower loss under Order A. Together, these results validate PQF as an operatorial framework capable of detecting structural novelty beyond probabilistic or metric paradigms. Keywords Possest–PQF, Recursio Intensitatis, filtration, recursion, persistent homology, bottleneck distance, topological entropy, Betti curves, AI diagnostics, operatorial complexity Communities Philosophy of Science Complexity Science Artificial Intelligence Topological Data Analysis Related/Referenced DOI Schimmelpfennig, Y. (2025). Possest–PQF: An Operatorial Theory of Filtration, Intensity, and Topological Complexity. Zenodo. https://doi.org/10.5281/zenodo.17230263