PageRank, Normal Factors, and Eigenvector Centrality as Filtrational Stabilizations in Possest–PQF

This paper should be read as a technical extension of the main theoretical article, “Fixed Points as Filtrational Stabilizations: A Possest–PQF Reconstruction of the Generalized Markov–Kakutani Theorem” (DOI: 10.5281/zenodo.19423489).

Where the main article develops the general operatorial architecture of common admissibility cores, affine semigroups, recursive normal-factor composition, and filtrational stabilization, the present paper derives a concrete downstream realization of that framework in the domain of ranking procedures. More precisely, it reconstructs PageRank, personalized PageRank, and eigenvector centrality as bounded architectures of admissible redistribution whose stationary profiles should be read not as neutral measures of importance, but as filtrational stabilizations produced within a controlled operator envelope.   

The conceptual sequence is precise. The main article establishes the generalized fixed-point logic: persistence of a common admissibility core under layered affine composition, including recursively structured noncommutativity through normal factors. The present companion paper then shows how this logic becomes mathematically visible in ranking architectures, first in the standard PageRank setting, then in personalized redistribution, multi-layer systems, and finally in eigenvector centrality as a spectral boundary case.   

Taken together, the two papers form a single theoretical arc. The first provides the general theorem and operatorial grammar; the second demonstrates how this grammar governs concrete algorithmic ranking procedures. In that sense, this paper is not merely adjacent to the fixed-point reconstruction. It is one of its most explicit operational consequences.

Companion paper to:

Fixed Points as Filtrational Stabilizations: A Possest–PQF Reconstruction of the Generalized Markov–Kakutani Theorem

DOI: 10.5281/zenodo.19423489

Keywords

Possest–PQF, PageRank, personalized PageRank, eigenvector centrality, fixed-point theory, affine semigroups, filtrational stabilization, ranking algorithms, normal factors, spectral persistence