A Framework for Critical Positive Operator Families: Energy Representations, Degeneracy Mechanisms, and Renormalization

This repository contains the first complete draft of the manuscript“A Framework for Critical Positive Operator Families: Energy Representations,Degeneracy Mechanisms, and Renormalization” by Yovanys Verdecia. The manuscript develops a finite-dimensional framework for studying positivematrix/operator families whose coercivity degenerates in a limiting process.It introduces energy representations, degeneracy mechanisms, mechanism-adaptedrenormalization, and several model examples, including Brownian, Hilbert,hyperbolic Cauchy-type, and digamma boundary-drift families. The repository also includes supporting editorial and evidence-tracking filesused to distinguish proved results, conditional statements, computationalevidence, open problems, and corrected artifacts. Numerical or computationalclaims are treated as evidence unless accompanied by a proof or a reproducibleverification package. This version should be cited as a research preprint / working manuscript, notas a final peer-reviewed publication.