ON THE STRUCTURAL LIMITS OF PHYSICAL LAW — Collected Papers on Quantum Ultrametric Rigidity — Volume I — The Limits of Physical Law

This book is Volume I of a four-volume collected edition of the Rigidity Program, a research framework exploring the structural limits of predictive physical law and the informational foundations of spacetime geometry.The present volume establishes the conceptual and operational premises of the program. It argues that predictive physical law requires finite operational distinguishability within bounded regions, implying a finite effective physical content and a discrete underlying structure. Within this perspective, the mathematical continuum is interpreted not as fundamental reality but as a compressed representational regime emerging from deeper structural constraints.The collected papers introduce the core ideas that motivate Quantum Ultrametric Rigidity (QUR), including finite operational distinguishability, structural irreversibility, and the incompleteness of autonomous physical law.This volume includes:• Dialogue Concerning the Two Minimal World Systems • Finite Operational Distinguishability as a Structural Condition for Predictive Physical Law • Quantum Ultrametric Rigidity: Structural Irreversibility and the Incompleteness of Autonomous Physical Law