Polydimensional Layer Stack: Mathematical Foundations and Physical Implications of Composite Dimensionality

Polydimensional Layer Stack (PLS) is a comprehensive mathematical and physical framework in which spacetime is modeled as a countable family of geometrically distinct layers coupled through a superconnection. Each layer carries its own metric, curvature, and Dirac operator, while off‑diagonal link fields encode interactions between layers. The resulting structure produces a unified geometric mechanism for emergent mass, spin, electric charge, color, breakdown phenomena, and quantum measurement.This monograph develops the full mathematical foundations of the PLS framework, including:• layered metrics and curvature misalignment• the Jacob algebra and its graded structure• the superconnection and its curvature• the composite connection and composite Dirac operator• index‑theoretic derivations of emergent mass• geometric mechanisms for spin, charge, and color• breakdown, ghost states, and collapse geometry• a geometric derivation of the Born rule• cosmological implications, including early‑universe dynamics and structure formationThe text is organized in two parts. The main chapters present the conceptual and physical structure of the theory, while the appendices provide complete mathematical derivations, proofs, and technical background. A notation index and glossary support navigation of the formalism.This work is released under the Creative Commons Attribution 4.0 International License (CC BY 4.0) to encourage open scientific development, replication, and critical evaluation. It is intended as a mathematically complete and transparent foundation for further research in geometry, quantum theory, and gravitational physics.