Barry Marcovich

The Arithmetic Structure of the Divisor Mirror

This paper develops several arithmetic consequences of the divisor mirror invariant, building on the geometric framework of The Divisor Mirror (2026). Working from the excess function E(N)E(N), we collect and organize the explicit formulas the invariant admits: the zero-classific...

The Planck Boundary: A Structural Limit Between Quantum Potential and Relativistic Geometry

This paper proposes a structural resolution to the persistent failure of quantum mechanics (QM) and general relativity (GR) to unify within a single mathematical framework. Moving beyond technical obstacles, we introduce the Structural Floor Principle: a meta-invariant architectu...

The Divisor Mirror: A Geometric Invariant for Integer Structure

Every positive integer N carries a natural reflection symmetry whose deviations reveal its arithmetic structure. This paper introduces the divisor-mirror imbalance invariant W(N), defined through the total absolute distance of the divisors of N from the square-root axis. By measu...

The Structural Archive: A Universal Invariant for Physical and Logical Identity

Every discipline that reaches a sufficient depth of inquiry eventually encounters a structural boundary. Mathematics identifies such boundaries through incompleteness; physics through fundamental limits of scale; computation through undecidability; and cognition through the const...

The Geometry of the Self: A Structural Framework for Identity Integration, Psychopathology, and Therapeutic Translation

This paper proposes a structural framework for understanding mental health, identity, and psychotherapy. Traditional approaches treat trauma, anxiety, personality rigidity, and social conflict as separate phenomena, each addressed by different therapeutic modalities. This framewo...