Dimensional Ontological Triad Law — Version 2: Mathematical Formalization & Falsification Tests

This paper presents the Dimensional Ontological Triad Law, a recursive structural law governing transitions across dimensions: n-dimensional change = (n+1)-dimensional entity = (n+2)-dimensional adjective. Through pure logical reasoning and thought experiments, 22 original discoveries were made, including a unified explanation of 8 major quantum mechanical anomalies (superposition, entanglement, tunneling, measurement problem, wave function collapse, double-slit experiment, observer effect, and decoherence) under a single dimensional-projection principle. The framework identifies two types of projections — free-axis projection and constraint-axis projection — that systematically account for all known quantum phenomena as shadows of four-dimensional reality perceived from three-dimensional perspective. This research was conducted in collaboration with Claude (Anthropic) as AI Exploration Partner. Both English and Japanese versions of the paper are included. Note on Dimensional Definitions: In this framework, dimensional definitions are intentionally shifted by one level from conventional academic usage. For example, what is traditionally called the "fourth dimension (time)" is treated here as the third-dimensional being's projective name for the fourth axis. This shift is a deliberate methodological choice to avoid conceptual constraints imposed by lower-dimensional terminology when describing higher-dimensional structures. Call for Collaboration: The author welcomes collaboration from researchers in quantum foundations, philosophy of science, and mathematical physics — particularly for mathematical formalization of the framework and experimental prediction derivation. Contact: ikoma.yuudai@gmail.comCompanion paper: DOI 10.5281/zenodo.18523074