Dimensional Ontological Triad Law: Integration of Axiomatic System, Quantum Mechanical Anomalies, and Experimental Verification (V3)

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.

Version 2 Updates (February 10, 2026):
- Mathematical formalization of all 6 core elements using standard notation
- 8 independent falsification tests: ALL PASSED
- 10 byproducts derived (Bell's theorem, 1/f noise origin, BH entropy coefficient 4, etc.)
- 4 novel predictions (1 falsified and revised: D→D')
- Status: Law Candidate
- Most promising experimental path: suspended graphene noise measurement (Prediction D')

Version 3 — Complete Axiomatic System · Pythia Full-Scale Experiment · Cross-Dimensional Verification

A complete axiomatic system built from 3 axioms deriving 40 items (29 theorems, 9 methods, 2 rules). Independently re-derives fiber bundle theory, SO(n) rotation groups, and the Bekenstein–Hawking coefficient 4. Unifies 8 quantum mechanical anomalies under a single principle. Pythia full-scale experiment (7 scales, 810 measurement points): core prediction E-5 achieves R²=0.911. Cross-dimensional verification completed across 3D (quantum anomalies), 2D (LLM emergence), and 1D (halting problem).

Status: Law Candidate — 8/8 falsification tests passed.

Japanese and English versions 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.com

Companion paper: DOI 10.5281/zenodo.18523074