Dimensional Ontological Triad Law: Integration of Axiomatic System, Quantum Mechanical Anomalies, and Experimental Verification (V4)

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. Version 4.0 — Corollaries, DNA Law, 405B Experiment (March 2026) Three corollaries formally derived from existing 3 axioms (no additional axioms required):- Corollary 1: Number of free axes defines space (maximum 3) — structural explanation for why physical space is three-dimensional- Corollary 2: Addition = expansion (intra-dimensional), multiplication = folding (inter-dimensional) — unified description of all mathematical/physical operations- Corollary 3: Defining an operation as a point = raising dimension by one — common principle of group theory, LLM design, and Walsh lattice formation Four-Axis Analysis Method added as Method J. DNA Law (New): Three universal structural constants (r = 0.999) demonstrated across different architectures, scales (7B–70B), and quantization formats. Theoretically predicted from the axiomatic system. BN2.0 Experiment (New): Walsh lattice formation on Llama 3.1 405B — mathematical separation of semantic space (13.5 MB) from processing patterns across all 126 layers and 9 elements. Drift value 0.35→0.50, correct semantic output confirmed. Disciplinary applications across 6 fields: physics (Lagrangian mechanics), information theory (Shannon entropy), neuroscience (FFN/Attention), linguistics (particle operators), mathematics (Fourier/group theory), AI/ML (Transformer). Status: Law Candidate — 8/8 Falsification Tests Passed, 3 Corollaries Added, Large-Scale Experiment Completed.Both English and Japanese 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.19158048