This framework demonstrates conservation laws and resolves Godel's Incompleteness Theorems within physics.
Existing mathematical physics lacks a unified axiomatic system that can accommodate both the deterministic laws of General Relativity and the probabilistic nature of Quantum Mechanics. In this paper, we establish the "Three Grand Axioms" of Rough Operator Algebra (ROA). We propose that the universe is governed by a single conservation law of Energy-Roughness duality (E · α = κ), and that the logical structure of reality evolves dynamically with the roughness index α. This system resolves Godel's Incompleteness Theorems within the physical universe and provides the rigorous foundation for "Sunggil's Grand Unified Mathematics." Axiom 1 unifies Matter and Information. Axiom 2 unifies Quantum and Classical Logic. Axiom 3 unifies Gravity and Entropy. This work serves as the "Principia" of 21st-century physics.
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Lee Sung-gil (2025) studied this question.
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