Energy Primitivism: A Conceptual Framework for Unifying Physical Existence and Consciousness Experience

This paper presents a systematic application of Energy Elementalism to the field of discrete dynamical systems. The exposition proceeds along four progressive layers. At the first layer (foundational), we map every core element of the Collatz iteration into the conceptual system of Energy Elementalism, establishing a precise correspondence between positive integer states and the energy potential function. At the second layer (criterional), we rigorously prove a sufficient convergence criterion: if the long-term average of a trajectory's compression exponents exceeds log₂(3), then the trajectory must fall into the Optimal Differentiation Range. This criterion transforms the proof of the Collatz conjecture into an arithmetic-statistical problem concerning the sequence of compression exponents. Simultaneously, we prove a logarithmic upper bound on consecutive free chain lengths and construct a conservative truncation reduction that reduces verification of the infinite system to a maximum cycle mean computation on finite graphs. At the third layer (structural), we develop a "modular space metabolic structure" analytical method, proving local metabolic theorems modulo 2, 3, and 4, and describing the irreversible metabolic outlets through which non-survivor classes exit under the mapping. On this basis, we propose the "cross-modular survivor constraint" conjecture and prove the free-state frequency upper bound lemma: f₁ ≤ 1/3. At the fourth layer (synthetic), we construct a three-part exclusion argument by reductio. The first part (k̄>λ) is guaranteed by Theorem 1; the second part (k̄=λ) is excluded by the product inequality; the third part (k̄λ, hence all trajectories converge to {1,4,2}. A complete hand-computable verification at the modulo 64 level is provided, and n=27 is used as a case study to demonstrate the framework's diagnostic capability. This paper does not claim to have completed a final proof of the Collatz conjecture, but rather to provide a unified conceptual lens and a clear line of attack. It is an open research program.