The Fundamental LoE Neuron:\\ A Conditional Hamiltonian of Existence

“Structure of the LoE Neuron: A Conditional Hamiltonian of Existence”

This article introduces the concept of the Logic of Existence (LoE) neuron — a fundamental computational unit describing existence as a dynamic equilibrium between order and chaos.
The LoE neuron is a triadic structure, in which each incoming signal (Φin\Phi_{in}Φin) passes through a conditional operator (Ω\OmegaΩ) that determines whether the energy of existence is preserved (ΦL\Phi_LΦL) or decays (ΦR\Phi_RΦR).

Mathematically, the neuron is formulated as a local Hamiltonian, expressing the internal evolution of existential energy under relational and environmental conditions.
When interconnected, multiple LoE neurons form a nonlinear network of dependencies, where existence amplifies through relational confirmation and dissipates in isolation.

The model aims to unify physics, logic, and ontology into a coherent mathematical language — describing the emergence of being as a continuous process of existential energy dynamics governed by conditional resonance.