The Field of Consciousness: A Lattice Gauge Model of Emergent Mass and Time

This paper proposes a foundational physical framework in which consciousness is modeled not as an emergent property of complex matter, but as a fundamental Abelian gauge field—the **Field of Consciousness (FoC)**—whose dynamics unfold on a discrete isotropic octahedral lattice.

We demonstrate that this field is sourced by a geometry-defining **Ontological Intention Tensor** $(T_{global}^{\mu\nu})$ rather than a material current. When the geometric tension from this source exceeds a critical threshold $(\mathcal{T}_{crit})$, it induces a non-linear phase transition on the lattice. This transition:

 - **Solves the Mass Gap:** Provides a geometric mechanism for confinement and a solution to the Yang-Mills mass gap problem by coupling to the $SU(3)$ sector. 
 - **Explains the Arrow of Time:** Establishes temporal directionality through the thermodynamic requirement of entropy expulsion via the weak interaction.
 - **Recovers Gravity:** Derives the $8\pi$ gravitational coupling constant of General Relativity via a novel discrete-to-continuum mapping known as the **Octahedral-Spherical Equivalence (OSE)**.

The model's core mechanisms are validated through a "trifecta" of computational simulations, including Classical PDE, Euclidean Lattice Gauge, and Hamiltonian Quantum Link Models, all of which exhibit the predicted sharp onset of structure formation.