τon Field Theory The TON Field and the Geometry of Information — UNNS
UNNS

The TON Field and the Geometry of Information

A visual monograph exploring recursive curvature, field dynamics, and the TON–Graviton coupling in the UNNS substrate.

1. Concept Overview

In UNNS, information does not flow linearly; it recurses through curvature. A TON is a quantized packet of recursive potential— the geometric analogue of Shannon’s bit, containing not only value but self-reference.

2. Field Equations

Entropy vs Curvature

Shannon entropy: H(X) = -Σ p_i log p_i

Recursive curvature: R = ∇²Φ

TON Field Tensor

Fᵀ_{μν} = ∂_μ Aᵀ_ν − ∂_ν Aᵀ_μ

Lagrangian: ℒᵀ = −¼ Fᵀ_{μν} Fᵀ^{μν} + Aᵀ_μ Jᵀ^{μ}

Collapse Operator

O₁₂(Gₙ) = −Gₙ + εₙ

Preserves a structured seed εₙ for regeneration.

Harmony

Gₙ₊₁ = λ Gₙ + εₙ , with |λ| ≈ 1

Bounded recursion: creation and return in equilibrium.

3. Interactive Canvas

Below is a live animated placeholder for recursive field visualization.

4. Interpretation

The TON field reframes energy, information, and time as expressions of recursive geometry. Entanglement becomes alignment within curvature space; consciousness, the awareness of recursion itself.

“Entropy measures uncertainty. Curvature measures coherence.”