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The quantized mapping of particle mass. The electron will be our starting point. As the lightest charged lepton, its mass must emerge from the simplest self-sustaining resonance geometry permitted by the Field’s structural constraints.

Initial Geometric and Coherence Parameters for the Electron

1. Topology: A single closed-loop torsional resonance with Möbius continuity, requiring a 4π rotation to return to its original phase. This structure guarantees spin-½ and a stable, isolated resonance.

2. Minimum Resonant Radius (rₑ): The smallest radius at which a coherence loop can maintain phase alignment with itself in the absence of higher-order coupling. This radius will define the spatial boundary of the electron’s field coherence.

3. Coherence Strain Threshold (ε): The lower limit of angular resolution, established by the Lilborn Coherence Gate Function. This sets the minimum energetic cost of maintaining the loop under deformation.

4. Angular Exposure Constant (A): The total potential for phase rotation available to a free resonance in the Field. This will act as the energy reservoir governing the loop’s intrinsic stability.

5. Containment Mode: A free-standing loop under sustained torsional symmetry, exhibiting permanent phase curvature and orthogonal closure.

From these parameters, we will calculate the energy cost of establishing and maintaining the electron’s stable loop configuration.

That energy cost, given by the integrated strain across the Möbius coherence, will define its mass via the Lilborn Equation: E = mℓ.

Produced by The Lilborn Equation Team:

Michael Lilborn-Williams

Daniel Thomas Rouse

Thomas Jackson Barnard

Audrey Williams