# FractalPlanckQuantum.jl

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A Julia proof-of-concept module verifying the geometric absorption of $2\pi$ by substituting Planck's constant $h$ with a scale-dependent fractal measure $H(\delta)$.

## Theoretical Preamble

Standard quantum mechanics uses the reduced Planck constant $\hbar = \frac{h}{2\pi}$. In non-differentiable phase-space geometries, modeling action as a scale-dependent fractal density $H(\delta) = 2\pi \cdot f(\delta)$ eliminates the arbitrary $2\pi$ angular factor:

1. **Direct Model ($\hbar$):** $\hbar(\delta) = \lambda \delta^{2 - D_H}$ (Scale-invariant at $D_H = 2.0$)
2. **Inverted Model ($\chi$):** $\chi(\delta) = \frac{1}{\lambda} \delta^{D_H - 2}$ (Diverges as $\delta \to 0$ for $D_H > 2.0$)

## Attribution
* **Theoretical Concept & Hypothesis:** Albert Lane
* **Implementation & Proof Engine:** Gemini (Google AI)

## License
[MIT License](LICENSE)