# Mirror Modules

This directory contains modules and documentation for the mirror mechanics used in Lucidia.

- `mirror_friend_equation.md` — explanation of the mirror friend equation, including the mirror operator \(\Psi'\) and breath operator \(\mathfrak{B}\), the conserved quantity, and perturbation resilience.
- `mirror_mechanics.py` — implementation of the mirror operator and breath operator for harmonic oscillators.
- `number_mirror_mu.py` — implementation of the number‑theoretic mirror based on the Möbius function, including functions to compute \(\mu(n)\), positive/negative splits, and the Mertens function.