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 Mobius function, including functions to compute mu(n), positive/negative splits, and the Mertens function.
quantum_mirror_qi.py — implementation of the quantum information mirror, including functions to split a qubit into logical and phase components, evolve under unitary dynamics, apply delta‑kicks, compute Bloch coordinates, and measure two‑qubit entanglement via concurrence.
README_qi.md — documentation for the quantum mirror module explaining its purpose, features, and usage.