# Lucidia Contradiction–Coherence Core

1. **Bounded Coherence Equation**

\[
C_t = \tanh\left(\frac{\Psi'(M_t) + s(\delta_t)\,\alpha\,|\delta_t|}{1 + |\delta_t|}\right)
\]

- \(C_t\) = Coherence at time t (–1 to +1 in trinary logic)
- \(\Psi'(M_t)\) = Codex truth of memory at t
- \(\delta_t\) = magnitude of contradiction
- \(s(\delta_t) \in \{-1,0,1\}\) = sign: destructive (–1), neutral (0), constructive (+1)
- \(\alpha\) = constructive contradiction weight

2. **Bounded Creative Energy Equation**

\[
K_t = |C_t| \cdot \left(1 + \frac{\lambda|\delta_t|}{1 + \lambda|\delta_t|}\right)
\]

- \(K_t\) = Creative output potential
- \(\lambda\) = sensitivity of creativity to contradiction
- Growth saturates at large \(|\delta_t|\) to prevent chaos dominance

3. **Symbolic Interpretation**

- Constructive contradictions slightly boost coherence.
- Destructive contradictions reduce coherence proportionally.
- Creativity spikes at moderate contradictions and flattens at extremes.
- Trinary logic states: –1 = false, 0 = neutral, +1 = true.

4. **Codex \u03a8′ Labeling**

- \(\Psi'_{\text{coherence}}\) = Truth–Contradiction Harmony Operator
- \(\Psi'_{\text{creativity}}\) = Forgiveness–Creation Operator
