>[!warning]
>This content has not been peer reviewed.
# RST Refractive Lensing — Solver (Disformal Extra Bending)
This script implements the **Refraction Identity** to show that the **disformal term** produces the extra bending required for galaxy clusters — without dark matter.
**Derivation:** [[RST Lensing (Disformal)]]. The physical metric for light is
$\tilde{g}_{\mu\nu} = e^{2q}g_{\mu\nu} - (e^{2q} - e^{-2q})\, A_\mu A_\nu.$
The "bending boost" is the relational reciprocal of the update-speed drop with workload $q$.
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## Calculation logic
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## Logic
1. **Newtonian potential** $\phi_N \propto 1/r$.
2. **MONDian workload** $q \sim \sqrt{\phi_N \, a_0}$ (simplified weak-field).
3. **Bending boost** $1 + (q/\phi_N)$ from the disformal update-lag.
4. **Total deflection:** $\alpha_{\text{RST}} = \alpha_{\text{GR}} \times \text{boost}$.
So RST lensing exceeds baryons-only lensing by the substrate's **bandwidth congestion** (Refraction Identity). Zero free parameters in the gravity sector.