# PAPER_1167 UPDATE — Master Lagrangian 6-Term Form

**Original:** PAPER_1167 UQFF Master Lagrangian
**Update:** Session June 2026
**Status:** Update

## Session Extensions

The closed 6-term form is wired:
$$\mathcal{L}_{\rm UQFF} = \frac{R_{26}}{2\kappa_E} - \frac{1}{4}F^2_{\rm DPM} + \sum_i \beta_i U_g U_b + |U_m|^2 + \frac{1}{2}|\partial U_A|^2 + \frac{25}{12}\rho_{\rm SCm}\left[(U_A/v_{UA})^2 - 1\right]^2$$

### β_i ladder
$$\beta_i = \frac{3(5-n)}{20}\text{ with } n \in \{1,2,3,4\}$$
yielding β_1 = 0.6, β_2 = 0.45, β_3 = 0.30, β_4 = 0.15.

For n ≈ 0.98067 (fractional permitted): β = 0.6029 canonical.

### Variational stationarity
δS/δφ = 0 enforces F_U = 1 globally.
