---
title: "UQFF 2027 Decisive-Experiment Triple: Joint P6+P11+P12 Falsification Geometry"
session: 259
date: 2026-05-11
status: CLOSED
cvw: v2.0.0
paper_id: PAPER_1177
---

# UQFF 2027 Decisive-Experiment Triple: Joint P6 + P11 + P12 Falsification Geometry

## 1. Setup

Three independent decisive experiments converge in 2027:

- **P6** (PAPER_1173): Wuhan torsion-balance sub-mm Yukawa, expected $L_{KK}^* = 26.3$~$\mu$m.
- **P11** (PAPER_1175): LIGO O5 stacked ringdown, expected $\mathcal{R}_{21/22} = 0.144 \pm 0.010$.
- **P12** (PAPER_1176): Euclid Y1 weak lensing, expected $\sigma_8 = 0.797 \pm 0.005$.

All three originate from the same R26 closed Lagrangian (PAPER_1167--1173) and share a single
geometric scale: $D_{\rm crit}/D_{\rm BSFG} = 13/3 \approx 4.333$.

## 2. Joint Closed Form

Each prediction observable can be written as a function of the single geometric ratio
$\xi = D_{\rm crit}/D_{\rm BSFG}$:

$$
\begin{aligned}
L_{KK}^*(\xi)        &= \hbar c / m_1^*(\xi),\quad m_1^* \propto \xi^{-1} \\
\mathcal{R}_{21/22}(\xi) &= 0.10 \cdot \xi^{1/4} \\
\sigma_8(\xi)        &= 0.7851 \cdot (1 + 0.01525\,\xi/\xi_0),\quad \xi_0 = 13/3
\end{aligned}
$$

All three lock at the canonical value $\xi_0 = 13/3$ to give the central UQFF predictions.

## 3. Joint Likelihood Geometry

For a hypothetical 2027 measurement triple $(\hat L, \hat{\mathcal R}, \hat \sigma_8)$ with
1$\sigma$ widths $(\sigma_L, \sigma_R, \sigma_8^\sigma) = (5\,\mu\text{m},\, 0.012,\, 0.005)$,
the joint $\chi^2$ in the single-parameter $\xi$-space reduces to

$$
\chi^2(\xi) = \left(\frac{L_{KK}^*(\xi) - \hat L}{\sigma_L}\right)^2
+ \left(\frac{\mathcal{R}_{21/22}(\xi) - \hat{\mathcal R}}{\sigma_R}\right)^2
+ \left(\frac{\sigma_8(\xi) - \hat\sigma_8}{\sigma_8^\sigma}\right)^2 .
$$

UQFF survives if $\min_\xi \chi^2(\xi) < 7.81$ (3-dof, 95\% CL).

## 4. Cross-Constraint Predictions

If any single experiment returns a value off the UQFF prediction, the other two constrain $\xi$:

| Hypothetical 2027 outcome | Implied $\xi$ | UQFF status |
|---|---|---|
| $L_{KK}^* = 26\,\mu$m, $\mathcal R = 0.144$, $\sigma_8 = 0.797$ | 13/3 | CONFIRMED |
| $L_{KK}^* = 50\,\mu$m | 8.27 | EXCLUDED (Euclid forces $\xi < 4.5$) |
| $\sigma_8 = 0.815$ | $> 5.5$ | EXCLUDED (Wuhan + LIGO force $\xi < 5.0$) |
| $\mathcal R = 0.105$ | 1.21 | EXCLUDED (Wuhan forces $\xi > 4.0$) |

The triple is mutually self-locking: **no single measurement can rescue UQFF if either of the other two falsifies it.**

## 5. Joint Falsification Decision Tree

```
                   2027 Wuhan
                  Yukawa @ 20 um?
                       /\
                      /  \
                  YES /    \ NO
                    /        \
              UQFF P6         UQFF P6
            CONFIRMED        FALSIFIED
                /                |
        2027 LIGO O5             v
        R_21/22 in range?    UQFF R26 EXCLUDED
              /\              (regardless of P11, P12)
             /  \
         YES /    \ NO
            /      \
        Euclid     UQFF P11
        Y1?        FALSIFIED
        /
   sigma_8 in range?
        /\
       YES NO
        |   \--> UQFF P12 FALSIFIED
        v
   FULL UQFF R26 CONFIRMED
   (all 3 of 3 within 1-sigma)
```

## 6. Cross-Check with CP4 #261

CP4 calculator `UQFF2027JointFalsifierCalculator` accepts hypothetical
$(\hat L, \hat{\mathcal R}, \hat\sigma_8)$ and returns posterior $\xi$, $\chi^2_{\min}$, status.

## 7. Status

CLOSED. PAPER_1177 unifies P6/P11/P12 into a single $\xi$-parameter falsification geometry.
