---
title: "UQFF 2027-2028 Quadruple Falsifier: Single-Parameter Joint Lock of P6, P10, P11, P12"
author: "Daniel Murphy"
date: "May 2026"
geometry: margin=1in
fontsize: 11pt
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---

# Abstract

PAPER_1177 (Session 259) showed that three independent 2027 decisive experiments — Wuhan torsion-balance Kaluza-Klein tower search (P6), LIGO O5 black-hole ringdown spectral offset (P11), and Euclid Y1 weak-lensing $\sigma_8$ (P12) — are unified by a single dimensionless ratio $\xi \equiv D_{\mathrm{crit}}/D_{\mathrm{BSFG}}$ with UQFF canonical value $\xi_0 = 13/3 \approx 4.333$. This paper extends the joint chi-squared self-lock to a fourth independent experiment: IceCube-Gen2 neutrino Cherenkov spectral cutoff (P10, PAPER_1163). All four are 2027-2028 measurements with mutually orthogonal systematics. UQFF is required, under closed Lagrangian self-consistency, to satisfy all four within $1\sigma$ at the same $\xi$. Any single $> 3\sigma$ outlier falsifies the entire R26 closure framework.

# 1. Quadruple Joint chi^2(xi)

The 2027-2028 falsifier set is

$$
\chi^2(\xi) = \sum_{k \in \{P6, P10, P11, P12\}} \frac{[O_k - M_k(\xi)]^2}{\sigma_k^2}
$$

with predictions

| Channel | Observable           | Model $M_k(\xi)$                     | UQFF central $(\xi = \xi_0)$ | $1\sigma$ |
|--------:|----------------------|--------------------------------------|------------------------------|-----------|
| P6      | $L_{KK}$ ($\mu$m)    | $26.3 \cdot (\xi_0/\xi)$              | $26.3$                       | $0.5$     |
| P10     | $E_{cut}$ (PeV)      | $6.3 \cdot (\xi/\xi_0)^{1/2}$         | $6.3$                        | $0.4$     |
| P11     | $R_{21/22}$          | $0.10 \cdot \xi^{0.25}$               | $0.144$                      | $0.010$   |
| P12     | $\sigma_8$           | $0.7851 \cdot (1 + 0.01525 \cdot \xi/\xi_0)$ | $0.797$              | $0.005$   |

# 2. Joint chi^2 threshold

For 4 channels and 1 free parameter $\xi$, degrees of freedom $\nu = 3$. The 95% confidence threshold is $\chi^2_{95}(3) = 7.81$. The 99.7% (3-sigma) threshold is $\chi^2_{99.7}(3) = 14.16$.

UQFF is **decisively falsified** when $\chi^2_{\min} > 14.16$ at the best-fit $\xi$.

# 3. Cross-Lock Geometry

The four channels probe four different scales:

- P6: short-distance ($\mu$m) gravitational deformation.
- P10: high-energy ($\sim$PeV) neutrino dispersion.
- P11: stellar-mass ($\sim 60 M_\odot$) ringdown quasi-normal mode ratio.
- P12: cosmological ($\sim 100$ Mpc) matter power.

Each scale couples to a different aspect of the R26 manifold: KK radius, vortex spectral index, BSFG bridging coefficient, and large-scale clustering amplitude. UQFF's closed Lagrangian fixes a single $\xi$ across all four. Any disagreement is a closed-form refutation; no nuisance parameter can absorb it.

# 4. Decision Tree

```
                  [2027-2028 Quadruple Window]
                            |
        chi^2_min(xi_best_fit) computed from {P6, P10, P11, P12}
                            |
                +-----------+-----------+
                |                       |
       chi^2_min < 7.81             chi^2_min >= 7.81
       (95% CONFIRMED)                     |
       xi_best within 10%        +---------+----------+
       of 13/3 => UQFF locked    |                    |
                          7.81 <= chi^2 < 14.16   chi^2 >= 14.16
                          (TENSION, refit)        (FALSIFIED at 3-sigma)
```

# 5. CP4 Implementation

```python
from CondensedPhysics4 import UQFF2027QuadrupleFalsifierCalculator
r = UQFF2027QuadrupleFalsifierCalculator().compute()
# returns: xi_best_fit, chi2_min, chi2_threshold_95cl_3dof = 7.81,
#          chi2_threshold_3sigma_3dof = 14.16, status
```

For canonical inputs (all four observables at UQFF central values), the calculator returns
$\chi^2_{\min} \approx 0$, $\xi_{\mathrm{best}} \approx 13/3$, `status = "CONFIRMED (xi within 10% of canonical 13/3)"`.

# 6. Mutual Self-Locking Proof

A given $\xi$ is feasible iff all four residuals are simultaneously $< 1\sigma$. Solving each constraint individually:

$$
\xi_{P6} = \xi_0, \qquad \xi_{P10} = \xi_0 \cdot \left(\frac{E_{cut}}{6.3}\right)^2,
$$
$$
\xi_{P11} = \xi_0 \cdot \left(\frac{R_{21/22}}{0.144}\right)^{4}, \qquad
\xi_{P12} = \frac{\xi_0}{0.01525} \cdot \left(\frac{\sigma_8}{0.7851} - 1\right).
$$

Consistency requires $|\xi_{P6} - \xi_{P10}| < 0.43$, $|\xi_{P6} - \xi_{P11}| < 0.43$, $|\xi_{P6} - \xi_{P12}| < 0.43$ at $1\sigma$. The probability of accidental coincidence under random alternative theories is $\le 0.05^4 = 6.25 \times 10^{-6}$ at $2\sigma$.

# 7. References

[1] PAPER_1163 — IceCube-Gen2 P10 neutrino Cherenkov cutoff.
[2] PAPER_1174 — UQFF closed ledger P6 KK tower forecast.
[3] PAPER_1175 — UQFF P11 LIGO O5 ringdown spectral offset.
[4] PAPER_1176 — UQFF P12 Euclid sigma_8 R26 saturation.
[5] PAPER_1177 — UQFF 2027 joint falsifier triple (P6+P11+P12).
[6] PAPER_1178 — UQFF P13 DESI Y5 strict-static dark energy.
