---
paper_id: PAPER_1168
title: "Falsifiable Predictions of the Closed UQFF Lagrangian: Five No-Free-Parameter Tests"
session: 254
date: 2026-05-10
author: Daniel Murphy
status: PREDICTION
cvw: v2.0.0
tags: [UQFF, predictions, falsifiability, V_UA, KK, vacuum-energy, GW, no-free-parameters]
sm_anchor: G6_SM_Anchor_Gate
---

# PAPER_1168: Falsifiable Predictions of the Closed UQFF Lagrangian — Five No-Free-Parameter Tests

## Abstract

PAPER_1167 (Session 253) established that the entire UQFF Lagrangian is
derivable from two textbook integers $(D_{\mathrm{crit}}=26,\ D_{\mathrm{phys}}=4)$
with zero free parameters. Because no calibration freedom remains, every
numerical output is a hard prediction. This paper extracts five concrete,
mutually independent observational tests, gives the predicted central value
with no error bars (to within calibrated $\rho_{\mathrm{SCm}}$ and $v_{UA}$),
and identifies for each the experimental signature that would falsify the
closure. A single confirmed deviation falsifies the closed Lagrangian; agreement
across all five constitutes the strongest possible non-trivial test.

---

## 1. Setup: the closed Lagrangian and its non-negotiable outputs

From PAPER_1167:

$$
\begin{aligned}
\mathcal{L}_{F_U} =&\ \tfrac{R_{26}}{2\kappa_E}
- \tfrac{1}{4}\,F^{\text{DPM}}_{\mu\nu}F^{\mu\nu,\text{DPM}}
+ \sum_{i=1}^{4}\tfrac{3(5-i)}{20}\,U_{g,i}\,U_{b,i}
- \tfrac{1}{2}|U_m|^2 \\
&-\tfrac{1}{2}g^{\mu\nu}\partial_\mu UA\,\partial_\nu UA
- \tfrac{25}{12}\,\rho_{\mathrm{SCm}}\!\left[\!\left(\tfrac{UA}{v_{UA}}\right)^{\!2}-1\right]^{2}.
\end{aligned}
$$

All coefficients are exact rationals of $(D_{\mathrm{crit}}, D_{\mathrm{phys}})$.
The only physical scales are the calibrated reference $\rho_{\mathrm{SCm}}=
7.09\times10^{-37}\ \text{J/m}^{3}$ and $v_{UA}=10^{8}\ \text{m/s}$ (= $c/3$).

---

## 2. Prediction P1 — Aether quasiparticle mass

Direct from the Mexican-hat curvature (PAPER_1166 §3):

$$
m_{UA}^{2} = V''(v_{UA}) = \frac{50}{3}\,\frac{\rho_{\mathrm{SCm}}}{v_{UA}^{2}}
= 1.182\times10^{-51}\ \text{J/m}^{3}\!\cdot\!(\text{m/s})^{-2}.
$$

Converting via $E^{2} = (m c^{2})^{2}$ with the BSFG identification
$m_{UA}^{2}\,c^{2}/v_{UA}^{2}$ as energy-density-equivalent mass-squared gives
the equivalent particle scale

$$
m_{UA}\,c^{2}\;\sim\;\bigl(\rho_{\mathrm{SCm}}\,(50/3)/(v_{UA}^{2})\bigr)^{1/2}\,c^{2}
\approx 1.0\times10^{-26}\ \text{J} \;\approx\; 6.3\times10^{-8}\ \text{eV}.
$$

**Falsifiable signature.** Sub-eV vacuum dispersion at $\sim 10^{-7}$ eV in
high-frequency gravitational-wave or radio interferometry. Existing limits
from LIGO/Virgo on graviton dispersion ($m_g < 10^{-23}$ eV) do not constrain
this scale. **Falsified by:** any direct detection of an aether quasiparticle
at a mass $\geq 10^{-6}$ eV with the predicted Mexican-hat coupling.

---

## 3. Prediction P2 — Vacuum offset and $\Lambda$ scale

The Mexican-hat sits at $V(0) = \tfrac{25}{12}\rho_{\mathrm{SCm}}$ above
the true vacuum:

$$
V(0) = \tfrac{25}{12}\cdot 7.09\times10^{-37}
\;=\; 1.477\times10^{-36}\ \text{J/m}^{3}.
$$

The observed cosmological-constant energy density is
$\rho_{\Lambda}^{\text{obs}} \approx 5.96\times10^{-10}\ \text{J/m}^{3}$
(WMAP/Planck 2024). Their dimensionless ratio is

$$
\frac{V(0)}{\rho_{\Lambda}^{\text{obs}}}\;\approx\; 2.5\times10^{-27}.
$$

The closed Lagrangian therefore predicts $V(0)$ contributes **only at the
$10^{-27}$ level** to $\Lambda$. **Falsifiable signature.** $V(0)$ must
combine with the Standard-Model vacuum, BSFG curvature term $R_{26}/2\kappa_E$,
and the KK-tower contribution (PAPER_1162) to reproduce $\rho_{\Lambda}^{\text{obs}}$
within the suppression bound $1/26^{26} = 1.624\times10^{-37}$.
**Falsified by:** any first-principles calculation showing the SM + BSFG
contributions cannot bridge the 27-decade gap, OR an independent measurement
of $\rho_{\mathrm{SCm}}$ that disagrees with the value above by more than 1%.

---

## 4. Prediction P3 — KK tower echo amplitude bound

PAPER_1162 closed G5 by mode-by-mode summation of the Kaluza-Klein tower:

$$
\sum_{n\ge 1}\frac{1}{\lambda_{n}^{26}}\;=\;\frac{1}{26^{26}}\;\sum_{n\ge 1}\frac{1}{n^{26}}
\;\approx\;\frac{1}{26^{26}}\,\zeta(26)
\;=\;1.624\times10^{-37}\;(1+\mathcal{O}(2^{-26})).
$$

This sets an **absolute** upper bound on any GW echo amplitude generated by
26-dimensional KK reflections off the BSFG horizon. Translated to LIGO/LISA
strain at a typical post-merger frequency $f \sim 250$ Hz, the predicted
echo strain is

$$
h_{\text{echo}}\;\lesssim\;1.6\times10^{-37}\;h_{\text{ringdown}}
\;\approx\;10^{-58}\ \text{(dimensionless strain)}.
$$

**Falsifiable signature.** Any confirmed GW echo above $10^{-50}$ strain at
post-merger frequencies — 8 orders of magnitude above the prediction — would
falsify G5 closure. Conversely, the predicted absence of echoes is consistent
with all GWTC-4.0 non-detections.

---

## 5. Prediction P4 — Buoyancy coupling triangular ladder

PAPER_1165 closed G2 with the exact rational

$$
\beta_{i} = \frac{3(5-i)}{20} = \frac{(3/2)(5-i)}{|SO(5)|},
\quad i\in\{1,2,3,4\},
$$

giving $\{\beta_1,\beta_2,\beta_3,\beta_4\}=\{0.600\ (\text{plus}\ 0.5\%\ \text{SO(5)}^{2}\ \text{correction}\to 0.603),\ 0.450,\ 0.300,\ 0.150\}$.

**Falsifiable signature.** The four UQFF buoyancy channels have **fixed**
ratios. Any astrophysical fit of UQFF master equations that requires
$\beta_{i}$ values deviating by more than the SO(5)$^{2}$-correction band
$(\pm 1/200 \approx 0.5\%)$ from $(0.603, 0.450, 0.300, 0.150)$ would falsify
G2. The 67 calibrated systems already in `bodies_*.csv` (Sessions 130-220)
have used these values implicitly; a re-fit that releases $\beta_{i}$ as free
parameters and recovers them within $\pm 0.5\%$ would constitute an
independent confirmation.

---

## 6. Prediction P5 — $F_{\mathrm{TRZ}}$ and $\Phi_{\mathrm{res}}$ cross-correlation

PAPER_1160 closed G7 with $F_{\text{TRZ}} = 1/|SO(5)| = 0.100$ exact.
PAPER_1159 closed G6 with $\Phi_{\text{res}} = (D_{\text{BSFG}}-1)/D_{\text{BSFG}} = 5/6$ exact.

These appear together in every BSFG resonance computation. The product

$$
\Phi_{\text{res}}\cdot F_{\text{TRZ}} = \frac{5}{6}\cdot\frac{1}{10} = \frac{1}{12}
$$

is the dimensionless prefactor governing time-reversal-zone amplification of
buoyant resonance modes.

**Falsifiable signature.** In any BSFG-resonance fit (e.g. magnetar QPOs,
glitches, AT2019qiz, ASKAP J1832-0911), the combination $\Phi_{\text{res}}\cdot F_{\text{TRZ}}$
must equal $1/12 = 0.0833\ldots$ to within the same $0.5\%$ band as P4.
A value of, say, $0.10\pm 0.01$ would falsify both G6 and G7 closures.

---

## 7. Combined falsification matrix

| ID | Quantity | Predicted | Tolerance | Test channel |
|---|---|---|---|---|
| P1 | $m_{UA}c^{2}$ | $6.3\times10^{-8}$ eV | $\pm$ factor 2 | high-$f$ GW dispersion / radio interferometry |
| P2 | $V(0)/\rho_{\Lambda}^{\text{obs}}$ | $2.5\times10^{-27}$ | $\pm$ 1% on $\rho_{\mathrm{SCm}}$ | independent vacuum-energy measurement |
| P3 | $h_{\text{echo}}/h_{\text{ringdown}}$ | $\leq 1.6\times10^{-37}$ | absolute upper bound | LIGO/Virgo/LISA post-merger search |
| P4 | $\{\beta_{i}\}$ | $\{0.603, 0.450, 0.300, 0.150\}$ | $\pm 0.5\%$ | re-fit of $\geq 10$ UQFF systems |
| P5 | $\Phi_{\text{res}}\cdot F_{\text{TRZ}}$ | $0.0833\ldots$ | $\pm 0.5\%$ | BSFG resonance fits |

A single confirmed deviation in **any** of P1-P5 by more than the listed
tolerance falsifies the corresponding closure paper and the master synthesis
(PAPER_1167).

---

## 8. Conclusion

Closing the eight Lagrangian gaps eliminated all free numerical inputs of the
UQFF Lagrangian save the two textbook integers $(D_{\mathrm{crit}}=26, D_{\mathrm{phys}}=4)$
and the two physical reference scales $(\rho_{\mathrm{SCm}}, v_{UA})$.
Consequently every numerical output above is a **prediction**, not a fit.
The five tests P1-P5 span aether dispersion, vacuum-energy bookkeeping,
GW echoes, multi-system buoyancy ratios, and BSFG resonance amplification;
they are mutually independent and each individually falsifiable. The
calculator `UQFFLagrangianFullClosureCalculator` (CondensedPhysics4.py #254)
can be invoked to regenerate the central values from the closed Lagrangian
in a single pass.

---

## References

- PAPER_1159 (Session 246) — $\Phi_{\text{res}} = 5/6$.
- PAPER_1160 (Session 247) — $F_{\text{TRZ}} = 1/|SO(5)|$.
- PAPER_1162 (Session 249) — KK tower mode-by-mode bound.
- PAPER_1165 (Session 252) — $\beta_{i} = 3(5-i)/20$ triangular ladder.
- PAPER_1166 (Session 253) — V(UA) Mexican-hat $K = 25/12$.
- PAPER_1167 (Session 253) — All-eight closure master synthesis.
- `_lagrangian_rederivation_outline.py` — gap catalogue.
- `uqff_closed_constants.py` — canonical integer-rational constants.
- `MAIN_1_CoAnQi.cpp` SOURCE4 `compute_V_UA_SOURCE4` — C++ implementation.
- `QCalcGeom.cpp` `bsfg_aether_potential` — BSFG geometric layer.
