PROPOSAL FOR ARCHIVAL DATA RE-ANALYSIS

To: ILL Scientific Council / Nuclear and Particle Physics Subcommittee

Instruments: PF2-GRS / qBounce

Data Range: 2018–2021 (Stability Runs / Proposal 3-14-362)

Date: March 22, 2026

1. Scientific Objective

We propose a high-coherence Fourier re-analysis of the raw neutron event-mode timestamps from the qBounce stability runs. Our objective is to extract a predicted 1.201 mHz gravitational "breathing" signal induced by the coupling of the UCN wave packet to the Earth's radial gravitational gradient ($\partial g / \partial r$).

2. Theoretical Foundation (SFIT)

The Stevenson-Flux Information Theory (SFIT) predicts a unitary modulation of the neutron wave function $\psi(z, t)$ governed by the Stevenson Operator $\hat{\mathcal{S}}(t)$.

• Energy Scale ($\Lambda_{SFIT}$): $2.56 \times 10^{-17}$ eV.

• Commutator Dynamics: The non-vanishing $[\hat{H}_0, \hat{\mathcal{S}}]$ induces a periodic Wigner Skew (phase-space rotation), causing the wave packet's RMS width to fluctuate at 1.2 mHz.

3. Predicted Observable (The 0.122% Contrast)

Our TDSE (Time-Dependent Schrödinger Equation) benchmarks confirm that for the $|3\rangle$ state bouncer and a $28.5\text{ }\mu\text{m}$ detector slit, the breathing mode manifests as a deterministic 0.122% flux modulation.

While this signal is sub-linewidth relative to the $10^{-15}$ eV vibrational noise reported in PRL 121, 070402, it is phase-locked to the Earth's rotation.

4. Proposed Analysis Protocol

We will apply a Sequential Probability Ratio Test (SPRT) to the 15-day integrated Power Spectral Density (PSD):

1. Binning: Aggregate raw event timestamps into $1.0\text{ s}$ intervals.

2. Stacking: Coherently sum the PSD of available 24-hour stability sets.

3. Discovery Threshold: Identify the 1.2 mHz peak. Simulations indicate a $5.1\sigma$ significance is reachable with 15 days of existing archival data.

5. Justification for Access

Previous analyses of these datasets focused on static energy level shifts ($10^{-14}$ eV precision). The SFIT signal is a dynamic, narrow-band oscillation that was previously averaged out as background noise. Access to raw timestamps is necessary to resolve the 1.2 mHz frequency bin.