A QMU-Normalized Rotational Energy Analysis of Gravitational-Wave Events: Projection-Dependent Phase-Acceleration Structure in LIGO Strain Data

This paper introduces a QMU-normalized rotational observable for gravitational-wave analysis based on the gated phase acceleration of detector-pair phase differences. The observable is applied to publicly available LIGO/Virgo strain data from confirmed binary black hole merger events and is evaluated as a candidate probe of projection-dependent transverse rotational structure within the Aether Physics Model. Previous APM analyses emphasized scalar closure coherence metrics derived from inter-detector phase residuals. Those scalar observables showed weak statistical separation in interferometric data. In contrast, the present work examines the second temporal derivative of detector-pair phase,\[φ̈ᵢⱼ(t),\]and defines the rotational invariant\[Rᵢⱼ={1}{{F_q}^4}(d^2/dt^2Δφᵢⱼ)^2gated.\] Across the analyzed multi-detector events, the rotational invariant exhibits structured detector-pair ordering and a positive preliminary correlation with the geometric projection factor\[Pᵢⱼ=1-(k̂̂ᵢⱼ)^2,\]where \(k̂\) is the wave propagation direction and \(b̂ᵢⱼ\) is the detector-baseline unit vector. These results motivate a factorized response model,\[Rᵢⱼ=RsourcePᵢⱼ²D_iD_j,\]in which the measured rotational observable depends on intrinsic source excitation, detector geometry, and detector-specific coupling. The present dataset is limited and the reported statistical separations are modest, so the analysis is framed as exploratory rather than confirmatory. The paper defines falsifiable projection-dependent predictions for larger multi-detector gravitational-wave catalogs, including tests based on detector-pair ordering, projection-factor correlation, source-parameter scaling, and possible suppression of non-quadrupolar source classes. The work provides a QMU-native formalism for evaluating projection-dependent phase-acceleration structure in gravitational-wave strain data and proposes a foundation for future comparisons with modeled waveforms, standard antenna-pattern response, and complementary magnetic-flux-sensitive instrumentation.