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Motivated by Matsas et al. (2024), who demonstrated that time can serve as the sole fundamental dimension in place of traditional LMT dimensions, this study expands those results within the Minkowski and Tangherlini frameworks. Using a Lorentz transformation (LT) matrix approach, we validate the three-clock protocol, confirming that distance and newly discovered velocity expressions are derivable exclusively from proper times. The investigation is extended to Tangherlini's 4D spacetime to test whether absolute velocity is identifiable. While this resulted in velocity cancellation, a breakthrough was achieved by analysing the wave 4-vector geometric structure. By defining electromagnetic waves in transit as 'anonymous' — hosted by the ARF and unrelated to their original source frequency due to Doppler ambiguity at emission — we propose the Postulate of Anonymity, justified by the wave 4-vector structure in the Tangherlini framework. Using this concept, we successfully circumvented the "cancellation gap". We demonstrate that the ratio of spatial wave-vector components ky/kx (the tangent of the aberration angle) provides a direct, non-ambiguous measure of absolute velocity relative to the vacuum, reconciling with aberration methodologies utilised in the Planck 2013 mission. We prove that while the temporal component ω/c acts as a coordinate-dependent variable subject to sensor interaction, the spatial components tell the 'full truth' of the ARF. Consequently, we formally associate "peculiar velocity" with absolute velocity. The Andromeda Paradox is partially resolved as a coordinate artefact. We conclude that the wave 4-vector is a universal witness to an invariant, causal timeline anchored to the ARF.