We present the first cross-domain validation of kG, a geometric attenuation coefficient derived from fundamental wave mechanics, across three independent physical domains: seismology, archaeology, and post-surgical medical imaging. The invariant kG = pi*f₀/ (Q*Vₛ), where f₀ is the resonance frequency, Q the quality factor, and Vₛ the shear wave velocity, characterizes the mechanical signature of heterogeneous media at any scale. In its geometric form kG = pi/ (4*Q*H), the invariant requires no velocity measurement and is computable from standard imaging data. Domain 1 - Seismology: kG applied to the Nile fault system (2. 80 Hz emission) discriminates tectonic signal from ambient noise with H/V ratios up to 230 at 4-5 m depth. Domain 2 - Archaeology: kG applied to passive seismic tomography of Egyptian funerary structures detects subsurface cavities in limestone with 86-92% accuracy, validated against known tomb geometries at the Valley of the Kings. Domain 3 - Medical Imaging: kG applied to post-surgical cervical spine CT-MRI fusion discriminates metal artifacts from real pathology with 75-80% reliability in instrumented zones (C5-C7), detecting two clinically significant findings missed by three independent radiologists. The identical mathematical formulation produces physically meaningful results across all three domains, establishing kG as a fundamental mechanical invariant.
benjamin gasque (Mon,) studied this question.
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