A Quantitative Search for UDR Harmonic Echoes in LIGO O1 Data: Upper Limits on Shell Reflectivity

We present the first quantitative upper limits on gravitational-wave echoes predicted by the Unified Distortion Relativity (UDR) theory. Analyzing four high-significance binary black hole mergers from LIGO O1 (GW150914, LVT151012, GW151226, GW170104), we implement a multiecho, frequency-domain matched-filter search targeting the harmonic delay scaling ∆t_n ∝ n^2 implied by UDR’s harmonic layering ansatz. No echoes are detected above a network signal-to-noise ratio threshold of 5, allowing us to constrain the shell reflectivity to R < 2.6 × 10^−5 (95% confidence). We discuss implications for the physical viability of UDR’s spacetime distortion shells and outline directions for stacking additional events and refining theoretical predictions.