A Structural Bridge from Non-Singular Remnant Geometry to Gravitational-Wave Ringdown Observables

This paper develops a conservative, observation-facing bridge between bounded, non-singular merger remnants and gravitational-wave ringdown observables. Standard ringdown analyses model the post-merger object as an effectively point-like Kerr black hole whose quasi-normal modes are determined by its final mass and spin. This work explores a different structural possibility: if merger remnants satisfy continuity, bounded local deformation, exclusion of unbounded local collapse, and distributed interaction over domains of nonzero measure, then their late-time relaxation may be more naturally interpreted as the response of a bounded distributed remnant rather than the settling of an idealized terminal Kerr endpoint. To translate this structural picture into observable quantities, the paper introduces a minimal parameterized deformation model in which quasi-normal-mode frequencies and damping times acquire small, structured departures from Kerr expectations. These departures are governed by three effective remnant-response variables—residual structural capacity, deformation intensity, and redistribution strength—providing a disciplined interpretation of controlled departures from exact multi-mode Kerr consistency. The framework does not propose a modified theory of gravity, does not claim any detection of non-Kerr behavior, and does not rely on echo-centered phenomenology. Its purpose is strictly interpretive: to provide a conservative observational bridge between an inherited bounded, non-singular remnant framework and gravitational-wave ringdown inference. The paper also presents an observational workflow and illustrative toy models showing how different structural response regimes could project into measurable ringdown signatures. By preserving the Kerr solution as the zeroth-order reference while introducing a structured interpretation layer for possible future deviations, the framework provides a conservative and forward-compatible approach to gravitational-wave ringdown spectroscopy as observational precision continues to improve.