Radial Accommodation in the Ehrenfest Problem: A Conditional Layered-Ring Model with an Effective Covariant Phase-Stiffness Realization

This paper revisits the century-old Ehrenfest paradox and demonstrates that the contradiction between the Lorentz-contracted circumference and a supposedly unchanged radius arises from an unnecessary assumption of fixed material radius. A conditional layered-ring construction is presented: each concentric material ring is allowed to change its laboratory radius while preserving its summed local comoving (proper) circumference. The closure condition yields the radial map r(ρ) = ρ / √1 + ω^2 ρ^2 / c^2 , which simultaneously satisfies Euclidean laboratory geometry and the local tangential Lorentz relation. To give this kinematic map a dynamical foundation, an effective covariant phase-stiffness sector is introduced. Reducing the spatial phase-gradient action on a uniformly wound thin ring produces an explicit circumference-dependent energy Uwind(C) . In the strong-locking limit, the radial map is exact; at finite stiffness, a positive centrifugal correction and a local radial-stability condition are derived. A separate constrained time-dependent embedding in the zero-temporal-frequency sector provides the corresponding angular momentum and identifies the limit of the reduced branch. The construction thus supplies a closed, self-consistent model that resolves the Ehrenfest paradox without invoking non-Euclidean geometry or abandoning special relativity. The limitations of the thin-ring approximation and the open finite-stiffness Hamiltonian completion are honestly discussed, framing the work as a concrete step toward a more complete material theory of rotating relativistic bodies.