We formulate a gauge-aware proper-time criterion for asymptotic frequency growth in the bounded oscillatory near-core regime of a regularized black-hole interior with a saturating scalar closure. Starting from a companion numerical picture in which the interior core exhibits repeated oscillatory transitions between kinetic and potential dominance in coordinate time, we define a proper-time half-period sequence from successive core equipartition crossings and the central lapse, and prove that terminal chirp-like behavior is equivalent to the vanishing of these proper-time intervals. We derive general sufficient conditions for such chirp, including a lapse-assisted mechanism and a stiffness-driven mechanism, together with corresponding non-chirp criteria. The analysis is deliberately bounded: it does not establish exterior observability, Hawking evaporation, or a universal endpoint of the black-hole interior. Its purpose is to provide an analytic bridge from coordinate-time oscillatory numerics to physically interpretable terminal-frequency behavior in the core This record should be read as an analytic supplement to the companion numerical study of bounded oscillatory near-core dynamics in a saturating-scalar black-hole interior.
Michał Jerzy Drewnisz (Fri,) studied this question.