The usable time-dilation of a Kerr flyby is geodesic

A calculation of the observer-to-proper-time ratio available to a spacecraft that leaves an equatorial Kerr encounter, when the exit Δv is limited to published plasma and nuclear-thermal plants. A geodesic that returns to infinity has path-averaged R_t → 1. The encounter window r ≤ 50M yields 1.10–1.13. Interior-well captures show large R_t but do not escape. The cheapest mapped save requires Δv_φ ≈ 90–270 km/s. Published plasma and NTP do not buy that exit. Nuclear-electric propulsion can accumulate 89 km/s over months, far from the well. Orion and fusion-pulse figures are labelled study, not hardware. The usable time-dilation of a returning flyby is the escaping geodesic. Propulsion selects the worldline; it does not control time. This is an ElarionX research article, not an ElarionX CPMS technical note, and must not be deposited as a new version of Zenodo 10.5281/zenodo.21895568, 21895605, 21895647, 21895743, or 21895803. PDF (v1.3, marked): the-usable-time-dilation-of-a-kerr-flyby-is-geodesic-v1.3.pdfSHA-256: 526ffc34bb67cbb4a5cbf983679ef4a81bf5d992374d8bdfe39d1627cdbdf0a8Sidecar: the-usable-time-dilation-of-a-kerr-flyby-is-geodesic-v1.3.pdf.sha256This version adds the typeset PDF. Numerical claim unchanged from v1.3 / v1.0.