Preprint Shows Deceleration Can Increase Kinetic Energy in Maximal Proper Acceleration Spacetime

The work formulates particle dynamics on higher-order jet bundles where proper acceleration is capped at a fundamental scale. In the classical cavity example, the particle's four-acceleration couples to the metric such that energy gain occurs through the acceleration term itself rather than velocity alone. This produces an explicit counter-example to the usual monotonic link between speed and kinetic energy in special relativity.

The result revives and geometrizes Born reciprocity by treating velocity and acceleration as energetically dual variables. It also identifies a superluminal sector for massive particles once proper acceleration exceeds the bound, turning both c and a_max into sector-separation surfaces rather than absolute limits. The analysis stays classical yet points to measurable corrections in extreme-field regimes.

Existing maximal-acceleration proposals (Caianiello 1981, Brandt 1983) lacked this energetic equivalence; the jet-bundle treatment supplies the missing phase-space symmetry. No laboratory test yet exists, but the cavity scheme suggests controlled high-gradient RF structures as the natural probe.

Next steps require embedding the model in a quantized field theory and deriving falsifiable shifts in synchrotron spectra or laser-plasma acceleration thresholds above 10^20 eV.