Modified Horizon Radiation, Entropy Corrections, and Thermality Breakdown in Action-Limited Gravitational Collapse

Standard black hole physics suffers from the trans-Planckian problem and the loss of quantum unitarity during Hawking evaporation. Applying the non-linear action-limit model (NALM) to gravitational collapse, we treat spacetime as a bounded substrate with a universal coarse-graining scale σ_cut ≈ 100 nm. This eliminates trans-Planckian frequency shifts and modifies the Bogoliubov transformation matrices, resulting in non-thermal emissions that preserve phase correlations of collapsing matter. As collapse approaches the phase-action saturation bound ħ/2, divergent elastic back-pressure prevents central singularity formation and triggers a non-singular horizon bounce. We derive an analytical logarithmic correction to black hole entropy with a universal coefficient α = 1/3, offering testable gravitational-wave echo signatures for future observatories while resolving the black hole information paradox.