The Spectrum Above the Suppression: Extrapolation, Horizon Filtering, and What a Recovery Would Mean

What should the spectrum do above the suppression if standard propagation is the whole story? Continuing the ankle-region power law upward and then applying horizon filtering from the photopion loss lengths gives a definite shape: relative to the unfiltered extrapolation, the flux at 5e19 eV stands at a factor 4.346e-01, at 1e20 eV at 1.889e-01, and at 2e20 eV at 1.084e-01, with the filtered relative flux at 2e20 eV down to 2.566e-03 of its 5e19 eV unfiltered reference. A statistically significant recovery, in which the spectrum hardened back toward the extrapolation at the highest energies, would therefore signal either a local source population inside a few megaparsecs, a heavier composition whose fragments repopulate the top, or physics beyond standard propagation, in that order of prior plausibility. The density bound, inert at propagation densities, predicts no recovery, and a confirmed recovery should not be attributed to it without a mechanism that survives the density-ratio arithmetic. Simulated and computed; not a measurement.