Acceleration Time Against Loss Time: Where the Race Is Won in Candidate Sources

Acceleration is a race: a particle must gain energy faster than every loss channel drains it, and the finishing line of that race, not geometry alone, sets many real maximum energies. For an active-galactic-nucleus jet knot with a field of 5e-9 tesla and a flow speed of 0.9 c, the diffusive acceleration time at 1e20 eV is 2.747e+12 seconds against a proton synchrotron loss time of 5.680e+12 seconds, a ratio of 4.836e-01, so synchrotron losses do not stop protons there, though they would stop electrons at far lower energies. In a supernova remnant the acceleration time at 1e19 eV is already 1.113e+15 seconds, pressing the remnant's active lifetime and confirming its exclusion from the top of the spectrum. A formal acceleration floor from the critical shear, one over the critical rate, is 1.168e-33 seconds, shorter than every physical timescale in every source and therefore no constraint at all: the shear cap never wins the race because it never enters it. Simulated and computed; not a measurement.