My take is that you can't prove it, or at least not without access to technology not typically found in homes, garages or auto shops.
With mechanical abrasion or strong solvents like body shop silicone and grease removers/surface prep I tend to take it on faith that the LSP is gone (maybe two passes and a few towel changes with the panel prep). I wouldn't trust car shampoos no matter what the marketing hype says, isopropyl alcohol, dish soap, etc. nor would I trust lack of beading or sheeting or "doesn't feel slick."
I'd like to believe that Gtechniq Panel Wipe or Duragloss Squeaky Clean really gets it done but I'd like to see some evidence.