The Ceiling

Three snapshots of one system. A score that a watcher can never push above 1 — and a toucher can.

C₁₂ (snapshot 1 vs 2)
C₂₃ (snapshot 2 vs 3)
C₁₃ (snapshot 1 vs 3)
exact value for this gap

Flat grey line: the classical ceiling of 1. Gold curve: what re-preparing reaches, peaking at exactly 1.5 when the gap is 60°. The dot is where you are.

This is a toy, and the two modes are not on equal footing — that is the whole point of it. WATCH is a plain deterministic rotor, counted; nothing quantum is put into it, and the ceiling it hits is forced. TOUCH has the quantum rule for re-preparation put in by hand; it is not derived here and this page is not evidence that a clockwork world produces it. What the page shows is the gap between the two: no setting of the watcher ever crosses 1, and the toucher does. Nothing here is a claim about nature. Full scope, numbers and sources are in the article.