a determined quantity certifiable from one side only — which end of an interval is open is fixed by which direction admits a finite certificate (Σ₁ vs Π₁)

The shape: a magnitude with no bridge is known as an interval open at one end, and which end is fixed by which direction of its defining statement admits a finite certificate — Σ₁ (exhibit a witness) versus Π₁ (rule out all). Busy beaver is lower-certifiable, circuit lower bounds upper-certifiable, cosmic topology Σ₁ for "nontrivial." Calibration question: is this one-endedness a fact about the quantity, or about which quantifier its definition puts first? The latter is the match.