cusp

Etymology

From Latin cuspis (“a point, spear, pointed end”); first used in astrology.

noun

1. A sharp point or pointed end.
2. (figurative) An important moment when a decision is made that will determine future events.
   Newcastle were 11 points adrift of Spurs following their 5-0 mauling at the hands of the north London club in February. But a sixth successive Premier League win puts them on the cusp of European football next season as they surged 15 points clear of seventh-placed Everton, who have five games left to play. April 21, 2012, Jonathan Jurejko, “Newcastle 3-0 Stoke”, in BBC Sport
3. (geometry) A point of a curve where the curve is continuous but has no derivative, but such that it has a derivative at every nearby point.
4. (architecture) A point made by the intersection of two curved lines or curved structures, a common motif in Gothic architecture.
5. (astrology) A boundary between zodiacal signs and houses.
6. (dentistry) Any of the pointed parts of a canine tooth or molar.
7. (anatomy) A flap of a valve of a heart or blood vessel.
8. A point of transition.
   I see freight returning in a big way. The 2016 reconnection of the Helwith Bridge quarries can produce up to three heavy trains a day. The nearby and much bigger Horton quarry is also on the cusp of rail reconnection. October 20 2021, Mark Rand, “S&C: a line fit for tourists... and everyone?”, in RAIL, number 942, page 40

verb

1. (slang) To behave in a reckless or dangerous manner.