Cusp

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

Full definition of cusp

(plural cusps)

A sharp point or pointed end.
(figuratively) An important moment when a decision is made that will determine future events.

2012, April 21, Jonathan Jurejko, Newcastle 3-0 Stoke, 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.

(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.
(architecture) A point made by the intersection of two curved lines or curved structures. A common motif in Gothic architecture.Russell Sturgis, ed. (1902). A Dictionary of Architecture and Building: Biographical, Historical, and Descriptive. 3. Macmillan.
(astrology) A boundary between zodiacal signs and houses.
(dentistry) Any of the pointed parts of a canine tooth or molar.