The mark at two hundred and forty degrees
Fixed water ends and mutable fire begins when the Sun completes two hundred and forty degrees of ecliptic longitude, on 21 or 22 November. Mars gives the season to Jupiter, the lesser malefic to the greater benefic, and the mode changes from the most entrenched to the most restless in the same instant.
The two candidate dates are both ordinary. A tropical year exceeds a calendar year by close to six hours, so the crossing drifts later until a leap day resets it, and over four years it sweeps across roughly a day and a half.
Sidereal astrology moves this line by weeks
Anyone born in this window and used to Western dates will find Indian astrology giving a different sign, and the shift is larger than the boundary question itself. Sidereal zodiacs are measured from the fixed stars rather than from the equinox, and the two references have drifted about twenty four degrees apart since they last agreed.
That is more than three weeks of solar motion, so a tropical Sun in early Sagittarius is a sidereal Sun in Scorpio. The two systems are not rival calculations of the same quantity; they measure from different origins.
Why nobody is both
One longitude, one sign. There is no state of partial membership defined anywhere in the tradition, and the dignities, decans and aspects that make up a reading all assume a single placement.
The cusp of the popular phrase is a house cusp, a boundary between two of the twelve houses. Those are derived from the local horizon and meridian, they turn with the Earth, and they say nothing about which thirty degree arc the Sun occupies.
The two sides in their own right
Scorpio's final decan is Venus's, which the texts read as the most sociable band of a sign otherwise described as withheld. It is a Venus effect inside Scorpio, not an anticipation of Sagittarius.
Sagittarius opens under Mercury, an unusual pairing since Mercury is in its detriment there, and that gives the first degrees of the sign a talkative, scattered quality that the middle of the season loses. Neither band has anything to do with the boundary.
How to settle it
Take the year, the recorded time and the town of birth, and compare the resulting solar longitude against two hundred and forty degrees. The result is one sign, with no remainder.
If it turns out to be the sign nobody expected, the correction is limited to the Sun. Moon, Ascendant and everything else were derived from the same birth data and stand unchanged.
Questions people ask about this
Am I a Scorpio Sagittarius cusp?
No, because that placement does not exist. The Sun was either short of two hundred and forty degrees at your birth or past it, which makes you Scorpio or Sagittarius.
What date does the Sun move from Scorpio to Sagittarius?
21 or 22 November, depending on the year and on the time zone the birth is dated in. The instant is the same worldwide; only the local calendar date differs.
Do I have traits of both signs?
Popular astrology says so and sells the blend as a type. The chart does not show it: one Sun, one longitude, one sign. Other placements can of course sit in either sign.
What is a cusp in real astrology?
A house boundary. Houses are divided using the horizon and the meridian of the birthplace, and their cusps are genuine dividing lines within a chart.
How close to the boundary do I need to be to bother checking?
About forty eight hours either side. Inside that window the year and the birth time decide the answer; outside it, any date range gives the same result.