The first date past the line
Gemini's second decan begins at ten degrees. Across 1930 to 2035, a 1 June Sun at noon has stood between roughly ten and eleven and a half degrees, so it is inside that band in every year of the span, with the lower end of the range close to the boundary.
The day before is a genuinely split case and this one is not, which is a useful contrast. It shows how little movement is involved: a degree and a half of variation across a century is enough to make one date ambiguous and leave the next one settled.
The stability itself comes from the leap year cycle, which keeps a calendar date pinned to nearly the same point of the orbit rather than letting it drift. A century of 1 June noons fits inside a window narrower than the width of two full Moons.
Mars or Venus, depending on the scheme
The Chaldean order runs Mars, Sun, Venus, Mercury, Moon, Saturn, Jupiter, begun at zero degrees of Aries and carried through all thirty six faces. Counted through, the middle decan of Gemini falls on Mars. The triplicity scheme instead assigns a sign's decans to signs of its own element in order, so the air decans of Gemini go to Gemini, Libra and Aquarius, and the middle one is Libra's and therefore Venus's.
Mars and Venus is about as wide a gap as the two schemes ever produce. Tradition reads the Mars version as Gemini's quickness given an edge and a competitive turn, and the Libra version as the same quickness turned towards company and agreement. Neither is a measurement, and a description that does not name its scheme cannot be checked at all.
Why the calendar holds the position steady
The tropical year is a little under three hundred and sixty five and a quarter days. That quarter day accumulates over three common years and is cleared by a leap day, so a given calendar date returns to nearly the same solar longitude rather than drifting away from it.
Within a single year the Sun still moves a little under a degree a day, so a birth just after midnight sits nearly a degree behind one just before the next midnight. On this date that difference matters only for someone at the very bottom of the range, where the first decan is within reach.
What a June date cannot decide
The Moon covers around thirteen degrees a day, so on any single 1 June it occupies one sign or crosses into the next, and across a run of years it has been in all twelve. The rising sign changes completely about every two hours and depends on the birth latitude as well as the clock.
The widget above takes a year, an hour and a place and returns the Sun's degree and minute, the decan, and the distance to the nearest sign boundary. Here that last figure comes back wide, since Taurus ended around eleven days earlier and Cancer is about three weeks away.
That is the honest shape of what a birth date gives you. It fixes the Sun and nothing else, and the Sun is the placement shared with everyone born within a day of you anywhere on Earth.
Questions people ask about this
What decan is 1 June?
The second decan of Gemini, from ten to twenty degrees, in every year sampled at noon. The lower end of the range is near the boundary, so a very early birth in a low year is worth calculating rather than assuming.
Which planet rules that decan?
Mars under the Chaldean order and Venus, through Libra, under the triplicity scheme. The two schemes rarely diverge as widely as they do here, so the source of any description matters.
What degree of Gemini is 1 June?
Between about ten and eleven and a half, depending on the year and the hour. The widget above narrows that to a single degree and minute for a specific birth.
Is 1 June ever a Taurus birthday?
No. The Sun leaves Taurus around 20 or 21 May, so by the first of June there is well over a week of margin and no year in the sampled span comes close.
Does the decan affect compatibility readings?
Some practitioners use decan rulers when comparing charts, so it can change the emphasis of a reading. It does not change the sun sign, which is what most compatibility material is built on.
What still needs a birth time on this date?
The rising sign, the house positions, and the Moon in years where it changes sign during the day. None of those can be recovered from the date by itself.