Is the emission of pre-seminal fluid (madhy) and the growth of armpit hair among the signs of puberty?

Puberty for males occurs due to one of three things: completing fifteen years of age, growing pubic hair, or ejaculating semen with pleasure while awake or asleep. For females, a fourth sign is added, which is menstruation. The evidence for puberty being marked by ejaculation of semen is the Almighty's saying: "And when the children among you reach puberty, let them ask permission," and the Prophet's (peace be upon him) saying: "The pen is lifted from three... and from the boy until he reaches puberty." As for the growth of coarse hair around the pubic area, it is a sign of puberty for both boys and girls, as "we were presented to the Prophet (peace be upon him) on the day of [the Battle of] Qurayza. So, whoever had grown hair was killed, and whoever had not grown hair was left to go free." As for the discharge of pre-seminal fluid (madhy), or the growth of beard, mustache, or armpit hair, these are not signs of puberty.