The Birthday Gift is the unreduced day. Where the Birthday number turns the twenty-third into a five, this position keeps the twenty-three, and reads it as a specific inheritance sitting behind the general one.
The move is the same one the Compound number makes on the name side, and it exposes a tension that runs through the whole system. Reduction is the engine: every position is defined by adding digits until one is left, and the meanings attached to the nine resulting digits are the substance of the doctrine. But reduction throws information away, and a tradition that reduces everything has no way of distinguishing the fourteenth from the twenty-third, both of which give five. Positions like this one exist to put some of that information back.
The result is a system holding two incompatible instincts at once. Master numbers are exempt from reduction because they are held to be special. Karmic debt numbers are watched for at the two-digit stage because they are held to be dangerous. The Birthday Gift and the Compound preserve the two-digit form because it is held to carry detail. Meanwhile the meanings themselves are attached to single digits.
There are only thirty-one possible values here, of which ten are single digits and reduce to themselves, so for those births the Birthday Gift and the Birthday number are the same figure read twice. Practitioners generally treat the position as significant only where the day exceeds nine.