What is the phase of the impedance at each point on a resonant center fed half wave dipole?
Everyone knows that for an ideal center fed half wave dipole operated
at resonance, the impedance at the center is 73 + j0 ohms.

That's certainly not true.
From Wikipedia - dipole: -

Note that I've added on the vertical red lines and the horizontal blue and black lines that show the resistive and reactive parts of the impedance at exactly 0.5\$\lambda\$.

A true half-wave dipole is one half of the wavelength λ in length,
where λ = c/f in free space. Such a dipole has a feedpoint impedance
consisting of 73 Ω resistance and +43 Ω reactance, thus presenting a
slightly inductive reactance.

At slightly below the half-wavelength length of the input signal, the impedance will be truly resistive but at the ideal 0.5\$\lambda\$ point it's got significant reactance.

The answer that i'm not looking for is that the reactance is zero
everywhere on the antenna because it's resonant

The reactance IS NOT zero everywhere because at the feed-point it's not-zero AND, the feed-point is one point inside &quot;everywhere&quot;.