Unconditional modern producer for Richert (4.18) #
The proved fixed-witness Siegel theorem supplies the actual low-conductor primitive character estimate. The existing large-sieve/Vaughan argument and literal logarithmic-integral comparison then give the maximal prime-AP estimate. No analytic source proposition is assumed.
This is a modern replacement proof, not a transcription of Bombieri's Theorem 5 density argument or of an uninspected Prachar proof.
The exact raw interface is supplied by the proved, conductor-uniform quadratic L-value theorem.
The genuine nonprincipal primitive low-conductor Siegel--Walfisz input, with the smoothing function constructed rather than postulated.
Unconditional maximal Standard BV, before the literal li normalization
comparison.
Richert's exact nested integer-prefix and reduced-residue maximum,
with li(x) = integral_2^x dt/log(t) and the full stated modulus range.