N2: coincidence Wick square and revised diagnostics

The source reports relative differences at most $1.1\times 10^{-31}$ for a set containing

and two twisted cases with $\beta =0.3$.

For a second set containing

the retained earlier residual is $8.6\times 10^{-17}$.

The AB record reports that image terms had been cast to double complex. It further reports an omitted diffraction correction at a double approximation to $1/3$. After removing the cast, it reports N2 discrepancies at most $4\times 10^{-41}$, except $\alpha =\text{double}(1/3)$, for which the omitted term reportedly leaves $5.8\times 10^{-17}$. It reports N2/N3 reproduction at at most $6\times 10^{-39}$. All of these numbers and explanations are retained; none replaces a raw log or an error enclosure.

Two supplied values of $r^2{F}_0$ are

The exact second expression is $8/(48{\pi }^2)$. Pure diffraction at $\alpha >1/2$ and compatible finite images at exact quotient parameters are analytical conclusions, not consequences of those decimals.