What is reproduced analytically

Equations (eq:covsolution) and (eq:free) give an independent derivation of the quadratic Gaussian preparation evolution. Equation (eq:splitlaw) reproduces the normalized diagonal-filter outcome calculation in physical coordinates. These formula identities do not require numerical execution.

A useful restricted numerical comparison uses rounded design inputs:

For this diagnostic, thermal radiation is omitted and support noise acts during the boost but not the exactly flat free stage. Gravity is compared at the unsmeared continuous-sphere quadratic coefficient $A_0=G{M}^2/(2\hslash R^3)$. This is not a microscopic unsmeared collapse prescription.

The reference's rounded comparison values are $\sqrt{v_x}\approx 239$ nm at the split input, ${\xi }_0\approx 607$ nm, and ${\xi }_1\approx 121$ nm Pino2018 (Appendix A.5). The embedded artifact prints calculated values and discrepancies, rather than inventing a completed comparison record.

The subtraction $v_x{v}_p-c^2$ is severely ill-conditioned after boosting. The reference-formula diagnostic therefore uses 70-digit decimal arithmetic, not a determinant formed by subtracting large double-precision numbers. Higher arithmetic precision is not a physical error bound.