B04 Increment 24 — Optical Raster-to-Contour Bridge¶
Increment 23 proved only a finite-grid mask statement:
- exact-vector mask: 90032 occupied pixels;
- current dense loader: 96258 occupied pixels;
- all 6226 disagreements are dense false positives;
- mutual Chebyshev radius: 1 pixel.
That result must not be read as an 11.31 nm printed-contour EPE bound.
For SOCS
[ F(m)=\sum_j w_j |E_j(m)|^2, ]
write (D_j=E_j(\widetilde m-m)). Then exactly
[ F(\widetilde m)-F(m) = \sum_j w_j\left( 2\Re(E_j(m)\overline{D_j})+|D_j|^2 \right). ]
Thus if (|E_j(m)|\le A_j) and (|D_j|\le B_j) on the verification core,
[ |F(\widetilde m)-F(m)|_\infty \le \sum_j w_j(2A_jB_j+B_j^2)=:\delta_I. ]
If the reference threshold band of width at least (\delta_I) has certified
[ |\nabla F|\ge\kappa>0, ]
then the sharp level-set transfer gives
[ d_H(\Gamma_{\widetilde m},\Gamma_m)\le\delta_I/\kappa. ]
Under unique oriented-slab edge pairing:
- continuous contour EPE is at most (\delta_I/\kappa);
- paired CD error is at most (2\delta_I/\kappa).
The local benchmark is intentionally diagnostic. It chooses the 128x128 crop of the Increment-23 fixture with the largest exact-vs-dense disagreement, runs both masks through the same K24 Hopkins model over focus/dose nodes, and reports:
- max aerial-intensity discrepancy;
- thresholded printed-raster EPE;
- a grid finite-difference gradient diagnostic;
- the diagnostic ratio
delta_I / kappa_grid.
No continuous/certified contour claim is made until the gradient floor is replaced by an interval-certified full-band transversality bound.