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B04 Increment 25 — Exact-Vector Proof-Facing Cutover

Increment 24 showed that the legacy dense GDS rasterization is not a small representation perturbation on the tested fixture:

  • max K24 aerial-intensity difference: about 0.177;
  • threshold: 0.225;
  • diagnostic delta_I / kappa_grid: about 133--191 nm;
  • diagnostic printed-raster EPE maximum: 24 nm.

These numbers do not prove a lower bound on the best possible certified bridge, but they make the dense-loader certification branch strategically noncompetitive for a 2--3 nm theorem budget.

The proof-facing mask semantics are therefore frozen as:

GDS/OASIS
-> KLayout parser only
-> exact pixel-center vector indicator
-> canonical horizontal runs
-> direct normalized run spectrum
-> Hopkins/SOCS coefficient chain
-> interval continuous geometry

The legacy dense loader remains supported for public/legacy benchmarking and diagnostics, but it is no longer an admissible theorem dependency.

Exact-vector spectrum theorem

Let a square theorem tile have side length N, and let its binary occupancy indicator be partitioned exactly into disjoint row runs

[ R={(y,[a,b))}. ]

The direct run accumulator computes

[ c_m(k_x,k_y) = \frac{1}{N^2} \sum_{(y,[a,b))\in R} e^{-2\pi i k_y y/N} \sum_{x=a}^{b-1}e^{-2\pi i k_xx/N}, ]

which is exactly

[ \frac{1}{N^2}\operatorname{DFT}(m)(k_x,k_y). ]

No dense GDS rasterizer appears in this identity.

Consequently, relative to the declared EXACT_VECTOR_PIXEL_CENTER_INDICATOR semantics,

[ E_{\rm representation}=0. ]

This zero is not a statement about the approximation of arbitrary continuous polygon boundaries by a pixel-center indicator; quantization remains an explicit provenance assumption.

Next acceptance gate

Use a pinned public Sky130 GDS cell/layer as real geometry, choose a square exact-vector crop, and verify:

  1. canonical runs -> normalized spectrum;
  2. direct spectrum equals a materialized window of the same exact-vector source to floating replay tolerance;
  3. direct spectrum + K24 kernel spectrum reproduces Hopkins aerial intensity;
  4. no load_layout() / PIL rasterization is used anywhere in the proof path.

This is an algorithmic lithography benchmark under stated synthetic optics, not foundry calibration.