v0.9 Engineering Milestone

The implementation and validation described here are complete on the application v0.9 branch. A v0.9 release tag had not yet been created when this Pages update was prepared.

Main Focus

v0.9 adds an exact Hopkins/TCC/SOCS path and cross-validates it against the v0.8.1 Abbe reference. The milestone is deliberately about numerical and architectural equivalence. It does not change the public service default or silently introduce an approximate truncated result.

Exact TCC and Full-Rank SOCS

The implementation includes:

a guarded small-array discrete TCC reference using the same source points, weights, shifted pupils, FFT ordering, and defocus phase as Abbe
deterministic Hermitian full-rank SOCS construction
round-off-negative eigenvalue handling and phase-canonicalized modes
an exact HopkinsAerialImageBackend built through a source-space Gram matrix instead of a production-size explicit TCC
preserved backend-neutral process-window and CD measurement orchestration

On the 12 x 12 golden matrix covering six deterministic masks, dense7/dense11, and focus -0.15, 0.0, and +0.15 µm:

Comparison	Maximum absolute aerial error
Explicit TCC vs. Abbe	`3.66e-15`
Full-rank SOCS vs. Abbe	`6.55e-15`

Both passed the rtol=1e-9, atol=1e-11 equivalence gate. In the 18-condition backend-neutral PW/CD comparison, ordering, topology status, PASS grid, common-PW count, and sampled depth of focus were identical; maximum valid CD difference was 4.86e-16 µm.

Bounded Optical-Mode Cache

The exact Hopkins backend uses a thread-safe LRU keyed by raster shape, the complete immutable imaging configuration, and physical focus. Default bounds are eight entries and 128 MiB of retained NumPy mode payload. Diagnostics report hits, misses, evictions, oversized skips, entry count, and retained bytes.

For a deterministic 320 x 320 dense7 case at focus=+0.15 µm:

Measurement	Result
Warm Abbe median	`234.22 ms`
Hopkins first cache miss	`390.56 ms`
Hopkins cache-hit median	`115.10 ms`
Maximum aerial error	`2.66e-15`
Retained Hopkins mode payload	`45.31 MiB`

The cached evaluation was faster on this case, but the first miss was slower and used substantially more memory. These measurements support bounded reuse; they do not justify changing the service default.

Truncation Evaluation and Decision

Approximate SOCS truncation was evaluated separately with explicit mode-count, retained-energy, aerial-error, CD-error, runtime, and payload diagnostics.

On the 320 x 320 dense7 case, a 99% energy policy retained 25 of 29 modes but produced 9.82e-4 maximum aerial error and 2.22e-4 µm PW-case CD error.
Across 36 aerial cases covering six masks, dense7/dense11, and three focus values, even 99.99% energy passed only 21 of 36 strict cases.
Only 100% retained energy passed all 36 cases, and it truncated no modes.
The dense11 PW extension still measured 2.58e-5 µm maximum CD error at 99.99% energy.

No tested truncated policy meets the combined aerial and 1e-6 µm CD gates. Therefore no truncation policy is selected as a safe default. Abbe remains the service default, full-rank Hopkins remains the exact alternative, and truncated SOCS remains an explicitly labelled evaluation path.

Validation Summary