add mixed-resolution HighDensitySolverA12

[seveibar]

Summary

• add HighDensitySolverA12 in the A-series as the mixed-resolution complement to A11
• reuse A03's five-region topology with A11's feature-derived fine pitch, a 16-cell fine perimeter, and a 4x coarser middle
• keep A03 diagonal motion opt-in so existing A03 behavior is unchanged
• preserve exact endpoints/root-net metadata and reject geometry-invalid completed routes
• expose A12 in package exports, the debugger, and the Z04 benchmark CLI

HD30 result

At Pipeline 9 dimensions, seed 0, native bounds, and 100,000 iterations:

• 8/27 exact-valid solves
• 5 wins beyond A11; A11 + A12 union is 11
• 201,044 total states versus A11's 455,644 (55.9% fewer)
• 39,646 states on the largest node versus A11's 144,144 (72.5% fewer)
• zero invalid nominal solves, endpoint violations, timeouts, or exceptions

Diagonal edge conflicts are currently handled by the final geometry gate rather than repaired during search, so A12 is intended as a complementary portfolio stage.

Validation

• 15 A12 regression tests / 199 assertions
• A03 output-transform regressions
• TypeScript typecheck
• package build
• Cosmos site build
• format and diff checks

Stacked on #94 because A12 reuses A11's feature-derived pitch helper.

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Project	Deployment	Actions	Updated (UTC)
high-density-a01	Ready	Preview	Aug 30, 2026 11:36pm

[tscircuitbot]

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PR Rating: ⭐⭐⭐
Impact: Major

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