Tune getTunedTotalCapacity1 using via-size ratio and add regression tests (total 9.5% improvement)

[0hmX]

Motivation

• Improve capacity estimation for narrow/rectangular nodes by accounting for the limiting (narrow) side and how many vias can be packed across it.
• Build on PR Reduces MSE from 0.051 to 0.049 (~4% improvement, rounded values). #637's height-aware capacity model to reduce error on the high-density benchmark without changing single-layer capping behavior.

Description

• Extend getTunedTotalCapacity1 signature to accept an optional height and compute minSide so capacity reflects rectangular shapes.
• Introduce a narrowSideViaRatio and clamped viaRatioFactor to scale the effective node span by how many vias fit across the limiting dimension before computing viaLengthAcross.
• Add two regression tests in tests/auto-capacity-depth.test.ts to assert that thin rectangles yield lower capacity and that viaDiameter reduces capacity.

Testing

• Ran unit tests with bun test tests/auto-capacity-depth.test.ts, which passed all 4 added/affected tests.
• Ran sampled high-density benchmark experiments via the existing runBenchmarkWithWorkers path on the first 1200 cases to compare the PR-637 height-aware baseline against this tuned variant, yielding: baseline MSE 0.047537988117760326 (pass 1147/1200) and tuned MSE 0.04502167598365793 (pass 1147/1200).
• All automated checks and the benchmark runs completed successfully.

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Codex Task

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Project	Deployment	Actions	Updated (UTC)
capacity-node-autorouter	Ready	Preview, Comment	Mar 10, 2026 6:08pm

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/benchmark

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🏃 Autorouting Benchmark Results

📊 PR Results

Benchmark Results (1x effort)

+---------------------------+----------------+--------------------+-----------+----------+----------+
| Solver                    | Completed %    | Relaxed DRC Pass % | Timed Out | P50 Time | P95 Time |
+---------------------------+----------------+--------------------+-----------+----------+----------+
| AutoroutingPipelineSolver | 82.9% (🕒4.8%) | 1.9% (🕒4.8%)      | 5/105     | 6.6s     | 62.2s    |
+---------------------------+----------------+--------------------+-----------+----------+----------+

Scenarios: 105

📊 Main Branch Results

Benchmark Results (1x effort)

+---------------------------+-----------------+--------------------+-----------+----------+----------+
| Solver                    | Completed %     | Relaxed DRC Pass % | Timed Out | P50 Time | P95 Time |
+---------------------------+-----------------+--------------------+-----------+----------+----------+
| AutoroutingPipelineSolver | 77.1% (🕒10.5%) | 1.9% (🕒10.5%)     | 11/105    | 5.0s     | 73.0s    |
+---------------------------+-----------------+--------------------+-----------+----------+----------+

Scenarios: 105

📦 Artifact: https://github.com/tscircuit/tscircuit-autorouter/actions/runs/22907289006

[0hmX]

/benchmark

[0hmX]

@seveibar

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