Add 3DGS validation benchmark plan

Author: AdaWorldAPI

.claude/plans/3DGS-validation-benchmark-plan.md

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+# 3DGS Validation and Benchmark Plan — ndarray
+
+## Goal
+
+Create the reproducibility, correctness, and performance harness for the ndarray-side 3DGS work.
+
+This plan covers tests and benchmarks for:
+
+- splat covariance construction
+- EWA projection
+- CPU-SIMD projection/raster kernels
+- pillar certificates
+- quantized codecs
+- HHTL cascade decisions
+
+## Test tiers
+
+### Tier 0: compile gates
+
+Required gates:
+
+```bash
+cargo check -p ndarray --features std,linalg,splat3d
+cargo check -p ndarray --features std,linalg,pillar,splat3d
+cargo test  -p ndarray --features std,linalg,pillar,splat3d
+```
+
+### Tier 1: scalar reference tests
+
+Every SIMD path must have a scalar reference.
+
+Required tests:
+
+- scalar covariance construction
+- scalar EWA projection
+- scalar frustum rejection
+- scalar HHTL decision
+- scalar codec roundtrip
+
+### Tier 2: SIMD equivalence tests
+
+For each supported SIMD tier:
+
+- compare projected coordinates within tolerance
+- compare projected covariance within tolerance
+- compare rejection masks exactly where possible
+- compare aggregate counters exactly
+
+### Tier 3: deterministic pillar probes
+
+Run the active pillar probes twice in the same test and assert identical reports where expected.
+
+Required properties:
+
+- seed preserved
+- sample count preserved
+- pass/fail preserved
+- PSD rate stable
+- concentration values stable within tolerance
+
+### Tier 4: golden vectors
+
+Add small committed fixtures:
+
+```text
+tests/fixtures/3dgs/
+  tiny_splats_f32.json
+  tiny_camera.json
+  projected_reference.json
+  quantized_reference.json
+```
+
+Fixtures should be small enough for code review.
+
+## Benchmark groups
+
+Use Criterion where already available.
+
+Suggested benchmarks:
+
+```text
+splat3d_project_1k
+splat3d_project_10k
+splat3d_project_100k
+splat3d_project_1m
+splat3d_codec_f32_to_f16
+splat3d_codec_tile_i16
+hhtl_heel_frustum_100k
+hhtl_full_cascade_100k
+pillar_ewa_3d_probe
+```
+
+## Metrics to record
+
+- splats projected per second
+- rejected splats per second
+- blocks classified per second
+- bytes read per projected splat
+- allocations per call
+- max covariance error
+- max projected coordinate error
+- certificate generation time
+
+## Regression policy
+
+A benchmark regression is not automatically a correctness failure.
+
+Correctness failures:
+
+- non-deterministic certificate output
+- invalid PSD covariance accepted
+- scalar/SIMD divergence above tolerance
+- codec roundtrip above declared error
+- HHTL action mismatch between scalar and SIMD reference
+
+Performance warnings:
+
+- more allocations in hot path
+- throughput regression above configured threshold
+- unexpected branch-heavy behavior in SIMD path
+
+## CI recommendations
+
+Use two profiles:
+
+1. correctness profile
+   - fast
+   - runs on every PR
+   - scalar + default SIMD feature checks
+
+2. benchmark profile
+   - manual or scheduled
+   - records hardware and CPU features
+   - writes results to a stable report artifact
+
+## Acceptance criteria
+
+- A developer can run one command and verify 3DGS correctness.
+- A developer can run one command and benchmark 3DGS hot paths.
+- Every certificate includes enough metadata to reproduce the run.
+- All fixture files are small and human-inspectable.
+- No benchmark depends on network access.