Add 3DGS EWA SYRK BLAS MKL cross-pollination plan

Author: AdaWorldAPI

.claude/plans/3DGS-EWA-SYRK-BLAS-MKL-crosspollination-plan.md

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+# 3DGS EWA/SYRK/BLAS/MKL Cross-Pollination Plan — ndarray
+
+## Goal
+
+Fold the older PR-X12 BLAS/GEMM lens into the new 3DGS plan family.
+
+The new 3DGS plans should not rediscover this line:
+
+```text
+EWA sandwich
+  -> batched SYRK / GEMM form
+  -> backend dispatch: native / Intel MKL / OpenBLAS / AMX where available
+  -> shared Basis<T> / LinearReduce<T> substrate
+```
+
+## Existing canon to preserve
+
+Prior architecture docs already identify a high-value Plan C:
+
+```text
+Plan C — EWA SYRK-batched
+Replace per-Gaussian sandwich loop with batched cblas_ssyrk.
+Add backend dispatch: native / intel-mkl / openblas.
+Target file: src/hpc/splat3d/spd3.rs plus backend wiring.
+```
+
+This plan promotes that into the 3DGS roadmap.
+
+## Kernel identity
+
+The 3DGS projection core contains this sandwich:
+
+```text
+Sigma_image = J * W * Sigma * W^T * J^T
+```
+
+For many Gaussians, this is not only a per-splat loop. It can be batched:
+
+```text
+for each Gaussian block:
+  M = J * W
+  Sigma_image = M * Sigma * M^T
+```
+
+Batched form:
+
+```text
+many small SPD sandwiches
+        ->
+SYRK / GEMM-like backend
+        ->
+SIMD / MKL / OpenBLAS / AMX dispatch
+```
+
+## Why this matters
+
+The current CPU-SIMD path is valuable, but the older canon found a deeper win:
+
+```text
+3DGS projection is a BLAS workload in disguise.
+```
+
+The renderer should expose two tiers:
+
+```text
+small / scalar-ish batches:
+  native SIMD path
+
+large / stable batches:
+  BLAS backend path: SYRK / GEMM
+```
+
+## Proposed module layout
+
+```text
+src/hpc/splat3d/
+  spd3.rs
+  projection.rs
+  batch_sandwich.rs
+  backend.rs
+
+src/hpc/splat3d/backend/
+  native.rs
+  mkl.rs
+  openblas.rs
+  amx.rs
+```
+
+If the project prefers existing backend namespaces, adapt to that instead of inventing a second backend tree.
+
+## API sketch
+
+```rust
+pub enum Splat3dBackend {
+    NativeSimd,
+    IntelMkl,
+    OpenBlas,
+    AmxBf16,
+}
+
+pub struct SandwichBatchConfig {
+    pub backend: Splat3dBackend,
+    pub min_batch_for_blas: usize,
+    pub allow_bf16: bool,
+    pub require_deterministic: bool,
+}
+
+pub fn sandwich_batch_spd3(
+    transforms: &[Mat3x3<f32>],
+    sigmas: &[Spd3],
+    out: &mut [Spd2],
+    config: &SandwichBatchConfig,
+) -> Splat3dBatchReport;
+```
+
+## Backend dispatch rules
+
+```text
+NativeSimd:
+  always available
+  deterministic reference path
+  best for small batches
+
+IntelMkl:
+  feature-gated
+  best for large stable batches
+  must have numerical tolerance tests against NativeSimd
+
+OpenBlas:
+  feature-gated
+  portability backend
+  tolerance may differ by platform
+
+AmxBf16:
+  experimental / certified path only
+  requires pillar probe before becoming default
+```
+
+## Interaction with 4x4 carrier
+
+The 4x4 carrier plan remains compatible:
+
+```text
+Mat4 world/camera transform
+        ->
+extract spatial W / J path
+        ->
+3x3 SPD sandwich remains authoritative
+        ->
+optional 4x4 metadata/cognitive lane survives alongside
+```
+
+Do not replace 3x3 SPD covariance with 4x4 unless the extra lane has a formally defined meaning.
+
+## Certification hooks
+
+Add benchmark and proof links:
+
+```text
+Pillar-7 / EWA Sandwich 3D:
+  PSD preservation
+  concentration / CV tightness
+
+New backend parity test:
+  NativeSimd vs MKL/OpenBLAS/AMX within tolerance
+
+New performance test:
+  small-batch native wins
+  large-batch BLAS wins
+```
+
+## Acceptance criteria
+
+- Native SIMD remains the scalar-compatible reference.
+- BLAS backend results match reference within declared tolerance.
+- Backend selection is explicit and testable.
+- No hard dependency on MKL in default build.
+- Large-batch benchmark demonstrates why the BLAS path exists.
+- 4x4 carrier plan can call the same backend without breaking 3x3 covariance invariants.
+
+## Cross-repo link
+
+`lance-graph` owns SplatShaderBlas / BLASGraph orchestration and tile/block scheduling. `ndarray` owns this numerical kernel surface.