Add 3DGS certified field kernel substrate plan

Author: AdaWorldAPI

.claude/plans/3DGS-certified-field-kernel-substrate-plan.md

@@ -0,0 +1,168 @@
+# 3DGS Certified Field Kernel Substrate Plan — ndarray
+
+## Goal
+
+Generalize the ndarray-side 3DGS math into a domain-neutral certified field-kernel substrate.
+
+The 3DGS renderer is the first concrete consumer, but the numerical pattern is wider:
+
+```text
+local field block
+  -> kernel summary
+  -> SIMD / BLAS / tensor operation
+  -> error certificate
+  -> skip / refine / hydrate decision support
+```
+
+## What stays in ndarray
+
+`ndarray` owns reusable numerical kernels:
+
+```text
+EWA sandwich
+SPD covariance operations
+Mat4 / Sym4 / Block4 carriers
+SIMD HHTL scoring kernels
+BLAS/SYRK/GEMM backend dispatch
+popcount / distance / palette lookup kernels
+quantization and codec helpers
+pillar probes and parity tests
+```
+
+It does not own domain semantics.
+
+## Field kernel abstraction
+
+A field kernel is a compact local approximation of a larger signal.
+
+Examples:
+
+```text
+3DGS:
+  anisotropic Gaussian over 3D position, color, opacity, covariance
+
+Datalake:
+  statistics / centroid / covariance / bloom over a fragment
+
+RAG:
+  semantic centroid + provenance + uncertainty over a chunk family
+
+Ultrasound:
+  PSF covariance + amplitude / Doppler / phase over a frame block
+
+Genetics:
+  motif / transition / expression kernel over a sequence window
+
+Neuronal:
+  activation / edge uncertainty kernel over a microcircuit block
+```
+
+## Suggested module layout
+
+```text
+src/hpc/field_kernel/
+  mod.rs
+  block.rs
+  summary.rs
+  certificate.rs
+  decision_support.rs
+  simd_score.rs
+  blas_backend.rs
+  block4.rs
+```
+
+This can start as a plan only. Do not create a generic abstraction until two concrete consumers need it.
+
+## Core DTO sketches
+
+```rust
+pub struct FieldKernelSummary {
+    pub block_len: usize,
+    pub density: f32,
+    pub energy: f32,
+    pub variance: f32,
+    pub max_error: f32,
+    pub confidence: f32,
+}
+
+pub struct FieldKernelCertificate {
+    pub total_error: f32,
+    pub confidence: f32,
+    pub passed: bool,
+    pub reason_codes: Vec<FieldKernelReason>,
+}
+
+pub enum FieldKernelReason {
+    BelowErrorBudget,
+    AboveErrorBudget,
+    NonPsdCovariance,
+    QuantizationTooHigh,
+    SamplingTooSparse,
+    DependenceInflationHigh,
+    BackendParityFailed,
+}
+```
+
+## Relation to 3DGS
+
+3DGS remains the first hard implementation path:
+
+```text
+GaussianBatch / SplatBlockView
+  -> EWA projection
+  -> HHTL cascade
+  -> field-kernel summary
+  -> certificate
+```
+
+Do not weaken `splat3d` into an over-generic module too early. Extract common pieces only after they repeat.
+
+## Relation to 4x4 carrier
+
+The 4x4 cognitive-shader carrier is the preferred experimental block grammar:
+
+```text
+lane0: coordinate / source
+lane1: state / covariance / transition
+lane2: signal / activation / confidence
+lane3: time / provenance / role
+```
+
+The certified field-kernel substrate should be able to score and certify 4x4 block summaries, but it should not require every domain to become 4x4 on day one.
+
+## Backend types
+
+```text
+Native scalar reference
+Native SIMD
+BLAS / SYRK / GEMM
+AMX / BF16 experimental
+popcount / Hamming
+palette table lookup
+```
+
+Every backend must have a reference path and parity tests.
+
+## Acceptance criteria
+
+- 3DGS code remains concrete and fast.
+- Reusable kernel/certificate pieces can be extracted without domain semantics.
+- Backend parity is testable.
+- Field-kernel certificates can be consumed by `lance-graph` decisions.
+- No domain-specific adapter logic is added to ndarray.
+
+## Implementation trigger
+
+Do not implement this as a big abstraction immediately.
+
+Trigger extraction when at least two of these are active:
+
+```text
+3DGS splat blocks
+Datalake HHTL summaries
+RAG retrieval blocks
+Ultrasound PSF blocks
+4x4 cognitive-shader blocks
+```
+
+Until then, keep this as the north-star substrate plan.