Add 3DGS render depth certification plan

Author: AdaWorldAPI

.claude/plans/3DGS-render-depth-certification-plan.md

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+# 3DGS Render-Depth Certification Plan — ndarray
+
+## Goal
+
+Capture the mathematical-bounds cross-pollination for rendering depth, visibility, occlusion, and progressive refinement.
+
+This plan connects:
+
+```text
+3DGS EWA projection
+Cesium screen-space error
+Blender/CAD depth buffers
+CPU-SIMD HHTL traversal
+statistical error certificates
+```
+
+The renderer should not only decide what to draw. It should know how deep, how certain, and how much refinement is mathematically justified.
+
+## Core problem
+
+Depth in 3DGS and CAD/BIM scenes is not a single scalar problem.
+
+A view may contain:
+
+```text
+mesh surfaces
+transparent splats
+overlapping Gaussian support
+scan noise
+quantized local frames
+LOD substitutions
+query-relevant hidden objects
+```
+
+A naive depth test is insufficient for certified traversal.
+
+## Depth certificate components
+
+```rust
+pub struct RenderDepthCertificate {
+    pub min_depth: f32,
+    pub max_depth: f32,
+    pub depth_variance: f32,
+    pub projected_radius_px: f32,
+    pub occlusion_confidence: f32,
+    pub ordering_uncertainty: f32,
+    pub quantization_depth_error: f32,
+    pub covariance_depth_error: f32,
+    pub total_depth_error: f32,
+    pub passed: bool,
+}
+```
+
+## Error terms
+
+```text
+E_depth_total =
+    E_camera_transform
+  + E_local_frame_quantization
+  + E_covariance_projection
+  + E_splat_support_overlap
+  + E_sort_bucket_width
+  + E_lod_substitution
+  + E_sampling_discrepancy
+```
+
+The exact formula can evolve, but the certificate should keep terms separate for auditability.
+
+## Projection path
+
+For each splat or block:
+
+```text
+world/local center
+  -> view-space position
+  -> projected screen center
+  -> EWA image covariance
+  -> approximate depth support interval
+  -> depth certificate
+```
+
+Depth support interval:
+
+```text
+z_center ± k * sigma_z
+```
+
+where `k` is selected by the render budget / confidence target.
+
+## HHTL usage
+
+```text
+HEEL
+  reject blocks outside frustum or behind near/far planes
+
+HIP
+  estimate depth interval and projected radius
+
+TWIG
+  refine overlap/ordering uncertainty
+
+LEAF
+  exact projection and optional raster/composite path
+```
+
+## Blender/CAD relevance
+
+Blender/CAD scenes add exact mesh depth or proxy depth:
+
+```text
+mesh object depth
+  -> exact or rasterized depth interval
+
+3DGS texture/radiance skin
+  -> probabilistic splat depth interval
+
+combined object
+  -> mesh depth anchors splat depth confidence
+```
+
+This enables reality-skinned CAD/BIM:
+
+```text
+CAD mesh says wall is here.
+3DGS scan says visual surface is here.
+Certificate reports whether the visual skin aligns within tolerance.
+```
+
+## Cesium relevance
+
+Cesium-style traversal uses screen-space error.
+
+3DGS depth certification adds:
+
+```text
+screen-space error
+  + depth uncertainty
+  + ordering uncertainty
+  + occlusion confidence
+```
+
+This improves decisions for:
+
+```text
+skip LOD
+refine tile
+hydrate exact mesh
+render splat preview
+reject visually hidden block
+```
+
+## CPU-SIMD kernels
+
+Candidate kernels:
+
+```text
+batch view-space transform
+batch depth interval estimate
+batch frustum/depth rejection
+batch projected-radius estimate
+batch occlusion bucket assignment
+batch certificate reduction
+```
+
+The exact alpha compositing path may remain GPU/WGPU optional. CPU-SIMD owns planning, prefiltering, and certification.
+
+## Sorting and buckets
+
+Full exact splat sorting can be expensive.
+
+Use tiered depth buckets:
+
+```text
+coarse bucket
+  -> render/skip/refine decision
+
+uncertain bucket overlap
+  -> TWIG refinement or exact LEAF sort
+```
+
+Certificate reports whether bucket uncertainty is acceptable.
+
+## Acceptance criteria
+
+- Depth certificate DTO exists at plan/API level before implementation.
+- Scalar reference computes depth interval and projected-radius estimates.
+- SIMD path can batch depth rejection.
+- Certificate terms remain separate, not only one opaque score.
+- Blender/CAD mesh depth can be used as an anchor for 3DGS skin alignment.
+- Cesium-style SSE decisions can include depth uncertainty.
+
+## First demo
+
+```text
+one camera
+one mesh plane
+one small splat block near the plane
+  -> compute mesh depth
+  -> compute splat depth interval
+  -> report alignment / uncertainty / pass-fail
+```
+
+## Wall sentence
+
+```text
+Depth is not just where something is; depth is how confidently the renderer may stop looking behind it.
+```