Cartesian Nested Face Construction

Pseudocode

1. Start from one finalized Cartesian fixed line. In the current repo this means the finalized QW-PGDG fixed line used as the parent line for later atomic nesting work. Code: src/ordinary_mapped_backends.jl, src/ordinary_qiu_white_rg.jl

2. Choose one one-dimensional interval on that fixed line. The first primitive is local, not global: one interval of finalized parent functions that will be compressed into a smaller side space. Code: src/cartesian_nested_faces.jl

3. Build one local doside contraction on that interval. The retained span is not an arbitrary truncation. It is the low-order local coordinate content of the interval. Code: src/cartesian_nested_faces.jl Legacy model: GaussletModules/PureGaussianGausslet.jl getsideu(...), getside(...)

4. Form the retained side space by the legacy local moment/coordinate rule. In the current pattern:

   • start from local weights
   • build directions by repeated multiplication by the local coordinate
   • orthogonalize in the local metric
   • diagonalize the projected local coordinate operator
   • sign-fix with the local weights

   Code: src/cartesian_nested_faces.jl

5. Build one tangential face product from those side spaces. For one rectangular face:

   • contract the first tangential interval with doside
   • contract the second tangential interval with doside
   • take the product of the two retained side spaces

   Code: src/cartesian_nested_faces.jl

6. Restrict to face interiors so different faces remain disjoint. The first primitive shell language already depends on disjoint support between opposite or neighboring faces. Code: src/cartesian_nested_faces.jl

7. Assemble the first shell packet from those face pieces. The shell packet carries:

   • one shell coefficient map
   • shell overlap
   • one-body packet pieces
   • Gaussian-factor and pair-factor packet pieces

   Code: src/cartesian_nested_faces.jl

8. Stop at the first shell packet. This page is only the primitive page:

   • doside
   • tangential face products
   • first shell packet

   The full landed atomic nonrecursive route now lives in: Cartesian nested atomic nonrecursive route

References

• Legacy primitive model: GaussletModules/PureGaussianGausslet.jl
  • getsideu(...)
  • getside(...)
  • getsidexyznew(...)
  • face branches around the x-y face, x-z face, and y-z face code
• Upstream fixed-line framing: 1D distorted-gausslet PGDG refinement hierarchy
• Landed nonrecursive atomic route: Cartesian nested atomic nonrecursive route

What This Frames

This page records the local primitive language for Cartesian nesting:

• one-dimensional doside
• two-dimensional tangential face products
• one first shell packet with transferred operator data

It is no longer the source-of-truth page for the whole landed atomic nonrecursive route.

For emitted 2D/3D point-set diagnostics from this construction family, the repo viz/ viewers provide a lightweight inspection path. For the current public entry points, see Visualization utilities.

Current Repo Status

The repo now has the primitive pieces described on this page:

• dedicated one-dimensional doside helpers
• tangential face-product constructors
• first shell packet propagation on those face pieces

The repo has moved beyond this primitive stage for the active atomic line. For the landed nonrecursive fixed-block route, coverage rule, shell-plus-core, corrected complete-shell source, and fixed-block adapter, use: Cartesian nested atomic nonrecursive route

Relation To Other Pages

• This page is the primitive local-contraction page.
• Cartesian nested atomic nonrecursive route records the landed nonrecursive atomic fixed-block route built from these primitives.
• Qiu-White residual-Gaussian route records the later hybrid completion once a fixed block is already in hand.

Implementation Notes

Recommended code-comment style:

# Alg Nested-Face step 3: Build a local 1D doside contraction on one interval.
# See docs/src/algorithms/cartesian_nested_face_construction.md.

Guidelines:

• keep this page focused on local primitives
• do not use it as the source-of-truth page for the full atomic nonrecursive nesting route
• keep later fixed-block assembly and residual-Gaussian completion on their own algorithm pages