Current ordinary branch

This page is the shortest current user-facing status read for the newer ordinary Cartesian line.

What the ordinary branch is today

The current ordinary story is:

• Coulomb-expansion first, not 3D grid first
• one-dimensional mapped ordinary bases on each Cartesian axis
• an explicit backend split between validation and experimental PGDG-style analytic construction
• a separate paper-faithful Qiu-White residual-Gaussian reference path
• the friendlier hybrid/core-supported regime as the practical target

The hybrid motivation is the same as in the hybrid gausslet/Gaussian papers: the Gaussian supplement is there to improve the near-nuclear/core region while letting the gausslet backbone stay at a relatively moderate spacing, instead of asking the gausslets alone to resolve the whole core.

This line is still experimental, but it now has a clear current interpretation and should be read as a real second workflow in the package.

For terms involving residual Gaussians, the intended interaction stays in the same two-index integral-diagonal-approximation (IDA) representation used for the gausslet channel, rather than being treated as a four-index tensor with only diagonal index patterns retained.

Start here

Within the manual, the best supporting pages are:

• Examples
• Example guide
• First radial workflow

The radial tutorial is still useful context because the package’s operator and quadrature story was established there first.

Notes that are not yet migrated into the first site

The current ordinary-branch workflow and supporting notes still live in the flat docs/ tree for now. The most important filenames are:

• ordinary_coulomb_expansion_path.md
• mapped_ordinary_basis.md
• ordinary_cartesian_vee_validation.md
• ordinary_cartesian_hybrid_vee_validation.md
• ordinary_cartesian_residual_gaussian_interaction.md
• ordinary_cartesian_mwg_interaction.md
• ordinary_cartesian_legacy_he_s_adapter.md
• ordinary_cartesian_qiu_white_reference.md
• ordinary_cartesian_qiu_white_crossblock_correction.md
• qw_pgdg_base_milestone_note.md
• qw_pgdg_fixed_a_mapping_note.md
• ordinary_pgdg_hybrid_regime.md
• ordinary_sho_spectral_test.md
• ordinary_pgdg_hybrid_consolidation.md
• ordinary_pgdg_supporting_notes.md

Current interpretation

The wording discipline for the ordinary line remains:

• :numerical_reference is the validation route
• the PGDG-style analytic route is good enough in the friendly hybrid regime
• hard pure mapped small-c cases remain stress tests
• AsinhMapping is the current working map, not final truth
• for pre-nesting Cartesian convergence tests, the current default family is fixed a = 1/(2Z) with s solved from count and xmax rather than a fixed-s scan
• the radial branch remains numerical rather than PGDG-driven

That is much closer to the practical White–Lindsey-style hybrid picture than to the harsher pure mapped stress-test cases.

If you want the lower-priority architecture and note-history context after that, continue with:

• Developer Notes