# HiLiftAeroML native-point dual surface areas

This directory describes the case-local `boundary_dual_area_<case>.npy`
payloads used for area-weighted scoring on the native HiLiftAeroML boundary
meshes.

## Payload contract

For a case named `geo_LHCiii_AoA_j`, the payload is stored beside its source
boundary archive/VTU:

```text
geo_LHCiii_AoA_j/
  boundary_geo_LHCiii_AoA_j.vtu.tgz
  boundary_dual_area_geo_LHCiii_AoA_j.npy
```

Each payload is a one-dimensional little-endian float32 NPY with one value per
native boundary point, in the exact point order of
`boundary_<case>.vtu`. Values have units of square inches (`in^2`), matching
the native coordinate units.

## Definition

Each ordered native polygon `[v0, v1, ..., v{k-1}]` is fan-triangulated as
`(v0, vj, v{j+1})` for `j=1,...,k-2`. For each fan triangle `t` with area
`A_t`, `A_t/3` is added to each of its three vertices. Thus

```text
dual_area[i] = sum(A_t / 3 for fan triangles t incident on point i).
```

Coordinates are promoted to float64 before subtraction and cross products.
Accumulation and validation use float64. Only the final payload is cast to
float32. Consumers should likewise accumulate weighted metric statistics in
float64.

## Validation and provenance

`cases/<case>.json` binds each payload to canonical hashes of the source point,
connectivity, offset, and cell-type arrays and records topology histograms,
float64 surface-area closure, float32 storage closure, orphan-point counts,
payload SHA256, and runtime provenance. `manifest.json` aggregates completed
case records.

Do not reorder the NPY or apply it to an STL, resampled mesh, triangulation with
different point order, or processed PhysicsNeMo PDMsh. It is defined only for
the corresponding raw boundary VTU.