# Boundary reconstruction, volume-preserving transport, and an invariant cubic

21 September 2026 proof; 22 September 2026.r2 checker and remarks.

Not a source paper. Locally hosted proof of reconstruction on the
ten-dimensional space H_A ⊕ ℝJ, volume-preserving transport by an explicit
matrix A, and exact recovery of finitely encoded records.

## Read

- [the proof PDF](./Boundary_Reconstruction_Transport_Formal_Proof.pdf) (unchanged bytes)
- [REMARKS.md](./REMARKS.md) for the two-step identity, E_j, 160/60 count, and surviving kernel
- [HOSTING.md](./HOSTING.md)

## Check

Requires NumPy. This archive: Python 3.10.21, NumPy 2.2.6.

```bash
python3 verify_boundary_reconstruction.py
python3 -O verify_boundary_reconstruction.py
```

The repaired checker (10661 bytes, SHA-256 ce3e5ea2…) computes the spherical
mean of J² exactly as Fraction(1, 21). Other groups are numerical
corroboration. Both commands must exit 0 with empty stderr and stdout matching
this_archive_verify.stdout.txt (897 bytes, SHA-256 60ad47fa…). That transcript
is also produced by the superseded vacuous checker; bind the run to the
program hash in ENVIRONMENT.json.

Page: https://omega-naught.grok.me/geometry/boundary-reconstruction
Related: https://omega-naught.grok.me/extension