Research package: classify marked-cubic hyperplane slices

[ipitchford]

Summary

This draft PR adds a self-contained publication package for the normalized linear-times-quadratic factorization construction behind the July 2026 three-dimensional Keller counterexample.

Main theorem

For

[
X_\ell={(L,Q):\operatorname{Res}(L,Q)=1,\ \ell(LQ)=1},
]

one has

[
X_\ell\cong\mathbb A^3
\quad\Longleftrightarrow\quad
\mathbb P(\ker\ell)
\text{ is tangent but not osculating to the twisted cubic}.
]

The proof separates:

1. universal étaleness of multiplication plus resultant;
2. generic degree three from the marked-simple-root interpretation;
3. the exceptional affine-space source, proved as two successive (\mathbb A^1)-bundles;
4. converse obstructions for the transverse and osculating hyperplane orbits.

Included artifacts

• public manuscript in Markdown and LaTeX;
• exact SymPy verifier over (\mathbb Q);
• GitHub Actions replay workflow;
• machine-readable claim ledger;
• citation and licensing metadata.

Reproduction

python -m pip install -r research/jacobian-hyperplane-slices/requirements.txt
python research/jacobian-hyperplane-slices/verify_all.py

This PR is deliberately left in draft for mathematical and provenance review. It should not be merged until the exact CI replay and independent geometric review are complete.