Exact low-brightness minimax risk for quartic Gaussian energy
Scott Schubr, Luminary Oddities

main.pdf is the manuscript. main.tex is its complete editable source.
The paper determines the exact low-brightness quantum critical relative risk
for quartic energy of an unknown centered single-mode Gaussian state, gives
an attaining pilot-adapted procedure, and proves sharp quantum and standard
heterodyne constants at vanishing risk.

Build with Python 3 and Tectonic:
  python build.py --engine tectonic --output-dir build

Run the exact finite algebra controls (Python standard library only):
  python verify_quartic.py
  python -O verify_quartic.py

The verifier prints JSON and writes no files. It enumerates all 105 ordered
Wick pairings, independently integrates the heterodyne projection moments,
and checks rational instances of the uniform bounds and Poisson equalizer.
Its Wick enumeration adapts the author's earlier public Gaussian quartic
verifier. The manuscript supplies the all-parameter and asymptotic proofs.

citation.json supplies bibliographic metadata. MANIFEST.sha256 lists the
hashes of all other public members.
