[qmc] JOE: chiral-graviton NQS for Challenge 15

[Joe-Nor]

Team

Team name	JOE
Members	Bei Qiao (乔北), Institute of Physics, Chinese Academy of Sciences

Challenge

Row
Challenge	Construct an exchange-antisymmetric, SO(3)-equivariant neural quantum state for the ν = 1/3 chiral graviton and compute Δ = E(L=2) − E(L=0).
Catalog issue	Addresses #15.
Track	qmc — Variational Monte Carlo / Neural Quantum States.

Result and evidence

The scientific submission contains only the Challenge 15 registration.
Challenge 121 has been moved to a separate branch, solution folder,
repository, and PR. This branch temporarily mirrors the independently tested
two-file Ubuntu prerequisite fix from #264 because current upstream main
otherwise fails its own test workflow; those files contain no challenge
content.

For (N=4), the VMC calculation gives

$$ \Delta_4/E_C=0.132556\pm0.002941, $$

while exact diagonalization gives

$$ \Delta_4^{\mathrm{ED}}/E_C=0.131856754927. $$

The values differ by (0.24) Monte Carlo standard errors. This is a
small-system validation, not a thermodynamic-limit claim.

Latest projected-CF Pfaffian attempt

The reviewer-ready snapshot also contains a coordinate-space projected-CF
Pfaffian rank-two broken-pair tangent. At (N=4), its two active channels span
the complete (\mu_2=2) multiplicity space. The deterministic oracle reports

|E₂(Pfaffian) − E₂(ED)| = 4.44×10⁻¹⁶
maximum fivefold splitting = 4.44×10⁻¹⁶
maximum coordinate-symmetry residual = 2.83×10⁻¹⁵
maximum ‖(L²−6)ψ‖ residual = 1.31×10⁻¹³

This is a deterministic small-system certificate, not a Monte Carlo result.
It does not establish large-(N) convergence, a thermodynamic-limit gap, or
chirality.

• Concise reviewer report
• Projected-CF Pfaffian report
• Reproduction guide
• Machine-readable Pfaffian oracle
• Immutable reviewer-ready snapshot a74b92a

Validation at the linked snapshot: 84 project tests and 61 independent
Stage-1 Fock-oracle tests passed.

[Joe-Nor]

Working repository:
https://github.com/Joe-Nor/JOE-Harnessing-Quantum-2026

• Challenge [challenge]: Symmetric neural-network ansatz for the chiral graviton in ν = 1/3 fractional quantum Hall state #15 — Chiral-graviton NQS: https://github.com/Joe-Nor/JOE-Harnessing-Quantum-2026/tree/main/challenges/15-chiral-graviton
• Challenge [challenge]: Sign-problem free hunter #121 — Sign-problem-free hunter: https://github.com/Joe-Nor/JOE-Harnessing-Quantum-2026/tree/main/challenges/121-sign-free-hunter

The registration PR will remain in Draft while the challenge work is developed in the external repository. We will mark it ready for review after the final report is complete.