Add the LLL-projected C4 moire model and its interaction map

[changkai-zhang]

Adds a spinless-fermion model for a C4 moire potential projected onto the lowest Landau level on a cylinder, together with the interaction map that enumerates its terms, and registers both in registry.yaml.

The interaction map emits every one-body slot and every ordered pair admitted by momentum conservation and the orbital bounds, computed in closed form on the index differences. It carries no index cutoffs: truncation belongs to the model builder, which is the only stage that sees the interaction parameters.

The model builder assembles the one-body matrix from the four C4 reciprocal harmonics and precomputes the screened-Coulomb table through a nonoscillatory form of the momentum integral. Coupling truncation is relative to a per-channel reference scale rather than absolute, so a scan over either the potential amplitude or the interaction strength keeps the same accuracy throughout, and the discarded weight is logged and exposed for audit.

The two-body term uses the half-weighted convention, summed over ordered pairs alone, equivalent to 1/2 times the unrestricted four-index sum. This is documented on ordered_pair_W, since it fixes the interaction scale relative to the potential amplitude and differs by a factor of two from sources that write the sum unrestricted.

Verification

• Interaction coefficients agree with an independent quadrature of the projected matrix element to 8e-15.
• The ordered-pair enumeration is identical to brute force over all N^4 quadruples for N = 5..9.
• With the potential switched off, DMRG at N = 12 and half filling reproduces exact diagonalization of the same Hamiltonian to 2e-14.
• python tools/verify_registry.py passes on all four entries.

Not included

No regression test, as the repository currently has no test infrastructure beyond the digest check.