Liouvillian builders accept H whose diagonal differences overflow and return a non-finite generator (present on main)

[marcohost33-maker]

A Hamiltonian with finite entries whose differences overflow is accepted, and the resulting Liouvillian contains non-finite entries. Nothing after the build checks that the generator is finite.

Reproduction (origin/main, 38f8652 lineage; checked 2026-09-11)

import numpy as np
from liouscope.core.lindblad import build_liouvillian
H = np.diag([1e308, -1e308]).astype(complex)
L = build_liouvillian(H, [])
np.all(np.isfinite(L))   # False — accepted without error

Control: diag(1, -1) is accepted and L is finite, so the probe discriminates.

Why it gets through

The Hermiticity gate works on the gauge-fixed scale of H, which is finite here. But the coherent part -i[H, ·] contains the diagonal differences H_jj − H_kk = 2e308, and those overflow. So the gate checks the input, and nobody checks the output.

Found while reviewing PR #127, where the reviewer (Equalita) and the author (Codie) reproduced it independently. It also happens on main, so it is not caused by #127 and should be fixed separately.

Suggested fix

After building, check np.all(np.isfinite(L)) (dense) or np.all(np.isfinite(L.data)) (sparse). Reject with the same error family as the other non-representable-input guards. Tests should cover:

• a before-test on the case above;
• a control that must stay accepted;
• both builders.

Related

• fix(numerics): make trace-preservation norms underflow/overflow-safe #130 (overflow-safe trace-preservation norms, closed): it covers the norms, not the generator entries.
• Hermiticity validation uses an absolute tolerance on the energy-dimensioned H (fail-open for small H) #109 (absolute Hermiticity tolerance).