Abstract
<jats:p>Sample-based quantum diagonalization (SQD/QSCI) selects determinant subspaces from quantum-circuit samples for classical diagonalization; its iron–sulfur demonstrations anchor utility-scale quantum-chemistry claims, and a recent critique disputes them at matched subspace dimension. Both sides benchmark on energy-based diagnostics, not spin identity. We introduce a rotation-invariant spin audit: exact determinant-space ⟨S²⟩, invariant S²-Gram spectra over quasi-degenerate manifolds, and higher spin moments (⟨S⁴⟩ through ⟨S⁸⟩) that bound the spin-sector decomposition, and apply it to the public [2Fe-2S] and [4Fe-4S] benchmarks, IBM's shipped qiskit-addon-sqd pipeline, and IBM's published hardware data. No audited execution returned the named singlet at competitive energy; for published states unavailable to direct audit, the energy-only records do not establish singlet identity. Classical selected-CI growth converges to a spin-contaminated attractor (⟨S²⟩ ≈ 4.7 on [2Fe-2S]); samples drawn from it preserve the contamination; spin-inversion completion permits spin symmetry without producing it; and the released [2Fe-2S] hardware samples yield no energy advantage over the uniform-random control. A scalar mean does not identify these states: two audited arms share ⟨S²⟩ ≈ 2.00, one a triplet eigenstate (Var(S²) = 3×10⁻⁶), the other a 2:1 singlet–quintet mixture whose triplet weight its third moment bounds below 10⁻⁴. At the largest published dimension (5.625×10⁷ determinants, reconstructed here from the released support), the numerically stable lowest root lies 170 mHa below the published energy at ⟨S²⟩ = 1.3711 (stable under an 18.6-fold residual tightening to 1.1% of the 0.285 mHa gap), with Var(S²) = 6.9 and first two moments excluding any decomposition confined to S ≤ 2. Near-singlet character survives only as a non-stationary superposition: selection does not commute with S². Energy-only SQD benchmarks therefore do not establish convergence to the named target state; we propose measured spin moments as a mandatory benchmark output, with spin control active rather than passive.</jats:p>