QMA-hardness of the electronic Coulomb ground energy in the full continuum, with unit nuclear charges

Unit-charge paper, Theorem 1.1: the promise problem for the electronic Coulomb infimum with distinct rational nuclear positions, all charges 1, unary electron number and thresholds separated by at least $L^{-1}$ is QMA-hard under deterministic polynomial-time many-one reductions; the reductions output polynomially many nuclei and electrons and threshold gap at least 1, with no basis, magnetic field or extra potential. Companion: the same with binary-encoded, possibly exponentially large charges. No membership in QMA, no spectral-gap or binding assumption, and no claim about chemically natural instances.

Unit-charge paper, Theorem 1.1: the promise problem for the electronic Coulomb infimum with distinct rational nuclear positions, all charges 1, unary electron number and thresholds separated by at least $L^{-1}$ is QMA-hard under deterministic polynomial-time many-one reductions; the reductions output polynomially many nuclei and electrons and threshold gap at least 1, with no basis, magnetic field or extra potential. Companion: the same with binary-encoded, possibly exponentially large charges. No membership in QMA, no spectral-gap or binding assumption, and no claim about chemically natural instances.