What is the definition of 'ground state',considering H- ion = -14.35eV

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If 'ground state' is the lowest energy state, and H atom takes -13.6eV to ionise while H- takes -14.35eV, why is H- not considered the 'ground state'?

Is that definition wrong? What is the definition of 'ground state' that "fixes" this?
 
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Ground state of an electron in a proton-electron system (by which I mean the system consisting of one proton and one electron) would be the lowest energy state available to the electron.

H- is not a proton-electron system. That's a different system with a different set of energy levels available to the electrons.
 
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OK, got it.

In orbital notation, what is the H- ion? Is it 1s2?