The quantum mechanical identity of indiscernibles for fermions is encoded in the Pauli exclusion principle, which presupposes exact mass-energy degeneracy across all particles of a given kind.

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Identity of indiscernibles(One of the conclusions Leibniz derives using the PSR.): The principle that no two distinct entities can share all the same properties — if two things are indiscernible, they are identical.
Mass-energy degeneracy(what the statement says is presupposed by the principle): The condition where multiple particles have identical mass and energy values, making them physically indistinguishable from each other.
Pauli exclusion principle(the specific law that encodes the identity principle for fermions): A physics rule discovered by scientist Wolfgang Pauli stating that two identical fermions cannot occupy the exact same quantum state at the same time.
Quantum mechanical(describing the level of physics being discussed): Related to the science of how tiny things like atoms and particles behave—which follows different rules than everyday objects.

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