= Solution
In old covariant quantization, an open-string <physical string state> obeys
$$
(L_0-1)|\psi\rangle=0,
\qquad
L_n|\psi\rangle=0\quad(n>0),
$$
with analogous left- and right-moving conditions for a closed string. A <spurious string state> is a <Virasoro descendant> orthogonal to every physical state. A <null string state> is both physical and spurious; it has zero norm and zero inner product with every physical state, so quotienting by null states removes gauge redundancy without removing observable states.
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