= Solution
Introduce anticommuting matter fields $\psi^\mu$ as <worldsheet Majorana fermions>, transforming as target-spacetime vectors and two-dimensional spinors. The <RNS string> pairs them with $X^\mu$ through <worldsheet supersymmetry>. In flat superconformal gauge the matter action is, up to the conventional fermion normalization,
$$
S=-\frac1{4\pi\alpha'}\int d^2\sigma\left(\partial_aX\cdot\partial^aX-i\bar\psi^\mu\rho^a\partial_a\psi_\mu\right),
$$
and the field equations split $\psi$ into left- and right-moving components. The supersymmetry constraints include both the stress tensor and the supercurrent, so unphysical polarizations are removed rather than interpreting every fermionic worldsheet component as a physical particle.
The possible <spin structures> produce two sectors. On the closed chiral circle, or the doubled open string, the <Neveu–Schwarz sector> has $\psi(\sigma+2\pi)=-\psi(\sigma)$ and half-integer modes $b_r$. The <Ramond sector> has periodic $\psi$ and integer modes $d_n$, including $d_0$. Canonical quantization replaces the classical Grassmann variables by operators satisfying
$$
\{b_r^\mu,b_s^\nu\}=\eta^{\mu\nu}\delta_{r+s,0},\qquad
\{d_m^\mu,d_n^\nu\}=\eta^{\mu\nu}\delta_{m+n,0}.
$$
In particular $\Gamma^\mu=\sqrt2d_0^\mu$ obeys $\{\Gamma^\mu,\Gamma^\nu\}=2\eta^{\mu\nu}$. This is the <Ramond zero-mode Clifford algebra> in covariant form. Its ground-state space must carry a representation of the <Clifford algebra> of the target metric, and hence transforms as a <spinor>, not a scalar vacuum. Indeed the zero-mode Lorentz generators proportional to $[\Gamma^\mu,\Gamma^\nu]/4$ act on it as the spin representation. This is the essential mechanism converting anticommuting worldsheet matter into spacetime spinorial states.
The zero-mode supercurrent constraint on a Ramond ground state is proportional to $k\cdot d_0$. It becomes
$$
\boxed{k_\mu\Gamma^\mu u(k)=0,}
$$
the momentum-space <Dirac equation>. The <Ramond level operator> has zero intercept, so the ground state is massless. Exciting bosonic or nonzero fermionic oscillators gives tensor-spinor excitations; the Clifford ground-state factor is retained. In the Neveu–Schwarz sector there is no fermionic zero-mode degeneracy. Its ground state is a scalar and its excited states carry integer-spin tensor representations, despite the anticommuting oscillator construction. Thus worldsheet fermionic oscillators do not by themselves make every target-space state a fermion.
Consistent projection also matters. The <GSO projection> removes the NS tachyon and selects a definite Ramond chirality in the standard supersymmetric spectrum. At the critical dimension ten, the projected massless NS vector has eight transverse polarizations, while the projected Ramond ground state has eight physical spinor polarizations after the massless Dirac constraint and the <Majorana-Weyl spinor> conditions. The projection permits their organization into spacetime supersymmetry multiplets. The assignment of spacetime fermionic statistics is compatible with spinorial transformation, vertex-operator locality and the <Spin-statistics theorem>; it is not just a relabeling of the Grassmann variables in the classical action.
For a closed string the left and right sectors can be chosen independently subject to level matching and the consistent spin-structure sum. The <NS-NS sector> and <Ramond–Ramond sector> have bosonic spacetime representations; a pair of Ramond spinors produces integer-spin fields. The mixed <NS-R sector> and <R-NS sector> instead carry one spinor factor and yield spacetime fermions, including <gravitino> and <dilatino> states. Opposite versus equal chiralities of the two Ramond sectors distinguish the <type IIA superstring theory> and <type IIB superstring theory> choices.
Quantum consistency of this RNS matter-plus-gauge system requires $d=10$: its matter central charge is $d+d/2$, the reparameterization ghosts contribute $-26$ and the commuting <superconformal ghosts> contribute $11$, so the total is $3d/2-15$. \b[Spacetime fermions arise through Ramond matter zero modes, their Clifford/spinor representations and the physical-state/projection conditions.] The anticommuting $b,c$ gauge-fixing ghosts already present in the bosonic path integral are not such matter fields and do not create physical spacetime fermions.
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