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We prove that genus-zero and genus-one stationary Gromov–Witten invariants of P1 arise as the Eynard–Orantin invariants of the spectral curve x=z+1∕z, y=lnz. As an application we show that tautological intersection numbers on the moduli space of curves arise in the asymptotics of large-degree Gromov–Witten invariants of P1.
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