CK Vul is a star whose outburst was observed in 1670-72. A stellar-merger event was proposed to explain its ancient eruption. Aims: We aim to investigate the composition of the molecular gas recently discovered in the remnant of CK Vul. Methods: We observed millimeter and submillimeter-wave spectra of CK Vul using the IRAM 30m and APEX telescopes. Radiative-transfer modeling of the observed molecular features was performed to yield isotopic ratios for various elements. Results: The spectra of CK Vul reveal a very rich molecular environment of low excitation ($T_{rm ex} lesssim$12 K). Atomic carbon and twenty seven different molecules, including two ions, were identified. They range from simple diatomic to complex polyatomic species of up to 7 atoms large. The chemical composition of the molecular gas is indicative of carbon and nitrogen-driven chemistry but oxides are also present. Additionally, the abundance of F may be enhanced. The spectra are rich in isotopologues that are very rare in most known sources. All stable isotopes of C, N, O, Si, and S are observed and their isotopic ratios are derived. Conclusions: The composition of the remnants molecular gas is most peculiar and gives rise to a very unique millimeter and submillimeter spectrum. The observation of ions and complex molecules suggests the presence of a photoionizing source but its nature (a central star or shocks) remains unknown. The elemental and isotopic composition of the gas cannot be easily reconciled with standard nucleosynthesis but processing in hot CNO cycles and partial He burning can explain most of the chemical peculiarities. The isotopic ratios of CK Vul are remarkably close to those of presolar nova grains but the link of Nova 1670 to objects responsible for these grains is unclear.
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