Is one obligated to fulfill a vow written on paper, intending to perform a Qur'anic litany and seek forgiveness for five days during the last ten days of Ramadan, knowing that the paper was lost after it was found, and the intention was not restricted to the writing itself? And what is the expiation for breaking this vow?

Fulfilling the covenant with Allah is a religious obligation, and it is a stringent one, as Allah Almighty says: (And fulfill the covenant; indeed, the covenant will be questioned). The covenant is considered a vow if it is intended to obligate oneself to obedience, and it is obligatory to fulfill it and to offer an expiation for an oath (kaffarat yamin) if its time has passed.