Al-Ghayb, A Formal Mathematical Definition of the Unseen

The Qur'anic concept of al-ghayb (the Unseen) is central to Islamic theology, but most scholarship treats it through exegetical, theological, mystical, or anthropological analysis. This paper develops a formal, time-indexed representation that separates actual discovery from accessibility in principle. Let Omega denote a fixed, stipulated domain of obtaining states of affairs within created reality. Let A be the class accessible in principle to independent creaturely inquiry, and let M at time t be the cumulative part of A actually established by historical epoch t. The relative Unseen at time t consists of accessible states not yet established. Let G be the class outside A and therefore inaccessible to independent creaturely inquiry. The total Unseen relative to the inquiry record combines these two classes. The paper shows that the historical residue, meaning what remains unseen across all epochs, is not automatically identical to G, because it also includes accessible states that inquiry never happens to establish. The two coincide only if historical inquiry eventually establishes every state accessible in principle. Divine disclosure is represented separately rather than treated as independent inquiry. Historical cases from electromagnetic radiation and gravitational-wave astronomy illustrate only that absence from the established record at one time does not entail non-existence. The construction does not prove that the independently inaccessible class is non-empty, identify any member of it, or use scientific unobservables as evidence for theological claims.