Formalising Istishab in Islamic Legal Theory: A Persistent Homology Model of Legal Continuity under Doubt

Siti Nurul Azizah; Shofaatullayli; Tutik Hamidah

doi:10.55927/ijis.v5i10.97

Authors

Siti Nurul Azizah Universitas Islam Negeri Maulana Malik Ibrahim Malang
Shofaatullayli Universitas Islam Negeri Maulana Malik Ibrahim Malang
Tutik Hamidah Universitas Islam Negeri Maulana Malik Ibrahim Malang

DOI:

https://doi.org/10.55927/ijis.v5i10.97

Keywords:

Istishab, Persistent Homology, Algebraic Topology, Usul Al-Fiqh, Legal Continuity

Abstract

The presumption that an established legal status continues until a valid defeater appears (istishab) governs how Islamic jurists handle doubt, yet its structure over time has not been formalised. This qualitative-conceptual study maps the elements of istishab onto persistent homology, separating a normative admission rule for defeaters from a topological reading of continuity, and tests the model on four illustrative cases (ablution, ritual impurity, a missing person, and a contract with doubtful clauses). The initial status corresponded to a homology class that persisted until a valid defeater closed it, while doubt appeared as short-lived bars that left the class intact. Four barcode-reading rules give an auditable record of legal continuity without replacing ijtihad. Expert validation is the next step.

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