Farāʾiḍ Engine

Islamic inheritance computed from 4 irreducible axioms — not case-by-case if/else.

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Key Results

4 Irreducible Axioms

Every blocking rule, every share, every normalization step follows from α₁, α₂, β, γ. No hardcoded cases.

27 Heir Types

All recognized heirs in classical fiqh mapped to a 5-dimensional integer vector (g, j, d, q, c).

6 Extension Families

Munāsakhat, Mafqūd, Dhawī al-Arḥām, Ḥaml, Khunthā, Gharqā — all instances of one unified (S, w, A) schema.

Exact Arithmetic

Shares computed as exact rationals over ℚ using BigInt. No floats, no rounding errors.

Packages

Package	Purpose
`@faraid/core`	Pure math engine — 4 axioms, 6 phases, no strings
`@faraid/domain`	Canonical types: HeirType, schemas, madhhab presets
`@faraid/extensions`	12 extension instances via the (S, w, A) primitive
`@faraid/api`	User-facing wrappers + BaseSolver class hierarchy
`@faraid/server`	Hono HTTP server (Cloudflare Workers)
`@faraid/client`	Generated RPC client
`@faraid/web`	Interactive web application

Source Hierarchy

faraid/           ← Primary Arabic source texts (16 files, ~940 KB)
  └─ findings/    ← Mathematical formalism derived from sources (17 docs)
       └─ packages/core/   ← Engine implementing the formalism
            └─ packages/api/ packages/server/ packages/web/

The engine never hardcodes juristic decisions found in faraid/. Every rule is derived through findings/ and encoded as a mathematical axiom or exception.