ι = 0 — Verified On-Chain

Shariah Compliance Proof

Every value on this page is read live from our verified smart contracts on Arbitrum Sepolia. No trust required — verify it yourself on Arbiscan.

Live On-Chain Verification

Mark Price (OracleAdapter)—

Index Price (OracleAdapter)—

F computed = (Mark−Index)/Index—

F on-chain (FundingEngine.getFundingRate)loading...

ι (interest parameter)0 ← hardcoded constant

Insurance Fund—

Values refresh every 10–15 seconds from Arbitrum Sepolia (chainId 421614).

Islamic Finance Principles

01No Riba (ι = 0)ENFORCED

The funding rate formula F = (Mark − Index) / Index contains no interest floor or riba component. The parameter ι is hardcoded to zero in FundingEngine.sol and cannot be changed — it is a constant, not a variable. This is proven by Ackerer, Hugonnier & Jermann (2024), Theorem 3 / Proposition 3: when r_a ≈ r_b (both parties use the same stablecoin), the no-arbitrage condition uniquely determines ι = 0.

02No Maysir (Excessive Speculation)ENFORCED

Maximum leverage is hardcoded as MAX_LEVERAGE = 5 in ShariahRegistry.sol (a constant, not a settable parameter). Every position open call passes through validatePosition() which reverts if leverage > 5. Utility-focused framing: the protocol is designed for hedging, not pure speculation.

03No Gharar (Uncertainty / Hidden Risk)ENFORCED

All 21 contracts are verified on Arbiscan — source code is public. No proxy contracts, no upgradeable contracts (OZ upgradeable deliberately NOT installed). No admin backdoors. The only governance is a 48-hour timelock with Shariah board veto. All fees, liquidation parameters, and funding mechanics are visible on-chain. 21-pass internal audit completed with 302 findings fixed.

04Takaful Insurance FundPARTIAL

An on-chain insurance fund holds collateral to cover bad debt from insolvent positions. 50% of all liquidation penalties flow to this fund. No yield is generated on idle capital (no staking or lending of insurance funds). This is the seed of a full Takaful structure planned for Layer 3.

05Halal Asset ApprovalENFORCED

ShariahRegistry.sol requires each collateral asset to be approved by the Shariah board multisig. The approval stores an IPFS hash pointing to the fatwa document on Pinata. Testnet USDC is approved — fatwa CID QmVztQvWd5QkD5euhiUb2ycwr2SHL928Y2AC9rnWCMn7c2 is recorded in ShariahRegistry.fatwaIPFS[USDC]. PAXG and XAUT pending formal board review for mainnet.

06Everlasting Options — κ-Rate Pricing (Layer 2)DEPLOYED

EverlastingOption.sol implements the actuarially fair takaful pricing formula from Ackerer, Hugonnier & Jermann (2024) Proposition 6 at ι = 0: Π(x, K) = [K^{1−β} / (β₊ − β₋)] · x^β, where β = ½ ± √(¼ + 2κ/σ²). The κ-rate (convergence intensity) replaces the interest rate r entirely — no riba in the formula. 759/759 tests pass including fuzz and invariant suites. Deployed to Arbitrum Sepolia (2026-03-10). This is the pricing engine for Layer 2 Perpetual Sukuk and Layer 3 Takaful.

Mathematical Proof (Ackerer et al. 2025, Mathematical Finance)

Grand Valuation Equation (Ackerer Theorem 3):

F = (r_a − r_b − ι) × x + (Mark − Index) / Index

For stablecoin-margined perps (USDC):
r_a ≈ r_b (both legs use USDC, same borrowing cost)
∴ r_a − r_b = 0
∴ F = −ι × x + (Mark − Index) / Index
No-arbitrage + Proposition 3 uniquely determines ι = 0

∴ F = (Mark − Index) / Index [no riba term]

Reference: Ackerer, D., Hugonnier, J., & Jermann, U. (2025). Perpetual Futures Pricing. Mathematical Finance, DOI:10.1111/mafi.70018. The Baraka implementation follows Theorem 3 / Proposition 3 precisely — see NatSpec comments in FundingEngine.sol. The κ-rate monetary framework and everlasting option pricing (Proposition 6) are developed in Ahmed (2026), SSRN 6322778 / 6322858 — available at baraka.arcusquantfund.com.

Why Not Black-Scholes / Merton?

BSM is the industry standard for option pricing. It is also structurally incompatible with Islamic finance. Here is why — and how the AHJ everlasting option framework resolves it.

BLACK-SCHOLES / MERTON — HARAM

C = S·N(d₁) − K·e^(−rT)·N(d₂)

d₁ = [ln(S/K) + (r + σ²/2)T] / σ√T

↑ r appears twice. Removing it breaks the model.

AHJ EVERLASTING OPTION — HALAL

Π(x,K) = [K^(1−β) / (β₊−β₋)] · x^β

β = ½ ± √(¼ + 2κ/σ²)

↑ No r. No e^(−rT). No discounting at interest.

Discount factor

K · e^(−rT) ← this is riba

None — no discounting required

Maturity

Fixed T (days/months/years)

None — random stopping θ ~ Exp(κ)

Pricing parameter

r = risk-free rate (interest)

κ = convergence intensity (no interest)

Where rate comes from

Central bank / LIBOR / T-bills

On-chain perpetual convergence dynamics

Set r/ι = 0?

Breaks the model

Required by Theorem 3 — model works perfectly

Products priced

European options only

Perps · options · sukuk · takaful · iCDS

Shariah status

Structurally haram (r is riba)

Halal by construction (ι = 0 proven)

BSM prices options by discounting at the rate lenders charge for money over time — that is riba. AHJ prices everlasting options by the rate at which markets converge to equilibrium — that is not. The economic content is different even when the numerical values are similar. See Ahmed (2026), SSRN 6322858 for the full derivation.