● Interest-free Layer-1 · κ in consensus · single-node devnet

The world's first interest-free blockchain.

Built for a world after interest-based money.

κ is native. ι = 0 is the substrate.

Interest (ι) isn't banned by policy here — it's removed from the foundation. In its place, this Cosmos-EVM Layer-1 agrees a measured convergence rate κ in consensus and serves it to the EVM as block.kappa, as native as block.timestamp. Finance rebuilt from the foundation — interest-free by construction, not a compliance stamp on a conventional chain.

connecting…
See what's liveThe honest line
3 channels
independent recoveries of one κ
ι = 0
interest, by construction
0%
inflationary issuance
block.kappa
0x…0900 · 7 active precompiles
Two kinds of “different κ” — both proofs

The three panels above are independent recoveries of κ (axis 1 — different kinds of measurement). The rows inside a panel are the second proof (axis 2 — one channel, many markets): in Convergence, Bitcoin, Ether and WTI carry distinct κ — the same formula, different markets, each market's own funding decontaminated. WTI is the clincher — the moment a TradFi perp has funding, the Separation Theorem works on it too, not just crypto. And a market at parity reads “no funding this interval”, never a flattering 0 — the board doesn't lie.

What is — and isn't — enforcing today

The whitepaper is a running chain.

Everything buildable as software is built and tested. We split it into two buckets — what runs on the devnet every block, and what is coded and wired but stays OFF until the Shariah board seeds the allowlist and switches it on. We never blur the two.

Running on the devnet now — every block

κ in consensus

Every block, validators submit an index price in their ABCI++ vote extension → a stake-weighted median (≥⅔ power) → the FBA basis → κ. v10 is LIVE: it also strips each venue's interest floor per-market in consensus — the Separation Theorem made live, so ι = 0 in the published κ. No external oracle, no trusted feed.

block.kappa

An EVM precompile at 0x…0900. A Solidity contract reads κ exactly like block.timestamp — κ is a state primitive, not an app feature. v10 is LIVE — it serves a distinct, real-time per-market κ across 18 markets in three independent channels: 15 perp (crypto + gold/silver/oil/copper/equities, interest-decontaminated funding) + credit (USIG/USHY) + loss (agri takaful). Markets with real funding publish their own κ (BTC/ETH/oil distinct); a market at parity this interval honestly reads 0, not a placeholder — and a symmetric slow funding smoother lets an intermittently-funded perp carry a stable κ across its 8h funding gaps, tracking real funding without inventing it. Seven precompiles are now active — block.kappa/perp 0x…0900, takaful 0x…0901, credit 0x…0902, sukuk 0x…0903, the κ-yield curve 0x…0904, the Shariah board 0x…0905, and the κ-ladder 0x…0906.

On-chain κ-yield curve

A live term structure (Paper 2a), read in the EVM at 0x…0904 — a per-tenor stake-weighted-median grid with interpolation, the most-reused primitive (sukuk prices its distribution off it at tenor). Flat-seeded from the single κ today until a real per-tenor feed exists (bring-up); on-chain NSS fitting is deliberately omitted — a float solver would be non-deterministic.

A real FBA market

Uniform-price frequent batch auction + a 30-block mark TWAP, with a defense stack (median · ±75bp clamp · gated blend · CUSUM glass-monitor · depth rule) that simulation puts at 72×–2,739× costlier to manipulate. v10 (LIVE) hardens it per-market — a 1/K_m depth cap (thin perps capped 100–350× tighter than BTC, since ~$27K moves a thin mark the 0.10% that costs $9.4M on BTC) + a regime-corroboration monitor that freezes κ only when a jump is depth-unexplained AND credit is calm (no crisis false-trip).

Funded perp market

The funding & liquidation engine settles positions every block. The market is capitalized by the protocol's own seed, behind a real-coin escrow + solvency gate (deposits pause if the buffer can't back them, vault ≥ external claims). There are no external depositors on this devnet; open external collateral at size is Phase-3, not live.

Riba-free block reward

Zero inflationary issuance — validators are paid only from real fees, no money bred from the passage of time — plus a wakala 60/20/20 split to a tabarru fund and the board treasury.

x/shariah gate

Consulted before every fill: an asset whitelist, board-adjustable leverage caps (10× ceiling), and an emergency halt.

Two-sided depth cap

Every block, κ's move is bounded by min(cost-side, value-side). Cost-side (1/K_m) tightens with order-book shallowness (BTC 1× … thin 350×). Value-side (valueCap = S/(OI·dP/dκ), dP/dκ=1.0) caps the move so the repriceable value of the chain's own open interest can't exceed bonded stake — now live, a no-op until real exposure approaches the protocol's backing.

Built & board-activatable — wired, switched OFF

These compile and are wired into the ante / order path. On the running devnet the switch is OFF and the allowlist unseeded, so they reject nothing yet — activation is a board action, deliberately. Honest status: built, not currently enforcing.

ι = 0 EVM gate

built · off

A permissioned-EVM gate: only board-approved contracts execute, so an arbitrary app can't be called and can't reintroduce riba. (Not autonomous interest-detection — that's undecidable — but a deliberate permissioning choice: this is a permissioned EVM, not a decentralisation claim.) Coded into the ante; activates when the board seeds the allowlist.

R1–R4 product gates

built · off

Deliverable underlying (R1) + Track-A board approval for cash-settled synthetics (the open SBR-5 fatwa, as a coded gate). Possession / qabd (R2) and insurable interest (R3) are now enforced on-chain registry facts — not self-attested booleans — checked at the order path; tabarru (R4) wired into takaful contributions. Per-market, board-activated.

How κ is made

From a vote to block.kappa, every block.

01

Agree the index

Each validator reports an index price in its precommit vote extension. The PreBlocker takes the stake-weighted median over ≥⅔ of voting power — the agreed, manipulation-resistant index.

02

Clear the market

The on-chain frequent batch auction clears resting orders at a single uniform price; that clearing price folds into a 30-block mark TWAP. No intra-block time priority — a latency race buys nothing.

03

Derive κ

basis = (mark − index) / index, clamped to ±75bp → the signed funding F_t; with the venue interest floor removed (the Separation-Theorem step), κ = |F − I| × 1095 (3 settlements/day × 365). Non-negative, market-measured, zero at parity.

04

Publish & guard

κ is written to state and surfaced by block.kappa. A two-sided Page-CUSUM glass-monitor and a thin-market gated blend freeze the print if the measurement is being warped.

Priced off the consensus κ

The κ-native instruments.

Each prices off the single consensus κ the chain produces — no SOFR wrapper, no benchmark markup, no discount term. The same KappaInstruments.sol proves these on the EVM layer too.

Perpetuals

x/perp

The κ-basis funding flow itself — longs pay shorts (or vice-versa) the signed F_t, zero when the perp is at parity. Not predetermined, outcome-contingent: riba-free by Paper 1's three-condition test.

Takaful

π* = κ · B

Mutual insurance where the fair contribution is just the expected loss — no cost-of-capital, no interest loading. Priced off the consensus κ in x/takaful.

Islamic CDS

s* = κ (1 − δ)

Credit protection priced as a hazard, not as a spread over a conventional benchmark. Structured as kafāla over an owned exposure in x/credit.

Perpetual Sukuk

x/sukuk

An asset-backed instrument (R1 deliverable / R2 qabd) whose distribution is priced off the κ-yield curve at the certificate's tenor — so a 1-year and a 10-year certificate differ once the curve has shape. A yield read from real convergence, never a coupon over an interest benchmark.

Look, don't imagine

Price an instrument off the consensus κ.

Move the inputs; the takaful contribution, iCDS spread and payout recompute off the κ the chain actually agreed. No interest rate appears anywhere in the formulas.

consensus κ0.0438read from block.kappa · BTCUSD · last-read
Benefit Btakaful cover · $1,000
Recovery δ40%
Notional NiCDS cover · $1,000
Takaful contribution
π* = κ · B
$43.80
iCDS running spread
s* = κ (1 − δ)
2.6280% / yr
iCDS credit-event payout
(1 − δ) · N
$600.00

Computed off the last consensus κ the chain agreed — not a fabricated number. The live feed is momentarily unreachable, so this shows the last-read value.

Don't trust this page — verify κ yourself

The κ above isn't hard-coded — it's the value the chain published this block. Read it straight from the live endpoint, then refresh and watch the block climb:

$ curl -s https://kappachain.site/api/kappa
→ {"market":"BTCUSD","kappa":0.0765,"block":…,"live":true}

The same κ a Solidity contract reads on-chain via block.kappa (0x…0900). Verifiable, not asserted.

The evidence — 90 analyses, 17 papers

κ is real across every domain.

Across credit, the perp basis, mortality, disaster, agriculture and the monetary base, κ behaves as one measurable intensity — non-negative, credit-ordered, term-structured, mean-reverting. Validated on a 17-provider independent dataset, reproduce-first, with refinements and nulls labelled rather than hidden.

90 analyses · 17-provider independent data · reproduce-first

Perp basis — the keystone

confirmed

ι=0 funding centres at 0; ι>0 is pinned at exactly 0.0001/8h — the interest floor. Removing ι removes the +1bp/8h drift, uniformly.

A59 · P1

Credit hazard — out-of-sample

confirmed

Ranked by 2016–18 κ̂, the three sovereigns that later defaulted came out #1, #2, #3 of 20 (Lebanon, Ukraine, Sri Lanka). κ front-ran the defaults.

A43 · P2

Credit levels

confirmed

κ̂ = OAS/(1−δ) reproduces the papers' levels exactly (US-HY 0.081, EM-HY 0.102), monotone AAA→B.

A4 · A24

κ-yield curve

confirmed

12/12 sovereigns upward-sloping; +2.86 bp/yr (t=4.7) on a fresh 921-bond panel (179k bond-days).

A12 · A22

κ ≠ a benchmark (not SOFR)

confirmed

Benchmark-free κ ranks bonds the same (Spearman 0.84); the only wedge is the reserve currency's own κ — it tracks UST through time, ρ=0.93.

A32 · A40

Mortality — life takaful

confirmed

Across 41 HMD life tables ln(μ) is linear in age — Gompertz; the force of mortality doubles every 7.4 yrs. κ as a clean hazard.

A53 · P2b

Disaster — catastrophe takaful

confirmed

Disaster arrivals are a country-specific Poisson κ: 194 countries, median 1.68/yr (flood 0.74, storm 0.48). Same hazard object.

A56 · P14

Agricultural takaful — fairness

confirmed

USDA RMA, $1.245tn liability: premium 9.60% ≈ expected loss 7.89% (loss ratio 0.82). π* ≈ E[loss] holds on a real market.

A61 · P2b

Monetary — the κ-Standard

confirmed

The κ-priced money base contracts −2.03% per +100bp ≈ the paper's −1.99% — countercyclical, on independent larger data.

A30 · P8

Separation theorem — r = κ + inflation

confirmed

(policy rate − credit κ) vs inflation: corr 0.96 across 12 countries — what r carries that κ doesn't is inflation.

A49 · V2

Manipulation resistance

confirmed

The frequent-batch auction is 2776× costlier to manipulate than continuous (≈ the paper's 2739×); a grind attack nets negative.

A71 · A72 · P3

κ ↔ CDS — softened

softened

κ tracks sovereign CDS strongly (0.81–0.92 for majors) — but the corpus's 0.97 headline is a specific construction; the broad-index figure is 0.79. Corrected.

A2

Cross-domain lead — a null

null (kept)

"Credit-κ leads mortality" (found on 8 points) did not survive pooling across 20 countries (p=0.58). Kept as a null, not dropped.

A38

Every figure here is reproducible — the full archive (19 packages, all 81 analyses A1–A90, reproduce-first) is on GitHub, and the complete corpus is one downloadable book.

Is κ just interest, relabeled?

The data locates the question.

ι = 0 removes interest's predetermined charge — the guaranteed, outcome-independent increment that defines riba — everywhere. What remains inside κ is a risk premium. The decomposition measures how much: negligible for takaful (you pay for events that actually occur), dominant for credit (priced, rarely realised). Move recovery δ — the ordering, and the gap, hold.

realised hazard risk premium

Takaful — riba-free in substance

Life takaful · mortality, measured18% premium
Agricultural takaful · USDA RMA, loss ratio 0.8218% premium
Sovereign sukuk · 0 defaults / 305 bond-yrs → ≥45% (Poisson bound)45% premium

Credit by rating — mostly risk premium

AAA · 0.00% PD · 56bp100% premium
AA · 0.02% PD · 77bp99% premium
A · 0.05% PD · 78bp97% premium
BBB · 0.16% PD · 98bp93% premium
BB · 0.90% PD · 245bp85% premium
B · 3.50% PD · 270bp48% premium
CCC · 9.00% PD · 380bp5% premium

Share = 1 − E[loss]/spread, the non-expected-loss part of the spread — an upper bound on the pure premium (it also holds liquidity/tax; our IG figures sit at the top of the credit-spread-puzzle band — Elton 2001 ~80%, Huang–Huang 2012 ~70–80% IG). Sovereign is a Poisson bound (≥45%), not a point — no sovereign USD sukuk has ever defaulted. CCC turns negative at low recovery (the model's edge). The one thing that survives every recovery assumption: the takaful-vs-credit gap (~18% vs the great majority) — a 3–5× difference that is δ-invariant.

Takaful is riba-free in substance — κ ≈ realised loss, a margin not a time-charge: the beachhead. For credit, what remains after ι = 0 is a contingent, loss-bearing risk premium — riba-free in form, but whether it is riba in substance is the one thing the data cannot settle. That is reserved to scholars (the open SBR-5 ruling); the contribution here is to reduce the verdict to a single measured quantity and show exactly where it bites.

The question we'd put to a Shariah board →
The boundary — what we do and don't claim

A clean baseline, honestly scoped.

The hard, novel core — proving interest is eliminable from pricing, in consensus — is done and demonstrably true. What remains needs counterparties saying yes, not more engineering. We draw the line ourselves.

Built — done in software (see what runs vs is board-activated above)

  • κ agreed in consensus + block.kappa precompile — running
  • A real FBA market + the full manipulation-defense stack — running
  • Real-coin collateral escrow + solvency gate — enabled, protocol-seeded
  • Zero-inflation, fee-only block reward + wakala split — running
  • x/shariah whitelist/halt — running · ι=0 EVM gate + R1–R4 — board-activated (off)
  • Takaful (π*=κ·B), iCDS (s*=κ(1−δ)) & sukuk — priced off the κ-yield curve, running
  • On-chain κ-yield curve at 0x…0904 — running, flat-seeded bring-up
  • R2 (qabd) & R3 (insurable interest) — enforced on-chain registries, board-activated
  • Validator Liveness Sleeve (Paper 12) — keeper built + tested, coin-wiring pending

Needs banks, scholars, capital — not more code

  • A multi-institution validator set — it runs on one node today, so the Byzantine-fault-tolerance is by design, not yet exercised
  • Untrusted external collateral at size — needs external market-makers + a κ-ladder-sized insurance fund
  • Real-world deliverable attestation — custodians proving an asset-backed underlying exists off-chain
  • A legal entity, licensing, KYC/AML and custody
  • A Shariah-board ruling on the cash-settled perpetual, independent of interest (the open SBR-5 question)

Stated precisely: it is a live devnet serving real, interest-decontaminated, per-market κ in consensus across three modalities — the thesis is a running system, not an assertion. It is not yet production: it runs on a single node (the multi-validator security model is designed, not exercised), there are no real positions or open interest (so valueCap and thin-market exposure stay correctly inert), and the riba-in-substance question is reserved to scholars — the chain runs the form (ι = 0, the predetermined charge removed); whether the residual risk premium is permissible is theirs to rule. The form is live and proven; the substance ruling, the multi-validator testnet, and the capital are the deliberate next gates — none of them more code to write blind.

The brief we'd put in front of a Shariah board →
The proofs

Read the work.

The full 17-paper corpus behind κ, in reading order (plus the κ-Chain whitepaper this site implements, on the author's SSRN page). The arc: 1–7 build the primitive and its instruments, 8–11 build money and its jurisprudence, 12–14 defend it under attack, and 15–17 prove, measure, and reduce it — converging on the one question that belongs to scholars. Seventeen papers in the pipeline.

BOOK

The complete corpus — one volume

All 17 papers + the whitepaper, bound with a full apparatus (355pp). Everything, in one place.

CODE

Reproduce it yourself ↗

The replication archive — 19 packages, all 81 analyses (A1–A90), reproduce-first, on GitHub. Audit me.

The foundation

1

The Interest Parameter in Perpetual Futures

PDF ↗SSRN ↗

On a live venue (dYdX v4) the funding has no interest term — only a premium. ι is optional; κ carries the price.

2

From Perpetual Contracts to Islamic Credit — the keystone

PDF ↗SSRN ↗

The perpetual price IS the Duffie–Singleton credit equation (κ↔λ, ι↔r). The bridge to riba-free sukuk, takaful, and credit.

The instruments — one primitive, three markets

2a

The κ-Yield Curve

PDF ↗SSRN ↗

The interest-free yield curve from real sovereign sukuk — κ is credit-ordered and upward-sloping.

2b

Stochastic Takaful

PDF ↗SSRN ↗

κ as a CIR process; fair contribution = expected loss, validated on real USDA crop-loss data.

2c

The Islamic CDS

PDF ↗SSRN ↗

A riba-free CDS; the fair spread is κ(1−δ) — the interest rate cancels out entirely.

The system

3

Integrated Simulation Framework

PDF ↗SSRN ↗

The adversarial test-bench — cadCAD + RL + game theory — where the manipulation defenses and attack frontiers are derived.

The synthesis

7

The κ-Framework — a riba-free foundation for Islamic monetary systems

PDF ↗SSRN ↗

The capstone: the whole programme in one document — decompose r, define κ, build the curve, the Shariah analysis.

Money without a rate

8

The κ-Standard

PDF ↗

Debt-free money — base money as κ-priced sovereign equity, not interest-bearing debt; a countercyclical supply.

9

Interest-Free Monetary Equilibrium (κ-DSGE)

PDF ↗

The general-equilibrium proof the κ-Standard is determinate (γ_s < e^κ̄−1, Dynare-validated).

Jurisprudence and its roots

10

Money as a Mirror

PDF ↗

The classical foundations — al-Ghazālī's money-as-a-measure, Ibn Taymiyyah on the integrity of the measure.

11

The Jurisprudential Boundaries

PDF ↗

Riba lives in the discount rate, not the contract; the four product gates; the cash-settled case reserved to scholars.

The frontier — a measured primitive under attack

12

Liveness under Macro Winters

PDF ↗

Mechanism design for fee-only chains — liveness + censorship-resistance through macro stress.

13

Warping the Glass

PDF ↗

Measurement integrity — the oracle-manipulation frontier (closed form) + a depth rule vs bonded stake.

14

The Safe Asset without the Risk-Free Rate

PDF ↗

The κ-ladder as a safe asset; the welfare cost of the missing riskless bond (~0.4–24 bp) — small but honestly nonzero.

Proof, measurement, reduction — the newest

15

The κ-Framework Meets the Data

PDF ↗SSRN ↗

81 pre-registered analyses on a 17-provider, ~1.1 GB dataset — κ is real, venue-independent, recovered three independent ways.

16

The Riba Question, Reduced

PDF ↗SSRN ↗

Decomposes κ into hazard vs risk premium (~18% takaful → the majority for sovereign credit); reduces the verdict to one measured quantity.

17

The Separation Theorem

PDF ↗SSRN ↗

The maths: interest is a removable parameter — κ>0 moves the pricing pole off the origin, making ι=0 regular. Builds on Ackerer–Hugonnier–Jermann, “Perpetual Futures Pricing” (Mathematical Finance, 2025).