Summary
We present a currency system where all issued currency returns through exponential decay — no human controller, no governance vote, no discretionary monetary policy. The system runs on Ethereum L2 (initially Base network) as eight smart contracts. The entire monetary policy is described by two exponential functions.
Full paper: SSRN (ID: 6483158)
Source: GitHub (CC0)
1. The Problem
Every object of economic exchange — labor, meals, services, time — is finite and returns upon consumption. Currency, the medium for exchanging these things, does not return. Gold persists. BTC is capped at 21M units forever. Fiat expands at discretion.
This asymmetry produces the Cantillon effect: newly issued currency reaches those closest to the source first; by the time it reaches the periphery, purchasing power is already diluted. Between 2020–2022, the net worth of the top 1% in the US increased by $11.8T. The bottom 50% gained $1.5T.
The root cause is not issuance policy — it is that currency does not return.
2. Design: Four Currencies, Two Equations
The system comprises four currencies. All are managed by smart contracts with no admin keys.
2.1 Base (Existence Guarantee)
Each participant deposits USDT (up to 1,000) and receives an equivalent Base balance. Used Base recovers exponentially:
where D is the deposit amount (capped at 1,000) and B(t) is the current balance. From zero, ~37 days restores 90%. This is the participant’s guaranteed floor — it always recovers.
2.2 Amortization (Return Currency)
The instant Base is spent, it enters the recipient’s Amortization wallet and begins returning through exponential decay:
The per-second rate r is set so the residual rate reaches 3% at T = 108 days:
No batch processing. No epoch boundaries. Continuous decay via lazy evaluation — only the last timestamp and balance are stored; residual value is computed on-read from elapsed seconds.
Amortization cannot be converted back to stablecoins. There is no escape route from a returning currency to a non-returning asset.
2.3 Torch (Pay-it-Forward)
Participants can convert their own Base into Torch. This permanently reduces their Base ceiling:
The converted amount c enters their Torch wallet (ceiling: 1,000, equal to Base). Simultaneously, 3c is generated in their IgnitionPool (IGP).
IGP can only be used to ignite another participant’s Torch. The recipient receives the ignited amount as Torch plus 3\times that amount as new IGP. Participants without USDT can enter the system by receiving an ignition.
This structurally reverses the Cantillon effect. Those with more Base can convert more → generate more IGP → but IGP can only be used for others. Wealth does not trickle down from center to periphery — it is lit as fire at the edges.
2.4 Creation (Creative Support)
Activated at 10M+ participants. Up to 100,000 Base granted for education, research, entrepreneurship. Evaluated by participants + decentralized AI. Spent Creation enters Amortization and returns through the same decay.
3. Smart Contract Architecture
Eight contracts, each with a single responsibility:
| Contract | Role |
|---|---|
DecayMath |
Library. Exponential decay computation |
AmortizationWallet |
Receives spent Base/Torch/Creation. Continuous decay |
BaseWallet |
Existence guarantee. Exponential recovery. convert() to Torch |
TorchWallet |
Pay-it-forward wallet. Ceiling 1,000 |
IgnitionPool |
3× multiplier vessel. ignite() for others only |
CreationWallet |
Creative grants. Same decay as Amortization |
StablecoinPool |
USDT backing. Full withdrawal anytime |
CreationModule |
Grant evaluation (DAO + AI deliberation) |
Initial deployment on Base network (Coinbase L2). Low gas fees enable continuous exponential calculations at practical cost. Long-term: migration to a more neutral L2 or a dedicated rollup inheriting Ethereum’s security.
4. Security Properties
4.1 Sybil Collusion (Mutual Ignition)
Attack pattern: A converts Base → Torch → acquires IGP → ignites co-conspirator B → B ignites A back.
This is economically irrational. The moment A converts, A’s Base ceiling is permanently reduced. Restoring it requires real USDT deposits — a genuine cost to the system’s infrastructure. The Torch and IGP gained through collusion have no exit: Torch wallet ceiling is 1,000, and IGP can only be used for others.
Sybil collusion always requires real cost upfront, and what is gained has no liquidation path.
4.2 Gresham’s Law
Concern: participants spend decaying Amortization while hoarding non-decaying Base.
Structurally resolved. The instant a payment is made from Base, it automatically transforms into Amortization. There is no selective spending — the transformation is embedded in the payment function itself. Amortization cannot be exchanged for stablecoins.
4.3 Asset Flight
Criticism: participants will flee into non-decaying assets (land, gold, BTC).
This system intentionally scopes itself to the currency layer — the medium of exchange. Asset layer design is a civilizational problem, not one a currency system should attempt to solve alone.
5. Design Constants
| Parameter | Value |
|---|---|
| Decay model | B(t+1\text{s}) = B(t) \times (1-r) |
| Internal constant T | 108 days |
| Residual at T | 3% |
| Daily decay rate | \approx 3.174\% |
| Base ceiling | 1,000 USDT |
| Recovery rate | 6% / day |
| Torch ceiling | 1,000 (equal to Base) |
| IGP multiplier | 3× |
| IGP ceiling | None |
| Creation activation | 10M+ participants |
The constants are 3 and 6. The system is fully described by two exponential functions: the decay of Amortization (3% residual) and the recovery of Base (6% daily).
6. Relation to Existing Work
Bitcoin solved “how to reach consensus without a trusted third party” but reinforced the storability of currency. 21M cap + HODL culture → speculative asset, not medium of exchange.
Gesell’s Freigeld proposed demurrage (linear decay). This system uses exponential decay — the same feedback structure as radioactive decay, thermal cooling, and ecosystem balance. Exponential decay is self-regulating: the more there is, the more decays. No parameter tuning needed as the system scales.
EIP-1559 introduced burn as a partial return mechanism for gas fees. This system embeds return into the currency itself, at the application layer.
7. Open Questions
- Oracle risk: Base ceiling restoration depends on USDT deposits. USDT depegging affects the system’s entry point.
- L2 dependency: Initial deployment on a single-operator L2 (Base network). Migration path to a neutral rollup is planned but unspecified.
- Creation governance: The DAO + AI deliberation model for Creation grants is deliberately left underspecified until the 10M participant threshold.
- Composability: How does a decaying currency interact with existing DeFi protocols that assume non-decaying balances?
System name: AMI — All Material is Impermanent
Hikari Amato | Paper (SSRN) | Source (GitHub, CC0)