V4Coin: A Peer-to-Peer Hooked Cash System

The V4Coin Contributors
v4coin.xyz · @V4CoinETH

Version 1.0 — 2026 · An homage to Nakamoto (2008), adapted to Uniswap v4

1.Introduction

Commerce on decentralized finance relies almost entirely on tokens whose issuance is controlled by their creators. Supply schedules are promised in documents, not enforced by code; "fair launches" routinely reserve large allocations for teams and insiders; and inflation can be turned on by whoever holds an admin key. What is needed is a coin whose scarcity is a property of the protocol itself, distributed to those who make it useful rather than to those who deployed it.

Bitcoin[1] solved exactly this problem for a new blockchain by tying issuance to proof-of-work. But recreating a proof-of-work chain to launch one token is wasteful and impossible to compose with existing liquidity. We instead observe that Uniswap v4[2] introduces hooks — contracts that execute at defined points in a pool's lifecycle — and that a hook is a natural place to run a monetary policy. We define a coin, V4C: a fixed launch offering of 10,000,000 is minted at genesis to bootstrap the market, and every coin thereafter — up to a hard cap of 21,000,000 — is minted by the hook and handed to those who stake, on a Bitcoin-style halving schedule.

2.Coins

We define the coin, V4C, as a standard fungible token. A one-time launch allocation is minted at genesis; after that, new coins come into existence in only one way: the token exposes a single privileged function, mine(to, amount), callable only by the emission hook and internally clamped so that total supply can never exceed the cap C = 21,000,000. There is no other mint path. When the hook's address is set to zero, mine can never be called again and the supply is sealed.

The problem, as in any cash system, is establishing who is entitled to the newly minted coins in a way that requires no trusted party. We solve this by making entitlement a verifiable, on-chain function of a scarce and productive resource: staked coins.

3.Supply Milestones

A monetary schedule needs a trigger. Bitcoin halves its block subsidy every 210,000 blocks — which is really a statement about how many coins have been issued. We adopt that idea directly: the halving is triggered by minted supply. Splitting the cap C into eras by supply, era k ends when the minted supply reaches

so era 0 mints C/2, era 1 mints C/4, and so on. The current era is simply the number of milestones the minted supply has passed — a value every observer computes identically from public on-chain state. If no one is mining, supply does not grow and the next halving simply waits.

4.Proof-of-Stake

In Bitcoin, the right to a block's subsidy is won by expending energy: a miner's share of the reward is, in expectation, their share of the network's hash rate. We replace expended energy with committed stake. Let Sᵢ be the amount of V4C that address i has staked, and S the total staked. Over any interval, participant i's claim on emission is

Staking is a productive commitment of the coin itself: to mine you must hold and lock V4C, aligning every miner with the very asset they are issued. The more of the supply that is staked, the less remains liquid to sell — so mining and scarcity reinforce one another rather than working against each other.

5.The Hook

Mining is driven by a staking contract; the Uniswap v4 hook is how it plugs into a live market. The hook runs at two points in the pool's life: after initialization (to bind itself to a single pool) and after each swap (to advance the mining clock). Staking itself — deposits, withdrawals, and claims — advances the same clock. It maintains one global accumulator, A, the lifetime emission per unit of stake, updated lazily whenever it is touched:

A miner who has staked Sᵢ since accumulator value Aᵢ is owed Sᵢ·(A − Aᵢ). This is the standard reward-accumulator construction[3], and it serves any number of miners in constant time: no per-participant loop is ever required, no matter how many are mining.

6.Incentive

By convention, the emission in an era is the block subsidy for that era. In era 0 the subsidy rate is r₀ coins per second; after k halvings it is r₀/2ᵏ. This steadily releases new coins into circulation, analogous to miners expending resources to add gold — except here the committed resource is the staked supply itself. The subsidy also incentivizes participants to keep their stake locked: unstaking stops one's mining entirely.

Once the cap C is reached, emission ceases and stakers are compensated purely by the swap fees of the v4 pool. In this way the incentive can transition to fees with no inflation, and the coin can remain hard-capped indefinitely. The incentive may help encourage participants to stay honest: a large staker has more to gain by supporting the coin than by attacking it.

7.Lazy Minting

Once the latest emission is spread into the accumulator, the individual coins owed need not be minted immediately. Coins are minted only when a miner calls harvest(), or when their position changes. Because the amount owed is recovered from the accumulator at any time, nothing is lost by deferring the mint. This keeps state compact — one number per active miner — and means the protocol never iterates over participants to pay them, no matter how many there are.

8.Verifying Your Rewards

It is possible to verify mining rewards without trusting the interface. The hook exposes a view, pendingReward(miner), which recomputes the accumulator up to the present moment and returns exactly what would be minted on harvest(). A miner can read this directly from the chain, or reconstruct it from emitted events, and confirm that the coins they receive match the published schedule for the current epoch. As long as the emission math and the cap are public and immutable, a miner need not trust the website, only the contract.

9.Staking and Unstaking

A miner may add to or reduce their stake at any time, with no lock-up. On every such change the contract first settles what is owed at the current accumulator value, then updates the stake and resets the miner's reward debt. Rewards earned at the old stake weight are therefore minted before the weight changes and can never be lost. Unstaking returns the principal in full alongside any pending rewards; an emergency exit is also provided that returns principal while forfeiting unclaimed rewards.

10.Privacy

The traditional banking model achieves a level of privacy by limiting access to information to the parties involved. The necessity to announce all liquidity events publicly precludes this method, but privacy can still be maintained by keeping addresses anonymous. The public can see that someone is mining a certain amount, but without information linking the address to a real identity. This is similar to the level of information released by stock exchanges, where the time and size of individual trades is made public, but without telling who the parties were.

11.Calculations

11.1 Convergence to the cap

By construction, era k mints exactly C/2^(k+1) coins. The total ever emitted is therefore the sum over all eras:

The supply converges to exactly the cap C and, because each step is capped at the next milestone and every emission is additionally clamped so that totalSupply + emission ≤ C, it can never exceed it. The cap is thus enforced twice: analytically by the series, and defensively by the clamp.

The one free parameter is pace. The per-second subsidy in era 0, r₀, only sets how quickly the first C/2 is mined under continuous staking. Choosing a target era length T (we use ~4 years, as in Bitcoin) gives

after which every subsequent era — having both half the coins and half the rate — lasts the same T, recovering Bitcoin's ~4-year cadence as an emergent property of a purely supply-driven rule.

11.2 Stake grinding

An attacker might attempt to stake a large amount immediately before an emission is credited and unstake immediately after, capturing a disproportionate share for near-zero exposure. Because the accumulator advances only in proportion to elapsed time, and emission between two touches at the same instant is zero, sandwiching a single update within one block yields nothing. To capture meaningful emission the attacker must keep capital staked across real time, forgoing its liquidity — precisely the committed behaviour the subsidy is meant to reward. Let q be the fraction of a window for which an attacker is actually staked; their captured share of that window's emission is at most proportional to q, so fleeting stake earns fleeting rewards.

The probability that transient, uncommitted capital out-earns committed stake drops toward zero as the settlement layer's ordering prevents same-block stake-and-unstake from spanning any elapsed time, much as the probability of an attacker catching up in Nakamoto's analysis falls exponentially with depth.

12.Conclusion

We have proposed a system for distributing a hard-capped digital coin without a trusted issuer. We began with the observation that a Uniswap v4 hook can serve as an autonomous monetary authority, and that staking is a natural, self-securing substitute for proof-of-work. The coin's schedule — a halving block subsidy summing to 21,000,000 — is fixed in immutable code, enforced by a hard cap, and distributed pro-rata to the participants who stake the coin. Participants vote with their stake, extending it by committing capital and stopping simply by unstaking. They rarely need to coordinate, since the schedule is objective and the accounting requires no trust. Any needed rules and incentives can be enforced with this mechanism.

References

1. S. Nakamoto, "Bitcoin: A Peer-to-Peer Electronic Cash System," bitcoin.org/bitcoin.pdf, 2008.
2. Uniswap Labs, "Uniswap v4 Core," github.com/Uniswap/v4-core, 2024.
3. MasterChef reward-per-share accounting, as popularized by SushiSwap, 2020.
4. H. Adkins et al., "Concentrated Liquidity and Just-in-Time Provision," DeFi research notes, 2023.

This document is an independent homage to the structure of Satoshi Nakamoto's 2008 paper. It reproduces none of its text. V4Coin is an experimental, open-source project and is not affiliated with Bitcoin or Uniswap Labs. Nothing herein is financial advice.