Multiswap: Redefining Onchain Capital Markets

Abstract

Multiswap is the first automated market maker (AMM) engineered to scale to traditional finance (TradFi) proportions, bridging DeFi’s potential with institutional-grade infrastructure. Unlike legacy AMMs that bleed value and fragment liquidity, Multiswap delivers a mathematically robust, capital-efficient trading ecosystem. With dynamic weights, unified liquidity, and an embedded launchpad, it rethinks the capital management value chain—merging exchange and portfolio into one. Powered by the CAV token, Multiswap lays the foundation for spot trading, lending, fixed income, and derivatives, poised to rival centralized limit order books (CLOBs) onchain and outpace NYSE-grade systems offchain.

Introduction

Decentralized finance (DeFi) commands a total value locked (TVL) of $100 billion, yet it remains a fraction of traditional finance (TradFi), where the New York Stock Exchange (NYSE) processes $150-$200 billion in daily volume. Conventional automated market makers (AMMs), such as Uniswap and Curve, rely on constant product formulas that constrain DeFi’s growth. These systems incur value leakage through slippage and impermanent loss—costs obscured by fee-focused metrics—while liquidity fragmentation across multiple pools limits scalability. Short-term reward structures further destabilize protocols, exposing liquidity providers (LPs) to volatility and incentivizing transient participation.

CavalRe introduces Multiswap, an AMM engineered to transcend these limitations and align DeFi with TradFi’s scale. Designed from first principles, Multiswap ensures capital preservation through robust mathematics, consolidates liquidity into a single, boundless pool, and optimizes trades with dynamic weights. An integrated launchpad facilitates equitable token distribution, while a restructured value chain merges exchange and asset management—casting LP tokens as shares in a yield-bearing index fund. Extending beyond spot markets, its modular framework supports lending, fixed income, and derivatives, positioning Multiswap to compete with centralized limit order books (CLOBs) onchain and exceed NYSE-grade performance offchain.

This whitepaper delineates Multiswap’s technical architecture, ecosystem design, and the CAV token’s pivotal role in fostering adoption. Scheduled for launch on May 8, 2025, with a $25M fully diluted valuation, Multiswap establishes a foundation to integrate DeFi’s innovation with TradFi’s magnitude—targeting the next trillion in onchain capital markets.

Technical Foundations

Multiswap redefines decentralized trading, engineered from five foundational financial principles—discrete mathematics, balanced value, internal numeraire, discrete self-financing, and dynamic weights—to bridge DeFi’s potential with traditional finance (TradFi) scale. These principles converge into a single-pool architecture that supports unlimited assets, eradicates value leakage, and rivals NYSE-grade throughput. Transcending conventional AMMs, Multiswap’s governing equation and pioneering design deliver institutional-grade efficiency, targeting a $25M FDV at its May 8, 2025 launch. This section outlines the technical foundations of Multiswap, illustrates its mechanics through practical examples, and explains its potential role in advancing onchain capital markets.

Discrete Mathematics

Legacy AMMs like Uniswap anchor their mechanics in continuous mathematics, epitomized by the constant-product formula, $\alpha_x \alpha_y = \text{constant}$. This model assumes a finite trade is split into infinitesimal steps, integrated from pre-trade to post-trade prices—an abstraction misaligned with real-world dynamics. The result? An effective mid-price execution where ~50% reflects the stale pre-trade price, leaking value as trades execute partially at outdated rates. Financial markets, however, operate discretely, with finite transactions driving tangible shifts in prices and reserves. Multiswap harnesses this reality, modeling trades as distinct events rather than integrated curves.

This paradigm shift unlocks a profound capability: a singular liquidity pool supporting unlimited assets without the inefficiencies of pairwise fragmentation. In a pool with $n$ assets, Multiswap automatically activates

$$\text{\# Trading Pairs} = \frac{n (n+1)}{2}$$

trading pairs with zero fragmentation of liquidity.

The entire TVL of each asset is available to trade against the entire TVL of any other asset. Multiswap’s testnet exemplifies this prowess, deploying a single pool with 504 tokens modeling the S&P 500 unlocking 127,260 pairs—all with zero fragmentation of liquidity. Contrast this with traditional AMMs, where supporting 504 assets would demand thousands of separate pools, each diluting liquidity, amplifying slippage, and crippling scalability. Multiswap consolidates capital into a boundless hub, optimizing efficiency and forging a scalable backbone for institutional-grade trading—extensible to thousands of assets without compromising depth, poised to rival TradFi’s vast infrastructure with unmatched precision.

No Leverage

From the perspective of the pool, LP tokens represent equity and tokens in the pool are assets. Multiswap’s second pillar mandates that the value of LP tokens precisely equals the value of all assets within the pool

$$V_0 = \sum_{i=1}^n V_i$$

meaning there is no leverage in the system.

This principle enables a key advancement: LP tokens serve as shares in a yield-bearing index fund. Beyond trading fees, LPs gain proportional ownership of the asset portfolio, uniting exchange efficiency with portfolio growth.

Internal Numeraire

Multiswap has no dependencies on external prices, instead adopting an internal measure of value called "scale". Each token $i$ carries a scale $s_i$, with its scaled price defined as

$$P_i = \frac{s_i}{\alpha_i}$$

—the value per token in scale units—and the pool’s total scale follows from no leverage and is given by the sum of the asset scales

$$s_0 = \sum_{i=1}^n s_i.$$

The post-trade scaled price adjusts to

$$P_i+\Delta P_i = \frac{s_i + \Delta s_i}{\alpha_i + \Delta \alpha_i}.$$

Asset weights are independent of the chosen numeraire and are given by $w_i = \frac{s_i}{s_0}$, and the price of token $i$ measured in terms of token $j$ emerges as the ratio

$$P_{i,j} = \frac{P_i}{P_j} = \frac{s_i / \alpha_i}{s_j / \alpha_j}.$$

Discrete Self-Financing

Multiswap’s discrete self-financing principle ensures value inflows equal value outflows so that no value is created or destroyed during trades. For token $i$, with quantity $\alpha_i$ and scaled price $P_i$ from Principle 3, the value change from $t$ to $t+1$ is

$$\Delta V_i(t,t+1) = \alpha_i(t+1) P_i(t+1) - \alpha_i(t) P_i(t),$$

which can be expressed in term of $\Delta\alpha_i$ and $\Delta P_i$ by rewriting this as

$$\Delta V_i(t,t+1) = \Delta \alpha_i(t,t+1) P_i(t+1) + \alpha_i(t) \Delta P_i(t,t+1).$$

Here,

$$\Delta \alpha_i(t,t+1) P_i(t+1)$$

is the change in value due to trading, i.e. trading flow, which depends on the post-trade price $P_i(t+1)$, and

$$\alpha_i(t) \Delta P_i(t,t+1)$$

is the change in value due to price movement which depends on the pre-trade position $\alpha_i(t)$.

Discrete self-financing mandates

$$\Delta \alpha_0 \frac{s_0 + \Delta s_0}{\alpha_0 + \Delta \alpha_0} = \sum_{i=1}^n \Delta \alpha_i \frac{s_i + \Delta s_i}{\alpha_i + \Delta \alpha_i}.$$

This fundamental governing equation ensures no value leakage. Unlike constant-product AMMs, where mid-price execution erodes capital, Multiswap’s post-trade $P_i(t+1)$ secures full integrity.

Dynamic Weights

Consider the scaled value flow

$$\Sigma_i = \Delta \alpha_i \frac{s_i + \Delta s_i}{\alpha_i + \Delta \alpha_i}.$$

Dynamic weights open an infinite design space for Multiswap with the only real constraint being changes in scale (and hence weights) must satisfy

$$\Delta s_0 = \sum_{i=1}^n \Delta s_i$$

In an attempt to reduce the design space, note that if we set

$$\Delta s_i = \Delta \alpha_i \frac{s_i}{\alpha_i},$$

we find that

$$\frac{s_i}{\alpha_i} = \frac{s_i + \Delta s_i}{\alpha_i + \Delta \alpha_i}$$

i.e. the pre-trade marginal price is equal to the post-trade marginal price, i.e. there is precisely zero price impact and we have

$$\Delta s_i = \Sigma_i.$$

Inspired by this observation, we define a 1-parameter dynamical weight model

$$\Delta s_i = (1 - \kappa_i) \Sigma_i$$

resulting in a new expression for scaled value flow

$$\Sigma_i = \Delta \alpha_i \frac{s_i}{\alpha_i + \kappa_i \Delta \alpha_i}$$

or

$$\Delta s_i = \Delta \alpha_i \frac{(1 - \kappa_i) s_i}{\alpha_i + \kappa_i \Delta \alpha_i}$$

Special Case: $\kappa_i = 0$

When

$$\kappa_i = 0$$

we have

$$\Delta s_i = \Sigma_i = \Delta \alpha_i \frac{s_i}{\alpha_i}$$

which we saw above corresponds to zero price impact.

Special Case: $\kappa_i = 1$

When

$$\kappa_i = 1$$

we have

$$\Delta s_i = 0$$

which corresponds to constant weights with significant price impact.

Special Case: $\kappa_i \to \infty$

When

$$\kappa_i \to \infty$$

we have

$$\Delta s_i \to -s_i$$

and

$$\Sigma_i \to 0$$

which means the post-trade price goes to zero, i.e. maximum price impact.

In summary, the parameter $\kappa_i$ models desired price impact with precision:

• $\kappa_i = 0$: yields dynamic weights with zero price impact,
• $\kappa_i = 1$: locks constant weights with significant price impact, and
• $\kappa_i \to \infty$: drives dynamic weights to extreme price impact, collapsing the post-trade price toward zero.

This simple yet powerful parameterization unlocks a vast design space. Inspired by volatility-dependent fee models such as those implemented by Kyber, LFJ's Liquidity Book and, more recently, Flowing Tulip, we envision tailored models where $\kappa_i$ responds directly to market volatility. For example, setting

$$\kappa_i(t) = \frac{\sigma_i(t)}{\sigma_0}$$

where $\sigma_i(t)$ denotes current volatility and $\sigma_0$ is a reference volatility, allows Multiswap to automatically deliver minimal price impact during stable market conditions and increased impact—akin to traditional constant-product AMMs—during periods of high volatility. Thus, Multiswap not only generalizes existing volatility-adaptive AMM approaches but elegantly integrates them into a robust, mathematically rigorous framework suitable for institutional-grade finance.

Target Weights

Multiswap extends its dynamic weights mechanism by introducing the concept of target weights, enabling sophisticated and responsive asset allocation within the liquidity pool.

In this model, each asset in the Multiswap pool has a predefined target weight, clearly distinguishing between two asset states:

• Underweight Assets: Assets whose current weight is below their target.
• Overweight Assets: Assets whose current weight exceeds their target.

Zero-Price-Impact Trades

When an underweight asset is deposited, or an overweight asset is withdrawn, the asset moves toward its target weight. Multiswap ensures that such trades experience precisely zero price impact (i.e., $\kappa_i = 0$) until the target weight is reached.

If the deposit or withdrawal surpasses the target weight threshold, the trade transitions smoothly from zero price impact into the dynamic weight model described below.

Trades with Price Impact

Conversely, when an overweight asset is deposited or an underweight asset is withdrawn, the trades immediately experience price impact according to Multiswap’s dynamic weight model. Specifically, the price impact is governed by the parameter $\kappa_i$, calculated via a piecewise quadratic function

$$\kappa_i = k_i (r_i - r_i^\tau)^2$$

where $k_i > 1$ is a predefined constant and

$$r_i = \frac{\Delta\alpha_i}{\alpha_i^\tau}, \quad r_i^\tau = \frac{\Delta\alpha_i^\tau}{\alpha_i^\tau}.$$

This quadratic formulation elegantly ensures minimal price impact for small deviations and increasingly significant price impacts as actual weights diverge substantially from their targets.

Computing Target Reserves

To practically implement target weights, Multiswap computes target reserves from target weights. The relationship between changes in reserve and weight is given explicitly as

$$\Delta s_i^\tau = s_0 \frac{\Delta \omega_i^\tau}{1 - \omega_i^\tau}, \quad \Delta \alpha_i^\tau = \frac{\Delta s_i^\tau}{s_i}\alpha_i$$

ensuring that adjustments toward target weights are seamless, transparent, and computationally efficient.

Strategic Implications

This innovative target-weight model provides Multiswap unparalleled control over liquidity distribution, risk management, and asset allocation strategies, positioning it ideally for sophisticated DeFi applications including decentralized index funds, strategic asset allocation for institutional investors, and risk-managed liquidity provisioning.

Rethinking Impermanent Loss

Impermanent loss (IL) constitutes a central limitation in conventional automated market makers (AMMs), such as Uniswap, constraining their scalability and economic efficiency within decentralized finance (DeFi). IL quantifies the divergence in value between holding assets passively and providing liquidity to a pool as market prices shift. For a pool at time $t$ with reserves $\alpha_x(t)$ of asset X and $\alpha_y(t)$ of asset Y, the value of holding the assets outside the pool until $t+1$ would be

$$V_{\text{hold}}(t,t+1) = \alpha_x(t) P_{X,Y}(t+1) + \alpha_y(t)$$

Following a trade that adjusts the pool reserves, the pool’s value at $t+1$ is

$$V_{\text{pool}}(t,t+1) = \alpha_x(t+1) P_{X,Y}(t+1) + \alpha_y(t+1)$$

Impermanent loss is defined as

$$IL(t,t+1) = \frac{V_{\text{pool}}(t,t+1) - V_{\text{hold}}(t,t+1)}{V_{\text{hold}}(t,t+1)}$$

which can be written as

$$\begin{align*} IL(t,t+1) = \frac{\Delta \alpha_x(t,t+1) P_{X,Y}(t+1) + \Delta\alpha_y(t,t+1)}{\alpha_x(t) P_{X,Y}(t+1) + \alpha_y(t)} \end{align*}$$

The numerator

$$\Delta \alpha_x(t,t+1) P_{X,Y}(t+1) + \Delta\alpha_y(t,t+1)$$

typically yields a negative value under price divergence for constant-product AMMs, reflecting a reallocation of reserves that disadvantages liquidity providers (LPs) relative to holding.

This phenomenon can be reframed through the lens of value flow, offering a precise diagnostic of IL’s mechanics. Here

$$\Sigma_{X,Y} = \Delta \alpha_x(t,t+1) P_{X,Y}(t+1)$$

represents the value flow for $X$, while

$$\Sigma_{Y,Y} = \Delta\alpha_y(t,t+1)$$

denotes the value flow for $Y$. In traditional AMMs, IL manifests as an imbalance in these flows when $P_{X,Y}(t+1)$ decreases below the initial pool price

$$P_{X,Y}(t) = \frac{\alpha_y(t)}{\alpha_x(t)}$$

the pool gains X (inflow) but surrenders a greater value of Y (outflow), dictated by the constant-product formula. This value leakage, obscured in fee-centric metrics, represents a significant expense and undermines LP capital efficiency and scalability.

Multiswap reengineers this paradigm by enforcing a discrete self-financing condition, ensuring that value inflows precisely equal value outflows for each trade. The post-trade price

$$P_{X,Y}(t+1) = \frac{\alpha_y(t+1)}{\alpha_x(t+1)}$$

satisfies

$$\Delta \alpha_x(t,t+1) P_{X,Y}(t+1) + \Delta\alpha_y(t,t+1) = 0$$

nullifying the IL numerator and resulting in

$$IL(t,t+1) = 0.$$

This formulation eradicates single-trade IL, aligning with Multiswap’s no-leverage principle and discrete mathematics foundation, which eschews the continuous approximations of legacy AMMs. By securing capital preservation, Multiswap establishes a robust framework for institutional-grade liquidity provision.

This approach extends to an LP token-based valuation, where $P_{X,L}(t) = \frac{\alpha_L}{2 \alpha_x(t)}$ and $P_{Y,L}(t) = \frac{\alpha_L}{2 \alpha_y(t)}$ define asset prices in terms of the pool’s LP token supply $\alpha_L$. It can be shown that if we define an effective price as

$$P^{\text{eff}}_{i,L}(t,t+1) = \frac12 \left[P_{i,L}(t) + P_{i,L}(t+1)\right]$$

so that

$$\Delta\alpha_x P^{\text{eff}}_{X,L}(t,t+1) + \Delta\alpha_y P^{\text{eff}}_{Y,L}(t,t+1) = 0$$

we derive the constant-product formula, illustrating that Uniswap executes swaps on stale prices with a 50% weight on the pre-trade price. This is the source of IL the reliance on outdated pricing leaks value to arbitrageurs, undermining LP capital efficiency. Multiswap, by contrast, executes swaps solely at the post-trade price $P_{X,Y}(t+1)$, eliminating this leakage and aligning with its discrete self-financing principle. This design underpins Multiswap’s superior efficiency, positioning it as a scalable, mathematically rigorous solution capable of supporting DeFi’s ascent to TradFi proportions while preserving LP value with precision.

Infrastructure Innovations

To fully realize Multiswap's potential as an institutional-grade decentralized trading protocol, CavalRe developed key infrastructural innovations addressing fundamental technological challenges common in existing DeFi systems. These innovations ensure Multiswap delivers unmatched robustness, scalability, and precision.

High-Precision Floating-Point Math Library

Numerical inaccuracies pose subtle yet critical limitations in decentralized finance. Existing protocols predominantly rely on fixed-point arithmetic, resulting in rounding errors and numerical instability—especially when handling very large or extremely small token amounts. While developing Multiswap, we encountered these limitations firsthand. Rigorous testing revealed small, pervasive rounding errors, undermining confidence in the system’s mathematical integrity.

Rather than overlook these issues, as commonly done in the industry, CavalRe took a rigorous approach by developing a bespoke floating-point math library from the ground up. Our new library enables Multiswap to manage quotes of virtually any magnitude—from as minuscule as $10^{-1000}$ to as enormous as $10^{1000}$—with at least 18 digits of decimal accuracy. This unprecedented precision ensures mathematical correctness and robustness across all trades, positioning Multiswap uniquely among DeFi protocols.

By pioneering this high-precision numerical solution, Multiswap now stands as the most numerically robust protocol available, ready to serve institutions and users demanding absolute reliability in financial transactions.

Modular Router Architecture

To address evolving DeFi market requirements and regulatory changes while maintaining security and decentralization, Multiswap introduces a robust and highly modular Router/Module architecture inspired by the Diamond Standard (EIP-2535).

Router Contract

At the core of this architecture is the Router contract, serving as a central gateway for all interactions. The Router delegates function calls dynamically to specialized Modules based on the function signatures invoked by users. This delegation is facilitated through a flexible mapping from function selectors to Module addresses

• Dynamic Delegation: Incoming calls are routed via a fallback function, leveraging efficient Solidity assembly calls (delegatecall) to Modules, ensuring minimal overhead and maximum performance.
• Upgradeable and Extendable: Modules can be easily added, replaced, or removed at runtime, granting unparalleled adaptability without compromising the protocol’s integrity or requiring complete redeployment.

Module Contract

The Module contract defines the basic framework for individual modules, enforcing consistent patterns across implementations:

• Ownership Management: Each Module tracks its own owner, enhancing security by ensuring that only authorized entities can manage module-specific logic.
• Explicit Interface Definition: Modules explicitly declare their supported function selectors (commands), enabling the Router to automatically integrate new functionality seamlessly.

Strategic Advantages

This modular approach provides Multiswap with a robust, secure, and agile infrastructure capable of rapidly adapting to new financial products, regulatory demands, and user requirements. By clearly separating concerns and enabling dynamic function delegation, Multiswap’s Router/Module architecture sets a new standard for scalability and flexibility in DeFi protocol design.

Multitoken Contract

The Multitoken contract provides a sophisticated, scalable bookkeeping framework integral to Multiswap's operational precision and institutional readiness. Built explicitly to support advanced financial practices, Multitoken introduces a novel hierarchical subaccount system, enabling comprehensive management of reserves, collateral, liquidity positions, staking, governance, and rewards—all unified within a single contract.

Hierarchical Subaccounts

At the core of Multitoken is its innovative hierarchical tree data structure:

• Distinct Token Trees: Each root within the hierarchy represents a unique token, facilitating simultaneous, organized tracking of multiple tokens within the ecosystem.
• Flexible Naming Conventions: Every account, including root tokens, can be assigned meaningful, human-readable names, enhancing transparency and ease of administration.

Double-Entry Accounting

Multitoken natively supports rigorous double-entry accounting practices:

• Debit Accounts (Assets): Track tangible assets, liquidity, and reserves.
• Credit Accounts (Liabilities and Equity): Precisely monitor obligations and capital structures.

This dual-accounting capability ensures precise financial record-keeping and transparency, crucial for institutional compliance and advanced financial reporting.

Strategic Advantages

By consolidating bookkeeping functions into a versatile and robust structure, Multitoken positions Multiswap to efficiently handle complex DeFi operations such as large-scale staking programs, governance token distribution, liquidity management, and reward allocation. Its scalable design ensures Multiswap remains adaptable, capable of seamlessly integrating new tokens, financial products, and regulatory requirements, thus laying a strong foundation for future expansion and institutional adoption.

Ecosystem Design

Staking Rewards Framework

One of the primary challenges in designing staking rewards systems is mitigating mercenary farming—where users stake tokens solely to extract rewards and exit once incentives diminish. Traditional models, such as those employed by Aave, Synthetix, and Compound, distribute rewards like a firehose, allocating them uniformly over a fixed period. While this attracts short-term liquidity, it often results in rapid outflows when rewards cease. To address this, we propose a generalized staking rewards framework that discourages opportunistic behavior and incentivizes long-term commitment. This model, applicable to any decentralized protocol, shifts from a firehose approach to an airdrop-based system with vesting and forfeiture mechanics.

Core Mechanics

Our staking rewards system operates by distributing rewards based on users’ staked positions at the moment rewards are added to the protocol. Unlike traditional models, these rewards are not immediately claimable—they enter a pending state and vest into available rewards over time. This vesting process, combined with forfeiture and redistribution mechanisms, ensures that long-term stakers are disproportionately rewarded.

1. Pending vs. Available Rewards
   When rewards in token $i$ are distributed at time $t$, they are recorded as total unclaimed rewards earned by user $j$, denoted $T_i^j(t)$. These rewards are split into pending rewards, $P_i^j(t)$, which vest over time, and available rewards, $A_i^j(t)$, which can be claimed immediately once vested

   $$A_i^j(t) = T_i^j(t) - P_i^j(t)$$

   At the aggregate level

   $$T_i(t) = \sum_j T_i^j(t), \quad P_i(t) = \sum_j P_i^j(t), \quad A_i(t) = \sum_j A_i^j(t)$$

   When new rewards $\Delta T_i(t, t+1)$ are added to the aggregate pool between $t$ and $t+1$, the increase in total unclaimed rewards for user $j$, denoted $\Delta T_i^j(t, t+1)$, is proportional to their staked amount $S_i^j(t)$ relative to the total stake $S_i(t) = \sum_j S_i^j(t)$

   $$\Delta T_i^j(t, t+1) = \frac{S_i^j(t)}{S_i(t)} \Delta T_i(t, t+1)$$

   The total unclaimed rewards $T_i^j(t_f)$ at time $t_f$ are the cumulative sum of these increases over time from $t=0$ to $t_f-1$

   $$T_i^j(t_f) = \sum_{t=0}^{t_f-1} \frac{S_i^j(t)}{S_i(t)} \Delta T_i(t, t+1)$$

   If the user’s stake $S_i^j(t)$ is constant from $t_0$ to $t_f$ (i.e., $S_i^j(t) = S_i^j(t_0)$), we can factor it out

   $$T_i^j(t_f) = T_i^j(t_0) + S_i^j(t_0) \sum_{t=t_0}^{t_f-1} \frac{\Delta T_i(t, t+1)}{S_i(t)}$$

   The term

   $$\sum_{t=t_0}^{t_f-1} \frac{\Delta T_i(t, t+1)}{S_i(t)}$$

   depends only on the aggregate rewards and total stakes, not on the individual user $j$. We define this as the total reward accumulator

   $$\phi_i^T(t_f) = \sum_{t=0}^{t_f-1} \frac{\Delta T_i(t, t+1)}{S_i(t)}$$

   Thus, for a constant stake

   $$T_i^j(t_f) = T_i^j(t_0) + S_i^j(t_0) \left[ \phi_i^T(t_f) - \phi_i^T(t_0) \right]$$

   For pending rewards, a discount factor $e^{-r(t_f - t)}$ is applied to reflect vesting over time. The pending rewards for user $j$ are the cumulative sum of discounted increases

   $$P_i^j(t_f) = \sum_{t=0}^{t_f-1} e^{-r(t_f - t)} \frac{S_i^j(t)}{S_i(t)} \Delta T_i(t, t+1)$$

   If the stake is constant from $t_0$ to $t_f$

   $$P_i^j(t_f) = e^{-r(t_f - t_0)} P_i^j(t_0) + S_i^j(t_0) \sum_{t=t_0}^{t_f-1} e^{-r(t_f - t)} \frac{\Delta T_i(t, t+1)}{S_i(t)}$$

   The term $\sum_{t=t_0}^{t_f-1} e^{-r(t_f - t)} \frac{\Delta T_i(t, t+1)}{S_i(t)}$ is independent of the user. We define this as the pending reward accumulator

   $$\phi_i^P(t_f) = \sum_{t=0}^{t_f-1} e^{-r(t_f - t)} \frac{\Delta T_i(t, t+1)}{S_i(t)}$$

   So

   $$P_i^j(t_f) = e^{-r(t_f - t_0)} P_i^j(t_0) + S_i^j(t_0) \left[ \phi_i^P(t_f) - e^{-r(t_f - t_0)} \phi_i^P(t_0) \right]$$

   At $t=0$, we assume no rewards: $T_i^j(0) = P_i^j(0) = A_i^j(0) = 0$. Aggregate rewards $T_i(t_f) = \sum_{t=0}^{t_f-1} \Delta T_i(t, t+1)$ and $P_i(t_f) = \sum_{t=0}^{t_f-1} e^{-r(t_f - t)} \Delta T_i(t, t+1)$ are updated whenever new rewards are added.

2. Forfeiture on Unstaking
   If a user unstakes a portion of their position before pending rewards fully vest, they forfeit a proportional amount of those pending rewards. For example, unstaking 25% of their stake results in forfeiting 25% of $P_i^j(t)$. Mathematically, if user $j$ reduces their stake from $S_i^j(t)$ to $S_i^j(t) - \Delta S_i^j(t)$, the forfeited pending rewards are

   $$\text{Forfeited } P_i^j(t) = P_i^j(t) \frac{\Delta S_i^j(t)}{S_i^j(t)}$$

   Available rewards, $A_i^j(t)$, remain unaffected—once vested, they are permanently owned by the user.

3. Redistribution of Forfeited Rewards
   Forfeited pending rewards are not discarded; instead, they are redistributed to remaining stakers, amplifying rewards for those who maintain their positions. This creates a compounding effect. At the aggregate level, forfeited rewards increase $\Delta T_i(t, t+1)$ for the next distribution, proportionally allocated based on each user’s stake

   $$\Delta T_i^j(t, t+1) = \frac{S_i^j(t)}{S_i(t)} \Delta T_i(t, t+1)$$

Flexible Reward Distribution

Rewards can be contributed by any user, not just the protocol itself. This flexibility enables external entities—such as DAOs, foundations, or partners—to boost staking incentives by sending additional rewards, which are then processed through the same vesting and distribution mechanics.

Conclusion

This staking rewards framework transcends the limitations of traditional firehose-style systems by integrating vesting, forfeiture, and redistribution. Grounded in a robust mathematical structure, it ensures that long-term participants reap the greatest benefits, making it a versatile solution for decentralized protocols seeking sustainable staking incentives.

Dual Governance

Multiswap's innovative new dual governance model leverages the general staking rewards model to ensure rewards flow fairly and efficiently to participants who contribute to the protocol’s stability and growth.

Key Participants

The dual governance model involves two key participant groups:

1. Liquidity Providers: LP token holders stake to determine target weights of assets in the pool, i.e. the target weight of an asset is the percentage of LP tokens staked to that asset. By staking LP tokens to an asset, users earn boost rewards and transaction fees in that asset for real organic yield.

2. CAV Holders: CAV holders stake to determine the allocation of emissions. The proportion of staked CAV tokens to an asset dictates the share of total emissions directed to that asset. This allows governance participants to dynamically adjust incentives based on market conditions.

Incentives

As described in the staking rewards model, anyone can send rewards to the system, enabling both internal and external strategic incentives that vest over time. Multiswap utilizes this powerful flexibility for the following incentives:

Emissions & Boosts

To help attract liquidity providers and bootstrap TVL, CAV token emissions and other boosts from strategic partners in order to boost yields for liquidity providers and attract TVL.

Transaction Fees

A key innovation in Multiswap’s dual governance model is the redistribution of transaction fees as staking rewards. Fees collected from swaps within the protocol are automatically allocated to stakers based on their participation. This ensures that rewards are directly tied to protocol usage.

Vesting Rewards

As in the general staking model, rewards are not immediately claimable but enter a pending state, gradually converting into available rewards over time. Users who unstake before full conversion forfeit a proportional amount of their pending rewards, which are then redistributed to remaining stakers.

Advantages

• No Lockups or Rebasing: Avoids market distortion mechanisms common in other DeFi models.
• Direct Incentive Alignment: Encourages long-term participation without artificial constraints.
• Governance-Driven Emissions: Ensures rewards are directed where they are most effective.
• Sustainable Yield Model: Staking rewards are tied to actual protocol usage and fees rather than unsustainable inflation.

Conclusion

Multiswap’s staking rewards system represents a significant innovation in DeFi incentive design. By allowing LPs to influence target weights and CAV holders to direct emissions, the model creates a fair and adaptive rewards structure. This ensures long-term sustainability while maximizing incentives for active participants in the Multiswap ecosystem.

Launchpad

Traditional token sales suffer from major inefficiencies. Presales at discounted rates create immediate sell pressure as early investors look to exit at a profit. Vesting doesn't help because locking up a liquid asset only distorts market prices and creates pent up sell pressure. Meanwhile, large team allocations concentrate supply and reduce liquidity in circulation. On top of that, artificially hyped public sales often result in unsustainable price spikes, followed by crashes when speculative interest fades.

Multiswap’s Launchpad is designed to fix these problems by enabling organic price discovery and gradual liquidity growth without distortions.

The Role of Surplus in Price Discovery

Rather than conducting a large pre-sale or simply injecting the full token supply into the liquidity pool, the Launchpad introduces a surplus mechanism:

• Minting into Surplus: Instead of allocating all tokens to reserves, most of the supply is minted into a surplus account.
• Balanced Reserves: A smaller portion is placed in the pool’s reserve to enable balanced pricing.
• Gradual Release: When traders buy the token, the tokens are taken from the surplus instead of the reserve.
• Treasury Capture: Proceeds from surplus sales are directed to the protocol’s treasury.

This approach creates a fair launch while maintaining a liquid and accessible market.

Eliminating Unnecessary Price Impact

A key innovation of the surplus mechanism is that it does not affect price impact. Whether a token is sourced from surplus or reserve, traders experience the same pricing behavior. This ensures that price discovery remains fair and organic, without artificial distortions or early dumping.

Recall that without surplus the post-trade scaled price is given by

$$P_i^\text{Reserve} = \frac{s_i+\Delta s_i^\text{Reserve}}{\alpha_i+\Delta\alpha_i^\text{Reserve}},$$

where $\Delta\alpha_i^\text{Reserve}$ is the change in the reserves and $\Delta s_i^\text{Reserve}$ is the change is scale from the dynamic weight model. If the token is taken from surplus instead of reserve, we have

$$P_i^\text{Surplus} = \frac{s_i+\Delta s_i^\text{Surplus}}{\alpha_i}$$

since there is no change in reserves. In order for the post-trade price to be the same whether the token is taken from reserves or surplus, we must have

$$\Delta s_i^\text{Surplus} = \alpha_i \left(\frac{s_i+\Delta s_i^\text{Reserve}}{\alpha_i+\Delta\alpha_i^\text{Reserve}}\right) - s_i.$$

Conclusion

The Multiswap Launchpad introduces a sustainable, fair, and transparent model for token distribution. By leveraging surplus-based releases and avoiding common pitfalls of presales and inflationary allocations, Multiswap enables projects to launch with strong liquidity foundations and genuine price discovery. This approach not only benefits new token launches but also lays the groundwork for a more efficient trading ecosystem that rewards long-term participation.

Tokenomics

The CAV token is a key driver of the Multiswap ecosystem, designed to align incentives across community, team, and investors, fostering sustainable adoption and long-term growth. With a total supply of 5 million tokens and an initial fully diluted valuation (FDV) of $25 million at $5 per token, the tokenomics ensure a balanced distribution that supports the launch phases and incentivizes ecosystem participation. At Token Generation Event (TGE) on May 8, 2025, all tokens will be minted to a multisig address controlled by the CavalRe team, with plans to fully decentralize within three years through iterative governance development.

• Community Incentives: 35% (1.75M tokens, $8.75M). This allocation drives user adoption through deposit rewards and post-launch emissions. 10% (500K tokens) will incentivize early deposits for whitelisted assets from April 8 to May 8, 2025, transferred to the staking rewards module at pool activation, convertible to claimable with a 60-day halflife; unstaking forfeits rewards, which are redistributed to stakers. The remaining 30% (1.5M tokens) will support post-launch emissions, such as liquidity provision, staking, or trading incentives, distributed at a rate of approximately 1.25% monthly (62,500 tokens, $312,500) over 2 years, held in the multisig for future distribution.
• Public Sale (Surplus): 20% (1M tokens, $5M). These tokens will be transferred from the multisig to surplus for gradual release via swaps starting May 8, 2025, with proceeds funding the treasury (up to $5M at $5/token). A controlled release will be implemented: 25% (250K tokens, $1.25M) at launch, with the remaining 75% over 6 months. If treasury needs are met, the team may redirect unsold tokens to alternative uses, with plans to decentralize this process via governance.
• Team & Advisors: 20% (1M tokens, $5M). This allocation rewards contributors while ensuring long-term alignment. The founder receives 15% (750K tokens) with a 3-year vesting schedule (1-year cliff, 5% per month for 24 months), reflecting their critical role in single-handedly building Multiswap, from foundational research to implementation, alongside 91% equity ownership. Two partners receive 1% each (50K tokens total), vesting over 2 years (5% per month for 20 months), reflecting their 9% equity. Advisors receive 3% (150K tokens total), vesting over 2 years. Tokens will be transferred to a vesting contract managed by the multisig.
• Private Sale: 10% (500K tokens, $2.5M). Allocated to seed round investors via SAFT notes at a $20M valuation cap, vesting over 2 years (10% at TGE, 6-month cliff, 18-month linear vesting), supporting early funding efforts starting March 19, 2025. Tokens will be transferred to the same vesting contract as Team & Advisors.
• Exchange Liquidity: 15% (750K tokens, $3.75M). Set aside as reserves, with an initial portion deposited at pool activation on May 8, 2025, proportional to the value of other assets collected during the deposit phase, receiving LP tokens in exchange; LP tokens are held by the team (effectively locked), earning platform fees, while remaining tokens are held for future use, such as multichain expansion.

Roadmap

Multiswap’s development and deployment follow a structured timeline to ensure technical excellence and ecosystem growth. Key milestones include:

• May 8, 2025: Token Generation Event (TGE) and Multiswap launch on the initial EVM chain, with unified liquidity pool activation and CAV token integration.
• Q3 2025: Expansion to additional EVM-compatible chains and launch of a lending protocol to complement spot trading.
• Q4 2025: Enablement of cross-chain swaps, enhancing interoperability without centralized bridges.
• Q1 2026: Introduction of fixed income products, including onchain yield curves, to broaden financial offerings.
• Q2 2026: Launch of derivatives markets, establishing Multiswap as a full-spectrum capital markets platform.

Post-launch, Multiswap will prioritize ecosystem expansion through strategic partnerships, multichain scalability, and progressive decentralization of governance, ensuring long-term sustainability and adoption.

Future Vision

Multiswap is engineered to redefine onchain capital markets, targeting the next trillion dollars in Total Value Locked (TVL) by bridging DeFi’s innovation with traditional finance’s scale. Beyond spot trading, its modular architecture lays the groundwork for lending, fixed income, and derivatives—financial primitives poised to rival centralized limit order books (CLOBs) onchain and outpace NYSE-grade systems offchain. Through regulatory engagement and direct onchain listings for stocks and bonds, Multiswap aims to disrupt legacy intermediaries, positioning itself as the decentralized backbone of global capital markets. Institutional adoption, continuous innovation, and a scalable liquidity framework will cement Multiswap’s dominance, rendering centralized exchanges obsolete.

Conclusion

Multiswap transcends conventional AMMs, delivering a mathematically robust, capital-efficient ecosystem that preserves LP wealth and unifies liquidity at scale. With its high-precision floating-point math library, modular router architecture, and multitoken contract, it sets a new standard for DeFi infrastructure. The CAV token aligns incentives across stakeholders, driving sustainable growth from the May 8, 2025 launch onward. As Multiswap scales to rival TradFi giants, it invites developers, traders, liquidity providers, and visionaries to join the onchain frontier—shaping the future of decentralized finance. The revolution starts here.