FPSSL (Single-Sided Liquidity)

Fairly Paired Single-Sided Liquidity architecture immunizing Bitcoin treasuries against impermanent loss.

The Unit of Account Illusion

Historically, Automated Market Makers (AMMs) forced divergent market participants into an unnatural compromise. A Bitcoin treasury measures its success strictly by accumulating more BTC. A stablecoin yield fund measures success strictly in USD. Their risk preferences, positioning, and definitions of "profit" are fundamentally asymmetric.

Yet, legacy DeFi models force both participants into a unified liquidity calculation that dictates a single "Unit of Account" (almost always USD) to measure Impermanent Loss and Yield Distribution.

This creates a fatal contradiction. If a pool's performance is measured in USD, the BTC purist is told they are "losing money" whenever fiat exchange rates fluctuate, entirely defeating their fundamental strategy of stacking native Bitcoin. The industry falsely assumed that a unified liquidity pool must enforce a unified risk metric.

The FPSSL Axiom: Asymmetric Risk Sovereignty

Fairly Paired Single-Sided Liquidity (FPSSL) is an exclusive mathematical framework developed by OnNexus to shatter this contradiction. It proves a foundational economic truth: Liquidity pairing does not require a shared unit of measurement.

FPSSL allows institutions to deposit strictly one asset (e.g., pure BTC or pure USD) and mathematically decouples their risk exposure. The routing engine pairs their liquidity to execute trades, but the protocol evaluates Impermanent Loss and Fee Yields strictly in the native currency of the depositor.

If the pool generates fee yield, the BTC depositor logs a pristine gain in BTC, and the USD depositor logs an identical percentage gain in USD. FPSSL respects the absolute sovereignty of your chosen risk profile.

Mathematical Fairness Theorem

The foundation of FPSSL rests on a strict uniqueness theorem ensuring Equal Native-Percentage Performance.

When a BTC-only institution deposits BTC, and a USD-only institution deposits USD, the protocol logically pairs them at entry price $P_{0}$. At the time of withdrawal ($P_{1}$), the protocol asserts two axioms:

1. Conservation: The sum of both allocations must equal the total mathematical pool value.

2. Symmetry: Each holder must experience the exact same percentage return measured in their native unit of account.

Symmetric Impermanent Loss

Under the FPSSL dynamic allocation weights, if the price of BTC drops, creating an Impermanent Loss scenario of $-1.0$, the mathematical proof guarantees that the BTC depositor loses exactly $-1.0$ of their BTC, and the USD depositor loses exactly $-1.0$ of their USD.

Unlike naive 50/50 splits where directional price swings create massive windfalls for one party while destroying the other, FPSSL forces shared exposure exclusively driven by AMM curve mechanics.

Provably Fair Fee Yields

The symmetry applies equally to transaction fees. If the pool accrues $+5.0$ in fee yield via arbitrage flow, both the BTC-holder and USD-holder will register a pristine $+5.0$ gain in their respective settlement assets.

It achieves this by weighting the value allocation at the time of withdrawal based on dynamic ratio distributions:

$\alpha_{BTC} = \frac{P_{1}}{P_{0} + P_{1}}$ $\alpha_{USD} = \frac{P_{0}}{P_{0} + P_{1}}$

Protocol Implementation

At the protocol layer, this allows institutions to plug strictly native BTC into the 3/3 Nexus State Channels. The Protocol Node dynamically rebalances the internal Commitment Transactions to ensure that the asset values strictly adhere to the $\alpha$ weights.

By abstracting away the secondary asset, Nexus ensures asset managers can deploy pure-BTC yields against market-neutral strategies without bridging into synthetic stables.