Mathematical Security Model

Osito Protocol's mathematical security model calculates safe lending limits without relying on oracles or price feeds. This model addresses the question: "how much BERA could be extracted in the worst-case scenario?" to ensure protocol solvency.

The Core Borrow Limit Formula

The central formula that enables Osito's oracle-free lending approach is:

max_borrow = pool_BERA - extractable_BERA

Where:

  • pool_BERA is the BERA locked in the liquidity pool
  • extractable_BERA is the maximum BERA that could be extracted by selling all circulating tokens into the pool

This formula ensures that the protocol remains solvent even in worst-case scenarios.

Extraction Calculations

The calculation for extractable_BERA depends on the AMM pool type:

For CPMM Pools (Constant Product Market Maker)

extractable_BERA = (pool_BERA * pool_tokens) / (pool_tokens + dumpable_tokens)

Where:

  • pool_BERA is the BERA in the pool
  • pool_tokens is the tokens in the pool
  • dumpable_tokens = total_supply - pool_tokens - total_staked - total_deposited

This applies the constant product formula (x*y=k) to determine the result of selling all dumpable tokens into the pool.

For CLMM Pools (Concentrated Liquidity Market Maker)

extractable_BERA = (dumpable_tokens * pool_BERA/pool_tokens / 2)

This accounts for the price impact in CLMM pools.

Numerical Example

Here's how these calculations work in practice:

Initial Conditions:

  • pool_BERA = 1,000 BERA
  • pool_tokens = 10,000 TOKEN
  • total_supply = 20,000 TOKEN
  • total_staked = 2,000 TOKEN
  • total_deposited = 3,000 TOKEN

Calculation:

  1. dumpable_tokens = 20,000 - 10,000 - 2,000 - 3,000 = 5,000 TOKEN
  2. extractable_BERA = (1,000 * 10,000) / (10,000 + 5,000) = 10,000,000 / 15,000 = 666.67 BERA
  3. max_borrow = 1,000 - 666.67 = 333.33 BERA

In this example, the protocol can safely lend 333.33 BERA against this token.

Position-Level Borrow Limits

For individual positions, the borrow limit is calculated as:

position_max_borrow = (tokens_in_position / total_tokens_deposited) * max_borrow

This formula ensures that each position's borrowing limit is proportional to its share of the total deposited tokens.

Non-Monotonic Borrowing Power

The lending formula creates an interesting economic dynamic where:

  • Depositing tokens reduces dumpable supply, potentially increasing the global borrowing limit
  • But also dilutes individual borrowing power as total deposits increase

This creates the rationale for staking as a separate activity from borrowing, providing a way to reduce dumpable supply without diluting borrowing power.

Key Protocol Requirements

This mathematical model necessitates several protocol features:

1. Fixed Supply Requirement

Tokens must have fixed supply because:

  • The dumpable_tokens calculation requires a known total supply
  • Variable supply would make it impossible to calculate safe lending limits

2. Real-Time Risk Assessment

Since extraction depends on current pool states, the protocol:

  • Re-queries pool data at each significant interaction
  • Recalculates borrowing limits
  • Adjusts lending parameters in real-time

3. Liquidation Mechanism

The liquidation system follows from the model:

  • Positions become liquidatable when borrowed BERA exceeds recalculated max borrow
  • Liquidators ensure protocol solvency by closing underwater positions

Benefits of the Mathematical Approach

This mathematical approach provides several advantages:

  1. No Oracle Dependence: No price feeds that can be manipulated or fail
  2. Minimal Governance Requirements: Few subjective decisions about token quality or parameters
  3. Permissionless Integration: Any token meeting objective criteria can be used
  4. Verifiable Security: Lending limits based on observable on-chain data

The Revolutionary Implications

This mathematical approach provides several revolutionary advantages:

  1. Zero Oracle Dependence: No price feeds that can be manipulated or fail
  2. No Governance Risk: No subjective decisions about token quality or parameters
  3. Permissionless Integration: Any token meeting objective criteria can be used immediately
  4. Mathematical Certainty: Security guarantees based on pure mathematics

By deriving everything from a single adversarial design principle, Osito creates a lending system that's fundamentally different from and more resilient than traditional DeFi lending protocols.

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