feels

Fee System Specification

1. Overview

In the Feels Protocol, fees are not arbitrary percentages. They are emergent properties of the system's physics:

  • Instantaneous Fees (Trading) emerge from the Gradient of the potential field (resistance to movement).
  • Continuous Fees (Funding/Yield) emerge from Conservation Laws (cost of maintaining position over time).

This document details the fee mechanisms, calculation formulas, and safety protocols.

2. Instantaneous Fees (Trading)

Instantaneous fees apply to any action that changes the system's state (e.g., Swaps, Opening Positions). They represent the work done against the potential field.

2.1 Calculation Formula

The base fee is the path integral of the gradient along the trade vector:

W=∇V(P)⋅ΔP⃗W = \nabla V(P) \cdot \Delta \vec P

The actual fee charged to the user is calculated as:

  1. Surcharge: dyn_bps=min⁡(W⋅Πamount_in⋅104,MAX_SURCHARGE)\text{dyn\_bps} = \min\left( \frac{W \cdot \Pi}{\text{amount\_in}} \cdot 10^4, \text{MAX\_SURCHARGE} \right)

  2. Total Fee: fee_bps=base_bps+dyn_bps\text{fee\_bps} = \text{base\_bps} + \text{dyn\_bps}

2.2 Rebates (Negative Fees)

If a trade moves the system "downhill" (improving balance, W<0W < 0), the user receives a rebate instead of paying a dynamic surcharge.

R=min⁡(η∣W∣Π,captx,capepoch)R = \min(\eta |W| \Pi, \text{cap}_{tx}, \text{cap}_{epoch})

  • η\eta: Rebate participation factor (0.0 to 1.0).
  • Caps: Rebates are strictly limited by the protocol's accumulated buffer to ensure solvency.

3. Continuous Fees (Yield & Funding)

Continuous fees represent the cost of time and risk. They are delivered via Multiplicative Rebasing, meaning user balances change smoothly over time.

3.1 Mechanism

Balances are updated using an exponential growth factor: g=erΔtg = e^{r \Delta t}

  • Lenders: See balances grow (r>0r > 0).
  • Borrowers: See debt grow (r>0r > 0).
  • Traders: See positions rebase based on funding rates (rr can be positive or negative).

3.2 Conservation Laws (Solvency)

To guarantee that value is never created from thin air, every rebase epoch must satisfy the Sub-domain Log-Sum Conservation Law:

∑i∈domainwiln⁡(gi)=0\sum_{i \in \text{domain}} w_i \ln(g_i) = 0

Example: Lending Domain wdepositln⁡(gdeposit)+wdebtln⁡(gdebt)+wbufferln⁡(gbuffer)=0w_{deposit} \ln(g_{deposit}) + w_{debt} \ln(g_{debt}) + w_{buffer} \ln(g_{buffer}) = 0

This ensures that the yield paid to lenders comes exactly from the interest paid by borrowers (plus/minus the protocol buffer).

4. Safety & Resilience

4.1 Staleness & Fallbacks

The system relies on Keepers to update the physics parameters that determine fees. If Keepers go offline, the system degrades gracefully.

  1. Grace Period: For short outages (< 30 min), the system uses the last known good physics parameters.
  2. Fallback Mode: If staleness > threshold, the system switches to Bounded-Spread Routing.
    • Complex gradient calculations are disabled.
    • Fees revert to a simple, conservative percentage model (e.g., fixed 0.3%).
    • Rebates are disabled to prevent gaming stale state.

4.2 Testing Matrix

To ensure fee correctness and solvency:

  • Loop-Work Theorem: ∮∇V⋅dP⃗≥0\oint \nabla V \cdot d\vec P \ge 0. Proves that no sequence of trades can extract infinite value (no perpetual motion).
  • Rebase Conservation: Verifies that ∑wiln⁡(gi)=0\sum w_i \ln(g_i) = 0 holds exactly for every epoch.
  • Stress Tests: Verifies fee behavior under extreme volatility and utilization.

5. User Experience

  • Transparency: Instantaneous fees are shown upfront. Continuous fees are visible as real-time balance changes.
  • No Claiming: Yield and funding are auto-compounding; users never need to manually "claim" rewards.
  • Liquidation-Free: Positions compress via rebasing rather than facing sudden liquidation events.