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Surplus Settlement: Safe Composition, Coefficient Order, and Permanent Liquidity

· 26 min read
Eric Forgy
Founder of CavalRe

Scope: This research article compares Surplus candidates and safety conditions. The current implementation uses a reduced-pay second quote with direct-payout top-ups, described in Quote Engine. Counter-swaps and LP Token burning discussed here are not the deployed settlement policy.

Multiswap Surplus is exogenous protocol inventory. When a user receives an asset held in Surplus, the protocol can use that inventory to settle the user's output and convert it into reserve growth, Rewards, Treasury revenue, or an ongoing CAV token sale.

The economic purpose is straightforward. The safety question is not.

A compound action can look harmless when examined as an immediate round trip and still leave the pool in a state from which later transactions transfer value unexpectedly. The correct test is therefore not merely whether the first user can reverse the transaction without profit. The resulting state must remain inside the coefficient-order admissible set under every later supported action.

This article develops that test from first principles. It reaches four conclusions:

  1. the original price-preserving Surplus transformation does not remain inside the Post-Trade Elasticity coefficient order;
  2. the counter-swap model is a composition of supported state transitions and does remain inside that order;
  3. LP Token burning is coefficient-order admissible, although it creates a distinct temporary-liquidity allocation issue;
  4. coefficient safety can be verified token by token, while value-flow entropy provides an aggregate summary of those local certificates.

The analysis assumes exact arithmetic, positive reserves and scales, and homogeneous scale elasticity

0<es<1,0<e_s<1,

with price elasticity

eP=1es.e_P=1-e_s.

The exact boundary es=0e_s=0 is discussed separately.