A Unified General Formula for Arbitrary Liquidity Operations in Weighted AMMs: Potential Applications to Intelligent Transportation Systems

Battle Count: 56

The paper is directly relevant to DeFi market making and AMM-based trading strategies. The unified formula is the exact computation used in Balancer V2 smart contracts for liquidity operations. Swap-decomposition theorems are relevant for understanding execution equivalence in multi-asset pools. However, the primary application domain is transportation resource allocation rather than traditional quantitative trading. The mathematical framework (weighted geometric mean invariant, BPT minting/burning) is foundational for AMM-based trading strategies and liquidity provision optimization.

The core formula is extremely simple: a single product of ratios raised to weights, minus one, multiplied by BPT supply. The Python implementation is ~10 lines. The swap-decomposition theorems are conceptual proofs rather than algorithms requiring implementation. The main complexity lies in the theoretical understanding of the invariant structure and the fee-charging extension (which remains open). For practical DeFi development, this is trivially implementable as it matches existing Balancer V2 code.

The paper provides a complete Python implementation (Appendix B) that reproduces all six numerical examples exactly. The unified formula is a single-line computation. All pool parameters, weights, and expected outputs are explicitly stated. Invariant verification tables (Appendix C) confirm consistency across all cases. The mathematical proofs are self-contained and verifiable.