Per-Subnet Estimation of Effective Pool Weights

Estimate the effective AMM weight parameter w (equivalently, the CEV exponent β) separately for each Bittensor subnet using on-chain data to disentangle the causes of the observed attenuation in the realized variance–price elasticity relative to the constant-product prediction β=1/2.

Background

The variance elasticity test predicts a slope of −1 in a regression of log(variance) on log(price) after controlling for pool depth and flow volatility when β=1/2 for constant-product AMMs. Empirically, the median slope is −0.86, close to but less than −1.

The paper suggests several potential explanations, including jump-like flows, measurement noise from overlapping windows, and the possibility that some pools operate with effective weights above 1/2 (e.g., due to concentrated liquidity). The authors state that per-subnet estimation of effective pool weights is needed to separate these effects and is deferred.