Directional Transfer Taxes from Smoothed Relative-Price Velocity

This report examines a Solidity rate engine that assigns a buy-side rate when a smoothed relative price is above its reference and rising, and a sell-side rate when it is below its reference and falling. The implementation maintains exponential averages of price, reference value, and relative-price velocity. We release its source snapshot and a dependency-free Foundry test harness, and report eleven passing tests executed with Solidity 0.8.35. In synthetic ten-step price sequences with a constant reference, the engine returns 381 basis points for a growing premium and 392 basis points for a growing discount. A stationary premium returns zero, while a return of spot price to parity after the premium sequence leaves a lagging buy rate of 345 basis points. This last output is a library rate, not an actual tax charged by the surrounding vault, which imposes additional spot-direction and cap rules. A high-precision comparison also finds a decay approximation error of approximately 6.53 × 10^-9 at one tested interval, exceeding the source comment's stated bound. The results characterize deterministic behavior and its integration limits. They do not establish peg stability, profitability, financial inclusion, or fair treatment of market participants. Preparation of this report was assisted by Codex. The research programme is directed toward human agency, financial inclusion, and evidence-based accountability. Intended social benefits are distinguished from measured technical results in the manuscript. The manuscript and newly authored analysis are offered under CC BY 4.0. Any supplied source files retain the license terms stated in the supplement; the record license does not replace third-party source licenses.