Summary
The follow-on to The Geometric Siphon and The Hidden Microstructure answers the question the latter closed on. Why is the directional asymmetry of dust flows stronger on volatile–volatile pairs, where the numéraire theorem that explains it does not apply? The answer is the operator itself. Rebalances fire on trigger lines inside the range bounds, ranges sit asymmetrically around price through the manager’s own rounding arithmetic, and an exact first-passage law converts that placement into the firing asymmetry with slope one. The numéraire mechanism, exact where the earlier paper proved it, is bounded one to two orders below the execution factors at production scale. The paper the study was designed to write would have confirmed the mechanism; the paper it produced measures its ceiling.
Abstract
On a production concentrated liquidity position manager, the USD-valued dust flows credited at rebalances are directionally asymmetric. The first companion paper explains the volatile–stable case through a numéraire theorem; the second closes on the observation that the asymmetry is stronger on volatile–volatile pairs, outside that theorem’s domain. This paper decomposes it into a frequency channel and a value channel, measured on the V9 production dataset (126,339 rebalances, 48 pools, Aerodrome Slipstream on Base). A directional firing proposition gives the frequency channel as an exact first-passage law with no free parameters. A second proposition and its corollary give the swap-free per-event dust credit in closed form, with its sign inversion under token-order reversal, verified to machine precision against a direct V3 mint. The first-passage barriers are the operator’s trigger lines, not the range bounds, recovered from the data as a discontinuity in the firing-position distribution. With barriers so placed the theory slopes match their predicted value of one wherever the regressor carries signal, intercepts are indistinguishable from zero, and a replay test attributes the one remaining null to a noise-dominated regressor. The volatile–volatile excess is attributed to asymmetric range placement, a grid-quantisation artefact, jump-driven exits and labelling artefacts ruled out. The value channel, from joining each rebalance to its corrective swap, is the near-cancellation of two large opposing execution factors, with the residual direction-conditioned. The numéraire component, exact in its domain, is bounded at production scale one to two orders below the execution factors. The directional asymmetry of production dust flows is carried by operator microstructure. All results are single-operator; the law’s form and the trigger-measurement recipe are portable, and cross-operator replication is the immediate test.
The barriers are not where you think
The empirical subtlety is that the first-passage barriers are not the range bounds. The manager fires when price comes within a configured fraction of the range width of either bound, so the effective barriers are the trigger lines inside them. The fraction is recoverable from public chain data alone, as sharp steps at exactly and in the distribution of the price’s position within the range at firing. Fits against the raw bounds produce systematically attenuated slopes; against the trigger lines, the law holds. The volatile–volatile excess that motivated the paper is then placement arithmetic. Those pools sit ranges with the price systematically above the midpoint, because the manager centres each new range by rounding the current tick down to the pool’s tick-spacing grid. The first-passage law converts that rounding bias into the observed firing excess with slope one.
Cite as
@techreport{ryan2026operatormicrostructure,
author = {Ryan, K. R.},
title = {Operator Microstructure: Decomposing the Directional Asymmetry of Concentrated Liquidity Dust Flows},
institution = {SSRN},
type = {SSRN preprint},
number = {7164459},
year = {2026},
month = jul,
url = {https://papers.ssrn.com/sol3/papers.cfm?abstract_id=7164459},
}Third paper in the sequence begun by The Geometric Siphon, whose numéraire theorem this paper bounds at production scale, and The Hidden Microstructure, whose closing observation it explains. The two fronts left open here have since closed. Quantisation Microstructure derives the per-event law of the value channel, and Operator Fingerprinting runs the cross-operator replication named as the immediate test.