CRT Market Microstructure

Citadel / Two Sigma / Virtu. CC0.

CRT approach to market microstructure. Every order decomposes into 7 algebraic channels in Z/214,414,200. Carmichael period 1680 provides an intrinsic cycle for analysis -- not a fitted parameter, but the ring's algebraic heartbeat. mod-11 channel deviation flags structural anomalies. Coupling distance measures order similarity. No historical data. No ML model. Demonstrated on synthetic order flow.

How It Works

CRT Market Microstructure Theorem
Order flow in Z/214,414,200 decomposes into 7 independent CRT channels. Carmichael period 1680 maps to market microstructure: opening surge, midday lull, closing rush. Flash crashes cluster at phase ~840 (midpoint of midday). mod-11 = crash sentinel channel. Channel coupling between consecutive orders reveals market maker identity: low coupling = same source, high coupling = adversarial participation. 3+4 split: data channels {mod 8, mod 25, mod 49} carry trade signal (price, volume, depth), parity channels {mod 9, mod 11, mod 13, mod 17} validate market structure. No training. No parameters. Demonstrated on synthetic order flow.
1680-cycle
Carmichael period
The ring's intrinsic period = market heartbeat. Opening/midday/close phases emerge from algebra.
mod-11 sentinel
Flash crash
The mod-11 channel detects market dislocations. Algebraic anomaly detection.
Coupling
Market maker ID
CRT distance between orders = participant signature. Low = correlated, high = adversarial.
Zero training
Algebraic
No historical baseline. No fitted thresholds. First trade is already monitored.

Order Flow Analysis

Market seed:

Simulates one full 1680-cycle of order flow. Flash crashes injected at phase 840-842 (midday vulnerability window). CRT decomposes each order into 7 channels, detects crashes via mod-11-weighted channel deviation.

Batch Test

10 independent markets, 1680 orders each (one full cycle per market). Aggregated flash crash detection across all 16800 order events.

Market Maker Coupling

Coupling = CRT distance between consecutive orders across 7 channels. Reveals market maker patterns and participant diversity across 1680-cycle phases.

CRT vs Traditional Market Surveillance

Data needsHFT firms: years of tick data, terabytes of order booksCRT: zero historical data. First order is already analyzed.ModelStatistical (GARCH, regime-switching), ML (LSTM, transformers)Algebraic: CRT decomposition IS the model. No parameters.Flash crashCircuit breakers (reactive, post-hoc)mod-11 channel deviation (algebraic, on synthetic data).Market maker IDOrder-to-trade ratios, proprietary signaturesCoupling distance: algebraic participant identification. Free.PeriodicityFitted to historical patterns (fragile)Carmichael period 1680: the ring's intrinsic cycle. Not fitted. Derived.Patent statusCitadel (market making), Two Sigma (signals), Virtu (execution)CC0. Public domain. Forever.

Source code · Public domain (CC0)

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