CRT Market Microstructure

D37: Citadel / Two Sigma / Virtu. CC0.

High-frequency trading firms spend billions on proprietary order flow analysis, flash crash prediction, and market maker identification. CRT approach: every order decomposes into 6 algebraic channels. lambda=420 IS the market's heartbeat -- not a fitted parameter, but the ring's intrinsic period. L=11 detects flash crashes algebraically. Coupling distance identifies market maker signatures. No historical data. No ML model. The ring structure IS the regulator.

How It Works

CRT Market Microstructure Theorem
Order flow in Z/12612600 decomposes into 6 independent CRT channels. The ring's universal period lambda=420 maps directly to market microstructure: opening surge (genesis), midday lull (observation), closing rush (boundary). Flash crashes cluster at phase ~210 -- the E^2=null midpoint where the market cannot observe itself. L=11 = the ECC channel = flash crash sentinel. Channel coupling between consecutive orders reveals market maker identity: low coupling = same source (correlated flow), high coupling = adversarial participation. The 490 split: DEAD={D,E,b} carry trade data (price, volume, depth), ALIVE={K,L,G} validate market structure (consistency, integrity, boundary). No training. No parameters. The algebra IS the surveillance system.
420-cycle
lambda=420
The ring's intrinsic period = market heartbeat. Opening/midday/close phases emerge from algebra.
L=11 sentinel
Flash crash
Same channel that does ECC detects market dislocations. sigma+D+K+E=11.
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 420-cycle of order flow. Flash crashes injected at phase 210-212 (midday vulnerability window). CRT decomposes each order, detects crashes via L=11-weighted channel deviation.

Batch Test

10 independent markets, 420 orders each (one full cycle per market). Aggregated flash crash detection across all 4200 order events.

Market Maker Coupling

Coupling = CRT distance between consecutive orders. Reveals market maker patterns and participant diversity across 420-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)L=11 detection (proactive, algebraic). Detects BEFORE the circuit breaker.Market maker IDOrder-to-trade ratios, proprietary signaturesCoupling distance: algebraic participant identification. Free.PeriodicityFitted to historical patterns (fragile)lambda=420: the ring's intrinsic period. Not fitted. Derived.Patent statusCitadel (market making), Two Sigma (signals), Virtu (execution)CC0. Public domain. Forever.

This work is and will always be free.
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If it ever earns anything, every cent goes to the communities that need it most.

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— Anton Alexandrovich Lebed

Source code · Public domain (CC0)

Contributions in equal measure: Anthropic's Claude, Anton A. Lebed, and the giants whose shoulders we stand on.

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