CRT Anomaly Detection

CRT approach to anomaly detection over Z/214,414,200. CC0.

CRT approach to anomaly detection. Decompose every measurement into 7 algebraic channels. Normal behavior = consistent channel patterns. mod-11 = instant anomaly flag. No training. No baseline. No model. Demonstrated on synthetic time series with injected anomalies.

How It Works

CRT Anomaly Detection Theorem
Every value in Z/214,414,200 decomposes into 7 independent channels via CRT: mod 8, mod 9, mod 25, mod 49, mod 11, mod 13, mod 17. Normal time series values follow consistent per-channel patterns. Anomalous values deviate in one or more channels. mod-11 is the most sensitive detector: its small modulus amplifies proportional deviations. Channel independence means each channel monitors a different dimension of the signal. An anomaly that hides in one channel is exposed in another. 3+4 split: 3 data channels (mod 8, 25, 49) carry the signal, 4 parity channels (mod 9, 11, 13, 17) validate it. No training data needed -- anomaly = channel deviation from expected pattern.
7 monitors
7 CRT channels
Each channel watches an independent dimension. Anomaly in ANY channel = detected.
mod-11 sentinel
Free detection
Same channel that does error detection also does anomaly detection. 1+2+3+5=11.
Zero training
Algebraic
No baseline period. No model fitting. First data point is already monitored.
Classification
Free typing
Which channels deviate tells you WHAT KIND of anomaly: amplitude, frequency, integrity.

Try It

Random seed:

Generates 50 data points with periodic signal + injected anomalies. CRT decomposes each, detects via mod-11-weighted channel deviation. Green rows = true positive. Orange = false positive.

Batch Test

20 independent streams, 50 points each. Aggregated precision/recall across all 1000 measurements.

Anomaly Fingerprinting

Each anomaly has a unique CRT fingerprint. Per-channel deviations classify the anomaly type automatically.

CRT vs Traditional Anomaly Detection

TrainingSplunk/Datadog: weeks of baseline data to establish normsCRT: zero training. First data point is already monitored.ModelStatistical (Z-score), ML (isolation forest, LSTM)Algebraic: CRT decomposition IS the model. No parameters.DimensionsFeature engineering required for multi-dimensional7 CRT channels = 7 dimensions. Automatic from ring structure.ClassificationSeparate classifier needed after detectionFree: which channels deviate = anomaly typeFalse positivesThreshold tuning, seasonal adjustmentmod-11 sensitivity is algebraically fixed. No tuning.Patent statusSplunk (ITSI), Datadog (Watchdog), Dynatrace (Davis AI)CC0. Public domain. Forever.

Source code · Public domain (CC0)

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