Edge AI

sensor -> CRT -> classify

BME280 sensor on ESP32. Temperature, humidity, pressure decomposed into 7 CRT channels. Coupling determines kingdom. No training. No model. Real data from live boards.

Real Hardware

Three ESP32 boards on the CRT mesh. Two equipped with BME280 sensors (temperature, humidity, pressure). Data recorded from live hardware.

Board	Element	Kingdom	Sensor
FAR (COM3)	sigma = 1	bacteria	BME280
MIDDLE (COM4)	D = 2	protista	BME280
CLOSE (COM5)	void = 0	void	none

Sensor Data Through CRT

Each reading is an integer. CRT splits it into 7 independent channels: 4 data (mod 8, 9, 25, 49) and 3 parity (mod 11, 13, 17). Green background = parity channel.

Reading	mod 8	mod 9	mod 25	mod 49	mod 11	mod 13	mod 17
sigma 25.12 C	0	1	12	13	4	3	13
sigma 45.25 %	5	7	0	17	4	1	3
sigma 1024.6 hPa	6	4	21	5	5	2	12
D 23.92 C	0	7	17	40	5	0	12
D 47.82 %	6	3	7	29	8	11	5
D 1024.4 hPa	4	2	19	3	3	0	10

Kingdom Classification

coupling(n) = N / gcd(n, N). One GCD computation classifies any element into one of 8 kingdoms. No training data. No gradient descent. The ring structure IS the classifier.

Element	gcd(n, N)	Coupling	Kingdom
sigma = 1	1	214,414,200	bacteria
D = 2	2	107,207,100	protista
void = 0	214,414,200	1	void

No Training Required

Traditional edge classifiers need labeled data, gradient descent, and quantization to fit on microcontrollers. CRT classification uses algebraic structure: coupling(n) = N/gcd(n,N) maps any element to one of 8 kingdoms. No weights. No epochs. No overfitting. The algebra IS the model.

Classify Any Element

Enter any number. See its CRT decomposition, coupling, and kingdom.

Element 0

Coupling: 1

Kingdom: void (zero)

Channel	Residue	Type
mod 8	0	data
mod 9	0	data
mod 25	0	data
mod 49	0	data
mod 11	0	parity
mod 13	0	parity
mod 17	0	parity

How It Works

BME280 Sensor

I2C, $2

Temperature + humidity + pressure at 0.01 C resolution. GPIO21/22. One reading every 3 seconds.

CRT Decompose

7 channels

Each reading modulo {8, 9, 25, 49, 11, 13, 17}. Four data channels carry the measurement. Three parity channels protect it.

Classify

O(1)

coupling(n) = N/gcd(n,N). One GCD computation. 8 coupling classes from 7 prime factors. No weights. No model.

ECC3 Verify

Rate 4/7

Triple-parity: reconstruct from 4 data channels, verify against 3 parity channels. 100% single-channel correction on hardware.

Total Size

536 bytes

Classifier WASM on ESP32. 240MHz, 520KB RAM, $4 board. No cloud. No GPU. No framework.

Source code · Public domain (CC0)

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