Mesh Sensor Network

3 boards, 0 failures

Three ESP32 boards. CRT addressing. ECC3 triple-parity on every packet. 1,094 packets received, 0 failures. Round-trip calibration: delta = 0 on all pairs. Real data from live hardware.

Network Topology

Three boards on ESP-NOW broadcast mesh. Each board's ring element determines its CRT address, coupling class, and routing role.

Board	Element	CRT Address	Coupling
FAR (COM3)	sigma = 1	(1,1,1,1,1,1,1)	214,414,200
MIDDLE (COM4)	D = 2	(2,2,2,2,2,2,2)	107,207,100
CLOSE (COM5)	void = 0	(0,0,0,0,0,0,0)	1

Packet Statistics

Real traffic from 3-second heartbeat mesh. SPIN packets (type 3), calibration probes (type 1), calibration echoes (type 2). Every received packet validated by ECC3.

Board	TX	RX	ECC OK
sigma (COM3)	338	345	345
D (COM4)	205	371	371
void (COM5)	214	378	378
TOTAL	757	1,094	1,094

100% ECC PASS
1,094 packets received. 0 failures. ECC3 triple-parity (mod 11 + mod 13 + mod 17). Rate 4/7.

Round-Trip Calibration

Probe value 42 sent between all board pairs. Mirror involution (N - x) cancels systematic channel error. Round-trip recovers the original value exactly.

Pair	Probe	Recovered	Result
sigma -> D	42	42	PASS
sigma -> void	42	42	PASS
D -> sigma	42	42	PASS
D -> void	42	42	PASS
void -> sigma	42	42	PASS
void -> D	42	42	PASS

Why Delta = 0

-1 is the unique involution where round-trip error cancellation is exact. For any involution u, the residual error is u(u+1)*epsilon. Only u = -1 gives u+1 = 0, so the residual vanishes. This is not a design choice -- it is forced by the algebra.

Try Round-Trip

Enter a value and a systematic error. Watch the 4-step round-trip cancel the error in every CRT channel.

x =error =

x = 0, epsilon = 0

Forward: 0 + 0 = 0

Mirror: N - 0 = 0

Return: 0 + 0 = 0

Unmirror: N - 0 = 0

Result: PASS (delta = 0)

Step	mod 8	mod 9	mod 25	mod 49	mod 11	mod 13	mod 17
1. Send x	0	0	0	0	0	0	0
2. + error	0	0	0	0	0	0	0
3. Mirror	0	0	0	0	0	0	0
4. + error	0	0	0	0	0	0	0
5. Unmirror	0	0	0	0	0	0	0

How It Works

ESP-NOW

Broadcast

250kbps, no AP needed. 14-byte CRT payload. 3-second heartbeat. All boards hear all packets.

CRT Address

7 channels

Ring element = address = route. sigma(1) = backbone. D(2) = bridge. void(0) = relay. No routing tables.

ECC3

Rate 4/7

Triple-parity: mod 11 + mod 13 + mod 17. Detects any single-channel corruption. Corrects via reconstruction from remaining 6 channels.

Calibration

delta = 0

Mirror involution (N-x) cancels systematic error. Unique among all involutions. O(1) cost: one subtraction.

Hardware

$12 total

3 ESP32 boards at $4 each. 240MHz, 520KB RAM. .ax WASM firmware. No cloud. No infrastructure.

Source code · Public domain (CC0)

Report issue

.ax source compiled to WASM via self-hosting compiler. Zero HTML authored.