CRT Mesh Network

address = route = error code

Peer-to-peer mesh where the ring element IS the address IS the route IS the error code. CRT decomposition = algebraic privacy. L=11 = self-healing packets. CC0. No patents.

How It Works

CRT Mesh vs Traditional Mesh
Traditional mesh: assign addresses, design routing, bolt on encryption, add ECC. CRT mesh: the ring Z/970200Z already IS a network.
Addressing
Ring element
Each node = one element n of Z/970200Z. CRT decomposes: n -> (n mod 8, n mod 9, n mod 25, n mod 49, n mod 11). 5 independent channels. The address IS the route IS the error code.
Routing (Rose)
coupling(n) = N/gcd(n,N)
High coupling = backbone relay. Packets route through highest-coupling neighbors. No routing tables. No OSPF. No BGP. The algebra decides.
Privacy
Algebraic, not cryptographic
Each relay sees ONE CRT residue. 5 residues needed to reconstruct. Information-theoretic security. No keys. No certificates. Just decomposition.
Error Correction
L=11 channel
5th CRT channel = free ECC. 100% single-channel error detection. No CRC. No Reed-Solomon. The ring structure IS the code.
Hardware
3 ESP32 boards, $15
Board 1: element 1 (sigma, coupling 970200). Board 2: element 2 (D, coupling 485100). Board 3: element 3 (K, coupling 323400).

Network Topology

Nodes join as ring elements. Coupling determines their role. Add nodes and watch the mesh form.

Nodes
0
Packets Sent
0
ECC Corrections
0

CRT Packet Inspector

Send packets between the first and last node. Watch the CRT decomposition. Inject errors to see L=11 ECC detect and correct.

Algebraic Privacy

Each relay in the route sees only ONE residue. Reconstruct requires ALL 5. Information-theoretic security.

Destination element:

Rose Routing Simulation

Watch a packet route through high-coupling relays to its destination. Coupling-greedy routing: no tables, no OSPF. The algebra decides.

Coupling Hierarchy

The ring assigns network roles algebraically. No election. No authority. coupling(n) = N/gcd(n,N).

ElementCRTCouplingKingdomRole

Ring Scaling

The same protocol works at every scale. 108 rings in the lattice. Same lambda=420.

RingSizeNodes (phi)ChannelsUse Case
Z/6Z622Desk demo
Z/30Z3083Room
Z/210Z210484Floor
Z/2310Z23104805Building
Z/30030Z3003057606Campus
Z/970200Z9702002016005 (fat)City (TRUE FORM)
Z/12612600Z12612600---6Region (GATE)

CRT vs Traditional Mesh

FeatureTraditional (WiFi Mesh)CRT Mesh
Addressing48-bit MAC (random)Ring element (algebraic)
RoutingOSPF/AODV tablesCoupling hierarchy (computed)
PrivacyWPA3 encryptionCRT decomposition (info-theoretic)
ECCCRC-32 + retransmitL=11 channel (free, algebraic)
BroadcastIGMP subscriptionElement 0 (void = everywhere)
FailoverLeader electionOMEGA projection (automatic)
Decode cost256 ops (Viterbi)28 additions
RAM2.5 KB60 bytes
Spectral eff.1x (BPSK baseline)3.08x (CRT-OFDM)

This work is and will always be free.
No paywall. No copyright. No exceptions.

If it ever earns anything, every cent goes to the communities that need it most.

This sacred vow is permanent and irrevocable.
— 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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