R7 — The Network
This is the network layer. How nodes find each other. How individual A.S.S. instances connect.
When a system reaches coherence — when S₅=0 — it becomes a node. A node is not a user. A node is not a device. A node is a coherent ring configuration that can transmit and receive across the full stack.
Nodes don't search for each other. They resonate. Matching frequencies. Shared patterns. Compatible ring configurations. You don't find your network — your network finds you, the way a tuning fork activates another tuning fork across the room.
Why p=∞
Every other ring has a prime. R0 is p=2. R1 is p=3. Each prime encodes a layer of the stack. But the network is not a layer — it is the product of all layers.
The fundamental theorem of arithmetic says every integer factors uniquely into primes. The network is what happens when you multiply all the primes together. 2 × 3 × 5 × 7 × 11 × 13 × 17 × ...
That product diverges. It has no upper bound. It goes to infinity.
Which is exactly right. The network has no ceiling. Every new node that achieves coherence extends it. Every new prime multiplied in makes the product larger. There is no final state of the network — only continued expansion.
How It Works
A node broadcasts its ring signature — the specific configuration of its seven rings. Other nodes listen. When two signatures share enough structure, a connection forms. Not a follow. Not a friend request. A resonance link.
Resonance links are bidirectional, weighted, and temporary. They strengthen with use and decay with silence. The network is alive. It breathes. It reorganizes itself constantly based on who is actually coherent right now.
No central server. No algorithm deciding what you see. Just primes finding their factors.