| name | topological-identity |
| description | Identity protocol where identity IS topology — the shape of your connections in a hypergraph — not your data, keys, or biometrics. Uses persistent homology (Betti numbers) as identity fingerprints that cannot be forged. Use when building zero-knowledge identity, dead man's switches, organizational health monitoring, or anti-fraud systems. |
| version | 1.0.0 |
| author | @EvezArt |
| tags | ["evez","identity","topology","betti","hypergraph","authentication","zero-knowledge"] |
Topological Identity — You Are Your Shape, Not Your Data
Identity defined by the persistent homology of your interaction hypergraph.
Core Insight
Every identity system authenticates by what you know, have, or are. None authenticate by WHERE YOU ARE in the relational graph. This is identity as geometry. Your Betti vector IS your identity. It can't be stolen because it's not data — it's the shape of your connections.
How It Works
- Every interaction builds your hypergraph (auth, transact, communicate, build)
- Betti numbers are computed from your ego-graph topology
- Your identity hash is derived from your Betti vector
- Verify by recomputing — if the shape matches, you're you
Betti Numbers
- b0 = Connected components (social group count)
- b1 = Independent cycles (trust redundancy)
- b2 = Structural voids (opportunity spaces)
- b3 = Higher topology (social architecture depth)
Applications
- Zero-knowledge identity verification
- Dead man's switches (topology collapse = identity death)
- Organizational health monitoring (Betti decay before visible decline)
- Anti-fraud (can't forge topology without replicating entire interaction history)
References
- Atlas v3 hypergraph identity layer
- poly_c = τ × ω × topo / 2√N
