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Topic · Layer 2 of Digital Space Algebra

Two islands, one shared space.

A connection isn't a search. It's an intersection. The algebra behind how identities connect without a central authority that knows both.

Two islands, live

Kernel: this.me 4.2.1 (npm) ⓘ

1 · Two islands

Each identity is its own island: a who and a secret derive a seed, the seed an identity hash. Claiming a namespace is a signed proof anyone can check, without learning the secret.

ana: · bob: 
 
      


      

        
2 · An island keeps its secret

        
A secret scope narrows who can read a branch to its owner. Not a rule checked at a door: the branch is encrypted.

        
 
      


      

        
3 · A bridge for one reader (OR)

        
To share, ana wraps a content key to bob's public key. bob opens it; eve, holding a different key, cannot. One wrap per member is an OR audience.

        
 
      


      

        
4 · Copying is not reading (T ⊥ A)

        
ana's whole island can be copied to bob. The public part reads; the secret stays sealed, and the copy carries neither the value nor its key.

        
 
      


      
AND (XOR shares), minus and groups: in the v4.2.1 source, not exported by npm. See Audiences.

    


    

      
Read

      

        

          
          
The Algebra of Encrypted Audiences III

          
The essay: I_AB = I_A ∩ I_B, contextual sovereignty, verifiable intersection, structural privacy.

          

            ES
            JA
          

        

        
          
Robots × Encrypted Audiences — Infographic

          
The same algebra applied to embodied agents: one object, four contexts, zero copies.

        
      

    


    

      
Status in this.me 4.2.1

      

        

          Kernel: this.me 4.2.1

          OR / AND (XOR shares) / minus — implemented and tested in the 4.2.1 source; not exported by the npm 4.2.1 package.

          From npm 4.2.1 — OR by wrapping one secret per recipient with ME.wrapSecretV1. Concept and status per implementation: Audiences.

          group:name — partial (Cleaker roles only). surface[a+b] / audienceSeed and key distribution — not implemented.
        

      


import ME from "this.me"; // 4.2.1
const a = await ME.generateP256KeyPair(), b = await ME.generateP256KeyPair(), out = await ME.generateP256KeyPair();
const S = "content-key-123";
const Wa = await ME.wrapSecretV1({ secret: S, recipientPublicKey: a.publicKey, kid: "a", class: "identity-key" });
const Wb = await ME.wrapSecretV1({ secret: S, recipientPublicKey: b.publicKey, kid: "b", class: "identity-key" });
await ME.unwrapSecretV1(Wa, a.privateKey, "utf8");   // "content-key-123"
await ME.unwrapSecretV1(Wb, b.privateKey, "utf8");   // "content-key-123"
await ME.unwrapSecretV1(Wa, out.privateKey, "utf8"); // throws: OperationError

    


    

      
Technical docs

      

        
          
Audiences

          
OR, AND, minus: the concept, a verified npm 4.2.1 example, and status in TypeScript, Rust and Python.

        
        
          
Axioms — The Kernel's Invariants

          
Stealth disclosure and secret-scope: the guarantees the audience algebra is built on.

        
        
          
Primitives

          
The kernel primitives secret-scoped, audience-gated paths are made of.

        
        
          
Seed

          
Where audience derivation actually starts — the kernel seed.