cleaker

The Algebra of Me ​

Let us define the universe of the system:

𝕌 = the set of all possible namespaces. A namespace is a composite structure: N = (domain, port)

Each component may be present or absent.

Base Rule: "More specific ⇒ Subset" ​

When additional components are introduced (subdomain, port, path), the covered region becomes smaller.

  • cleaker.me contains cleaker.me:8161
  • cleaker.me contains jabellae.cleaker.me
  • jabellae.cleaker.me contains jabellae.cleaker.me/board

Formally: if A is less specific than B, then B ⊆ A.

A0 — Namespace as Region ​

A namespace N is a region defined by a set of coordinates:

N = { domain, port?, path?, subdomain?, … }

There exists a refinement operator (⊑) such that: if B adds coordinates to A, then B ⊑ A and B ⊆ A.

A1 — Relation as Function ​

A relation R is a function that maps a viewer namespace to a target namespace:

R : N_viewer → N_target

A2 — Relation Refinement ​

A relation R_B refines R_A if for all viewer namespaces, the target of R_B is more specific than that of R_A.

A3 — Relation Composition ​

Given R_A : N_viewer → N_intermediate and R_B : N_intermediate → N_target, their composition is:

R_C(N_viewer) = R_B(R_A(N_viewer))

A4 — Identity Relation ​

The identity relation I maps any viewer namespace to itself:

I(N_viewer) = N_viewer

A5 — Existence Relation ​

An existence relation E maps any viewer namespace to a base existence namespace:

E(N_viewer) = N_existence

A6 — Semantic-to-Routing Resolver ​

The .me language expresses semantic paths; Cleaker resolves them into routing targets.

  • Semantic (.me): cleaker.me/@username/device/suiGNMacBookAir/PORT/profile
  • Routing (cleaker): username.cleaker.me:suiGNMacBookAir:8161/profile

Interpretation:

  • .me defines the meaning (device, PORT, namespace, identity).
  • cleaker performs the resolution (semantics → routing).
  • monad.ai is the surface.

This preserves a clean separation: language (meaning) → dictionary (resolver) → storage (ledger).