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Space Algebra

.me thinks in spaces.

Not schemas. Not tables. Not object classes.

A space is a region of meaning that can contain other spaces.

Everything else follows from set laws.

Core Rule

A space can contain spaces.

txt
space ⊇ subspace ⊇ subspace ⊇ subspace

Examples:

  • profile is a space
  • profile.contact is a subspace of profile
  • wallet.hidden is a subspace of wallet
  • friends[age > 18] is a selected subspace of friends

In .me, paths are how we navigate nested spaces:

ts
me.profile.name("Abella");
me.profile.contact.email("abella@neurons.me");
me.wallet["_"]("vault-key");
me.wallet.hidden.note("private");

Namespace

A namespace is a named space.

Examples:

  • self
  • kernel
  • ana
  • family.photos

In protocol form:

txt
me://self:read/profile
me://kernel:export/snapshot
me://family.photos:read/2026.vacation.cover

So:

  • namespace names the space
  • selector states the operation
  • path identifies the subspace

Set View

We can describe a space by the sets that act on it:

  • A = audience set
  • T = topology set
  • C = capability set
  • P = path / subspace set

These are not different ontologies. They are different views of the same space.

Space Predicates

The common adjectives are just set statements:

  • public space: the readable audience is broadly open
  • private space: the audience is tightly bounded, often {self}
  • shared space: the audience contains more than one principal
  • encrypted space: readable membership is enforced cryptographically
  • replicated space: the topology has multiple carriers

Examples:

  • wallet may be a private encrypted space
  • family.photos may be a shared replicated encrypted space
  • profile.public may be a public space

No new noun is required beyond space.

Refinement

More specific spaces are subsets of less specific spaces.

txt
profile.contact.email ⊆ profile.contact ⊆ profile
wallet.hidden ⊆ wallet

This same law appears across the system:

  • deeper path -> smaller semantic region
  • tighter audience -> smaller readable set
  • tighter context -> smaller resolution set
  • tighter capability -> smaller action set

Encryption As Membership

Encryption does not create a different universe. It creates a stricter readable membership over a space.

Examples:

  • a private space may have A = {self}
  • a shared encrypted space may have A = {me ∪ wife}

The topology can be large while the readable audience stays small:

txt
T = {home-daemon, office-daemon, phone}
A = {me, wife}

That means the same space may be replicated widely without becoming readable widely.

Why This Matters

This gives .me one ontology instead of many.

  • .me declares, creates, and navigates spaces
  • cleaker records, routes, and transports spaces
  • monad.ai serves, resolves, and persists spaces

The system stays unified because everything still reduces to:

txt
space inside space inside space

And all of it follows set law.