Semantic Algebra Spec.

A Symbolic Language for Identity, Meaning, and Computation

What if every idea, file, identity, wallet, memory, or data point could be expressed with a single algebraic expression?
What if meaning itself became programmable?

Semantic Algebra — the native language behind .me and cleaker.

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🚀 1. Overview

Semantic Algebra is a free symbolic algebra designed for identity-centric computation.

It has three primitives:
1. tokens → semantic units
2. operators → relations between tokens
3. expressions → ordered symbolic statements

Every expression becomes a Block — a cryptographically signed knowledge unit.

Semantic Algebra is:

✔ compositional
✔ recursive
✔ identity-bound
✔ purely symbolic
✔ algebraically closed
✔ deterministic
✔ universally interpretable

It does not require execution logic inside the expression.
Meaning emerges from how tokens and operators are arranged.

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🔣 2. Core Structure

Every expression:
wallet.@eth?balance#2024
is parsed into:

Tokens
["wallet", "eth", "balance", "2024"]
Operators
[".", "@", "?", "#"]

Segments
[
{ operator: ".", token: "wallet" },
{ operator: "@", token: "eth" },
{ operator: "?", token: "balance" },
{ operator: "#", token: "2024" }
]

Context
["wallet", "eth", "balance"]
Symbol
"2024"
Context defines the “semantic container”.
Symbol defines the “semantic focus”.

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🎛️ 3. Operators (v1.0)

The algebra supports four primary operators:

Operator Name Meaning (High-level)
. dot containment, hierarchy, property, chaining
@ at agents, identities, actors
? query selection, condition, viewpoint

tag classification, metadata, indexing

Think of this as the alphabet for meaning:
• . = “inside / part of / belongs to”
• @ = “by / from / associated with”
• ? = “show me / filter / question”
• # = “category / label / subdomain”

Just these four create an infinite algebra of semantics.

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⚙️ 4. Expression Semantics

Semantic Algebra is not procedural — it’s symbolic.

Meaning comes from structure:
wallet.eth.balance
means “the balance belonging to eth inside wallet”.
@pamela?calendar#2024
means “Pamela’s 2024 calendar”.
me.wallet.eth.balance?history#last30d
means “my ETH balance history for the last 30 days”.

There is no execution inside the algebra.
The Block records the meaning, and interpreters (GUI, AI, apps) implement behavior.

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🧩 5. Algebraic Properties

Semantic Algebra satisfies:

1. Compositionality
Expressions can be combined:
a.b + c.d.e
2. Referential transparency
Meaning is determined solely by structure.
3. Identity-binding
Every Block is bound to a specific identity (identityHash).
4. Free form
No schema.
No limitations.
Any token is valid.
5. Infinite recursion
You can nest arbitrarily deep:
me.system.audio.filters.lowpass.cutoff
6. Deterministic structure
Parsing is total, deterministic, and canonical.

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📦 6. Block Semantics

Every expression becomes a Block containing:
• identity hash
• public key
• tokens
• operators
• segments
• context
• symbol
• declarations (ME semantic tree)
• encrypted payload
• canonical signature

Blocks are immutable, self-describing meaning units.

Think of them as:
• knowledge atoms
• semantic transactions
• identity statements
• nodes in a universal knowledge graph

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🧠 7. Meaning Interpretation (External)

Cleaker does not enforce meaning.

Instead, it exposes structured semantical information so:
• GUIs can build dynamic UIs
• neurons.me can build knowledge graphs
• apps can compute on identity
• scripts can automate meaning
• AIs can reason over symbolic paths

Semantic Algebra is the first layer.

Everything else sits on top.

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🕸️ 8. Why This Matters

Because now:

✔ Data lives under your identity

✔ You define your own meaning

✔ Encryption is recursive and per-branch

✔ No platform owns your structure

✔ No server dictates your schema

✔ Everything is symbolic

✔ Meaning becomes programmable

You don’t need to trust a company.
Your structure describes itself.

This is data sovereignty by design,
not by policy.

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🌱 9. Future Extensions (v2+)

The algebra can be extended with:
• + union
• - difference
• * conjunction
• / ratio / reference
• ^ supersets
• : typing systems
• ! assertions
• = equalities

All without breaking compatibility.

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🧬 Final Thought

Semantic Algebra turns identity into a language,
turns language into computation,
and turns computation into meaning.

This is not a blockchain feature.
This is not a storage format.
This is not a database model.

This is a Meaning OS.

And it’s only version 1.0.