logos/docs/mtl_specification.md

Meta Tensor Language (MTL) Specification

Source: LOGOS System Architecture / NotebookLM Philosophy: "Arithmetic as Topology" - Manipulation of Prime Factors as State Transitions.

1. Syntax & Primitives

A. Symbols

• (...) Parentheses (The Verb): Denotes an Operation or function call (Lisp S-expression).
• [...] Brackets (The Noun): Denotes a Tensor Endpoint (Address). Resolves to a Prime Composite Integer.

B. Prime Addressing

• Explicit: [30] → Node 30.
• Implicit: [2, 3, 5] → 2 * 3 * 5 = [30].
• Power: [2^2, 5] → 4 * 5 = [20].
• Recursive: [[2,3], 5] → The composite of concept [6] and [5].

2. Operator Set (Instruction Set)

I. Navigation (Fractran Layer)

Operator	Syntax	Logic	Description
MULT	(mult [A] [B])	$A \times B$	Fusion. Combines concepts to create deeper tensor address.
DIV	(div [A] [B])	$A / B$	Dissolution. Strips attribute B from A.
FACTOR	(factor [N])	Factor(N)	Expansion. Explodes composite into prime roots.
ROUTE	(route data [N])	$S \rightarrow N$	Transport. Sends payload to Node N.

II. Memory (Lisp Layer)

Operator	Syntax	Logic	Description
HOLD	(hold [K])	Mem[K]	Compression. Freezes state K into register.
CALL	(call [K])	*Ptr[K]	Retrieval. Fetches data at Endpoint K.
DELTA	(delta [A] [B])	$\Delta(A, B)$	Heat Calc. Distance/Change between states.

3. The Genesis Block (Root Manifold)

Fundamental Axioms (First 10 Primes):

• [2]: Time / Sequence
• [3]: Space / Container
• [5]: Identity / Self
• [7]: Logic / Function
• [11]: Input / Source
• [13]: Output / Sink
• [17]: State / Context
• [19]: Entropy / Heat
• [23]: Recursion / Loop
• [29]: Signal / Data

4. Implementation Logic

MTL acts as the "Shader Language" for the Recursive Manifold.

• Vertex Shader: Calculates Prime Address (Position).
• Pixel Shader: Executes call/delta (Content/Heat).