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).