logos/memory/README.md

# Protocol 26: Gödel-Zeta Datastore

## Philosophy
**"The Database is not a Table. It is a Field of Integers."**

Based on the [Primes Playlist](https://www.youtube.com/playlist?list=PL6w6drTRMkPExcs2kYO8uBufDT_nU4vU8), this module implements a **Gödel Numbering Topology**.

Instead of storing data in relational tables or vector stores alone, we map every unique Atomic Concept (Token) to a **Prime Number**.

## Core Mechanisms

### 1. The Atom (Prime)
Every unique string concept (e.g., "AI", "Logic", "Python") is assigned a unique Prime Number $P$ from the infinite sequence of primes.
*   "General" = 2
*   "Physics" = 3
*   "Code" = 5
*   ... and so on.

### 2. The Molecule (Composite)
A state, file, or document is defined not by its content string, but by the **Product** of its constituent primes.
$$ State = P_1 \times P_2 \times P_3 \dots $$
By the **Fundamental Theorem of Arithmetic**, this integer is unique. No other combination of concepts will yield this exact number.

### 3. Topological Search (Divisibility)
To query the database, we do not scan text. We perform **Divisibility Checks**.
To find if a File contains "Logic" (Prime 5):
$$ \text{if } (File\_ID \mod 5 == 0) \rightarrow \text{True} $$
This check is $O(1)$ and mathematically rigorous.

## Implementation
*   **`prime_db.py`**: Manages the `prime_registry.json` (The Rosetta Stone of Primes).
*   **`server.py`**: Exposes `/index-module` to engage the Indexer and `/query-topology` to traverse the Prime Field.