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, 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. $$State=P_1\times P_2\times P_3\dots State\; =\; P\_1\; \backslash times\; P\_2\; \backslash times\; P\_3\; \backslash dots$$ 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): $$\text{if }(File\mathrm{\_}ID\mathrm{m}\mathrm{o}\mathrm{d}5==0)\to \text{True}\backslash text\{if\; \}\; (File\backslash \_ID\; \backslash mod\; 5\; ==\; 0)\; \backslash rightarrow\; \backslash text\{True\}$$ 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.