logos/docs/periodic_table.md

The Periodic Table of Matroska AI Elements

This document defines the fundamental "elements" of the Logos Matroska System, inspired by the IBM AI Periodic Table but adapted for the Recursive Manifold architecture. These elements serve as the atomic units for the "Matroska Tool Token Assignment" and "Semantic Gravity".

I. Primitives (The Nucleus)

Fundamental building blocks that cannot be broken down further within the domain.

Symbol	Element	Description	Logos Mapping
Pr	Prompt	The initial input wave or instruction.	State Buffer Input
To	Token	The atomic unit of semantic meaning.	Text Tokens / Image Patches
Ve	Vector	Numerical representation of meaning (Semantic Gravity).	Heat Codes / Embeddings
Mo	Model	The dense compute node (LLM).	Gemma, RNJ-1, Local LLMs
Me	Memory	Persistence of state.	Manifold Storage
Co	Code	Executable logic functions.	Tools / Python Functions

II. Compounds (The Molecules)

Combinations of primitives that form functional units.

Symbol	Compound	Formula	Description
Rag	Retrieval	Pr + Ve + Me	Fetching context based on semantic gravity.
Ch	Chain	Pr -> Mo -> Pr	Linear sequence of model calls.
Fu	Function	Mo + Co	LLM calling a specific tool (Tool Use).
St	State	Me + time	The evolving context over recursive loops.

III. Organisms (The Agents)

Self-organizing structures capable of goal-directed behavior.

Symbol	Organism	Formula	Description
Ag	Agent	Ch + Fu + St	A recursive loop with tools and memory.
Sw	Swarm	Ag + Ag + ...	Multiple agents coordinating via the Hyper-Graph.
Ma	Matroska	Sw^n	Nested domains of swarms (The Logos System).

IV. The Periodic Laws (Rules of Interaction)

1. Law of Semantic Gravity:

   • Elements with similar Ve (Vectors) attract each other.
   • Routing is determined by the "Heat" (Dissonance) between the Pr and Mo.

2. Law of Recursive Synthesis:

   • Compounds are formed effectively when St (State) is preserved across loops.
   • A stable Ag (Agent) requires a harmonic balance of Dissonance (Entropy).

3. Law of Matroska Embedding:

   • Higher-order organisms (Ma) can contain lower-order elements as "Tokens".
   • An entire Ag can be treated as a To for a higher-level Router.