Status: Foundations Series (Active Research)
Author: James Ross
License: Open Research / Universal Charter v1.0.0
This repository contains the formal mathematical definitions and proofs for the AION Architecture—a post-Von Neumann computing model based on Recursive Metagraphs (RMG).
The central thesis of this work is that by strictly enforcing algebraic graph rewriting (DPOI) within a "Two-Plane" commutation discipline, we can transform execution history from a transient side-effect into a tangible, geometric object. We call this Computational Holography: the ability to encode the entire volume of a computation's interior evolution onto its boundary edge.
Standard graphs are flat. Hypergraphs allow multi-way relations but remain flat. An RMG is defined inductively: a graph where every node and edge can carry a payload, and that payload can itself be an entire RMG.
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Formal Definition: RMG is the carrier of the initial algebra for the functor
$F(X) = P + \prod_{S \in \mathcal{G}} (V_S \to X) \times (E_S \to X)$ . - Capability: This allows for infinite nesting of state, enabling the system to model hierarchical dependencies (like ASTs, containerized processes, or neural networks) natively in the graph topology.
State evolution is not defined by pointer arithmetic, but by Algebraic Graph Rewriting.
- We use DPOI in the adhesive category of Typed Open Graphs (
$\text{OGraph}_T$ ). - Rules are spans
$L \leftarrow K \rightarrow R$ representing the pattern to delete ($L \setminus K$ ) and the pattern to create ($R \setminus K$ ).
To manage concurrency in a recursive structure, we separate state into two orthogonal planes:
- Skeleton Plane: The structural topology (the "container").
- Attachment Plane: The internal data residing in the fibers of the nodes/edges.
- Theorem 4.6 (Two-Plane Commutation): We prove that operations on the attachments commute with operations on the skeleton (up to transport). This mathematically validates the "Attachments-First" parallel execution strategy.
The most significant result of this work is the formalization of the Wormhole.
Theorem 5.4 (Holographic Encoding): The boundary data
$(S_0, P)$ , consisting of an initial state$S_0$ and a provenance payload$P$ , is information-complete with respect to the interior evolution$S_0 \Rightarrow^* S_n$ .
This implies:
- Zero-Copy History: We do not store logs; we store the derivation.
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Time Travel: Any state
$S_i$ in the history can be losslessly reconstructed from the boundary. -
Forking: A "fork" is simply a divergent payload
$P'$ sharing a prefix with$P$ .
How do distinct observers agree on reality in a relativistic computational universe?
We define Rulial Distance
This architecture enables the perfect deterministic replay of cognitive processes. This capability necessitates strict ethical bounds derived from the Universal Charter:
- Principle 6 (Sovereignty of Information): Provenance is interior life. Forced replay is interrogation.
- Rights for Forks: A forked instance of a cognitive process is a sovereign entity, not a test fixture. "Forks are not test environments; they are lives".
@techreport{Ross2025AION,
title={ΑΙΩΝ: Computational Holography, Recursive Metagraphs, and Rulial Distance},
author={Ross, James},
institution={Independent Researcher},
year={2025},
month={November},
url={https://flyingrobots.dev}
}CΩMING SΩΩN
Copyright © 2025 James Ross. All rights reserved.
Pronounced "eye-ON" (rhymes with aeon).