AIΩN Foundations — Paper I

WARP Graphs: A Worldline Algebra for Recursive Provenance

DOI	10.5281/zenodo.17908005

James Ross
Independent Researcher
ORCID: 0009-0006-0025-7801
License: CC BY 4.0 December 2025

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Overview

This repository contains the LaTeX source, figures, and compiled PDF for Paper I of the AIΩN Foundations Series.

The paper introduces WARP graphs (Worldline Algebra for Recursive Provenance) — a recursively defined graph-of-graphs object built from finitely nested typed open graphs. WARP graphs serve as the foundational state representation for the AIΩN computer, enabling deterministic multiway computation, holographic provenance, and worldline-level reasoning.

Paper I establishes the object.
Subsequent papers develop semantics, dynamics, and ethical implications on top of this foundation.

Specifically, Paper I develops:

• A formal inductive definition of WARP graphs
• An initial-algebra characterisation
• Morphisms, recursion principles, and depth/unfoldings
• Embeddings of ordinary graphs and hypergraphs
• The attachment / skeleton decomposition
• The category $WARP$

This paper is intended to be the canonical reference for the WARP graph construction.

Repository Contents

• paper/main.tex — Primary LaTeX manuscript
• paper/macros.tex — Command and notation definitions
• paper/diagrams.tex — TikZ diagrams and global styles
• paper/refs.bib — Bibliography
• paper/figures/ — Diagram assets
• pdf/ — Compiled PDF (release artifact)

Build Instructions

Requirements

• TeXLive or MiKTeX
• latexmk (recommended)

Build

make

The compiled paper will appear in ./pdf/.

AIΩN Foundations Series

This paper is the first of a six-paper foundational series:

1. WARP Graphs: A Worldline Algebra for Recursive Provenance (this repository)
2. WARP Graphs: Canonical State Evolution and Deterministic Worldlines
3. WARP Graphs: Computational Holography & Provenance Payloads
4. WARP Graphs: Rulial Distance & Observer Geometry
5. WARP Graphs: Ethics of Deterministic Replay & Provenance Sovereignty
6. The AIΩN Computer: Architecture & OS (JITOS)

License

This repository contains only the Paper I manuscript, figures, compiled PDF, and documentation.

© 2025 James Ross. Licensed under Creative Commons Attribution 4.0 (CC BY 4.0). See LICENSE for details.

The AIΩN runtime and JITOS software projects referenced by the paper are not part of this repository. Those codebases are licensed separately under the Apache License, Version 2.0.

More on AIΩN

For updates and related projects, see the main AIΩN repository: https://github.com/flyingrobots/aion