DOI	10.5281/zenodo.17934512

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

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

Paper I introduced WARP graphs as a well-founded “graphs all the way down” state object: a finite skeleton whose vertices and edges carry recursively nested WARP attachments. Paper II provides the dynamics by equipping WARP states with an operational semantics based on double-pushout rewriting with interfaces (DPOI) over a category of typed open graphs.

At a high level, the paper treats computation as a two-plane process:

• The skeleton plane performs structural rewrites of a typed open graph G ∈ OGraph_T.
• The attachment plane performs local rewrites inside the attachments α, β (without changing G).

The central results and core objects are:

• WARP states as two-plane objects U = (G; α, β), with attachments over vertices and edges.
• Ticks as the unit of concurrency: a tick commits a scheduler-selected batch of independent skeleton rewrites together with attachment-plane updates.
• A footprint-based independence discipline (delete/use sets) for deciding when skeleton matches can be batched.
• Tick-level confluence on the skeleton plane: within a tick, serialisation order does not change the committed successor (up to typed open graph isomorphism).
• Two-plane commutation: attachment updates commute with skeleton publication up to canonical transport along preserved structure (formalised via a projection π: WState → OGraph_T equipped with chosen reindexing/transport functors τ_g).
• Tick receipts and a tick-event poset: deterministic conflict resolution is recorded as a partial order over candidate events (accepted vs rejected), serving as a provenance-ready audit object for Paper III.

When the scheduler is a total function of state, these ingredients compose into deterministic worldlines: the ℕ-indexed sequence of committed tick transitions.

• paper/main.tex — Primary LaTeX manuscript (Paper II)
• paper/aion.cls — AIΩN Foundations class file
• paper/macros.tex — Notation and helper macros
• paper/diagrams.tex — TikZ diagrams and global styles
• paper/refs.bib — Bibliography
• Makefile — Convenience build (latexmk + jobname/output directory)
• pdf/ — Compiled PDF + LaTeX build artifacts

Requires:

• TeX Live or MiKTeX
• latexmk recommended (used by the Makefile)

Build from the repo root with:

make

Clean + rebuild:

make clean
make

The compiled paper appears in ./pdf/ as aion-paper-02-canonical-state-evolution-deterministic-worldlines.pdf.

This paper is part of a six-paper foundational series:

1. WARP Graphs: A Worldline Algebra for Recursive Provenance
2. WARP Graphs: Canonical State Evolution and Deterministic Worldlines (this repo)
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)

This repository contains the Paper II manuscript, figures, compiled PDF, and documentation. These materials are © 2025 James Ross and 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; they live in separate repositories under their own licenses.

For updates, see the main AIΩN repository:
github.com/flyingrobots/aion