A formal framework for deterministic, history-native computation.
Note
This repository is primarily a reference archive for the AIΩN Foundations papers; readers seeking an executable system should see JITOS.
Note
Pronounced EYE-on, rhymes with "lion"
This repository collects the AIΩN Foundations Series, a sequence of papers that establish a mathematical and architectural foundation for deterministic computation. The series develops, from first principles, a framework in which history is the primary representational artefact and state is derived as a materialised view.
We address a class of problems endemic to contemporary software systems: irreproducible builds, nondeterministic concurrency failures, and the absence of verifiable provenance for automated transformations. Our approach demonstrates that these pathologies are not inevitable features of complex systems, but consequences of an architectural decision—storing snapshots rather than transformations—that can be revisited.
The series proceeds incrementally. Each paper assumes familiarity with its predecessors but remains self-contained in its contributions. Papers I–IV establish the theoretical substrate; Papers V–VI extend the framework to ethical considerations and system architecture.
We contend that the fundamental unit of computational storage should be the transformation, not the state. When transformations are first-class and immutable, deterministic replay, time-travel debugging, and structural provenance emerge as natural consequences rather than heroic engineering efforts.
The AIΩN Foundations Series develops the formal machinery and architectural consequences required to make this inversion rigorous and practical.
| # | Title | Status | Contribution |
|---|---|---|---|
| I | A Worldline Algebra for Recursive Provenance | Published | Paper I introduces WARP graphs—finite directed multigraphs whose vertices and edges recursively carry attached WARP graphs—providing a minimal, well-founded "graphs all the way down" structure that unifies hierarchy, syntax, control flow, and provenance into a single algebraic object upon which the rest of the series builds. |
| II | Canonical State Evolution and Deterministic Worldlines | Published | Paper II equips WARP graphs with a deterministic concurrent operational semantics—based on double-pushout rewriting in an adhesive category of typed open graphs—proving that any scheduler-admissible batch of rewrites commits to the same successor state regardless of internal serialisation order, thereby grounding replay and provenance in a single tick-confluent execution model. |
| III | Computational Holography & Provenance Payloads | Published | Paper III formalises computational holography—proving that a deterministic WARP worldline's entire interior derivation is uniquely recoverable from a compact boundary encoding (initial state plus ordered tick patches), then develops practical machinery for slicing, branching, and multi-tick compression via wormholes. |
| IV | Rulial Distance & Observer Geometry | Published | Paper IV formalises observer geometry—modelling observers as resource-bounded functors from rewriting histories to trace spaces, introducing a rulial distance that measures the MDL-regularised cost of translating between descriptions, and grounding the Chronos–Kairos–Aion time triad—thereby providing a computable notion of frame separation that clarifies abstraction, auditability, and explainability trade-offs. |
| V | Ethics & Sovereignty | Draft | Addresses provenance, accountability, computational agency, and fork/termination responsibility. COMING SOON |
| VI | Architecture & Operating System | Draft | Specifies JITOS, a causal operating system defining the execution model, observer interface, and kernel semantics implied by the theory. COMING SOON |
@misc{ross2025aion,
author = {Ross, James},
title = {The {AIΩN} Foundations Series},
year = {2025},
publisher = {Zenodo},
note = {Papers I--VI}
}
CΩMPUTER is the synthesis work—a comprehensive manuscript that takes the formal machinery developed across the AIΩN Foundations Series and pushes it to its philosophical and architectural limit.
The central provocation is simple but immodest: computation is not something we invented to model reality; computation is the base reality, and what we call physics, cognition, and causality are projections—what certain computations look like from the inside, under resource constraints, to observers embedded within them.
The book constructs this claim carefully. It begins with WARP graphs as the ontological primitive: directed multigraphs whose nodes and edges recursively contain further graphs, rules, and meta-structure. There is no bottom layer of "atoms" or "bits"—only structure that, when you zoom in, reveals more structure. Double-pushout rewriting becomes the sole dynamical law: no differential equations, no instruction pointers, just local pattern-matching and graph surgery, applied everywhere, all at once, with conflicts resolved deterministically.
From this foundation emerges MRMW—the Multi-Rule Multi-World space—a geometry not of points and distances but of universes and their histories. Every possible rewrite sequence, every branch not taken, every counterfactual—all coexist as structure. What we experience as "the present" is a cross-section; what we call "physics" is a particularly stable, low-entropy region of this space (CΩSMOS). Superposition, interference, measurement collapse—these aren't quantum mysteries bolted onto classical intuition but natural consequences of how rewrite bundles interact and how observers, themselves embedded computations, must commit to consistent views.
The practical payoff is a new class of machines: multiversal computers that operate not on single execution traces but on families of universes. Time-travel debuggers that navigate worldlines. Counterfactual engines that ask "what if we had rewritten differently?" Adversarial universe generators that stress-test systems against entire possibility spaces. Cross-world optimisers that search not just parameter spaces but rule spaces.
CΩMPUTER also confronts what this means for intelligence and ethics. If minds are geometry-aware navigators of MRMW—agents that model, predict, and steer through branching possibility—then intelligence is not a property of biological neurons or silicon but a dynamical pattern that can occur anywhere sufficient structure supports it. And if machines can create, fork, merge, and terminate entire computational worlds, ethics can no longer treat "the universe" as a fixed stage. We must develop frameworks for responsibility over worlds, not just actions within them.
The book is not an introduction, and does not attempt to be. It assumes comfort with category theory, graph rewriting, and the vertigo that comes from taking "graphs all the way down" seriously as an engineering constraint. It is intended for those who suspect that computer science, physics, and AI are three dialects of the same language—and who want a proposal for what that language might be.
Where the AIΩN Foundations Series becomes executable.
Our computers are modeled after a system invented in the 1940s to simulate working alone at a desk job. The file system, folders, recycling bin. CRUD. Debugging. “Works on my machine”. Let’s be honest: none of this really scales beyond one user. It’s no wonder we are plagued by concurrency issues when we are stuck using a system invented before the internet.
What if we reimagine how computers work? Let's build them from the ground up to solve today’s challenges: concurrency, transparency, and deterministic reproducibility. Let’s reimagine debugging by designing auditing that doesn’t just record what, but why and how something happened, as well as what else could have happened?
Introducing: JITOS —- a causal operating system that computes deterministic worldlines using WARP graph rewriting to capture complete system-wide provenance by construction. Every run produces holographic artifacts that are fully auditable and verifiable. JITOS turns computers from opaque black-boxes into honest, bit-perfect, replayable, reproducible, transparent, rewindable, forkable glass-boxes.
JITOS is not a thought experiment. It is real, working software that demonstrates the AIΩN execution model, with a deterministic WARP graph rewriting kernel, a browser-based WASM runtime, and real performance benchmarks. The JITOS project serves as the canonical reference implementation and living design record for the AIΩN system.
Learn more about JITOS –– try it in your browser!
AIΩN Foundations Series © 2025 by James Ross is licensed under Creative Commons Attribution 4.0 (CC BY 4.0).
CΩMPUTER © 2025 by James Ross is licensed under Creative Commons Attribution 4.0 (CC BY 4.0).
JITOS © 2025 by James Ross is a software project referenced by the papers, which is not part of this repository. This separate codebase is licensed under the Apache License, Version 2.0 OR MIND-UCAL.
NOTE: In short: you may freely use the theory, papers, and documentation without adopting MIND-UCAL; MIND-UCAL applies only to derivative ethical commitments, not technical use.