TetraKlein: A Unified Architecture

TetraKlein is a unified computational, cryptographic, and extended-reality (XR) architecture developed by Baramay Station Research Inc., a Canadian non-profit research organization.
This repository publishes the mathematical framework, AIR constraint system, XR physics formulations, digital-twin convergence rules, and verification pipeline defining the TetraKlein system.

TetraKlein integrates:

• Post-quantum cryptography (Kyber, Dilithium, Module-LWE/SIS)
• Zero-knowledge proof systems (AIR, STARKs, IVC, folding, FRI)
• Verifiable compute engines (SP1, RISC Zero, Brevis, zkSync-derived provers)
• XR physics and rendering pipelines (TK-U, XR-TSU kernels, foveation models)
• Digital-Twin Convergence (DTC lineage, projection operators)
• Hypercube ledger topology (HBB, Recursive Tesseract Hashing)
• IPv6-native mesh identity and routing (Yggdrasil, PQC-authenticated overlays)
• Cross-layer AIR constraints enabling recursive multi-domain verification

This repository is intended for researchers, engineers, cryptographers, XR developers, and academic institutions looking to analyze, extend, or experimentally validate a unified verifiable-compute architecture.

The current version of the TetraKlein architecture is an early-stage, research-oriented framework. It is not a production system and makes no claims of operational readiness, security guarantees, clinical or industrial safety, or real-world deployment feasibility. All mathematical models, AIR constraints, XR physics bindings, digital-twin operators, and ledger constructs are subject to heavy scrutiny, independent validation, and long-term peer review. The material in this repository should be treated strictly as a research roadmap—a foundation for future work that will require extensive testing, reproducibility studies, formal verification, adversarial analysis, and multi-year refinement by the broader scientific and engineering community before any practical use is considered.

The TetraKlein Virtual Machine provides a deterministic, low-degree constrained execution environment:

• XR frame physics evolution
• pose + camera kinematics
• TSU-compatible energy constraints
• DTC projection
• hypercube-ledger synchronization
• ZK-friendly opcode semantics
• verifiable state transitions

All TK-VM semantics map directly into algebraic AIR constraints.

TetraKlein supports:

• AIR-constrained STARK proving
• recursive IVC frame folding
• multi-epoch ledger commitment
• verifiable rendering pipeline
• deterministic cross-domain proofs (XR → DTC → Ledger)

Every XR frame, physics update, and identity transition is provable.

Identity and routing combine:

• Kyber-1024 key-encapsulation
• Dilithium-V signatures
• MLWE/SIS identity kernels
• Yggdrasil IPv6 self-authenticating mesh
• PQC-bound routing and handshake protocol
• hypercube-coordinate ledger addressing

The ledger uses a hypercube topology:

• adjacency enforced by AIR constraints
• spectral operators (E1–E4)
• Recursive Tesseract Hashing
• multi-epoch finality and spectral stability
• provable routing correctness
• deterministic fragment propagation

The digital-twin framework provides:

• XR → DTC projection operator
• inverse-projection (Ledger → DTC → XR)
• multi-agent DTC coupling
• Lyapunov-style stability envelopes
• convergence-time bounding
• real-world sensor model coupling (non-invasive)

TetraKlein adopts a dual-license structure:

Creative Commons Attribution 4.0 (CC-BY-4.0)
All mathematical material, papers, equations, AIR tables, and technical documentation.

MIT License (simple, permissive)
Apache License 2.0 (patent-safe, industry standard)

This ensures maximum compatibility with:

• Ethereum / zkSync
• RISC Zero / SP1
• StarkWare-style STARK ecosystems
• academic reproduction
• open-source research

This repository includes the full, unmodified original paper:

“TetraKlein: A Post-Quantum, Zero-Knowledge, Multidimensional Cryptographic Network for Mid–21st Century Civilization Infrastructure”
Michael Tass MacDonald — November 22, 2025

This archival version is included as-is for historical reference.
It may contain:

• speculative or unverified early-stage ideas
• preliminary constructions
• non-peer-reviewed material
• conceptual frameworks later replaced or refined

The unified monograph supersedes this original document.

• Unified 1,600+ page architecture
• TK-VM execution model
• AIR tables (TK-U … TK-Z)
• PQC identity system
• XR physics + DTC
• Hypercube ledger + RTH
• Recursive folding pipeline (TK-Y / TK-Z)

• minimal TK-VM interpreter
• TK-W ledger sponge (Poseidon-style)
• hypercube router (TK-V)
• proving-fragment diffusion (TK-X)
• SP1 / RISC-Zero test harness

• OpenXR prototyping
• XR-physics frame pipeline
• real-time DTC–ledger synchronization

• Coq/Isabelle/HOL formalization
• independent reproducibility testing
• security analysis
• academic peer review and conference submissions

A full permanent Zenodo DOI will be provided

MacDonald, M. T. (2025). TetraKlein: A Unified Architecture. Baramay Station Research Inc. Public Edition. CC-BY-4.0 / MIT / Apache-2.0.

Baramay Station Research Inc.
Canadian Non-Profit R&D (Saskatchewan)
Director & Principal Investigator: Michael Tass MacDonald Contact

TetraKlein aims to advance:

• open, verifiable computation
• transparent scientific methodology
• reproducible XR and digital-twin research
• post-quantum cryptography
• zero-knowledge trust frameworks
• decentralized, identity-bound networks

This project is released to help researchers, developers, and institutions build provable, reliable, and safe computational systems for the coming decades.