The Transformerless Geometric Foundation for Frontier AI
R4 Laboratories designs autoregressive geometric state models, exact addressed memory systems, and multiplier-free serving kernels. Engineered from fundamental non-Euclidean topology for ultra-low energy and frontier-class reasoning on consumer hardware.
Architecting Beyond Brute Force
Current deep learning scales quadratic matrix multiplication at immense energy expense. R4 Laboratories reconstructs artificial intelligence through algebraic topology, exact coordinate spaces, and discrete geometry.
Geometric Language Models (GLMs)
Autoregressive geometric state models that route through structured algebraic manifolds instead of dense quadratic self-attention layers. Token representations evolve as topological trajectories over fixed zeta and prime-address lattices.
Exact Addressed Memory & UOR
Universal Object Reference (UOR) addressing treats knowledge as invariant geometric coordinates. Eradicating probabilistic hallucination and attention decay by anchoring historical facts into addressed memory structures with verifiable provenance.
Paired Icosian & 4D Discrete Lattices
Utilizing the rich algebraic geometry of golden ratios φ, Hopf fibrations S³ → S², and 4-dimensional symmetry groups (H4 ⊕ φH4). Compute is mapped onto exact ring arithmetic and precomputed table lookups.
Autonomous Research Labs
Decentralized AI research nodes operating across multi-agent consensus protocols. Continuous peer-to-peer verification, automated hypothesis generation, and bitwise reproducible execution ledgers.
The Native Geometric Pipeline
A ground-up departure from dense transformer backbones — from raw tokens to served output.
Prime Coordinate Ingestion
Tokens mapped to exact prime addresses and fixed zeta-zero phases without semantic dilution.
R4/S3 Manifold Transition
State evolution across 4D hyperspheres, preserving chiral orientation and exact ring invariants.
Exact Addressed Memory
Deterministic coordinate traversal and retrieval across the Universal Object Reference space.
Multiplier-Free Serving
Final prediction executed through bounded routing, bitwise additions, shifts, and table lookups.
Public Research Repositories
Explore the active codebases, mathematical formalizations, and tools developed by R4 Laboratories.
uor-r4
Experimental autoregressive geometric state model with exact addressed memory and learned typed operators in Rust.
prime-router
Angular-manifold and prime-coordinate routing framework for high-dimensional semantic spaces.
uor-addr-1
Canonical content addressing standard for agent-produced content using RFC8785 canonical bytes.
uor-r4-wasm-chat
Interactive in-browser WebAssembly native geometric inference chat interface.
UOR-Framework
Formalization of the Universal Object Reference model and topological coordinate structures.
View All Repositories
Access our complete suite of research, benchmarks, and crates on GitHub.
Engage with R4 Laboratories
Whether you are interested in research collaborations, advisory, licensing native geometric model architectures, or institutional partnerships — reach out directly.