The Path to Physical AI
sgdl bridges the gap between symbolic reasoning and statistical learning, enabling AI to perceive, decide, and act in the real world.
Why sgdl
A Foundation Unlike Any Other
40 Years of R&D
Founded on Jean-François Rotgé's doctoral thesis on the Arithmetics of Forms, sgdl has built a comprehensive mathematical framework over four decades of continuous research.
21 Interconnected Patents
A mature portfolio of 21 interconnected patents covering spatial encoding, volumetric computation, and cryptographic applications — forming an interlocking fortress of intellectual property ready for industrial deployment.
CPU-Native & Zero Hallucination
Unlike GPU-dependent statistical approaches, sgdl runs on standard CPUs with deterministic results — 100% mathematically validated, zero approximation.
The Paradigm Shift
From Prediction to Action
The AI landscape is evolving from systems that predict to systems that act. Physical AI requires machines that can perceive environments, make precise decisions, and interact with the real world — from autonomous vehicles and surgical robots to synthetic cities, low-altitude economy, and robotic teleoperation.
The Virtuous Link
Connecting Rules and Data
The Arithmetics of Forms translates physical objects into high-precision BigNums, creating a permanent, self-feeding communication cycle between symbolic rules and statistical data.
Proof of Traction
Trusted by World-Class Partners
Canadian Space Agency
Developed a robotic arm simulator for the International Space Station's Canadarm, used successfully for 6 years.
CERN
Collaborating on 4 projects including spatial intelligence for volumetric brain imaging and structural anomaly detection.
Spineart
Creating real-time alignment solutions between 3D preoperative and 2D intraoperative imaging for spinal implants.
AOUSD
Contributing non-anthropomorphic spatial reasoning expertise to advance open standards for 3D simulations and AI-driven workflows, alongside NVIDIA, Apple, Amazon.
Ready to explore the mathematics of Physical AI?
Learn how sgdl's Arithmetics of Forms can power your next breakthrough.