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.

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.

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.

Symbolic AIReasons with rulesStatistical AILearns from dataPhysical AIPerceives, decides, actsSymbolic AI + Statistical AI = Physical AI
Symbolic AIMachine, Factory, RobotAdFArithmetics of FormsStatistical AIAI Agents, LLM, LWMPhysical AI1. Rules transmitted to data processing2. Data enhanced with precision3. Data quality improves4. Rules are refined

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.

Trusted by World-Class Partners

CSA / ASC

Canadian Space Agency

Developed a robotic arm simulator for the International Space Station's Canadarm, used successfully for 6 years.

CERN

CERN

Collaborating on 4 projects including spatial intelligence for volumetric brain imaging and structural anomaly detection.

Spineart

Spineart

Creating real-time alignment solutions between 3D preoperative and 2D intraoperative imaging for spinal implants.

AOUSD

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.