Pioneering
Verifiable Spatial AI
Verifiable Spatial AI
The New AI Frontier:
From Language to Spatial Intelligence
From Language to Spatial Intelligence
The AI industry is at a major inflection point, shifting from mastering language (LLMs) to solving the far more complex challenge of spatial intelligence.
The Challenge:
Spatial intelligence is the ability to perceive, understand, reason about, and interact with the 3D world. This capability is fundamental for the next wave of AI in robotics, drug design, and autonomous systems.
The Emergence of LWMs:
Large World Models (LWMs) are emerging to create interactive virtual worlds for training AI agents.
The Critical Gap:
While current generative models create photorealistic worlds, they cannot guarantee physical consistency, a "fatal flaw" for high-stakes applications where mathematical precision and verifiability are required.
This gap between plausible appearance and verifiable reality is the frontier we conquer.
SGDL vs. World Models: Logic, Not Prediction
World models simulate reality. SGDL provides the logical foundation for it. This is a fundamental difference in approach and capability.
World Models (e.g., World Labs)
Approach: Use massive neural networks to learn a predictive, statistical model of the world from data.
Function: They are powerful simulators that make educated guesses about what might happen next.
Limitation: Their understanding is probabilistic and approximate. They are powerful guessing engines.
SGDL AI
Approach: Use a formal language and the "Arithmetic of Forms" to define space with exact mathematical equations.
Function: It is a perspective engine that operates on verifiable, logical truth.
Advantage: Our system provides absolute, mathematical certainty. It doesn't guess; it proves.
The Bottom Line
We are not building a better simulator. We are building the verifiable, logical framework that all intelligent systems will require to operate safely and reliably in the real world.
Our Technological Foundation
The Foundational Discovery: The SGDL Exolanguage
Our entire ecosystem is built on the Spatial Geometry Description Language (SGDL), the first exolanguage designed for machines to reason about space. It is the breakthrough that maps topology and geometry directly to logic, enabling our three technological pillars.
Our Three Pillars:
Pillar 1: The Arithmetic of Forms
A discovered, mathematically exact system that replaces approximation with verifiable logic. It allows us to perform arithmetic on geometry itself.
Pillar 2: Boustrophedonic Indexing
A novel method using space-filling curves that enables instantaneous data retrieval and analysis without searching.
Pillar 3: Viator & The Tool Ecosystem
The practical software that applies our core technology, including our LLM Connector and Perspective toolkit for enterprise use.
Problem, Opportunity & Solution
The Problem
The current AI landscape, dominated by LLMs, lacks true spatial intelligence. Generative models can create photorealistic worlds but cannot guarantee physical consistency—a fatal flaw for high-stakes applications.
The Opportunity
This creates a multi-billion dollar market for a platform that provides the "reasoning layer" for AI , enabling machines to acquire unprecedented capabilities in autonomous learning and cross-robot transfer learning.
Our Solution
SGDL AI's cloud-based platform delivers a reasoning and indexing layer as a service. We give control, performance, and cost-savings back to the customer by turning their expensive database into a simple, commoditized storage layer.
Traction & Validation
Mission-Critical Validation:
Our technology is battle-tested and proven in environments where failure is not an option, including International Space Station (ISS) with the Canadian Space Agency and the Mars Rover mission.
x6 Cost Reduction:
We secured a paid Proof-of-Concept (PoC) with swiss pharmaceutical leader , to demonstrate a six-fold cost reduction in vector search.
Prestigious Recognition:
We are the recipient of the Cosmos Prize at Pamoramai 2025 and were invited to join the official Swiss delegation to the RAISE Summit in Paris.
Landmark Public Launch (July 7-11, 2025):
Our official launch takes place in a matter of days at the AI for Good Global Summit in Geneva.
We unveil our full AI ecosystem and officially launch our program for research centers and universities.
Our Vision: The "Intel Inside" of Spatial Intelligence
The Goal: Become the Industry Standard
Our vision is to become the indispensable reasoning and indexing framework for the spatial and enterprise AI ecosystems. We aim to be the de facto standard for verifying logical integrity in any AI system that interacts with the physical world.
The Philosophy: Reverse Learning
As Founder & CEO Alex Kummerman explains, "The idea of SGDL is to establish a reverse learning process (eXplainable AI) between the machine and the human".
The Impact:
A New Foundation for AI We are not just building a product; we are enabling a new paradigm of intelligent interaction with data. We are building a more reliable and intelligent foundation for AI itself.
The New AI Frontier: Spatial Intelligence and World Models
The Paradigm Shift: From Language to Spatial Intelligence
The AI industry is at a major inflection point, shifting from mastering language (LLMs) to solving a far more complex challenge: spatial intelligence.
This is the ability to perceive, understand, reason about, and interact with the 3D world. This capability is fundamental to unlocking AI applications that operate in the physical world, from robotics and drug design to the emerging low-altitude economy.
The Emergence of Large World Models (LWMs)
LWMs are generative AI systems designed to learn internal representations of real-world environments. They aim to create interactive virtual representations of the world for training and testing AI agents in robotics, autonomous vehicles, and digital twins.
The Critical Gap: The Need for Verifiability and Ground Truth
While current generative LWMs achieve stunning photorealism, they are probabilistic and lack ground truth. For highstakes applications, "plausible" is not enough; mathematical precision, logical consistency, and verifiability are required. This is the gap SGDL AI fills. We are not a competitor to generative LWMs; we are a necessary complement, providing the deterministic, verifiable "fact-checker for physics" that anchors these models in reality.
SGDL vs. World Models: Logic, Not Prediction
World models simulate reality. SGDL provides the logical foundation for it. This is a fundamental difference in approach and capability.
World Models (e.g., World Labs)
Approach: Use massive neural networks to learn a predictive, statistical model of the world from data.
Function: They are powerful simulators that make educated guesses about what might happen next.
Limitation: Their understanding is probabilistic and approximate. They are powerful guessing engines.
SGDL AI
Approach: Use a formal language and the "Arithmetic of Forms" to define space with exact mathematical equations.
Function: It is a perspective engine that operates on verifiable, logical truth.
Advantage: Our system provides absolute, mathematical certainty. It doesn't guess; it proves.
The Bottom Line
We are not building a better simulator. We are building the verifiable, logical framework that all intelligent systems will require to operate safely and reliably in the real world.
SGDL AI + LLMs = Spatial Intelligence
LMs generate SGDL code; SGDL executes symbolic-geometric logic.
An LLM produces SGDL non anthropomorphic code that encodes volume, contact constraints, and geometric continuity — entirely within a symbolic volumic expression. This demonstrates how SGDL represents not just shapes, but intelligent forms — ones that carry structure, behavior, and algebraic definition.
LLM Generates SGDL Code that allows machines to understand and reason about multidimensional forms
Why it matters:• Enables symbolic manipulation of physical structure• Supports generative, certifiable design processes• Opens the door to real-time neuro-symbolic agents reasoning in physical space
Target Markets:
Where Precision is Mission-Critical
Where Precision is Mission-Critical
SGDL AI is initially focusing on three primary verticals where our value proposition is immediate and substantial. Our position at the intersection of AI, robotics, and biotech aligns perfectly with Switzerland's strongest deep tech verticals, which are attracting significant capital inflows.
Pharma & Genomics
AI-driven drug discovery with 30% CAGR
Space-Tech & Robotics
Mission-critical physical reasoning
Enterprise Databases
Adaptive indexing for performance
Dealing with Space
Pharma and Genomics (Biotech)
Modern pharmaceutical R&D is inherently three-dimensional. Our platform offers a powerful new capability: performing symbolic geometric reasoning on biological structures.
Our PoC with leading swiss pharma is focused on RNA-Proteomics computing, and shall prove its value in a market for AI-driven drug discovery growing at 30% CAGR. This success aims to fit the forecast that the integration of AI/ML with TechBio will drive the next wave of breakthroughs in the Swiss ecosystem.
Space-Tech and Robotics
In aerospace, defense, and advanced robotics, the ability for an AI to reason about the physical environment is mission-critical. Our technology directly addresses the need for a formal geometric reasoning framework to solve complex industrial problems in scientific simulation. Its proven use in mission simulation software for On Orbit Real-Time Simulation of the ISS Mobile Servicing System as well as for the Mars Rover serves as the ultimate validation of its reliability.
Mission-Critical Applications
Our technology has been deployed in environments where failure is not an option, including the International Space Station International Space Station and the Mars Rover mission.
Formal Geometric Logic & Reasoning
We provide the framework needed to solve complex industrial problems in scientific simulation with logical and mathematical precision.
Ultimate Validation
The use of our technology in space exploration serves as the strongest possible proof of its reliability and precision.
Enterprise Databases &
Adaptive Indexing
Adaptive Indexing
The Pain
Large enterprises are trapped by the limitations of their database vendors. Every complex, multi-turn query forces a fresh, brute-force scan of massive indexes, causing latency to skyrocket and exploding compute bills from providers like Oracle. This performance wall is a major friction point in modern data-driven operations.
The Cure
Our Perspective toolkit provides the cure. Instead of relying on the database vendor's inefficient query planner, our tools analyze the query and use our core technology to build the perfect, optimal index on-the-fly. It speaks SQL, vectors, and graphs alike, creating a unified logical layer. This eliminates costly scans and dramatically reduces latency.
The Proof & Vision
This technology is not theoretical. The same principles allowed us to cut vector-search costs six-fold in our biopharma PoC. The core Arithmetic of Forms is trusted for precision On Orbit Real-Time Simulation of the ISS Mobile Servicing System. Our vision is to drop the Perspective toolkit between an enterprise's applications and their database backend. This turns the expensive database into a simple, commoditized storage layer, giving control, performance, and cost-savings back to the customer.
The SGDL AI Ecosystem: A Symbolic Framework for Verifiable World Models
Our ecosystem provides the essential tools for building physically grounded and logically coherent Large World Models. By connecting to LLMs with symbolic reasoning's logical precision, we create AI systems that can truly understand and interact with the physical world.
Arithmetic of Forms
Exact mathematical and logical representation of geometry
Boustrophedonic Indexing
Efficient multi-dimensional data access
SGDL Exolanguage
Universal language for spatial reasoning
Perspective Toolkit
Practical implementation for enterprises
Onto semantic space
The Foundational Layer: A History of Rigorous Mathematical Innovation
SGDL AI's technology is the culmination of a century of progress in mathematical logic and computability theory. Our work stands on the shoulders of giants like Thoralf Skolem, Alonzo Church, and Kurt Gödel, whose foundational inquiries into the nature of proof, computation, and formal systems created the intellectual bedrock for our approach.
Skolem's Finitism
Work on recursive functions championed a constructive, computable approach to mathematics, seeking to avoid the paradoxes of the infinite. This aligns directly with our goal of creating a finite, exact, and computable system for reasoning about forms.
Gödel's Arithmetization
Showed that complex logical statements could be encoded into unique numbers, allowing a system to reason about its own structure. This revolutionary idea of making logic computable is the philosophical ancestor of our ability to arithmetise geometry.
Church's Lambda Calculus
Defined computation in terms of pure function abstraction and application, proving that complex operations could be built from simple, elegant rules. This inspires our representation of forms not as static data, but as dynamic mathematical functions.
Discovery of the SGDL Exolanguage
In his Ph.D. thesis at the University of Montreal, Dr. Jean-François Rotgé discovers the mapping between topology, projective geometry on the one hand, and logic and primitive recursive functions on the other. These results are formalized in the Arithmetics of Forms system and the SGDL language: a geometric extension of the Lambda calculus. These results make it possible to transform the representation and control of Large World models into intelligent and logical machine expressions.
By synthesizing these historical insights, SGDL AI has developed a platform built on three distinct but synergistic technological pillars.
The First Pillar: The Arithmetic of Forms
This is our foundational logic. It addresses the core problem that all modern 3D systems are built on approximations. Our Arithmetic of Forms replaces approximation with mathematical exactitude.
Exact Representation
We do not draw a shape; we define it with a precise mathematical equation. This moves from an inexact shape to an exact Form.
Projective Geometry
By grounding our calculations in projective geometry, we eliminate the ambiguities and errors (like division-by-zero) that plague traditional computational geometry, ensuring our calculations are always robust and correct.
Symbolic Reasoning
Because a Form is an equation, we perform arithmetic on it and embed logical rules and physical properties directly into its definition. This is the heart of our symbolic AI capability.
The Second Pillar: Boustrophedonic Geometry, Encoding and Indexing
Having an exact Form is not enough; one must be able to navigate and query it efficiently. This is our second, more recent, and commercially critical innovation. We call it Boustrophedonic Geometry, named after the "as the ox plows" path of our indexing method.
Space-Filling Curves and Metacurves
We employ a new form of advanced space-filling curves called Metacurves, that are newly discovered to map a multi-dimensional Form onto a single, one-dimensional index.
We encode the data in "bigNum" to allow arithmetic processing.
We encode the data in "bigNum" to allow arithmetic processing.
Bijective & Instantaneous Access
This mapping is bijective, meaning every point in the N-dimensional space corresponds to a unique point on the 1D line, and vice-versa. The implication is groundbreaking : to find any data point, we no longer need to search. We calculate its 1D index and go there directly.
Indexing Heterogeneous Data
This method is not limited to 3D. We can index hyper-volumes containing any number of dimensions, allowing us to perform incredibly fast and complex queries on heterogeneous datasets.
The Third Pillar: The Viator Ecosystem
This is where our foundational technology becomes a practical solution. The Viator ecosystem provides the software tools for developers and machines to apply our core logic to solve real-world problems.
Viator :
The core engine for creating, manipulating, and reasoning about Forms using our Arithmetic of Forms navigator.
Perspective Toolkit:
The commercially critical implementation for enterprise databases. It analyzes complex queries and builds the perfect index on-the-fly, eliminating costly database scans and dramatically reducing latency.
LLM Connector:
A crucial interface that combines the strengths of our symbolic, verifiable logic with the pattern-recognition capabilities of modern Large Language Models (LLMs).
Configurators & Viewers:
A suite of tools, including a 3D configurator and a WebGL viewer, designed to visualize complex spatial structures and space-filling curves without requiring intermediate formats.
The Synthesis: The SGDL Ecosystem
The combination of these three pillars creates our product: an ecosystem of tools that provides the missing logical backbone to modern Large Language Models.
A query is no longer a search for "nearby vectors in a cube"; it becomes an exact geometric Form that carves out the precise, logically defined data required from the data space. This is the foundation of our symbolic offering.
A query is no longer a search for "nearby vectors in a cube"; it becomes an exact geometric Form that carves out the precise, logically defined data required from the data space. This is the foundation of our symbolic offering.
LLM Connector
Leverages pattern recognition and learning capabilities of modern Large Language AI
Symbolic Component
Provides logical reasoning and verifiable operations on data
Integrated Framework
Combines the strengths of both approaches for robust AI systems
The SGDL Exolanguage and Adoption Strategy
The entire ecosystem is built around the Spatial Geometry Description Language (SGDL), the first exolanguage designed for machines to reason about space. It is a universal language dedicated to the intelligence of modeling, simulation, and communication of geometric information.
Go-to-Market Strategy
Drive Grassroots Adoption
By empowering researchers and students, we aim to establish SGDL as the standard for spatial reasoning, building a new generation of developers who think in our framework.
Foster a Community
An open approach will create a vibrant ecosystem of users who can share knowledge, develop novel applications, and provide invaluable feedback, accelerating the maturation of our tools.
Validate and Expand Use Cases
The academic community will explore applications beyond our initial target markets, uncovering new opportunities and providing third-party validation of our technology's capabilities.
This strategy has been officially launched at the AI for Good Global Summit, marking our commitment to building an open and collaborative foundation for the future of spatial intelligence.
Team
SGDL AI brings together world-class experts in AI, mathematics, computer science, and business development. Our team combines deep technical knowledge with proven commercial experience, positioning us to deliver on our ambitious vision.
Leadership Team
Experienced executives with proven track records in scaling deep-tech ventures
Internal Scientific Team
Pioneering researchers and engineers developing our core technology
Innovation Focus
Dedicated to pushing the boundaries of what AI can accomplish
Leadership Team
Alex Kummerman
Founder & CEO
A serial AI entrepreneur with a proven track record of building and scaling deep-tech companies. Alex co-invented the SGDL AI ecosystem and drives the strategic vision and commercial execution for SGDL AI.
Dr. Jean-François Rotgé
Founder & Chief Scientist
The inventor of the Arithmetic of Forms and Boustrophedonic Geometry. Dr. Rotgé is a pioneer of symbolic geometric modeling and continues to guide the company's fundamental R&D.
Dr. Stefano Maddalena
Head of Legal
With a PhD in law, and strong focus on data and entreprise solutions, and business development. He now leads our Administrative and corporate development efforts.
Laurent Raeber
(CIO)
Leads the innovation strategy with experience in positioning and marketing deep-tech technologies.
Marc Aubert
Chief Operating Officer (COO)
Brings deep operational and organizational development and communication expertise, ensuring SGDL AI's operational efficiency.
Dr. Paul-Olivier Dehaye
Chief AI Scientist
With a PhD in mathematics from Stanford, computer science, and AI, bringing crucial interdisciplinary expertise.
Laurent Daniel, MSc
AI Engineer
Brings essential expertise to our engineering team, focusing on the development and optimization of our spatial reasoning capabilities.
Michel Bernard
Head of industrial parnerships
Focused on industrial junction and acceptability — showing how our technology can work within existing CAD, BIM, and OpenUSD systems.
Jérémie Farret, Dipl. Eng.
AI/LLMOps & Standardization
Expert Sr.
Expert Sr.
A key member of our technical team, specializing in the integration of Large Language Models (LLMs) and technical expert in Standardization. He has years of experience in International Standards (ASTM / ISO) and Standards Council of Canada. His AI & LLM expertise is core to our platform's generative interface.
Competitive Landscape and Strategic Positioning
Our competitive advantage is durable, rooted in a fundamental philosophical difference that translates into a distinct class of problems we can solve.
Proprietary IP and Patents
Our core AoF and boustrophedonic geometry methods are protected by issued patents, a strong legal barrier to entry.
First-Mover in Verifiable AI
While others pioneer generative spatial AI, we are the first to market with a scalable platform for verifiable spatial intelligence.
Enabling New Capabilities
Our platform allows machines to acquire unprecedented capabilities in autonomous learning and cross-robot transfer learning.
Deep Team Expertise
Our team includes the inventors of the core technology and possesses unique, hard-won experience.
Traction and Roadmap
SGDL AI has achieved significant progress in validating our technology and market demand.
Key Traction and Announcements
Prestigious Awards and Recognition
Recipient of the Cosmos Prize at Pamoramai 2025 and invited to the official Swiss delegation at the RAISE Summit in Paris.
Commercial Validation
Paid PoC with a leading Swiss pharmaceutical company.
High-Profile Public Launch
Our official launch was at the AI for Good Global Summit (ITU, Geneva, July 2025). It has been a landmark event where we unveild our new AI ecosystem built around the SGDL exolanguage, and presented the first physical spatial structures generated by our tools, exhibited three original artistic forms designed by our AI. This event has also been the mark the official launch of our program for research centers and university networks.
Our Vision: The "Intel Inside" of Spatial Intelligence
Our goal is to establish the SGDL platform as the essential, ubiquitous framework for any AI system that reasons about the physical world or complex data.
For AI Systems:
We will become the de facto standard for verifying the logical integrity of spatial and enterprise AI.
For the Industry:
We are not just building another application; we are building a more reliable and intelligent foundation for AI itself
An Invitation to Build the Future of AI
Our official was launch at the AI for Good Global Summit From July 7-11, 2025, marking our public debut and the start of our global community-building initiative.
Contact us :
SGDL AI
Alex Kummerman
Avenue Eugène-Pittard 56
1206 Geneva
Switzerland
Alex Kummerman
Avenue Eugène-Pittard 56
1206 Geneva
Switzerland
Connect with us on : Linkedin
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