SLWM
The world model. It writes an exact world from these operations and proves what it says.
When synthetic and logical models meet natural data
Primitive Recursive Protocol
for Multiscale World Models
SGDL is a formal exolanguage designed for deterministic communication between artificial intelligence and autonomous robotic systems, encoding environmental architectures from the planetary scale to the molecular scale as primitive recursive functions.
“When synthetic and logical data meet natural data”
A primitive recursive protocol for multi-scale world models
SGDL is a formal exolanguage for deterministic communication between artificial intelligence and autonomous robotic systems, encoding environmental architectures from the planetary scale to the molecular scale as primitive recursive functions.
SLWM · ONE EXOLANGUAGE, EVERY SCALE
From the planetary scale to the molecular scale.
The SLWM — the world model — writes the planet, the city, the engine and the molecule in one exolanguage: non-anthropomorphic, made for machines, built on primitive recursive functions. Where neuralese produces statistical approximations, it states invariant mathematical truths. The gold thread is that expression, writing each scale on a grid of integers that never moves.
The SLWM plate, alive in three dimensions: a turning wireframe planet with a satellite in orbit, a city of exact solids where a drone circles inside its safety bubble, an engine whose gears mesh and turn, a spinning molecular lattice with an electron orbit — side by side on one grid of integers, and a single gold thread writes itself from the planet to the lattice, then returns from the molecule to the planet, igniting and extinguishing a node at each scale, ten million metres down to one nanometre and back.
SGDL+ARIADNE GROUP · GENEVA · MONTREAL
One group, one intellectual property: exact geometry, patented, standardized.
SGDL Innovation SA holds the SGDL language — Spatial General Descriptive Language —, its Gray metacurves and its Arithmetics of Forms: a way of writing space in integers, where a solid is an expression, where a point is interior, boundary or exterior, and where the computation produces its proof with its result. The work is five operations. The intellectual property is built on them. SGDL Innovation SA, in Geneva, and Ariadne Geometry Inc., in Montreal, hold it.
WHAT WE DO
Five operations. The intellectual property is built on them.
Modelling, simulation, indexation, encryption and communication of spatial information. Twenty-one patents, filed as three families, serve these five. How the assets sit on them.
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01 Modelling
A solid is an expression. A point is interior, boundary or exterior, written in integers. The encoding family and the Arithmetics of Forms are this writing.
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02 Simulation
The same expression is run. The result is the computation, from the planetary scale to the molecular scale.
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03 Indexation
Gray metacurves give every cell one address. A query follows the space, or the data. The taxonomy.
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04 Encryption
A signal is scrambled along the same curve that addresses the space. That is the image-and-encryption family.
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05 Communication
Machines describe objects and spatial constraints to each other in the exolanguage, independent of any one model.
PRODUCTS
The SLWM and WMCP apply modelling, simulation, indexation, encryption and communication.
These are products, not the operations themselves. A result can be proved in Lean and shown as an image. Each result carries a certificate of computation.
WMCP
The protocol. A language model asks a spatial question and receives a computation.
Held.
21 patents, filed as three families — encoding, n-dimensional indexing, image and encryption — and built on five operations: modelling, simulation, indexation, encryption and communication.
Recognized.
Since MPEG-4 AFX (ISO/IEC 14496-16, 2003; synthetic and logical data in 2006): the Alliance for OpenUSD, the Open Geospatial Consortium, Khronos, and ISO/ASTM 52915. The contribution is the interface. The mechanism stays patented.
Published.
A thirty-year theory — the Arithmetics of Forms (thesis, Université de Montréal, 1997), SGDL-Scheme (2000), the SGDLscript manual (2003), the exolanguage charter — and 1,962 kernel theorems (2026), verified by Lean 4, which a third party replays with one command.
TWO INTERACTIVE CASE STUDIES
Run the operations yourself.
Two studies computed on real data. Each one runs in the page: move a point, move an error, and read what the exact computation answers.
Interactive · Indexation
A 10 m tile on a round Earth.
A 10 m tile is not 10 m at the pole, and two neighbouring grids do not agree at their seam. One Gray metacurve walks the six faces of the cube and gives every cell one address, from Geneva to Svalbard.
- Move a point from Geneva to the pole
- Pull the cube into the sphere
- Walk the index across the six faces
Interactive · Modelling · Simulation
The scanner on the radiograph, to the proven millimetre.
A pre-operative CT registered on an intra-operative radiograph: six exact numbers, a bounded error, and a Lean verdict that certifies the pose or refuses it. Twelve real cases, replayable.
- Blend measurement and model
- Move the error by hand
- Watch the certificate decide
Four fields
How to provide spatial truth to an AI. Five ways were tried. One is integer-exact. Four fields are written on it.
Low-altitude economy
Corridors and exclusion volumes as named solids, from the tunnel to the air.
Planetary
Exact terrain and GNSS-free autonomy, anchored to public elevation models.
GEO-TRUST-SPACE
Observational data, filtered by exact solids an AI can verify.
Mining 4.0
Zone entry is a ternary verdict: interior, frontier or exterior.
Corporate development, strategic partnerships, institutions, press.
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