INTELLECTUAL PROPERTY
The group models, simulates, indexes, encrypts and communicates spatial information. Twenty-one patents, filed as three families — encoding, n-dimensional indexing, image and encryption — are built on that work. The documents are available to investors under a confidentiality agreement.
The patent factory writes applicative intellectual property: patents specific to one field, which may be assigned or licensed in that field. SGDL Innovation SA holds the generalizing intellectual property. Those patents remain the technological asset.
A solid is written as an expression. A point is interior, boundary or exterior. The Arithmetics of Forms (Rotgé, Université de Montréal, 1997) is this writing. The encoding family (2011), held by Parallel Geometry Inc. (Ariadne Geometry), codes a space as a sequence of integers that preserves neighbourhood. An examiner has cited it in the file of another applicant.
The same expression is evaluated. The run goes from the planetary scale to the molecular scale. Simulation uses the encoding: there is no second geometry for the run.
N-dimensional indexing by metacurves. Each cell receives one address, contiguity is kept, and counts are exact. Held by SGDL Innovation SA. Gray metacurves, 2025–2026: a method and system for indexing an n-dimensional object. International examination recognized the novelty and inventive step of the claims. The encoding family is the basis of the index. The taxonomy is set out with the use cases.
Image and encryption. The same geometry renders an image to the byte and scrambles a signal along a space-filling curve. Held by SGDL Innovation SA. Filed on 27 October 2022, published on 27 April 2024: a method and system for generating an image and using it to encrypt information. Signing an access is one use — the image is shown, the signature stays private. Cited by the patent office of another country in the files of national applicants.
The exolanguage: machines describe objects and spatial constraints in one language, independent of any one model. Published as a charter (2026), and carried since MPEG-4 AFX, where synthetic and logical data entered in 2006. The mechanism stays patented.
The theory is published. The application is protected. Indexation, the taxonomy of Gray metacurves, is explained with the use cases. Primitive recursive functions, and the lambda calculus that writes them, are set out on that page too.
One geometry, carried where each field writes its interface. The contribution is that interface: how to describe, query and certify an exact solid. The patented mechanism stays out of the text. No contribution commits a licence.
| Body | Since | What is carried there |
|---|---|---|
| ISO/IEC MPEG-4 AFX | 2003 | First inclusion in ISO/IEC 14496-16. Synthetic and logical data introduced in 2006 (AFX, extension 21). |
| Alliance for OpenUSD | March 2026 | Member. Active participation in the applicative and core groups. |
| Open Geospatial Consortium | August 2026 | Member. A new working group is in preparation. |
| Khronos Group | 2026-2027 | Member. ANARI, interoperable with OpenUSD. |
| ISO/ASTM 52915 | 2026 | Member. 3D representations compatible with the Arithmetics of Forms. A work item is possible. |
The publications room — his own texts, and the work of SGDL, opened by an SGDL signature.
The kernel, formalized in Lean — the Arithmetics of Forms, verified wall to wall.
