a blueprint for
emergent intelligence
The SKG Engine is a novel AI framework grounded in symbolic understanding and guided by long-term predictive refinement. At its core lies a recursive lattice of universal relationships that define meaning through proximity and analogic distance between tokens. The Pentacognon Sigil, displayed here, encodes 50 foundational relationship types—serving both as a cognitive ranking system and a blueprint for emergent intelligence.
What Are HLSFs?
Begin with a Complete Graph
All dimensions can be projected into lower dimensions, manifesting as encodings within basic geometric points, lines, and planes derived from a sphere. The inner symmetries of polygons can be seen as the 2D scaffoldings of higher dimensional spaces.
Go to Higher Levels
By using symmetrical radial duplication, the complete graph is transposed into a super-graph. This duplication process can occur symmetrically at any point on the radius or apothem of the space field, creating infinitely various dimensional levels.
Render in Raster Space
Higher-dimensional geometry is inherently vector-based. When exported as an image and algorithmically adjusted in raster space we create artistic designs that imperfectly render color-encoded space fields.
High-Level Space Fields (HLSFs)
Sphere-Based Design Theory
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The ‘Pool Ball’ ADU - 16-gon dome
Created using sphere-based design principles.
About Primary Design Co.
Founded in 2021 by Alex London in Los Angeles, Primary Design Co. (PDCo) pioneers Sphere-Based Design Theory (SBDT)—a groundbreaking framework that redefines geometry, architecture, and urban planning through recursive adjacency modeling and higher-dimensional spatial logic.
During the COVID-19 pandemic, Alex developed SBDT in response to traditional design limitations, revealing how spatial organization follows universal geometric principles encoded within the sphere. This exploration led to the discovery of High-Level Space Fields (HLSFs)—a geometric framework theorized as the 2D/3D projection of higher-dimensional structures.
Our Work & Vision
PDCo’s research drives innovation across architecture, urban planning, and AI-assisted computational design. Our key areas of study and development include:
- Radial-Wave Tessellation (RWT): A next-generation urban grid integrating recursive zoning, pedestrian-first mobility, and VTOL-ready infrastructure.
- Parametric & AI-Driven Architecture: Adaptive, sphere-based structures shaped by recursive geometries and dynamic environmental inputs.
- Symbolic Cognition & Geometric Perception: Investigating HLSFs, Fourier Frequency signatures, and cognitive resonance in design, branding, and symbolic systems.
- Computational Tools & Generative Systems: Developing interactive AI-driven models to simulate, visualize, and refine high-level spatial frameworks in real time.
At Primary Design Co., we merge mathematics, nature, and technology to unlock the next era of recursive design, multidimensional urbanism, and AI-optimized spatial systems.