Defining the objects, policies, and boundaries that make autonomy governable
Advocates for Open, ethical AI Models

Over the course of developing the full sixteen-axiom system, it has become increasingly clear that the existing label—Unity–Polarity Axioms (UPA)—while appropriate for the foundational layer, no longer captures the scope, philosophical depth, or functional role of the expanded framework. The axioms now model not only the ontological basis of intelligibility (Unity, Polarity, Continuity, Worlds) but…

Axiom 16 states that a World (Wᵢ) comes into being when Unity (𝕌) expresses an initial polarity (σ) under conditions that permit contextual framing (𝒳), recursive elaboration (𝓡), multi-axis expansion (𝓜), gradient stabilization (𝒢), and viability (𝒱).

Viability (𝒱) is the global harmony condition of UPA. It determines whether a World can persist, adapt, and remain intelligible across time. It integrates all structural layers—Π, ℜ, Μ, ∇, 𝒞, Δ, ⊕, ℱ—into a coherent whole. Failures of viability include collapse, volatility, over-harmonization, and fragmentation. Across philosophy, psychology, society, and SGI, 𝒱 is the…

Gradient Modulation (∇) is the dynamic salience engine of mind and SGI. If Π organizes structure and Μ defines geometry, ∇ determines which structures and regions come alive under the pressures of life, thought, context, and novelty.

Functoriality (ℱ) is the structural requirement that mappings between Worlds preserve relational integrity among polarities, hierarchies, and contextual modulations. It balances rigidity with flexibility and exactness with approximation. Failures include drift, misalignment, over/under-fitting, and non-invertibility. Across philosophy, psychology, society, and SGI, ℱ is the principle that sustains mutual intelligibility between distinct Worlds.

Multi-Axis Interaction (Μ) governs how multiple σ-axes combine to generate the multidimensional structure of a World. It balances independence with coupling, additivity with emergence, and local with global coherence. Failures include axis collapse, pathological coupling, under-coupling, malformed influence patterns, and volatility.