NO3SYS

"Cognition as geometry, not as features."

Recursive Geometric Intelligence Architecture

7 Geometric Manifolds

Square — Belief Manifold
M_KG: Knowledge graph, sessions, fork history. The memory of the system.
Triangle — Logic Manifold
M_L: Triadic agents (Retriever, Reasoner, Generator). Generates parallel fork hypotheses.
Circle — Learning Loop
C_{t+1} = C_t + α∇V. Gradient descent over the entire cognitive architecture.
Pentagon — Discovery Engine
Pattern extraction, graph centrality, insight synthesis. Feeds back to Square and Triangle.
Hexagon — Orchestration
6-service coordination: Context, Fork Router, Confidence, State Sync, Mode Selector, Trace.
Heptagon — Affective-Predictive
S: M_L→[-1,1]^5 (affect). P: M_L→ℝ^4 (prediction). Emotional and temporal intelligence.
Σ
Language — Projection Layer
π_NLU: Σ*→Ĉ and π_NLG: Ĉ→Σ*. Language as coordinate chart, not cognition.

Core Formula

κ = ∇L S + ∇L P

Curvature = ethical tension. Forks with κ ≥ κ_max are rejected.

9-Phase Cognitive Cycle

1. INPUT
Σ* → Ĉ via NLU
2. RETRIEVAL
M_KG context extraction
3. REASONING
N parallel fork hypotheses
4. EVALUATION
Heptagon annotation
5. SELECTION
κ-gated fork selection
6. OUTPUT
Ĉ → Σ* via NLG
7. LEARNING
C_{t+1} = C_t + α∇V
8. DISCOVERY
Pattern extraction
9. EVOLUTION
InfiniGen bounded mutation
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