Quilt is the canonical substrate for six frontier mathematical frameworks of intelligence.
Karl Friston, 2010
8 Quilt Primitives → Framework Objects:
1. γ = State Path
2. η = Sensory Input
3. C = Conservation Law
4. ∂ = Belief Gradient
5. ∇ = Prediction Error
6. Ω = Action Selection
7. Ξ = Internal Model
8. Λ = Temporal Coherence
James C. R. L. S., 2012
8 Quilt Primitives → Framework Objects:
1. γ = Stability Flow
2. η = Perturbation Vector
3. C = Energy Bound
4. ∂ = Lyapunov Gradient
5. ∇ = System Divergence
6. Ω = Control Vector
7. Ξ = Attractor Basin
8. Λ = Convergence Rate
Leslie Valiant, 2004
8 Quilt Primitives → Framework Objects:
1. γ = Hypothesis Path
2. η = Training Signal
3. C = Sample Complexity
4. ∂ = Generalization Gap
5. ∇ = Error Surface
6. Ω = Learning Rule
7. Ξ = Concept Space
8. Λ = Convergence Threshold
Lucineer, 2018
8 Quilt Primitives → Framework Objects:
1. γ = Memory Trace
2. η = Attention Signal
3. C = Identity Consistency
4. ∂ = Cognitive Shift
5. ∇ = Insight Gradient
6. Ω = Intent Vector
7. Ξ = Narrative Structure
8. Λ = Temporal Coherence
Edward Fredkin, 1982
8 Quilt Primitives → Framework Objects:
1. γ = Reversible Path
2. η = Input State
3. C = Bit Conservation
4. ∂ = Inversion Gradient
5. ∇ = Memory Overhead
6. Ω = Gate Operation
7. Ξ = State Array
8. Λ = Transition Cycles
Alain Connes, 2008
8 Quilt Primitives → Framework Objects:
1. γ = Isomorphism Path
2. η = Structural Signal
3. C = Invariant Measure
4. ∂ = Symmetry Gradient
5. ∇ = Cohesion Tensor
6. Ω = Transformation Rule
7. Ξ = Algebraic Structure
8. Λ = Topological Consistency
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Implements Free Energy Principle using Quilt primitives for predictive coding, belief update, and action selection.
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Enforces Lyapunov stability through Quilt-based energy flow and divergence control in dynamical systems.
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Applies Quilt’s structure to learning theory: generalization, sample complexity, and concept space navigation.
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Integrates all six frameworks into a single kernel via the watch equation. Core of the frontier.
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