Frame System, Attentional Canvas, and Consciousness Core
Frame System (FS)
H_F = ⊕_i H_i
Structure
Direct sum of Hilbert spaces H_i, each representing a distinct cognitive frame or content module.
Function
Encodes all available perceptual, memory, and conceptual information as quantum-like states.
Properties
Orthogonal decomposition, frame fidelity F_f, load capacity L_max.
Attentional Canvas (AC)
Π_AC: H_F → H_AC
Projection Operator
Maps frame states to attentional focus subspace via projection operator Π_AC.
Attention Weight
Scalar attention α ∈ [0,1] determines proportion of FS content in AC.
Dynamics
OU process governs stochastic evolution: dA = θ(μ_A - A)dt + σ_A dW.
Consciousness Core (CC)
S_id ⊂ H_CC, β = rank(Π_CC)
Identity Subspace
S_id represents the integrated self-model within the consciousness Hilbert space.
Unified Awareness
β measures the effective dimensionality of conscious content integration.
Awareness Condition
β > α required: consciousness rank must exceed attention threshold for awareness.