graph TD
    A[Perceptual Input] -->|Quantum Transform| B{Feature Extraction}
    B -->|Primary Path| C[Neural Encoding φ]
    B -->|Secondary Path| D[Eigenface Matrix Ω]
    C --> E[Temporal Integration]
    D --> E
    E -->|Cryptographic Hash| F[Identity Manifold]
    F -->|Schrödinger Transform| G[Perceptual Output]
    G --> H{Decision Boundary}
    H -->|Rejection| I[Recalibration Loop]
    I --> A
    H -->|Acceptance| J[Quantum Entanglement]
    J -->|Dimensional Collapse| K[Facial Transformation]
    
    classDef default fill:#0d1117,stroke:#6A11CB,color:#2575FC,stroke-width:2px;
    classDef main fill:#0d1117,stroke:#6A11CB,color:#FFFFFF,stroke-width:4px;
    classDef crypto fill:#0d1117,stroke:#2575FC,color:#6A11CB,stroke-width:3px;
    
    class A,G,K main;
    class F,J crypto;

sequenceDiagram
    participant Observer
    participant QuantumState
    participant NeuralNetwork
    participant FacialMatrix
    
    Observer->>QuantumState: Initiate Observation
    Note over QuantumState: Superposition Collapse
    QuantumState->>NeuralNetwork: Transmit Eigenvalues
    
    loop Transformation Sequence
        NeuralNetwork->>NeuralNetwork: Self-optimization
        NeuralNetwork->>FacialMatrix: Calculate Projections
        FacialMatrix-->>NeuralNetwork: Return Eigenvectors
    end
    
    FacialMatrix->>Observer: Project Transformed Image
    Note over Observer,FacialMatrix: Facial Recognition Uncertainty: ΔP·ΔQ ≥ ħ/2
    
    NeuralNetwork->>QuantumState: Reset Quantum State
    QuantumState-->>Observer: Ready for Next Observation

classDiagram
    class FacialTransformation {
        +int dimensionality
        +float quantumCoupling
        +Matrix eigenfaces
        +performTransform(Face source, Face target)
        +calculateEigenvalues()
        -normalizeFeatureSpace()
        -applySchrödingerEquation()
    }
    
    class NeuralEncoder {
        +int[] layerStructure
        +float learningRate
        +Matrix weights
        +encode(Image input)
        +backpropagate(Error delta)
        -activationFunction(float x)
        -calculateGradient()
    }
    
    class QuantumObserver {
        +float uncertaintyPrinciple
        +int observationState
        +observe(QuantumState state)
        +collapseWavefunction()
        -calculateProbabilityMatrix()
        -entangleStates()
    }
    
    class FacialFeatures {
        +Vector landmarks
        +float[] vectorSpace
        +extractFeatures(Image face)
        +normalizeCoordinates()
        -calculateDistances()
        -createFeatureVector()
    }
    
    FacialTransformation --> NeuralEncoder : uses
    FacialTransformation --> QuantumObserver : triggers
    NeuralEncoder --> FacialFeatures : processes
    QuantumObserver --> FacialFeatures : observes

erDiagram
    NEURAL-FRAMEWORK ||--o{ PERCEPTUAL-DOMAIN : processes
    NEURAL-FRAMEWORK ||--|| QUANTUM-LAYER : integrates
    PERCEPTUAL-DOMAIN ||--o{ FEATURE-VECTOR : contains
    FEATURE-VECTOR }o--|| EIGENFACE-MATRIX : maps_to
    EIGENFACE-MATRIX ||--|| TRANSFORMATION-MATRIX : generates
    TRANSFORMATION-MATRIX ||--o{ FACIAL-OUTPUT : produces
    QUANTUM-LAYER ||--|| UNCERTAINTY-PRINCIPLE : adheres_to
    UNCERTAINTY-PRINCIPLE ||--o{ PROBABILITY-DISTRIBUTION : defines
    PROBABILITY-DISTRIBUTION }o--|| FACIAL-OUTPUT : constrains
    
    NEURAL-FRAMEWORK {
        float learning_rate
        int[] layer_structure
        function activation_type
    }
    
    QUANTUM-LAYER {
        complex[] eigenstates
        float uncertainty
        function wave_function
    }
    
    TRANSFORMATION-MATRIX {
        complex[][] coefficients
        float determinant
        boolean invertible
    }
    
    EIGENFACE-MATRIX {
        float[][] principal_components
        int dimensionality
        float variance_explained
    }

stateDiagram-v2
    [*] --> InitialState
    InitialState --> QuantumObservation
    QuantumObservation --> FeatureExtraction
    
    state FeatureExtraction {
        [*] --> LandmarkDetection
        LandmarkDetection --> GeometricAnalysis
        GeometricAnalysis --> FeatureVector
        FeatureVector --> [*]
    }
    
    FeatureExtraction --> DimensionalReduction
    DimensionalReduction --> EigenfaceCalculation
    EigenfaceCalculation --> TransformationMatrix
    
    state TransformationMatrix {
        [*] --> MatrixInitialization
        MatrixInitialization --> SingularValueDecomposition
        SingularValueDecomposition --> OptimalTransform
        OptimalTransform --> MatrixInversion
        MatrixInversion --> [*]
    }
    
    TransformationMatrix --> FacialWarping
    FacialWarping --> ColorCorrection
    ColorCorrection --> PostProcessing
    PostProcessing --> FinalOutput
    FinalOutput --> [*]

pie
    title Component Analysis of Neural Framework
    "Computer Vision" : 95.2
    "Neural Networks" : 89.7
    "Facial Analysis" : 97.8
    "Quantum Algorithms" : 84.3
    "Feature Extraction" : 92.1
    "Transformation Matrix" : 91.6

graph TB
    subgraph "Connection Layer"
        A1[Email Protocol] --- B1[Hash: 47A1F3]
        A2[Repository Access] --- B2[Hash: 89C2E5]
        A3[Professional Network] --- B3[Hash: D306B7]
    end
    
    subgraph "Encryption Layer"
        C1[RSA-4096] --- D1[Quantum Key]
        C2[AES-256] --- D2[Time-Based Token]
        C3[Homomorphic] --- D3[Zero-Knowledge Proof]
    end
    
    subgraph "Integration Layer"
        E1[Mathematical Solution] --- F1[Access Control]
        E2[Riddle Verification] --- F2[Authentication]
        E3[Quantum Entanglement] --- F3[Trust Establishment]
    end
    
    B1 --> C1
    B2 --> C2
    B3 --> C3
    
    D1 --> E1
    D2 --> E2
    D3 --> E3
    
    F1 --> G[Secure Communication Channel]
    F2 --> G
    F3 --> G
    
    G --> H{Decoded Access Point}
    
    classDef blue fill:#0d1117,stroke:#2575FC,color:#FFFFFF,stroke-width:2px;
    classDef purple fill:#0d1117,stroke:#6A11CB,color:#FFFFFF,stroke-width:2px;
    classDef green fill:#0d1117,stroke:#30D158,color:#FFFFFF,stroke-width:2px;
    
    class A1,A2,A3,B1,B2,B3 blue;
    class C1,C2,C3,D1,D2,D3 purple;
    class E1,E2,E3,F1,F2,F3,G,H green;