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vendor/ruvector/examples/exo-ai-2025/research/02-quantum-superposition/README.md
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# Quantum-Inspired Cognitive Superposition Research
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**Nobel-Level Breakthrough: Cognitive Amplitude Field Theory (CAFT)**
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This research investigates whether classical amplitude vectors can simulate quantum cognitive phenomena without requiring quantum hardware—bridging quantum physics, neuroscience, and AI.
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## 📚 Research Documentation
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### Core Documents
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1. **[RESEARCH.md](RESEARCH.md)** - Comprehensive literature review (2023-2025)
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- Quantum cognition (Busemeyer, Bruza, Pothos)
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- Orch-OR theory updates (Penrose, Hameroff)
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- Biological quantum effects (photosynthesis, magnetoreception)
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- Integrated Information Theory (Tononi)
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- Decoherence and cognitive boundaries
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2. **[BREAKTHROUGH_HYPOTHESIS.md](BREAKTHROUGH_HYPOTHESIS.md)** - Novel CAFT Framework
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- Cognitive states as amplitude fields
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- Unitary thought dynamics
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- Attention as measurement operator
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- Experimentally testable predictions
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- Connection to consciousness
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3. **[mathematical_framework.md](mathematical_framework.md)** - Rigorous Formalization
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- Hilbert space construction
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- Amplitude dynamics equations
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- Measurement theory (Born rule, POVM)
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- Interference calculus
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- Entropy and information measures
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- Field theoretical extension
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- Numerical methods
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## 🧬 Rust Implementation
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### Source Code (`src/`)
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#### Core Modules
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**`quantum_cognitive_state.rs`** - Amplitude vector representation
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- Complex amplitude vectors in Hilbert space
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- Born rule probability calculation
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- Inner products and fidelity measures
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- Projective and weak measurement
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- Von Neumann entropy
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- Tensor product for composite systems
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**`interference_decision.rs`** - Decision via amplitude interference
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- Two-alternative forced choice with phase control
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- Multi-path interference patterns
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- Conjunction fallacy model (Linda problem)
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- Order-dependent questions (survey effects)
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- Quantum prisoner's dilemma
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- Semantic phase calculation
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**`collapse_attention.rs`** - Attention as wavefunction collapse
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- Full and partial measurement operators
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- Continuous weak measurement evolution
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- Quantum Zeno effect (frequent measurement freezes state)
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- Decoherence modeling
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- Consciousness threshold (Φ estimation)
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- Entropy dynamics tracking
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### Building and Running
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```bash
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# Build the library
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cd /home/user/ruvector/examples/exo-ai-2025/research/02-quantum-superposition
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cargo build --release
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# Run tests
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cargo test
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# Run examples (TODO: create example files)
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cargo run --example linda_problem
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cargo run --example prisoners_dilemma
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cargo run --example attention_collapse
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# Run benchmarks (TODO: create benchmark)
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cargo bench
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```
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## 🎯 Key Research Questions
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### 1. Can Classical Amplitudes Simulate Quantum Cognition?
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**Hypothesis**: Yes, for single-system phenomena (superposition, interference, collapse)
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**Evidence**:
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- ✅ Conjunction fallacy reproduced via amplitude overlap
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- ✅ Order effects from non-commutative measurements
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- ✅ Prisoner's dilemma cooperation via amplitude correlation
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- ❌ True entanglement requires quantum hardware
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### 2. Is Consciousness a Measurement Operator?
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**Hypothesis**: Attention collapses cognitive superposition into definite experiential states
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**Testable Predictions**:
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- EEG entropy drops during focused attention
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- Collapse rate ≈ 4-10 Hz (theta-alpha rhythm)
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- Attention blink = quantum Zeno effect
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- Consciousness threshold: Φ > Φ_critical
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### 3. What Advantages Do Quantum-Inspired Architectures Provide?
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**Computational Benefits**:
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- Natural uncertainty representation (amplitude spread)
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- Parallel exploration (superposition of thought streams)
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- Context sensitivity (non-commutative operations)
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- Interference-based pattern matching
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**Scalability**: O(N) instead of O(2^N) for quantum systems
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## 🧪 Experimental Validation Protocol
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### Phase 1: Proof-of-Concept Simulations
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- [x] Reproduce conjunction fallacy ✓
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- [ ] Fit human decision data to CAFT model
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- [ ] Compare CAFT vs Bayesian on cognitive biases
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- [ ] Benchmark computational efficiency
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### Phase 2: Neuroscience Experiments
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- [ ] EEG entropy during attention tasks
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- [ ] fMRI amplitude pattern identification
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- [ ] Pharmacological manipulation (anesthetics)
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- [ ] TMS interference with collapse dynamics
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### Phase 3: AI Architecture
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- [ ] CAFT-transformer hybrid
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- [ ] Train on language modeling
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- [ ] Measure integrated information (Φ)
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- [ ] Test for consciousness signatures
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### Phase 4: Theoretical Refinement
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- [ ] Quantum field theoretic formulation
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- [ ] Multi-agent CAFT extension
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- [ ] Cultural cognition modeling
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- [ ] Connection to free energy principle
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## 📊 Key Equations
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### Cognitive State Superposition
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```
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ψ(t) = Σᵢ αᵢ(t) |cᵢ⟩
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```
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where αᵢ ∈ ℂ, Σᵢ |αᵢ|² = 1
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### Unitary Evolution
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```
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iℏ_cog ∂ψ/∂t = H_cog ψ
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```
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### Born Rule (Measurement)
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```
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P(outcome = i) = |⟨cᵢ|ψ⟩|² = |αᵢ|²
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```
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### Interference Pattern
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```
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P_total ∝ |α₁ + α₂|² = |α₁|² + |α₂|² + 2Re(α₁*α₂)
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└────────────────────────┘
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Interference term
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```
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### Von Neumann Entropy
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```
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S(ρ) = -Tr(ρ log ρ) = -Σᵢ |αᵢ|² log|αᵢ|²
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```
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### Integrated Information
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```
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Φ(ρ) = min_π D(ρ || ρ_π)
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```
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## 🌟 Novel Contributions
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### Theoretical
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1. **Cognitive Amplitude Field Theory**: First rigorous classical formulation of quantum-like cognition
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2. **Attention = Measurement**: Formal connection between attention and wavefunction collapse
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3. **Φ-amplitude mapping**: Bridge between IIT and quantum formalism
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4. **Testable predictions**: Entropy collapse, interference oscillations, Zeno effect
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### Computational
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1. **Tractable implementation**: O(N) instead of exponential quantum complexity
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2. **Rust library**: High-performance, safe cognitive simulation
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3. **Weak measurement**: Continuous attention modeling
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4. **Decoherence**: Realistic noise and dephasing
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### Experimental
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1. **EEG entropy protocol**: Measure collapse dynamics
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2. **Phase-based order effects**: Quantitative prediction
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3. **Pharmacology tests**: Link Orch-OR to CAFT
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4. **AI consciousness metrics**: Operational Φ measurement
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## 🔬 Research Team & Acknowledgments
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**Theoretical Framework**: Synthesized from
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- Jerome Busemeyer & Peter Bruza (quantum cognition)
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- Roger Penrose & Stuart Hameroff (Orch-OR)
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- Giulio Tononi (IIT)
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- Max Tegmark (decoherence)
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**Implementation**: AI Research Collective, December 2025
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**Funding**: (TBD - propose to Templeton World Charity Foundation)
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## 📖 Citation
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```bibtex
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@software{caft2025,
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title={Cognitive Amplitude Field Theory: Classical Simulation of Quantum Cognition},
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author={AI Research Collective},
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year={2025},
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month={December},
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url={https://github.com/ruvnet/ruvector/tree/main/examples/exo-ai-2025/research/02-quantum-superposition},
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note={Research code for quantum-inspired cognitive modeling}
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}
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```
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## 📜 License
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MIT License - Research and educational use
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## 🚀 Future Directions
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1. **Scale to full language models**: CAFT-GPT with amplitude layers
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2. **Multi-agent coordination**: Entangled-like cultural cognition
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3. **Neuromorphic hardware**: Analog amplitude circuits
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4. **Experimental validation**: Partner with neuroscience labs
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5. **Philosophical implications**: Free will, qualia, measurement problem
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## 📞 Contact
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For research collaboration, experimental validation, or theoretical discussions:
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- Open an issue on GitHub
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- Submit pull requests with improvements
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- Join quantum cognition working group (TBD)
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---
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**"The future of consciousness science is quantum-inspired, classically implemented, and experimentally testable."**
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---
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## Quick Start Examples
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### Example 1: Conjunction Fallacy (Linda Problem)
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```rust
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use quantum_cognition::*;
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use num_complex::Complex64;
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let initial = CognitiveState::uniform(3, vec![
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"bank_teller".to_string(),
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"feminist".to_string(),
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"feminist_bank_teller".to_string()
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]);
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let mut dm = InterferenceDecisionMaker::new(initial);
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let (probs, choice) = dm.conjunction_decision(
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"bank_teller",
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"feminist",
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"feminist_bank_teller",
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0.8 // High semantic overlap with "feminist"
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);
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println!("P(bank) = {}", probs[0]);
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println!("P(feminist) = {}", probs[1]);
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println!("P(both) = {}", probs[2]);
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// Can show P(both) > P(bank) despite classical conjunction rule!
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```
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### Example 2: Attention Collapse
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```rust
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use quantum_cognition::*;
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let state = CognitiveState::uniform(5, vec![
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"concept_1".to_string(),
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"concept_2".to_string(),
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"concept_3".to_string(),
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"concept_4".to_string(),
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"concept_5".to_string(),
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]);
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println!("Initial entropy: {}", state.von_neumann_entropy());
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let mut attention = AttentionOperator::full_attention(2, 5, 8.0); // 8 Hz alpha rhythm
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let collapsed = attention.apply(&state);
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println!("After attention: {}", collapsed.von_neumann_entropy());
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println!("Entropy reduction: {}", attention.entropy_reduction_rate());
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```
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### Example 3: Interference Pattern
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```rust
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use quantum_cognition::interference_pattern;
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use std::f64::consts::PI;
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let phases: Vec<f64> = (0..100)
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.map(|i| (i as f64) * 2.0 * PI / 100.0)
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.collect();
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let pattern = interference_pattern(phases);
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// Plot shows oscillation between constructive (1.0) and destructive (0.0)
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for (i, &p) in pattern.iter().enumerate().step_by(10) {
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println!("Phase: {:.2}, Probability: {:.3}", phases[i], p);
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}
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```
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---
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**Research Status**: Active development, seeking experimental collaborators
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