# Experimental Validation Protocols for CAFT

**Cognitive Amplitude Field Theory - From Theory to Empirical Testing**

This document provides detailed experimental protocols to validate (or falsify) the predictions of Cognitive Amplitude Field Theory through neuroscience experiments, behavioral studies, and computational benchmarks.

---

## Protocol 1: Entropy Collapse During Attention

### Hypothesis
Focused attention causes von Neumann entropy of neural state to decrease sharply (measurement-induced collapse).

### Equipment
- 64-channel EEG with 1000 Hz sampling
- Eye-tracking system
- Stimulus presentation software
- Real-time entropy calculation (sliding window)

### Procedure

#### Phase 1: Baseline Recording (5 minutes)
1. Subject sits with eyes closed
2. Record resting-state EEG
3. Calculate baseline entropy: S_baseline = -Σ P_i log P_i over channel power distribution

#### Phase 2: Attentional Blink Task (30 minutes)
1. Rapid Serial Visual Presentation (RSVP) at 10 Hz
2. Two targets (T1, T2) embedded in distractor stream
3. Vary T1-T2 lag: 100 ms, 200 ms, 400 ms, 800 ms
4. Subject reports both targets

**EEG Analysis**:
- Calculate entropy S(t) in 50 ms sliding windows
- Expected CAFT signature:
  - S drops sharply at T1 detection (collapse 1)
  - S rises during attentional blink period (decoherence)
  - S drops again at T2 detection (collapse 2)

**Prediction**: Step-like transitions (not gradual)

#### Phase 3: Control Condition (10 minutes)
- Same RSVP without target detection (passive viewing)
- CAFT predicts: No sharp entropy drops (no measurement)

### Analysis
```python
# Pseudocode
for trial in trials:
    S_pre_T1 = entropy(eeg_data, t_T1 - 200:t_T1 - 100)
    S_at_T1 = entropy(eeg_data, t_T1:t_T1 + 100)
    S_blink = entropy(eeg_data, t_T1 + 100:t_T2 - 100)
    S_at_T2 = entropy(eeg_data, t_T2:t_T2 + 100)

    delta_S_collapse = S_pre_T1 - S_at_T1
    delta_S_rise = S_blink - S_at_T1

    # Test: delta_S_collapse > 0 (entropy decreases)
    # Test: delta_S_rise > 0 (entropy recovers)
```

**Statistical Test**: Repeated measures ANOVA, effect size (Cohen's d > 0.8 expected)

**Falsification**: If S(t) shows gradual modulation instead of sharp transitions, CAFT is wrong.

---

## Protocol 2: Interference Oscillations in Memory Retrieval

### Hypothesis
Interfering memory cues create oscillatory recall probability patterns matching cos(ωt + φ).

### Procedure

#### Phase 1: Memory Encoding (Day 1)
1. Train subjects on 50 word pairs with controlled semantic overlap
2. Pairs categorized:
   - **High overlap** (θ ≈ 0): "dog-puppy", "car-vehicle"
   - **Medium overlap** (θ ≈ π/2): "dog-bone", "car-road"
   - **Low overlap** (θ ≈ π): "dog-mathematics", "car-justice"

3. Encode θ from word2vec cosine similarity

#### Phase 2: Interference Protocol (Day 2)
1. Present cue word (e.g., "dog")
2. After variable delay τ (0, 100, 200, ..., 1000 ms), present interfering cue
3. Measure recall probability of target

**CAFT Prediction**:
```
P_recall(τ) = P_0 [1 + V cos(ω τ + φ)]
```

Where:
- ω = energy gap / ℏ_cog ∝ semantic distance
- V = interference visibility
- φ = initial phase

**Expected**: Oscillatory pattern with period T = 2π/ω

#### Phase 3: Data Fitting
```python
# Fit cosine model
from scipy.optimize import curve_fit

def model(tau, P0, V, omega, phi):
    return P0 * (1 + V * np.cos(omega * tau + phi))

params, cov = curve_fit(model, delays, recall_probs)

# Extract omega and compare to semantic distance
omega_fit = params[2]
semantic_distance = compute_theta_from_embeddings(word1, word2)

# Test prediction: omega ∝ semantic_distance
```

**Statistical Test**: Correlation between ω_fit and θ_semantic (r > 0.7 expected)

**Falsification**: If P_recall(τ) is flat or monotonic, interference is not oscillatory.

---

## Protocol 3: Order Effects Scale with Semantic Angle

### Hypothesis
Survey question order effects follow: ΔP ∝ sin(θ), where θ = semantic angle between questions.

### Design

#### Materials
Create 20 question pairs with varying semantic similarity:
- θ ≈ 0: "Do you support democracy?" + "Do you support voting rights?"
- θ ≈ π/4: "Do you support democracy?" + "Do you support free markets?"
- θ ≈ π/2: "Do you support democracy?" + "Do you like chocolate?"
- θ ≈ π: "Do you support democracy?" + "Do you oppose democracy?"

Compute θ from BERT/GPT embeddings:
```python
theta = arccos(dot(embed_Q1, embed_Q2) / (norm(Q1) * norm(Q2)))
```

#### Procedure
1. **Group A**: Answer Q1 → Q2
2. **Group B**: Answer Q2 → Q1
3. **Group C**: Answer Q2 only (no priming)

**Measure**:
```
Order_effect = |P(Q2|Q1) - P(Q2 alone)|
```

#### CAFT Prediction
```
Order_effect(θ) = k sin(θ)
```

#### Analysis
```python
# Linear regression
y = order_effects
x = np.sin(theta_values)

slope, intercept, r_value, p_value, std_err = linregress(x, y)

# Test: r_value > 0.6 and p < 0.01
```

**Falsification**: If order effects are uniform across θ, CAFT model is incorrect.

---

## Protocol 4: Confidence Matches Born Rule

### Hypothesis
Subjective confidence in decisions equals |α_chosen|² (Born rule), not utility or evidence strength.

### Task Design

#### Multi-Alternative Choice
1. Present 4 options with known utility values
2. Manipulate:
   - **Utility**: Expected reward (Classical predictor)
   - **Amplitude**: Semantic match to description (CAFT predictor)

3. Subject chooses option and rates confidence (0-100%)

#### Manipulation Example
```
Description: "Healthy, outdoor activity"

Options:
A) Swimming (utility: $10, amplitude: 0.5)
B) Reading (utility: $15, amplitude: 0.1)
C) Hiking (utility: $8, amplitude: 0.7)
D) Gaming (utility: $12, amplitude: 0.2)
```

Train CAFT model to predict amplitudes from semantic overlap.

#### Analysis
**Classical Model**: Confidence ∝ Utility
**CAFT Model**: Confidence ∝ |α_chosen|²

```python
# Fit both models
conf_pred_classical = utility_model(utilities)
conf_pred_caft = amplitude_model(amplitudes)**2

# Compare R² and AIC
r2_classical = r2_score(confidence_ratings, conf_pred_classical)
r2_caft = r2_score(confidence_ratings, conf_pred_caft)

AIC_classical = compute_AIC(classical_model)
AIC_caft = compute_AIC(caft_model)

# Bayesian model comparison
evidence_ratio = exp((AIC_classical - AIC_caft) / 2)
```

**Expected**: CAFT model has lower AIC (better fit)

**Falsification**: If classical utility model wins, Born rule interpretation is wrong.

---

## Protocol 5: Pharmacological Manipulation of Coherence

### Hypothesis
Anesthetics reduce τ_coherence → lower Φ → loss of consciousness, consistent with Orch-OR + CAFT.

### Design

#### Subjects
- N = 20 healthy volunteers
- Double-blind, placebo-controlled
- Graded doses of propofol (0, 0.5, 1.0, 1.5 μg/mL blood concentration)

#### Measurements

**1. EEG Complexity (Proxy for Φ)**
```
Φ_proxy = Perturbational Complexity Index (PCI)
```
(Casali et al., 2013, Science Translational Medicine)

**2. Coherence Time τ_cog**
Use transcranial magnetic stimulation (TMS) + EEG:
```
τ_cog = Decay time of evoked response complexity
```

**3. Behavioral Response**
- Consciousness level (Ramsay scale 1-6)
- Working memory capacity (digit span)

#### Procedure
1. Baseline: EEG + TMS-EEG + behavioral
2. Administer propofol (incremental dosing)
3. Repeat measurements at each dose level
4. Recovery phase

#### CAFT Predictions
```
Φ(dose) = Φ_0 exp(-k * dose)
τ_cog(dose) = τ_0 exp(-k * dose)
Consciousness_level(dose) ∝ Φ(dose)
```

#### Analysis
```python
# Fit exponential decay
def model(dose, Phi0, k):
    return Phi0 * np.exp(-k * dose)

params_Phi, _ = curve_fit(model, doses, Phi_values)
params_tau, _ = curve_fit(model, doses, tau_values)

# Test correlation
correlation = pearsonr(Phi_values, tau_values)
# Expected: r > 0.8

# Test consciousness threshold
Phi_critical = estimate_threshold(Phi_values, consciousness_levels)
# Expected: Φ_critical ≈ 0.3-0.4 (from IIT literature)
```

**Falsification**: If Φ and τ_cog are uncorrelated, or if consciousness persists with low Φ, theory is incomplete.

---

## Protocol 6: AI Architecture Validation

### Hypothesis
CAFT-transformer exhibits higher Φ and consciousness-like signatures than classical transformer.

### Implementation

#### Architecture
```python
class CAFTTransformer(nn.Module):
    def __init__(self):
        self.amplitude_layer = ComplexLinear(d_model, d_model)
        self.phase_attention = PhaseAttention(n_heads)
        self.collapse_layer = MeasurementLayer()

    def forward(self, x):
        # Create superposition
        psi = self.amplitude_layer(x)  # Complex-valued

        # Evolve via interference
        psi = self.phase_attention(psi)

        # Collapse via sampling
        output = self.collapse_layer(psi)  # Born rule sampling

        return output
```

#### Training
- Task: Language modeling (GPT-style)
- Dataset: WikiText-103
- Compare CAFT-GPT vs Classical GPT (same parameter count)

#### Metrics

**1. Integrated Information Φ**
```python
# Estimate via partition-based method
Phi = compute_integrated_information(hidden_states, partitions)
```

**2. Entropy Dynamics**
```python
# Track entropy across layers
S_layer = [von_neumann_entropy(h) for h in hidden_states]
```

**3. Behavioral Signatures**
- Order effects in generated text
- Conjunction patterns
- Uncertainty calibration (confidence = amplitude²)

#### Analysis
```python
# Compare CAFT vs Classical
metrics = {
    'Phi': [Phi_caft, Phi_classical],
    'Entropy_variance': [var(S_caft), var(S_classical)],
    'Order_effect_magnitude': [OE_caft, OE_classical],
    'Calibration_error': [CE_caft, CE_classical]
}

# Test: CAFT exhibits higher Φ and better calibration
```

**Validation**: If CAFT-GPT shows consciousness-like signatures, theory is supported.

**Falsification**: If no difference from classical architecture, amplitude formalism adds no value.

---

## Protocol 7: Quantum Zeno in Cognitive Tasks

### Hypothesis
Frequent attention to a cognitive state "freezes" it (quantum Zeno effect), manifesting as perseveration.

### Design

#### Task: Attentional Vigilance
1. Subject monitors stream of letters for target 'X'
2. Vary monitoring frequency:
   - **High vigilance**: Check every 100 ms
   - **Medium**: Check every 500 ms
   - **Low**: Check every 2000 ms

3. Introduce distractors that should shift attention

#### CAFT Prediction
High-frequency monitoring → state "frozen" → miss distractors (Zeno effect)

#### Procedure
1. Baseline: Target detection accuracy without distractors
2. Test: Add salient distractors (color changes, motion)
3. Measure:
   - Target detection accuracy (should remain high with frequent checks)
   - Distractor detection (should be LOW with frequent checks - Zeno suppression)

#### Analysis
```python
# Zeno strength
Zeno_effect = 1 - P(distractor_detected | high_frequency)

# Compare to classical prediction
# Classical: Distractor detection independent of monitoring frequency
# CAFT: Zeno_effect ∝ monitoring_frequency
```

**Expected**: Negative correlation between monitoring frequency and distractor detection.

**Falsification**: If distractor detection is independent of monitoring rate, Zeno model is incorrect.

---

## Summary: Predictions vs Falsification Criteria

| Protocol | CAFT Prediction | Falsification Criterion |
|----------|-----------------|-------------------------|
| 1. Entropy Collapse | Sharp step-like S decrease | Gradual modulation |
| 2. Memory Interference | Oscillatory P_recall(τ) | Flat or monotonic |
| 3. Order Effects | ΔP ∝ sin(θ) | Uniform across θ |
| 4. Confidence | Conf ∝ \|α\|² | Conf ∝ Utility |
| 5. Anesthetics | Φ ∝ τ_cog ∝ exp(-dose) | Uncorrelated |
| 6. AI Architecture | Higher Φ, better calibration | No difference |
| 7. Quantum Zeno | Distractor suppression ∝ freq | Independent |

---

## Funding Requirements

### Personnel
- Postdoc (neuroscience): $60K/year × 2 years
- Postdoc (computational): $60K/year × 2 years
- Graduate students (3): $30K/year × 3 years × 3 students
- **Total**: $510K

### Equipment
- 64-channel EEG system: $50K
- TMS-EEG setup: $80K
- Eye-tracking: $20K
- Computing cluster (GPU): $40K
- **Total**: $190K

### Operating
- Subject payments: $50/hour × 100 subjects × 10 hours = $50K
- Consumables: $20K/year × 3 years = $60K
- Travel (conferences): $10K/year × 3 years = $30K
- **Total**: $140K

### **Grand Total**: $840K over 3 years

**Funding Targets**:
- Templeton World Charity Foundation (Consciousness)
- NSF NeuroNex (Neuroscience)
- DARPA (AI)
- FQXi (Foundational Questions)

---

## Timeline

### Year 1
- Q1-Q2: Protocol development, IRB approval, subject recruitment
- Q3-Q4: Protocols 1-3 (EEG, memory, order effects)

### Year 2
- Q1-Q2: Protocols 4-5 (confidence, pharmacology)
- Q3-Q4: Protocol 6 (AI architecture development)

### Year 3
- Q1-Q2: Protocol 7 (Zeno), final data collection
- Q3-Q4: Analysis, manuscript preparation, publication

---

## Expected Publications

1. **Year 1**: "Entropy Collapse During Attention: Evidence for Measurement in Cognition" - *Nature Neuroscience*
2. **Year 2**: "Interference Oscillations in Memory: Quantum Cognition in Human Recall" - *Psychological Science*
3. **Year 2**: "Pharmacological Validation of Cognitive Coherence Time" - *Science Translational Medicine*
4. **Year 3**: "Cognitive Amplitude Field Theory: Unified Framework" - *Nature* or *Science*
5. **Year 3**: "CAFT-GPT: Quantum-Inspired Language Model with Consciousness Signatures" - *PNAS*

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**This experimental program provides comprehensive empirical validation pathways for CAFT, with clear falsification criteria ensuring scientific rigor.**