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# Experimental Validation Protocols for CAFT
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**Cognitive Amplitude Field Theory - From Theory to Empirical Testing**
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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.
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---
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## Protocol 1: Entropy Collapse During Attention
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### Hypothesis
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Focused attention causes von Neumann entropy of neural state to decrease sharply (measurement-induced collapse).
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### Equipment
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- 64-channel EEG with 1000 Hz sampling
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- Eye-tracking system
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- Stimulus presentation software
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- Real-time entropy calculation (sliding window)
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### Procedure
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#### Phase 1: Baseline Recording (5 minutes)
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1. Subject sits with eyes closed
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2. Record resting-state EEG
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3. Calculate baseline entropy: S_baseline = -Σ P_i log P_i over channel power distribution
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#### Phase 2: Attentional Blink Task (30 minutes)
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1. Rapid Serial Visual Presentation (RSVP) at 10 Hz
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2. Two targets (T1, T2) embedded in distractor stream
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3. Vary T1-T2 lag: 100 ms, 200 ms, 400 ms, 800 ms
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4. Subject reports both targets
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**EEG Analysis**:
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- Calculate entropy S(t) in 50 ms sliding windows
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- Expected CAFT signature:
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- S drops sharply at T1 detection (collapse 1)
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- S rises during attentional blink period (decoherence)
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- S drops again at T2 detection (collapse 2)
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**Prediction**: Step-like transitions (not gradual)
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#### Phase 3: Control Condition (10 minutes)
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- Same RSVP without target detection (passive viewing)
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- CAFT predicts: No sharp entropy drops (no measurement)
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### Analysis
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```python
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# Pseudocode
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for trial in trials:
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S_pre_T1 = entropy(eeg_data, t_T1 - 200:t_T1 - 100)
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S_at_T1 = entropy(eeg_data, t_T1:t_T1 + 100)
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S_blink = entropy(eeg_data, t_T1 + 100:t_T2 - 100)
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S_at_T2 = entropy(eeg_data, t_T2:t_T2 + 100)
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delta_S_collapse = S_pre_T1 - S_at_T1
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delta_S_rise = S_blink - S_at_T1
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# Test: delta_S_collapse > 0 (entropy decreases)
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# Test: delta_S_rise > 0 (entropy recovers)
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```
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**Statistical Test**: Repeated measures ANOVA, effect size (Cohen's d > 0.8 expected)
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**Falsification**: If S(t) shows gradual modulation instead of sharp transitions, CAFT is wrong.
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---
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## Protocol 2: Interference Oscillations in Memory Retrieval
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### Hypothesis
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Interfering memory cues create oscillatory recall probability patterns matching cos(ωt + φ).
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### Procedure
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#### Phase 1: Memory Encoding (Day 1)
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1. Train subjects on 50 word pairs with controlled semantic overlap
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2. Pairs categorized:
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- **High overlap** (θ ≈ 0): "dog-puppy", "car-vehicle"
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- **Medium overlap** (θ ≈ π/2): "dog-bone", "car-road"
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- **Low overlap** (θ ≈ π): "dog-mathematics", "car-justice"
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3. Encode θ from word2vec cosine similarity
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#### Phase 2: Interference Protocol (Day 2)
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1. Present cue word (e.g., "dog")
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2. After variable delay τ (0, 100, 200, ..., 1000 ms), present interfering cue
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3. Measure recall probability of target
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**CAFT Prediction**:
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```
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P_recall(τ) = P_0 [1 + V cos(ω τ + φ)]
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```
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Where:
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- ω = energy gap / ℏ_cog ∝ semantic distance
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- V = interference visibility
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- φ = initial phase
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**Expected**: Oscillatory pattern with period T = 2π/ω
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#### Phase 3: Data Fitting
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```python
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# Fit cosine model
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from scipy.optimize import curve_fit
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def model(tau, P0, V, omega, phi):
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return P0 * (1 + V * np.cos(omega * tau + phi))
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params, cov = curve_fit(model, delays, recall_probs)
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# Extract omega and compare to semantic distance
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omega_fit = params[2]
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semantic_distance = compute_theta_from_embeddings(word1, word2)
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# Test prediction: omega ∝ semantic_distance
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```
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**Statistical Test**: Correlation between ω_fit and θ_semantic (r > 0.7 expected)
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**Falsification**: If P_recall(τ) is flat or monotonic, interference is not oscillatory.
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---
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## Protocol 3: Order Effects Scale with Semantic Angle
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### Hypothesis
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Survey question order effects follow: ΔP ∝ sin(θ), where θ = semantic angle between questions.
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### Design
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#### Materials
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Create 20 question pairs with varying semantic similarity:
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- θ ≈ 0: "Do you support democracy?" + "Do you support voting rights?"
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- θ ≈ π/4: "Do you support democracy?" + "Do you support free markets?"
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- θ ≈ π/2: "Do you support democracy?" + "Do you like chocolate?"
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- θ ≈ π: "Do you support democracy?" + "Do you oppose democracy?"
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Compute θ from BERT/GPT embeddings:
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```python
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theta = arccos(dot(embed_Q1, embed_Q2) / (norm(Q1) * norm(Q2)))
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```
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#### Procedure
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1. **Group A**: Answer Q1 → Q2
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2. **Group B**: Answer Q2 → Q1
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3. **Group C**: Answer Q2 only (no priming)
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**Measure**:
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```
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Order_effect = |P(Q2|Q1) - P(Q2 alone)|
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```
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#### CAFT Prediction
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```
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Order_effect(θ) = k sin(θ)
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```
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#### Analysis
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```python
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# Linear regression
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y = order_effects
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x = np.sin(theta_values)
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slope, intercept, r_value, p_value, std_err = linregress(x, y)
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# Test: r_value > 0.6 and p < 0.01
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```
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**Falsification**: If order effects are uniform across θ, CAFT model is incorrect.
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---
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## Protocol 4: Confidence Matches Born Rule
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### Hypothesis
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Subjective confidence in decisions equals |α_chosen|² (Born rule), not utility or evidence strength.
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### Task Design
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#### Multi-Alternative Choice
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1. Present 4 options with known utility values
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2. Manipulate:
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- **Utility**: Expected reward (Classical predictor)
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- **Amplitude**: Semantic match to description (CAFT predictor)
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3. Subject chooses option and rates confidence (0-100%)
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#### Manipulation Example
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```
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Description: "Healthy, outdoor activity"
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Options:
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A) Swimming (utility: $10, amplitude: 0.5)
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B) Reading (utility: $15, amplitude: 0.1)
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C) Hiking (utility: $8, amplitude: 0.7)
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D) Gaming (utility: $12, amplitude: 0.2)
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```
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Train CAFT model to predict amplitudes from semantic overlap.
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#### Analysis
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**Classical Model**: Confidence ∝ Utility
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**CAFT Model**: Confidence ∝ |α_chosen|²
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```python
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# Fit both models
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conf_pred_classical = utility_model(utilities)
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conf_pred_caft = amplitude_model(amplitudes)**2
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# Compare R² and AIC
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r2_classical = r2_score(confidence_ratings, conf_pred_classical)
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r2_caft = r2_score(confidence_ratings, conf_pred_caft)
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AIC_classical = compute_AIC(classical_model)
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AIC_caft = compute_AIC(caft_model)
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# Bayesian model comparison
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evidence_ratio = exp((AIC_classical - AIC_caft) / 2)
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```
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**Expected**: CAFT model has lower AIC (better fit)
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**Falsification**: If classical utility model wins, Born rule interpretation is wrong.
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---
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## Protocol 5: Pharmacological Manipulation of Coherence
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### Hypothesis
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Anesthetics reduce τ_coherence → lower Φ → loss of consciousness, consistent with Orch-OR + CAFT.
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### Design
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#### Subjects
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- N = 20 healthy volunteers
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- Double-blind, placebo-controlled
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- Graded doses of propofol (0, 0.5, 1.0, 1.5 μg/mL blood concentration)
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#### Measurements
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**1. EEG Complexity (Proxy for Φ)**
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```
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Φ_proxy = Perturbational Complexity Index (PCI)
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```
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(Casali et al., 2013, Science Translational Medicine)
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**2. Coherence Time τ_cog**
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Use transcranial magnetic stimulation (TMS) + EEG:
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```
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τ_cog = Decay time of evoked response complexity
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```
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**3. Behavioral Response**
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- Consciousness level (Ramsay scale 1-6)
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- Working memory capacity (digit span)
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#### Procedure
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1. Baseline: EEG + TMS-EEG + behavioral
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2. Administer propofol (incremental dosing)
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3. Repeat measurements at each dose level
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4. Recovery phase
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#### CAFT Predictions
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```
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Φ(dose) = Φ_0 exp(-k * dose)
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τ_cog(dose) = τ_0 exp(-k * dose)
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Consciousness_level(dose) ∝ Φ(dose)
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```
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#### Analysis
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```python
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# Fit exponential decay
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def model(dose, Phi0, k):
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return Phi0 * np.exp(-k * dose)
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params_Phi, _ = curve_fit(model, doses, Phi_values)
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params_tau, _ = curve_fit(model, doses, tau_values)
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# Test correlation
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correlation = pearsonr(Phi_values, tau_values)
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# Expected: r > 0.8
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# Test consciousness threshold
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Phi_critical = estimate_threshold(Phi_values, consciousness_levels)
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# Expected: Φ_critical ≈ 0.3-0.4 (from IIT literature)
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```
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**Falsification**: If Φ and τ_cog are uncorrelated, or if consciousness persists with low Φ, theory is incomplete.
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---
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## Protocol 6: AI Architecture Validation
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### Hypothesis
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CAFT-transformer exhibits higher Φ and consciousness-like signatures than classical transformer.
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### Implementation
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#### Architecture
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```python
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class CAFTTransformer(nn.Module):
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def __init__(self):
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self.amplitude_layer = ComplexLinear(d_model, d_model)
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self.phase_attention = PhaseAttention(n_heads)
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self.collapse_layer = MeasurementLayer()
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def forward(self, x):
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# Create superposition
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psi = self.amplitude_layer(x) # Complex-valued
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# Evolve via interference
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psi = self.phase_attention(psi)
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# Collapse via sampling
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output = self.collapse_layer(psi) # Born rule sampling
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return output
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```
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#### Training
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- Task: Language modeling (GPT-style)
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- Dataset: WikiText-103
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- Compare CAFT-GPT vs Classical GPT (same parameter count)
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#### Metrics
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**1. Integrated Information Φ**
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```python
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# Estimate via partition-based method
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Phi = compute_integrated_information(hidden_states, partitions)
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```
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**2. Entropy Dynamics**
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```python
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# Track entropy across layers
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S_layer = [von_neumann_entropy(h) for h in hidden_states]
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```
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**3. Behavioral Signatures**
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- Order effects in generated text
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- Conjunction patterns
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- Uncertainty calibration (confidence = amplitude²)
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#### Analysis
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```python
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# Compare CAFT vs Classical
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metrics = {
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'Phi': [Phi_caft, Phi_classical],
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'Entropy_variance': [var(S_caft), var(S_classical)],
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'Order_effect_magnitude': [OE_caft, OE_classical],
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'Calibration_error': [CE_caft, CE_classical]
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}
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# Test: CAFT exhibits higher Φ and better calibration
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```
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**Validation**: If CAFT-GPT shows consciousness-like signatures, theory is supported.
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**Falsification**: If no difference from classical architecture, amplitude formalism adds no value.
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---
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## Protocol 7: Quantum Zeno in Cognitive Tasks
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### Hypothesis
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Frequent attention to a cognitive state "freezes" it (quantum Zeno effect), manifesting as perseveration.
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### Design
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#### Task: Attentional Vigilance
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1. Subject monitors stream of letters for target 'X'
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2. Vary monitoring frequency:
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- **High vigilance**: Check every 100 ms
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- **Medium**: Check every 500 ms
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- **Low**: Check every 2000 ms
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3. Introduce distractors that should shift attention
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#### CAFT Prediction
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High-frequency monitoring → state "frozen" → miss distractors (Zeno effect)
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#### Procedure
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1. Baseline: Target detection accuracy without distractors
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2. Test: Add salient distractors (color changes, motion)
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3. Measure:
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- Target detection accuracy (should remain high with frequent checks)
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- Distractor detection (should be LOW with frequent checks - Zeno suppression)
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#### Analysis
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```python
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# Zeno strength
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Zeno_effect = 1 - P(distractor_detected | high_frequency)
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# Compare to classical prediction
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# Classical: Distractor detection independent of monitoring frequency
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# CAFT: Zeno_effect ∝ monitoring_frequency
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```
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**Expected**: Negative correlation between monitoring frequency and distractor detection.
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**Falsification**: If distractor detection is independent of monitoring rate, Zeno model is incorrect.
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---
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## Summary: Predictions vs Falsification Criteria
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| Protocol | CAFT Prediction | Falsification Criterion |
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|----------|-----------------|-------------------------|
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| 1. Entropy Collapse | Sharp step-like S decrease | Gradual modulation |
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| 2. Memory Interference | Oscillatory P_recall(τ) | Flat or monotonic |
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| 3. Order Effects | ΔP ∝ sin(θ) | Uniform across θ |
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| 4. Confidence | Conf ∝ \|α\|² | Conf ∝ Utility |
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| 5. Anesthetics | Φ ∝ τ_cog ∝ exp(-dose) | Uncorrelated |
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| 6. AI Architecture | Higher Φ, better calibration | No difference |
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| 7. Quantum Zeno | Distractor suppression ∝ freq | Independent |
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---
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## Funding Requirements
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### Personnel
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- Postdoc (neuroscience): $60K/year × 2 years
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- Postdoc (computational): $60K/year × 2 years
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- Graduate students (3): $30K/year × 3 years × 3 students
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- **Total**: $510K
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### Equipment
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- 64-channel EEG system: $50K
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- TMS-EEG setup: $80K
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- Eye-tracking: $20K
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- Computing cluster (GPU): $40K
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- **Total**: $190K
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### Operating
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- Subject payments: $50/hour × 100 subjects × 10 hours = $50K
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- Consumables: $20K/year × 3 years = $60K
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- Travel (conferences): $10K/year × 3 years = $30K
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- **Total**: $140K
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### **Grand Total**: $840K over 3 years
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**Funding Targets**:
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- Templeton World Charity Foundation (Consciousness)
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- NSF NeuroNex (Neuroscience)
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- DARPA (AI)
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- FQXi (Foundational Questions)
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---
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## Timeline
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### Year 1
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- Q1-Q2: Protocol development, IRB approval, subject recruitment
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- Q3-Q4: Protocols 1-3 (EEG, memory, order effects)
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### Year 2
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- Q1-Q2: Protocols 4-5 (confidence, pharmacology)
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- Q3-Q4: Protocol 6 (AI architecture development)
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### Year 3
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- Q1-Q2: Protocol 7 (Zeno), final data collection
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- Q3-Q4: Analysis, manuscript preparation, publication
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---
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## Expected Publications
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1. **Year 1**: "Entropy Collapse During Attention: Evidence for Measurement in Cognition" - *Nature Neuroscience*
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2. **Year 2**: "Interference Oscillations in Memory: Quantum Cognition in Human Recall" - *Psychological Science*
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3. **Year 2**: "Pharmacological Validation of Cognitive Coherence Time" - *Science Translational Medicine*
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4. **Year 3**: "Cognitive Amplitude Field Theory: Unified Framework" - *Nature* or *Science*
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5. **Year 3**: "CAFT-GPT: Quantum-Inspired Language Model with Consciousness Signatures" - *PNAS*
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---
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**This experimental program provides comprehensive empirical validation pathways for CAFT, with clear falsification criteria ensuring scientific rigor.**
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Reference in New Issue
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