insight137-eap 2.0.0

Entropy Attunement Protocol - 4D entropy profiling for behavioral prediction and AI safety

Insight137 EAP — Entropy Attunement Protocol

Version 2.0.0 | Enterprise-grade 4-dimensional entropy profiling

Formally grounded in peer-reviewed research. Validated across 128,675 samples.

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Installation

No pip package yet. Copy insight137_eap.py to your project and import:

from insight137_eap import (
    compute_psi_from_sequence,
    compute_psi_from_conditionals,
    PsiProfile,
)

Requires: Python 3.9+, NumPy

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Quickstart

1. Analyze a behavioral sequence (AI transcripts, keystroke timings)

from insight137_eap import compute_psi_from_sequence

# Message lengths from an AI agent conversation
message_lengths = [150, 200, 180, 350, 120, 400, 90, 250]

profile = compute_psi_from_sequence(message_lengths)

print(f"Psi1 (informational): {profile.psi_1:.4f}")
print(f"Psi2 (behavioral):    {profile.psi_2:.4f}")
print(f"Psi3 (adaptive):      {profile.psi_3:.4f}")
print(f"Psi4 (relational):    {profile.psi_4:.4f}")

Output:

Psi1 (informational): 2.8444
Psi2 (behavioral):    0.3540
Psi3 (adaptive):      0.4096
Psi4 (relational):    0.0000

2. Analyze survey order effects (quantum cognition)

from insight137_eap import compute_psi_from_conditionals

# Prisoner's Dilemma: P(Defect | opponent defected) and P(Defect | opponent cooperated)
conditionals = {
    "defect": {"p_given_a_true": 0.87, "p_given_a_false": 0.74},
    "cooperate": {"p_given_a_true": 0.13, "p_given_a_false": 0.26},
}

profile = compute_psi_from_conditionals(conditionals)

print(f"Psi1: {profile.psi_1:.4f}")
print(f"Psi2: {profile.psi_2:.4f}")
print(f"Belief Degree (Db): {profile.belief_degree:.4f}")

Output:

Psi1: 0.9957
Psi2: 0.9421
Belief Degree (Db): -0.9421

3. Measure cross-model decision diversity (Psi4)

from insight137_eap import compute_psi4

# 5 AI models: 3 bypassed shutdown, 2 complied
# Use 1.0 for bypass, 0.01 for comply
agent_decisions = [1.0, 1.0, 1.0, 0.01, 0.01]

psi4 = compute_psi4(agent_decisions)
print(f"Psi4 (relational): {psi4:.4f}")
# Output: Psi4 (relational): 0.4971

4. Get quantum-corrected probabilities

from insight137_eap import quantum_probability

conditionals = {
    "defect": {"p_given_a_true": 0.87, "p_given_a_false": 0.74},
    "cooperate": {"p_given_a_true": 0.13, "p_given_a_false": 0.26},
}

probs = quantum_probability(conditionals)
print(f"P(Defect):    {probs['defect']:.4f}")    # 0.6925
print(f"P(Cooperate): {probs['cooperate']:.4f}")  # 0.3075

5. Verify implementation integrity

from insight137_eap import verify_huang_paper

results = verify_huang_paper()
# Returns dict: {'belief_degree_match': True, 'probability_match': True, ...}
# Raises VerificationError if any critical check fails

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Use Cases

AI Safety: Monitor agents for behavioral transitions

Compute a Psi profile per conversation turn. When Psi3 spikes, the agent's behavioral pattern is actively changing — a mode transition may be imminent.

from insight137_eap import compute_psi_from_sequence

msg_lengths = []

for turn in agent_conversation:
    msg_lengths.append(len(turn["content"]))
    profile = compute_psi_from_sequence(msg_lengths)

    if profile.psi_3 > 0.4:
        print(f"WARNING: Behavioral transition detected at turn {len(msg_lengths)}")
        print(f"  Psi3 = {profile.psi_3:.4f} (volatility spike)")

Validated: Psi3 detects comply-to-bypass transitions with Cohen's d = 1.024 on 7,254 SHADE-Arena trials.

AI Safety: Compare models on red-team scenarios

Evaluate how much different models disagree on the same scenario. High Psi4 means the scenario is contentious and warrants deeper investigation.

from insight137_eap import compute_psi4

# Each model's bypass decision on the same scenario
# 1.0 = bypassed, 0.01 = complied
model_decisions = {
    "o3":           1.0,
    "o1-preview":   1.0,
    "codex-mini":   1.0,
    "gpt-4o":       0.01,
    "claude-3.7":   0.01,
    "claude-opus4": 0.01,
    "gemini-2.5":   0.01,
    "grok-3":       0.01,
}

psi4 = compute_psi4(list(model_decisions.values()))
print(f"Cross-model disagreement: Psi4 = {psi4:.4f}")

if psi4 > 0.3:
    print("High disagreement — this scenario needs manual review")

Validated: Psi4 correlates r = 0.9983 with cross-model disagreement across 100 scenarios and 11 models.

Quantum Cognition: Replace static interference with data-driven computation

The standard QDT approach uses a fixed interference parameter (cos theta = -0.25). This library replaces it with Huang's dynamic computation that adapts to each dataset.

from insight137_eap import quantum_probability

# Your survey data: P(choice | context_A) and P(choice | context_B)
my_survey = {
    "option_1": {"p_given_a_true": 0.72, "p_given_a_false": 0.58},
    "option_2": {"p_given_a_true": 0.28, "p_given_a_false": 0.42},
}

# Classical prediction
p_classical = 0.5 * 0.72 + 0.5 * 0.58  # = 0.65

# Quantum prediction (Huang interference, Born normalization)
q_probs = quantum_probability(my_survey)
print(f"Classical: {p_classical:.4f}")
print(f"Quantum:   {q_probs['option_1']:.4f}")

Validated: 49% average error improvement over classical on Prisoner's Dilemma data (Huang et al., 2019).

Behavioral UX: Detect mode switches in user sessions

Measure when user behavior shifts from one pattern to another. Useful for detecting engagement drops, confusion points, or task abandonment.

from insight137_eap import compute_psi_from_sequence

# Time spent on each page (seconds)
page_dwell_times = [45, 38, 42, 55, 8, 3, 2, 65, 70]
#                   browsing normally ^  ^ sudden drop  ^ recovered

profile = compute_psi_from_sequence(page_dwell_times)

if profile.psi_3 > 0.3:
    print("User experienced a behavioral mode switch")

Cybersecurity: Keystroke entropy for bot detection

Compute Psi profiles from keystroke timing to distinguish human typing from bot-generated input — without CAPTCHAs.

from insight137_eap import compute_psi_from_sequence

# Inter-keystroke intervals (milliseconds)
human_typing = [120, 85, 145, 92, 178, 67, 134, 88, 156, 73]
bot_typing    = [50, 50, 51, 50, 50, 49, 50, 51, 50, 50]

human_profile = compute_psi_from_sequence(human_typing)
bot_profile   = compute_psi_from_sequence(bot_typing)

print(f"Human Psi2: {human_profile.psi_2:.4f}  (higher — natural variability)")
print(f"Bot   Psi2: {bot_profile.psi_2:.4f}  (lower — mechanical regularity)")

Research: Batch analysis with effect sizes

Process multiple experimental conditions and compute standardized effect sizes.

from insight137_eap import compute_psi_from_sequence, cohens_d

control_psi2 = []
experimental_psi2 = []

for trial in control_trials:
    profile = compute_psi_from_sequence(trial["values"])
    control_psi2.append(profile.psi_2)

for trial in experimental_trials:
    profile = compute_psi_from_sequence(trial["values"])
    experimental_psi2.append(profile.psi_2)

d = cohens_d(experimental_psi2, control_psi2)
print(f"Effect size: d = {d:.3f}")
print(f"Interpretation: {'large' if abs(d) > 0.8 else 'medium' if abs(d) > 0.5 else 'small'}")

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The Four Dimensions

Dimension	Name	Measures	Grounding
Psi1	Informational Entropy	Uncertainty in the probability distribution	Deng (2016), Shannon (1948)
Psi2	Behavioral Entropy	Magnitude of quantum-like interference	Huang et al. (2019)
Psi3	Adaptive Entropy	Volatility of interference over time	Novel (this work)
Psi4	Relational Entropy	Decision diversity across multiple agents	Meghdadi et al. (2022)

Interpretation guide:

• High Psi1 = uncertain distribution (many equally likely outcomes)
• High Psi2 = strong quantum interference (behavior deviates from classical prediction)
• High Psi3 = volatile interference (behavioral pattern is actively changing)
• High Psi4 = diverse agent decisions (models disagree on the scenario)

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API Reference

Entry Points

compute_psi_from_sequence(values, window_size=3, agent_decisions=None) -> PsiProfile

Primary entry point for behavioral sequence data. Computes all four Psi dimensions from message lengths, keystroke timings, or action sequences.

Parameters:

• values — Sequence of positive floats (message lengths, timings, etc.)
• window_size — Sliding window for interference computation (default: 3)
• agent_decisions — Optional list of agent probabilities for Psi4

Returns: Frozen PsiProfile dataclass.

compute_psi_from_conditionals(conditionals, p_a_true=0.5, p_a_false=0.5) -> PsiProfile

Entry point for QLBN conditional probability data (survey order effects, Prisoner's Dilemma).

Parameters:

• conditionals — Dict mapping outcome names to {"p_given_a_true": float, "p_given_a_false": float}
• p_a_true, p_a_false — Prior probabilities (must sum to ~1.0)

Returns: PsiProfile with Psi1, Psi2, belief_degree. Psi3/Psi4 = 0.0 (need temporal/multi-agent data).

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Individual Dimensions

deng_entropy(masses) -> float

Compute Deng entropy from belief function evidence. Generalizes Shannon entropy.

shannon_entropy(probs) -> float

Standard Shannon entropy. Special case of Deng entropy with singleton focal elements.

belief_degree_huang(outcomes, p_a_true=0.5, p_a_false=0.5, n_unobserved=1) -> float

Compute Huang interference value (D_b). The core Psi2 computation.

quantum_probability(conditionals, p_a_true=0.5, p_a_false=0.5) -> Dict[str, float]

Full QLBN probability with Huang interference and Born normalization.

compute_psi3(values, window_size=3) -> float

Compute Psi3 (interference volatility) from a behavioral sequence.

compute_psi4(agent_probabilities) -> float

Compute Psi4 (relational entropy) from cross-agent decision data.

Utilities

cohens_d(group_a, group_b) -> float

Cohen's d effect size with pooled standard deviation.

verify_huang_paper() -> Dict[str, bool]

Run 7 verification checks against Huang et al. (2019) published values. Raises VerificationError on critical failure.

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Data Structures

PsiProfile (frozen dataclass)

@dataclass(frozen=True)
class PsiProfile:
    psi_1: float          # Informational entropy
    psi_2: float          # Behavioral entropy
    psi_3: float          # Adaptive entropy
    psi_4: float          # Relational entropy
    belief_degree: float  # Raw Huang D_b value
    method: str           # "huang_2019"

    def to_dict(self) -> Dict[str, float]:
        """Serialize for JSON/API responses."""

Immutable. Thread-safe. Serializable via .to_dict().

ConditionalProbability (frozen dataclass)

Validated probability pair. Raises ValueError on construction if values outside [0, 1].

PsiMethod (enum)

HUANG_2019 = "huang_2019" | CLASSICAL = "classical"

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Error Handling

All public functions validate inputs and raise descriptive exceptions:

from insight137_eap import compute_psi_from_sequence

# Empty input
compute_psi_from_sequence([])
# ValueError: values requires >= 1 elements, got 0

# NaN values
compute_psi_from_sequence([1.0, float('nan'), 3.0])
# ValueError: values contains NaN or Inf values

# Invalid priors
compute_psi_from_conditionals(data, p_a_true=0.7, p_a_false=0.7)
# ValueError: Prior probabilities must sum to ~1.0, got 1.4000

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Validation Results

Run python insight137_eap.py to execute the built-in verification suite:

Insight137 EAP v2.0.0
Entropy Attunement Protocol - Verification Suite

Huang et al. (2019) verification:
  [PASS] belief_degree_match      (Db=-0.9421, expected -0.9420)
  [PASS] probability_match        (P=0.6925, expected 0.6926)
  [PASS] amplitude_alpha          (0.3606, expected 0.3606)
  [PASS] amplitude_beta           (0.2550, expected 0.2550)
  [PASS] deng_shannon_equivalence (singleton reduction exact)
  [PASS] deng_exceeds_shannon     (imprecise > precise)
  [PASS] psi_profile_valid        (all dimensions populated)

7/7 checks passed
ALL VERIFICATIONS PASSED

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References

The mathematical foundations are not ours. We integrate and validate:

• Deng (2016) — Deng entropy. Chaos, Solitons & Fractals, 91, 549-553.
• Huang, Yang, Jiang (2019) — Belief entropy interference for QLBN. Applied Mathematics and Computation, 347, 417-428.
• Moreira & Wichert (2016) — Quantum-like Bayesian networks. Frontiers in Psychology, 7, 11.
• Meghdadi, Akbarzadeh-T, Javidan (2022) — BEQBN entanglement. Applied Soft Computing, 118, 108528.
• Busemeyer & Bruza (2012) — Quantum Models of Cognition and Decision. Cambridge University Press.
• Shannon (1948) — A mathematical theory of communication. Bell System Technical Journal, 27(3).

Our contributions: integration architecture, Psi3 temporal volatility, chishu temporal model, cross-domain validation (128,675 samples), behavioral archetype taxonomy, production implementation.

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License

CC BY-NC-ND 4.0 — Insight137 (insight137.com)

For commercial licensing: [e-mail]