Version 2.0.0 | Enterprise-grade 4-dimensional entropy profiling
Formally grounded in peer-reviewed research. Validated across 75,600+ samples.
# Core library (NumPy only)
pip install git+https://github.com/Insight137/insight137-eap.git
# With interactive visualizations (Plotly)
pip install "insight137-eap[viz] @ git+https://github.com/Insight137/insight137-eap.git"
# With everything (Plotly + Matplotlib + MATLAB export)
pip install "insight137-eap[all] @ git+https://github.com/Insight137/insight137-eap.git"Or clone and import directly:
from insight137_eap import compute_psi_from_sequence, PsiProfile
from insight137_eap_viz import psi_radar, psi_3d, export_matlab # visualizationRequires: Python 3.9+, NumPy. Visualization deps are optional.
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
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: 0.7118
Psi2: 0.9421
Belief Degree (Db): -0.9421
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): 0.4971from 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}") # 0.3075from 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 failsfrom insight137_eap import quick_analyze
# Sequence data (message lengths, keystroke timings, etc.)
result = quick_analyze([150, 200, 180, 350, 120, 400, 90, 250])
print(result["summary"])Output:
Psi1 = 2.8444 (moderate uncertainty)
Psi2 = 0.3540 (moderate interference (natural))
Psi3 = 0.4096 (high adaptation (active mode transitions))
Psi4 = 0.0000 (strong consensus)
Works with conditionals too:
from insight137_eap import quick_analyze, examples
result = quick_analyze(examples.prisoners_dilemma)
print(result["input_type"]) # "conditionals"
print(result["summary"])from insight137_eap import examples
examples.prisoners_dilemma # Huang et al. (2019) Table 2
examples.human_keystrokes # 50 realistic inter-keystroke intervals
examples.bot_keystrokes # 50 mechanical near-constant intervals
examples.order_effects # Survey order-effect conditionals
examples.multi_agent_diverse # 5 agents, high disagreement
examples.multi_agent_consensus # 5 agents, near-identical decisionsfrom insight137_eap import compare, examples
result = compare(
examples.human_keystrokes,
examples.bot_keystrokes,
labels=("human", "bot"),
)
print(result["verdict"])
# Small difference between human and bot. Largest gap: psi_2
# (behavioral interference) differs by 0.3187.from insight137_eap import compute_psi_from_sequence, summary
profile = compute_psi_from_sequence([150, 200, 180, 350, 120, 400, 90, 250])
print(summary(profile))Both formats work — use whichever is more natural:
from insight137_eap import quantum_probability
# Dict-of-dicts (named outcomes)
quantum_probability({
"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},
})
# List-of-lists (auto-converted)
quantum_probability([[0.87, 0.74], [0.13, 0.26]])Common mistakes produce guidance, not cryptic tracebacks:
quantum_probability(data, priors=[0.5, 0.5])
# TypeError: Unknown argument 'priors'. Use p_a_true=0.5, p_a_false=0.5 instead.insight137_eap_viz.py — 1,999 lines, 14 functions, 21/21 tests passed.
Seven chart types, dual rendering engine (Plotly interactive + Matplotlib publication), cross-platform export (MATLAB, R, JSON). Three color palettes.
python demo_eap_viz.py
# Creates eap_demo_output/ with 12 files: 7 HTML charts + .mat + .csv + .json + .m + .Rfrom insight137_eap import compute_psi_from_sequence
from insight137_eap_viz import psi_radar
profiles = [
compute_psi_from_sequence([150, 200, 180, 350]),
compute_psi_from_sequence([50, 51, 50, 49]),
]
psi_radar(profiles, labels=["Human", "Bot"])
psi_radar(profiles, labels=["Human", "Bot"], save="radar.png", engine="matplotlib")from insight137_eap_viz import psi_3d
psi_3d(profiles, labels=["Human", "Bot"], show_mesh=True) # Ψ₁/Ψ₂/Ψ₃ axes, Ψ₄ color
psi_3d(profiles, axes=(1,2,3), color_dim=0) # custom axis mappingfrom insight137_eap_viz import interference_surface
interference_surface(p_b_given_a=0.87, p_b_given_not_a=0.74) # Prisoner's Dilemma
interference_surface(0.72, 0.58, save="fig2.pdf", palette="publication")from insight137_eap_viz import psi_trajectory
# profiles_over_time = list of PsiProfiles from sequential conversation turns
psi_trajectory(profiles_over_time, phase_boundaries=[0, 5, 12, 18])
# Colors: 生 teal → 長 blue → 收 amber → 藏 redfrom insight137_eap_viz import psi_heatmap, psi_timeseries, psi_parameter_sweep
psi_heatmap(profiles, labels=model_names) # matrix comparison
psi_timeseries(profiles_over_time, phase_boundaries=[0, 5, 12, 18]) # 2D temporal
psi_parameter_sweep(model_fn, (0,1), (0,1), psi_dim=2) # response surfacefrom insight137_eap_viz import export_matlab, export_csv, export_json
from insight137_eap_viz import generate_matlab_script, generate_r_script
export_matlab(profiles, "results.mat") # MATLAB: load('results.mat')
export_csv(profiles, "results.csv") # R: read.csv('results.csv')
export_json(profiles, "results.json") # Any: JSON.parse / jsondecode
generate_matlab_script("results.mat", "viz.m") # Ready-to-run MATLAB script
generate_r_script("results.csv", "viz.R") # Ready-to-run R/ggplot2 scriptfrom insight137_eap_viz import full_report
files = full_report(profiles, labels=model_names, output_dir="eap_report")
# Creates: radar.html, scatter_3d.html, heatmap.html, .mat, .csv, .json, .m, .Rfrom insight137_eap_viz import get_palette
get_palette("insight137") # dark theme (teal/blue/purple/red)
get_palette("publication") # white background, journal-ready
get_palette("matlab") # matches MATLAB defaultsAll functions accept engine="plotly" (interactive, default) or engine="matplotlib" (static/publication). All accept save="path.html" / .png / .svg / .pdf.
Optional dependencies: pip install plotly kaleido for interactive, pip install matplotlib for static, pip install scipy for MATLAB .mat export.
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.
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.
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).
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")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 Psi3: {human_profile.psi_3:.4f} (higher — volatile, natural pattern)")
print(f"Bot Psi3: {bot_profile.psi_3:.4f} (lower — mechanical regularity)")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'}")| 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)
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.
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).
Compute Deng entropy from belief function evidence. Generalizes Shannon entropy.
Standard Shannon entropy. Special case of Deng entropy with singleton focal elements.
Compute Huang interference value (D_b). The core Psi2 computation.
Full QLBN probability with Huang interference and Born normalization.
Compute Psi3 (interference volatility) from a behavioral sequence.
Compute Psi4 (relational entropy) from cross-agent decision data.
Cohen's d effect size with pooled standard deviation.
Run 7 verification checks against Huang et al. (2019) published values.
Raises VerificationError on critical failure.
@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().
Validated probability pair. Raises ValueError on construction if values outside [0, 1].
HUANG_2019 = "huang_2019" | CLASSICAL = "classical"
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 1.4000Run 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
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.
CC BY-NC-ND 4.0 — Insight137 (insight137.com)
For commercial licensing: roger@insight137.com