cognitive-discovery-system 1.1.4

Pure Python computational science system — quantum simulation, FFT, optimization, probability, statistics, and more.

cognitive-discovery-system

Open-source computational science platform for research, simulation, and discovery.

CDS brings together quantum computing simulation, statistical analysis, signal processing, optimization, probability, and scientific computing in a single, dependency-light Python package. Every module is pure Python — no NumPy or SciPy required.

The system also includes built-in support for structured hypothesis generation, making it easier to explore ideas and connect them to simulation or analysis tools.

v1.1.4 stable release. Contributions welcome!

Documentation | Tutorials | Quick Start

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Latest Update: v1.1.4 — documentation, CI, and housekeeping cleanup. No API or behavior changes: removed cosmetic distractions from issue templates/docs, fixed CI workflow schemas, deleted ~3 500 lines of no-op autograd shim code never exercised at runtime, and aligned the PyPI distribution name (cognitive-discovery-system) with the repository name. The system spans 17 modules, 1165 tests, and ~99.6% coverage, all in readable pure Python.

Contents

• Why CDS?
• Citing CDS
• Modules
• Quick Start
• Intelligence over Brute Force
• ASCII Visualization & Tools
• Interactive Dashboard
• Scientific Case Studies
• Examples
• Architecture
• Vision
• Recent Improvements
• Contributing
• Automation and Maintenance Workflows
• Security
• License
• Contact

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Why CDS?

• Zero heavy dependencies — pure Python implementations you can read and learn from
• Quantum simulation — single & multi-qubit circuits with entanglement
• Built for discovery — hypothesis generation with structured outputs (assumptions, predictions, confidence) plus a Protocol for custom implementations
• Broad scope — 17 modules covering math, physics, stats, ML, signals, optimization, graph theory, ODEs, numerical integration, Monte Carlo, knowledge organization, and educational NLP (BPE + embeddings)
• 1165 tests (see CI) — thoroughly tested with ~99% code coverage
• Practical automation — workflows for PR checklists, dependency updates, and releases to keep maintenance manageable
• CLI included — interactive tools, demos, and ASCII visualization from your terminal

CDS vs other libraries

Need	CDS	NumPy/SciPy	SymPy	PennyLane
Pure-Python (no compile, no binary)	yes	no (C/Fortran)	yes	no (needs Qiskit/Cirq)
Quantum simulation	yes, single/multi-qubit	no	minimal	yes, full SDK
Hypothesis generation (structured)	yes	no	no	no
Educational NLP (BPE, embeddings)	yes, from-scratch	no	no	no
Single-package umbrella (math+physics+stats+ML+signals+NLP)	yes	no, split across 6+	partial	no, focused
Production-ready CI/CD (multi-OS matrix, signed releases)	yes	n/a	partial	yes
Educational / readable source	yes	no, large surface	yes	no
Edge runtime (no BLAS)	yes	no	partial	no
Heavy numerical performance (>10⁷ ops)	no, use NumPy instead	yes	no	yes (GPU)

When to use CDS: teaching, prototyping, scientific exploration, edge deployments, custom algorithm development. When to reach for NumPy/SciPy/PennyLane: production HPC, GPU-accelerated quantum, distributed compute.

Citing CDS

If CDS is useful in your research or publications, please cite it using the information in CITATION.cff at the repository root. This helps give proper credit and track adoption in scientific work.

Modules

Module	Description
cds.quantum	Single & multi-qubit simulation — Hadamard, Pauli, CNOT, SWAP, Toffoli, Bell/GHZ states, entanglement detection
cds.optimization	Gradient descent, Newton's method, Adam optimizer, golden section search
cds.ml	Pure Python Neural Networks — MLP, dense layers, Adam-based training
cds.signals	DFT, radix-2 FFT/IFFT (O(N log N)), 2D FFT/IFFT, convolution, power spectrum, filtering
cds.probability	Gaussian, uniform, exponential, binomial, Poisson distributions
cds.stats	Descriptive stats, Pearson correlation, linear regression, t-test, chi-square, ANOVA
cds.math_utils	Numerical calculus, O(N³) LU / QR / Cholesky, eigenvalue (power iteration), Gram-Schmidt, matrix inverse
cds.data_analysis	Mini-Pandas DataSet for filtering/grouping, CSV loading, ASCII visualization
cds.scientific	Physical constants, formulas (KE, gravity, gas law, Schwarzschild, de Broglie, escape velocity)
cds.graph	BFS, DFS, Dijkstra shortest path, Kruskal MST, topological sort, cycle detection
cds.modeling	Symbolic algebra — expressions, symbolic differentiation, simplification, LaTeX export, MathModel equation systems, root-finding & parameter fitting
cds.knowledge	Knowledge organization — concept graph with typed relations, research notes notebook, ranked structured retrieval (JSON persistence)
cds.montecarlo	Monte Carlo integration, π estimation, Buffon's needle, random walks (1D/2D)
cds.diffeq	Euler method, RK4, midpoint method, ODE system solver
cds.numerical_integration	Deterministic quadrature — trapezoid, Simpson 1/3 & 3/8, Romberg, Gauss-Legendre, adaptive Simpson
cds.nlp	Educational NLP from scratch — BPE tokenizer, sinusoidal embeddings, multi-head attention, Transformer block, scalar autograd (SGD/Adam), MiniGPT demo
cds.hypothesis	Structured hypothesis generation with prompt templates for custom research workflows

Quick Start

git clone https://github.com/Furox88/cognitive-discovery-system.git
cd cognitive-discovery-system
python -m venv .venv
source .venv/bin/activate
pip install -e ".[dev]"

# Run tests
pytest

# CLI usage
cds --help
cds constants
cds calc ke
cds modules
cds hypothesis "What causes the Hubble tension?"

Intelligence over Brute Force

CDS is built on the principle that algorithmic improvements matter more than raw loop speed. Pure Python cannot match C-extensions for tight loops, so CDS closes the gap where it can through better algorithms:

• Quantum Simulation: Instead of multiplying state matrices for every shot, CDS uses O(1) probabilistic sampling with explicit state collapse, which is significantly faster than the naive shot-by-shot approach.
• Linear Algebra: Uses O(N³) Partial Pivoting LU Decomposition in place of the naive O(N!) determinant expansion.
• Signal Processing: Zero-padded O(N log N) FFT and FFT-based convolution via the Convolution Theorem.
• Neural Networks: Adam optimizers with momentum state persistence.

See the full Intelligence & Performance Benchmark Report for detailed figures.

ASCII Visualization & Tools

You don't need heavy plotting libraries to inspect your data. CDS includes a built-in terminal visualization engine:

# Plot a sine wave or data series directly in your terminal
cds plot "1, 5, 3, 8, 4, 9" --title "My Data"

Outputs scale-aware ASCII line plots and bar charts.

Interactive Dashboard

CDS includes an Interactive Web Dashboard for scientific exploration. Launch it from your terminal:

pip install "cognitive-discovery-system[dashboard]"
cds dashboard

The dashboard includes a Hypothesis Engine, Quantum Circuit Simulator, Neural Network training visualizer, and Statistical testing lab.

Scientific Case Studies

Explore how CDS is used to solve real-world research problems:

1. Hubble Tension Analysis: Generating and testing hypotheses for the expansion rate of the universe.
2. Quantum-ML Integration: Using quantum circuit measurements as features for classical Neural Network training.

Examples

See the examples/ directory for runnable demos and docs/research-workflows.md for guidance on embedding CDS in research pipelines.

Hypothesis Generation (cognitive discovery)

# Basic demo
python examples/hypothesis_demo.py

# With stats / experiment sketch example
python examples/hypothesis_with_stats_demo.py

# Custom generator implementation (using the HypothesisGenerator Protocol)
python examples/hypothesis_custom_generator.py

# Or via CLI
cds hypothesis "What causes the Hubble tension?"

Quantum Circuit (single qubit)

from cds.quantum import QuantumCircuit, hadamard, pauli_x, simulate

circuit = QuantumCircuit().add(hadamard()).add(pauli_x())
result = circuit.run()
print(result.probabilities())

counts = simulate(circuit, shots=1000)
print(counts)  # {0: ~500, 1: ~500}

Multi-Qubit & Entanglement

from cds.quantum import (
    QuantumRegister, h_gate, cnot, bell_state,
    ghz_state, is_entangled,
)

# Bell state (|00⟩ + |11⟩) / √2
reg = bell_state(0)
print(is_entangled(reg))  # True
print(reg.measure_shots(shots=1000))  # {'00': ~500, '11': ~500}

# 4-qubit GHZ state
ghz = ghz_state(4)
counts = ghz.measure_shots(shots=1000)
print(counts)  # {'0000': ~500, '1111': ~500}

Optimization

from cds.optimization import gradient_descent, newton_method

# Find minimum of (x-3)²
result = gradient_descent(lambda x: (x - 3) ** 2, x0=10.0, lr=0.1)
print(f"x = {result.x:.6f}")  # ~3.0

# Find √2 using Newton's method
result = newton_method(lambda x: x ** 2 - 2, x0=1.5)
print(f"√2 = {result.x:.10f}")  # 1.4142135624

Signal Processing

from cds.signals import dft, fft_radix2, convolve, low_pass_filter

# FFT of a signal
signal = [complex(i) for i in range(8)]
spectrum = fft_radix2(signal)

# Convolution
result = convolve([1.0, 2.0, 3.0], [0.5, 0.5])
print(result)  # [0.5, 1.5, 2.5, 1.5]

Probability Distributions

from cds.probability import gaussian_pdf, binomial_pmf, poisson_pmf

# Gaussian PDF at x=0
print(gaussian_pdf(0.0, mu=0, sigma=1))  # 0.3989...

# Binomial: P(3 heads in 5 fair flips)
print(binomial_pmf(3, 5, 0.5))  # 0.3125

# Poisson: P(k=2, λ=3)
print(poisson_pmf(2, 3.0))  # 0.2240...

Statistics

from cds.stats import mean, stdev, correlation, linear_regression

data = [12.5, 14.3, 11.8, 15.1, 13.7]
print(f"mean={mean(data):.2f}, std={stdev(data):.2f}")

x = [1, 2, 3, 4, 5]
y = [2.1, 3.9, 6.2, 7.8, 10.1]
reg = linear_regression(x, y)
print(f"y = {reg.slope:.2f}x + {reg.intercept:.2f}, R²={reg.r_squared:.3f}")

Machine Learning

from cds.ml import Layer, MLP

# Simple XOR-like Neural Network
net = MLP([
    Layer(2, 4, activation="relu"),
    Layer(4, 1, activation="sigmoid")
])
X, y = [[0, 0], [0, 1], [1, 0], [1, 1]], [[0], [1], [1], [0]]

# Train with built-in Adam optimizer
history = net.train(X, y, epochs=50, lr=0.1)
print(f"Final loss: {history['final_loss']:.4f}")

Data Analysis & Visualization

from cds.data_analysis import DataSet, plot_bar

# Mini-Pandas DataSet for filtering and grouping
data = [{"name": "A", "score": 88}, {"name": "B", "score": 92}]
ds = DataSet(data)
filtered = ds.filter(lambda row: row["score"] > 90)
print(filtered.column("name"))  # ['B']

# Terminal Visualization
scores = {row["name"]: row["score"] for row in ds.to_list()}
print(plot_bar(scores, title="Scores"))

Scientific Computing

from cds.scientific import kinetic_energy, escape_velocity, get_constant

print(get_constant("c"))          # speed of light
print(kinetic_energy(10, 5))      # 125.0 J
print(escape_velocity(5.972e24, 6.371e6))  # ~11186 m/s

Graph Theory

from cds.graph import Graph, dijkstra, kruskal_mst, bfs

g = Graph(n_vertices=4, directed=False)
g.add_edge(0, 1, 1.0)
g.add_edge(1, 2, 2.0)
g.add_edge(2, 3, 3.0)
g.add_edge(0, 3, 10.0)

dist, prev = dijkstra(g, 0)
print(dist)  # {0: 0.0, 1: 1.0, 2: 3.0, 3: 6.0}

edges, total = kruskal_mst(g)
print(f"MST weight: {total}")  # 6.0

Mathematical Modeling

from cds.modeling import Variable, Sin, Exp, solve_equation

x = Variable("x")
expr = Sin(x) * Exp(x)        # sin(x) * e^x

# Symbolic derivative (chain + product rules)
print(expr.diff("x").to_str())

# Solve x^2 - 2 = 0  =>  x = sqrt(2)
root = solve_equation(Variable("x") ** 2 - 2, variable="x", x0=1.0)
print(root.x)                 # ~1.4142
print(root.converged)         # True

Knowledge Organization

from cds.knowledge import KnowledgeGraph, Notebook, search

kg = KnowledgeGraph(name="Cosmology")
kg.link_concepts("Dark Energy", "Hubble Constant", kind="affects")
kg.link_concepts("Hubble Constant", "CMB", kind="constrains")

# Shortest path across the (undirected) graph
print(kg.find_path("Dark Energy", "CMB"))
# ['Dark Energy', 'Hubble Constant', 'CMB']

nb = Notebook(name="Lab Book")
nb.add_note("n1", "Hubble Tension", "Local vs CMB H0 disagree.",
            tags=["experiment"], linked_concepts=["Hubble Constant"])

# Ranked retrieval across both concepts and notes
for hit in search(kg, nb, query="hubble"):
    print(hit.concept_name or hit.note_id, hit.score)

Monte Carlo Simulation

import math
from cds.montecarlo import estimate_pi, mc_integrate

if __name__ == "__main__":
    # Unit-circle method
    result = estimate_pi(n_samples=100_000, seed=42)
    print(f"PI approximation: {result.estimate:.4f}")

    # Integration
    area = mc_integrate(math.sin, 0, math.pi, n_samples=100_000)
    print(f"Integral of sin(x): {area.estimate:.4f}")

Differential Equations

from cds.diffeq import rk4, solve_system
import math

# dy/dt = -y, y(0)=1  =>  y(t) = e^(-t)
sol = rk4(lambda t, y: -y, t0=0, y0=1.0, t_end=2.0)
print(f"y(2) = {sol.y[-1]:.6f}")  # ~0.135335 (e^-2)

# Harmonic oscillator: x'' = -x
def harmonic(t, y):
    return [y[1], -y[0]]
t_vals, y_vals = solve_system(harmonic, 0, [1.0, 0.0], math.pi)
print(f"x(π) = {y_vals[-1][0]:.4f}")  # ~-1.0

Numerical Integration

import math
from cds.numerical_integration import simpson, gaussian_quadrature, romberg

# ∫_0^π sin(x) dx = 2
print(simpson(math.sin, 0, math.pi, n=100))  # ~2.0, O(h⁴)

# Gauss-Legendre: exact for polynomials up to degree 2n-1
print(gaussian_quadrature(lambda x: x**7, 0, 1, n=4))  # 0.125 (exact)

# Romberg reaches full machine precision on smooth integrands
result = romberg(math.exp, 0, 1, tol=1e-12)
print(f"∫e^x = {result.value:.10f}")  # ~1.7182818285

Architecture

src/cds/
├── quantum/        # Quantum circuit simulation (single & multi-qubit)
├── optimization/   # Gradient descent, Newton, Adam, line search
├── ml/             # Neural Networks (MLP, Layers, Adam training)
├── signals/        # DFT, FFT, convolution, filtering
├── probability/    # Probability distributions & sampling
├── stats/          # Statistical analysis & regression
├── math_utils/     # Calculus, linear algebra, eigenvalues, Gram-Schmidt
├── data_analysis/  # Mini-Pandas DataSet, CSV loading, ASCII viz
├── scientific/     # Physical constants & formulas
├── graph/          # Graph algorithms (Dijkstra, BFS, DFS, Kruskal MST)
├── modeling/       # Symbolic math (expressions, MathModel, solvers)
├── knowledge/      # Knowledge graph, concepts, notes, structured retrieval
├── montecarlo/     # Monte Carlo methods (π, integration, random walks)
├── diffeq/         # ODE solvers (Euler, RK4, midpoint)
├── numerical_integration/  # Deterministic quadrature (trapezoid, Simpson, Romberg, Gauss-Legendre)
├── nlp/            # Educational NLP (BPE, embeddings, attention, autograd, MiniGPT)
├── hypothesis/     # Hypothesis generation
├── core/           # Shared models, config
└── cli.py          # Command-line interface

examples/           # Runnable demo scripts
tests/              # 1165 tests (see CI)
docs/               # MkDocs documentation, tutorials, benchmarks

.github/workflows/ # Automation for PRs (labels + checklist), releases, and dependency updates

## Vision

The long-term goal of CDS is to provide a lightweight, dependency-free platform for scientific exploration and discovery.

We aim to combine solid numerical foundations (quantum simulation, FFT, linear algebra, statistics, differential equations, etc.) with higher-level tools for hypothesis generation and research workflows.

A distinctive part is the `cds.hypothesis` module, which generates structured, falsifiable hypotheses with explicit assumptions and predictions. The `cds hypothesis` CLI command and `examples/hypothesis_demo.py` make this side immediately usable. Recent work has focused on making the CLI and docs more practical for day-to-day use while keeping everything readable pure Python.

The project is still early but is being actively developed with a focus on code quality, test coverage, documentation, and usability for researchers and students.

Run `cds modules` after installation to explore the current modules.

## Recent improvements

Recent updates have aimed to make it simpler to generate and explore ideas within the platform:

- New CLI commands for browsing available modules and experimenting with hypothesis generation
- A dedicated example showing how to use the hypothesis features end-to-end
- Automation around pull requests, dependency management, and releases to free up time for core scientific work

The goal is to lower the barrier for using the discovery-oriented parts of the project and reduce time spent on routine tasks.

## Contributing

See [CONTRIBUTING.md](CONTRIBUTING.md) for setup and guidelines.

Looking for:
- Researchers with domain expertise
- People interested in pure-Python scientific computing
- Contributors for new modules (ML basics, PDE solvers, etc.)
- People who want to help make scientific tools easier to maintain and use


## Automation and Maintenance Workflows

A few GitHub Actions handle repetitive aspects of keeping the project running:

- Dependabot for regular updates to dependencies and GitHub Actions
- Automatic labeling and review checklists for pull requests
- An automated release pipeline: pushing a version tag builds, publishes to PyPI via Trusted Publishing (OIDC), cuts a GitHub Release with artifacts, and attests build provenance (sigstore)

These help ensure that time spent on the project goes more toward developing new modules, improving hypothesis tools, and supporting research use cases rather than manual upkeep.

See `.github/workflows/` for the current setup.

## License

MIT — see [LICENSE](LICENSE).

## Contact

- Maintainer: [@Furox88](https://github.com/Furox88)
- Issues & Discussions: [GitHub](https://github.com/Furox88/cognitive-discovery-system/issues)


## Security

Found a vulnerability? **Please do not open a public issue.** Report it privately:

- GitHub private advisory: [Report a vulnerability](https://github.com/Furox88/cognitive-discovery-system/security/advisories/new)
- Or email the maintainer directly.

Acknowledgement target: **48 hours** · Fix SLA: **7 days**. Full threat model,
supported versions, and out-of-scope items are in [SECURITY.md](SECURITY.md).


## Why These Automations Exist

The project is maintained by a small team (often solo). The workflows above exist so that routine tasks (labeling PRs, running checks, cutting releases, keeping dependencies fresh) take as little time as possible. This frees hours for actual research work: improving the hypothesis tools, adding new scientific modules, writing better examples, and exploring new discovery workflows.

If you're a researcher or educator using CDS, these automations mean you can focus on the science instead of repo housekeeping.