A geometric data oriented library unifying additive and multiplicative transports, Mellin coupling, submersion geometry, and Fisher–Rao pullbacks into a single coherent framework.

Originator & Lead Researcher: Sar Hamam

This library implements a research program proposed by Sar Hamam:

• Dual transports

  • Additive (Gaussian / heat semigroup)
  • Multiplicative (Poisson via log-map and Haar measure)

• Mellin coupling

  • Canonical balance point at s = 1/2
  • Emerges from additive–multiplicative duality

• Submersion backbone

  • Smooth map f=(τ,σ): M → ℝ²
  • Zero set Z = f⁻¹(0) with transversality checks

• Fisher–Rao pullback

  • Model-aware metrics from embeddings / logits

• Sparse numerics

  • k-NN graphs only
  • Solvers: Conjugate Gradient (CG/PCG) and Lanczos

git clone https://github.com/Sarhamam/NoeticEidos.git
cd NoeticEidos
python -m venv venv && source venv/bin/activate
pip install -r requirements.txt
pip install -e .  # Install package in development mode

import numpy as np
from graphs.knn import build_graph
from graphs.laplacian import laplacian
from solvers.lanczos import topk_eigs
from stats.spectra import spectral_gap, spectral_entropy

# toy dataset
rng = np.random.default_rng(0)
X = np.r_[rng.normal(0,1,(200,8)), rng.normal(3,0.5,(200,8))]

# additive geometry
G_plus = build_graph(X, mode="additive", k=16)
L_plus = laplacian(G_plus, normalized=True)
evals_plus, _ = topk_eigs(L_plus, k=16)
print("Additive gap:", spectral_gap(evals_plus))

# multiplicative geometry
G_times = build_graph(X, mode="multiplicative", k=16)
L_times = laplacian(G_times, normalized=True)
evals_times, _ = topk_eigs(L_times, k=16)
print("Multiplicative gap:", spectral_gap(evals_times))

Every feature must pass falsifiable tests:

1. Stability — metrics invariant under ±10% noise, different seeds
2. Separability — additive vs. multiplicative produce distinct spectra
3. Balance — s=1/2 maximizes stability score
4. Transversality — rank(J_f) = 2 and bounded cond(J_fᵀJ_f) on zero set Z
5. Fisher–Rao effect — measurable shift in spectral entropy on embeddings

# Run tests
pytest

# Run with coverage
pytest --cov=. --cov-report=html

# Lint & format
black .
ruff check . --fix
mypy . --ignore-missing-imports

┌─────────────────────────┐     ┌─────────────────────────┐
│    Additive Transport   │     │  Multiplicative Transport│
│    (Gaussian / Heat)    │     │  (Poisson / Log / Haar) │
└───────────┬─────────────┘     └───────────┬─────────────┘
            │                               │
            └───────────┬───────────────────┘
                        ▼
            ┌───────────────────────┐
            │     Mellin Balance    │
            │        s = 1/2        │
            └───────────┬───────────┘
                        │
                        ▼
            ┌───────────────────────┐
            │  Submersion Backbone  │
            │   f = (τ,σ): M → ℝ²   │
            │  Zero set Z = f⁻¹(0)  │
            │  Transversality check │
            └───────────┬───────────┘
                        │
                        ▼
            ┌───────────────────────┐
            │  Fisher–Rao Pullback  │
            │  Model-aware metrics  │
            └───────────┬───────────┘
                        │
                        ▼
            ┌───────────────────────┐
            │    Sparse Numerics    │
            │ k-NN Graphs, CG/Lanczos│
            │   Spectra & Curvature │
            └───────────────────────┘

This framework is based on the original theoretical and computational work of Sar Hamam. Please retain attribution in derivative works, documentation, and research papers.

If you use this framework in your research, please cite:

@software{hamam2025noetic,
  author       = {Hamam, Sar},
  title        = {Noetic Geometry Framework: Unifying Dual Transports and Topological Analysis},
  year         = {2025},
  url          = {https://github.com/Sarhamam/NoeticEidos},
  note         = {A geometric data oriented library unifying additive and multiplicative transports, Mellin coupling, submersion geometry, and Fisher-Rao pullbacks}
}

MIT License — see LICENSE for details.