Noetic Geometry Framework

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

✨ Overview

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

📦 Installation

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

🚀 Quick Demo

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))