sheaf-theory

Notes on how to use the internal language of toposes in algebraic geometry

A clean PyTorch / PyG implementation library of Sheaf Neural Networks as Message Passing comprising all variants and a benchmark suite with 14+ Datasets.

Full spectrum sheaf neural network over arbitrary CW complexes.

Sheaves library for graph abstractions based on NetworkX

From Cybernetics to Categorical Semantics in Distributed Software Organizations — Formalizing Organizational Viability in Open Source Software Governance

Open-source data plane primitives: arena storage, schema contracts, filesystem projection, tree-sitter AST, LSP integration

Open standard for processual awareness – machine-readable ontology of LifeNode

My master's thesis in the realm of Graph Neural Networks. In this work we propose a novel way to precompute the sheaf Laplacian motivated by the connection that exists between the global section of a sheaf and the minimization of the Dirichlet energy via graph convolution.

A sheaf theory planner created by LLMs. For research.

WDW: provably shift-invariant Fourier bispectrum features for algebraic neural networks. Exact recovery to float64 floor. 100% classification with 4 samples, zero augmentation. 32+ modules for symmetry discovery, rupture certification, and quantum-inspired machine learning.

Sheaf and hierarchy algorithms

Pre-alpha groupoid/sheaf/Riemannian aggregation prototype for federated learning; tested math components, not production FL.

Persistent sheaf cohomology — cellular sheaf Laplacians, Vietoris-Rips complexes, multi-modal data fusion

Repository containing the results of the paper: Art Beyond Semantics: Sheaf-Informed Contrastive Learning for Multi-Relational Representations, accepted at ECCV 2026.

Synthetic falsification harness for tissue-scale cellular-sheaf coordination signals.

GrainVDB: High-performance vector search engine written in native C++ and Metal. Optimized for Apple Silicon Unified Memory and local-first AI applications.

Sheaf Laplacians, parallel transport and holonomy on graphs: an expository account of GNN failure modes and their geometric fixes, with hand-checkable worked examples.

Runtime verification for language-model outputs: five conformally-calibrated validation gates with finite-sample guarantees. A cellular-sheaf logic gate reaches AUROC 0.990 on compositional inconsistencies in a pre-registered GSM8K field study.

Exploration des principes mathématiques derrière la frustration géométrique et ses applications en science des matériaux et au-delà.

Continuous-time, sheaf-theoretic optimization substrate implementing Girard's Geometry of Interaction via parallelized JAX Neural ODE self-synthesis loops.