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 standard for processual awareness – machine-readable ontology of LifeNode

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

A sheaf theory planner created by LLMs. For research.

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.

Template for composing multi-track active inference manuscripts — closed-form analytics, pymdp simulations, Lean 4 proofs, GNN/ontology notation — bound to shared sections by a typed sheaf engine with six machine-checked composition laws and a symbol gluing certificate.

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.

Five volumes, 4,020 pages: the meta-reasoning kernel of the Grothendieckian Programme. Reasoning native to a topos: a context is a site, evidence is a sheaf over it, and a conclusion is a global section that exists only where the local evidence glues. Open access, DOI 10.5281/zenodo.23538544.

SHRDLU II — a 2026 era modern symbolic substrate for AI agents. From blocks world to modern world models.

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.

Sheaf and hierarchy algorithms

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.

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

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

Sheaf-theoretic local-to-global data fusion for agent systems - gluing partial agent observations.