betti-numbers

Code for the NeurIPS 2019 paper: Topology-Preserving Deep Image Segmentation

DMT codes for the ICLR 2021 paper: Topology-Aware Segmentation Using Discrete Morse Theory

Computing Betti numbers from simplicial complexes.

Structure-Aware Image Segmentation with Homotopy Warping

Codes for the ICLR 2022 paper: Trigger Hunting with a Topological Prior for Trojan Detection

An advanced neuro-symbolic reasoning engine for the ARC-AGI visual abstraction challenge. Features multi-engine program synthesis (MCTS, Beam, Genetic Search), dihedral TTA consensus, persistent homology topological verification, continuous relaxed gradient search, and a modular object relation hypergraph builder

a mathematica notebook for computing homology groups of the vietoris-rips simplicial complex over the Z_2 ring

The SU(26) Dimension Polynomial — Complete Analytical Proof of Finiteness of Prime Values and Full Classification

Compute the linear strand

Three integers for any geometry file an agent writes: pieces, enclosed faces, Euler characteristic, from the arrangement rather than a render, shipped with the snap radius that decided them or a typed refusal.

Modeling the Gallium-Aluminum Wetting Transition via Topological Data Analysis of Interfacial Network Collapse with Python.

Betti Numbers for a Sub-Level Set of Volumetric Scalar Data

Detecting Topological Precursors to Technological Breakthroughs in the USPTO Patent Citation Network. Persistent homology applied to 8.4M patents and 118M citations.

Topological Early Warning Signals for Flash Crashes: A Proof-of-Concept using Topological Data Analysis (TDA) and Persistent Homology to detect structural market fragility and liquidity voids in Limit Order Books before a crash occurs.

Deterministic target-lock arbiter combining Vietoris-Rips persistent homology, Betti invariant verification, and rigid-body kinematic mass-flow constraints to defeat adversarial camouflage patches and inflatable decoys at the embedded edge.

Topology and geometry of Transformer hidden states via persistent homology. The manifold is a 1D arc (PC1=norm, r=0.999), not a torus or sphere. PC2=position, PC3=surprisal+POS. Validated up to 40B.

Clean-room verification suite for 'Betti Numbers as Cognitive Integrity Metrics: Topological Health Diagnostics for Deterministic Memory Systems' (Casey Lee Race, Calera Computing, Inc.)