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

Compute the linear strand

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

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.

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.

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

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

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.

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

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.