cohomology

Flexible and efficient persistent homology computation.

What C# can do for studying Finite Groups, quotient groups, semi-direct products, homomorphisms, automorphisms group, characters table, minimalistic rings and fields manipulations, polynomials factoring, fields extensions and many more...

R package porting Ripser-based persistent homology calculation engines from C++ via Rcpp. Currently ports Ripser (Vietoris-Rips complex) and Cubical Ripser (cubical complex).

A self-contained python library designed to apply Mathematical Surgery Theory over Manifolds.

A python CICY toolkit

Applying advanced the mathematics of cohomology to AI research (invented by Claude)

Basic abstractions and methods for computations in terms of group algebra Z[G] and automatic construction of cocycle translations for computation of cup-product.

Morphological Source Code (+QSD, /MOONLAPSED/cognosis branch) implemented in Python3 for contemporary hardware. Operates as a quantized kernel of agentic motility, akin to a Hilbert space kernel; augmented by an AdS/CFT Noetherian jet space enabling category-theoretic syntax-lift/lower, morphological differentiation, and morphosemantic integration.

Computes cohomology groups of certain chain complexes associated to pure or mixed states. For pure states this cohomology is a measure of entanglement. For more information see https://arxiv.org/abs/1901.02011.

An implementation of the Atiyah-Bott formula for the moduli space of genus 0 stable maps.

Computes the ranks of cohomology groups of certain chain complexes associated to pure or mixed states. For pure states this cohomology is a measure of entanglement. For more information see https://arxiv.org/abs/1901.02011.

S.T.A.R. Labs is a research program for investigating proposed relationships among arithmetic invariants, geometric and topological structure, symbolic fields, and physical/cosmological observables. The repository is both a computational research archive and a controlled-experiment framework.

Convergence-theoretic reformulation of the Hodge Conjecture for K3 surfaces, with flow-based projection methods, numerical experiments, and symbolic generalizations to abelian varieties and Calabi–Yau threefolds.

SageMath implementation of the restricted permutahedral model for computing the topology (cohomology, cup product, fundamental groups, asphericity criteria) of real parabolic arrangement complements associated to finite Coxeter groups.

Ontogeny and pedagogy of Morphological Source Code (MSC), implemented in Python3 for contemporary hardware. Operates as a quantized kernel of agentic motility, akin to a Hilbert space kernel; augmented by an AdS/CFT-dual Noetherian jet space enabling topos-invariant syntax-lift/lower, morphological differentiation, and morphosemantic integration.

we tryin to solve the hadamard conjecture! easy - right...? lol....

A Structural Reduction of the Hodge Conjecture in Lean 4 via Mumford-Tate Weight Gradings and Hodge-Riemann Bilinear Relations.

The M Conjecture proposes a collapse-theoretic foundation for understanding: Motives Mirror Symmetry The category of motives 𝕄_mot By reinterpreting them as functorially-generated fixed points of structural degeneration in the AK Collapse Theory.

Quantum Chevalley formula for partial flag varieties

Toeplitz determinantal formula for tetraquadric Calabi-Yau cohomology jumping with reproducible finite-field checks.