NoetherSolve Toolkit: Conservation Law Monitoring and Discovery for Numerical Simulations

We present NoetherSolve, an open-source Python toolkit for monitoring, validating, and discovering conservation laws in numerical simulations. The toolkit provides six tools covering three physical domains (point-vortex dynamics, chemical kinetics, N-body gravity) plus electromagnetism, Hamiltonian mechanics, and a domain-agnostic invariant discovery engine. Monitors based on a newly discovered Q_f invariant family detect numerical corruption at noise levels 100x lower than standard monitors. Available on PyPI (pip install noethersolve) with 102 tests.