rigorous-numerics

Library for validated numerics using interval arithmetic

Computing reachable states of dynamical systems in Julia

Library for computer-assisted proofs in dynamical systems

Certified finite positivity bands for a Riemann Xi defect kernel via endpoint moment bounds.

Lean 4 library + CLI for rigorous bounds in transformer computations (mechanistic interpretability)

Bernstein's constant to ten rigorously certified digits: beta = 0.2801694990, proved in interval arithmetic (Arb) where the 1985 Varga-Carpenter rigorous enclosure gives five. OEIS A073001. Every number re-derivable from the shipped data in exact arithmetic.

Rigorous ball/interval arithmetic for Python: sound enclosures with documented directed-rounding guarantees, plus certified interval-Newton root isolation.

Certified inertia and eigenvalue counting for symmetric matrices, in Arb ball arithmetic

Exact bottom-cluster and Feshbach reduction for the semilocal Weil prolate-proxy bridge, with reproducible code and audits.

Certified spectral instability of the excited De Gregorio profile f₃ - interval-arithmetic certificates, one-command reproduction, and diagnostics for CAP pipelines.

Certified global lower-bound improvement for the Erdos minimum-overlap problem: c_E > 0.38055925 via independent Arb and MPFI checks; the exact value remains open.

Computer-assisted existence certificates for self-similar blowup profiles in 1D fluid models. Includes a catalogue of six soundness gaps found while building it.

Certified lower bound on the length of a nontrivial positive Collatz cycle. Nothing new: a runnable, tested implementation of Sinisalo (2003) with current numbers, plus the audit that corrected a 4x-weaker first attempt.

Lean 4 formalization, research notes, and rigorous numerical certificates for CvS reductions in Riemann-hypothesis research.