Isomorphic < Holomorphic

For decades, the two-dimensional Hubbard model has been the standard minimal model of strongly correlated electrons, with benchmark studies relying entirely on floating-point numerical estimates. Today, my @SmartLedgerTech co-authors Shawn Ryan (@Sdot2121 & @Codenlighten1) and I are replacing those estimates with rigorous theorems. Our new paper certifies the ground-state energy of the periodic, half-filled 4x4 repulsive Hubbard model to at least 23 decimal places across eleven couplings, from U=1 to U=16. Alongside these energies, we've provided mathematically certified enclosures for key ground-state observables, including double occupancy, kinetic energy, and the full spin correlation function. Crucially, this isn't just a theoretical exercise. Our exact reduction technique condenses the problem from 165,636,900 states down to a 19,186-dimensional block. By separating the untrusted numerical production from our exact verification checkers, the entire certification pipeline including the Lean 4 formalization of the interlacing and Temple steps can be replayed and verified in minutes on a standard laptop without relying on a GPU or cluster. This level of precision even allowed us to identify an incompatibility with a previously published "exact" benchmark from Physical Review B at U=4. Check out the full paper and replay the certificates here: zenodo.org/records/23381094

We cut the critical logarithmic-control threshold for quasi-RH arguments from 10^{1778.3} down to ~10^{28.5} (certified optimal interval via obstruction witnesses). Explicit Littlewood bounds + Lean-checked certificates included. Paper + full release: zenodo.org/records/23400116 @OpenAI @AlexKontorovich @deancureton @KenOno691 @ObhishekSaha @Sdot2121 @Codenlighten1 @SmartLedgerTech This highlights the most dramatic quantitative advance (roughly 1,750 orders of magnitude improvement), emphasizes the certified/optimal nature of the result, and tags the key relevant accounts from the recent quasi-RH developments. It stays concise and high-signal for the analytic number theory and AI-math communities.