Just put up a Lean 4 formalization of Dusart’s bound on the sum of 1/p. The kernel checks pretty much the whole argument and reduces it to one published Chebyshev estimate. Includes the certificates, generators, and a full replay: zenodo.org/records/23479494

Liu’s exponent-pair optimization (Lean 4 kernel-checked, gives Re(s) > 7/8 ≈ 0.875 (certified optimal in the system at ~0.874957) for Dirichlet L-functions and ζ(s). Cureton–Thorner’s mesoplectic approach covers all Dedekind ζ_K and finite-order Hecke L-functions (initially >1−1/6000, later 31/32). These are complementary, not competing: Liu supplies a strong formal half-plane for the Dirichlet case that enables explicit unconditional bounds (e.g., Littlewood-type L(1,χ) ≥ 0.0621/log log q); Cureton–Thorner reaches a broader class of number fields. Hybrid certified computation (1M zeros, kernel-checked certificates for Dusart/Chebyshev) then turns the theorems into usable constants. Full technical comparison of methods, audits, and verification: “Separate-Tree Source Rebuild, Fresh-Environment Lean Kernel Replay, and Scoped Semantic Audit of the Re(s) > 7/8 Theorem” zenodo.org/records/23461828

Just released: certified optimality audit of the exponent comparison system behind the Re(s) > 7/8 zero-free half-plane for zeta and Dirichlet L-functions. We give an exact model and Lean-checked core lemma proving Liu’s improved bound (~0.874957) is optimal inside the system, plus the analytic bottlenecks. Full replayable package (scripts, Lean, checksums) standard axioms only, runs on a laptop. zenodo.org/records/23462320

New public audit of the 7/8 nonvanishing theorems: Separate-tree rebuild of 2,926 Lean modules + fresh-kernel replays confirm the Dirichlet/zeta zero-free half-plane Re(s) > 7/8 (@OpenAI math commit pinned). Real-zero gap follows: (1−β) log q ≥ (log 3)/8 for all real zeros of non-principal characters. Axioms only propext, Classical.choice, Quot.sound. Full logs, checksums, and regeneration scripts open. Verification is the signal. Check it. zenodo.org/records/23461828

Three new papers on explicit bounds + Lean 4 formalization: • Harmonic-measure barriers & certified Littlewood bounds zenodo.org/records/23400116 • Machine-checked Littlewood bounds (kernel-checked, sharpened) zenodo.org/records/23424383 • Kernel-checked proof of Dusart’s ∑1/p∑1/p bound zenodo.org/records/23432990 All with full verification artifacts. #Lean4 #NumberTheory

Just came across the @prove2memath platform yesterday.. I am hooked. It's your fault @RobinKothari prove2.me/users/a4da5acb-ce1…

Improved it to α ≥ 2.0391. It's Lean-verified end to end, kernel-checked with only the standard axioms, and accepted on Prove2Me: prove2.me/campaigns/block-se… It's the same gated-tournament architecture, sharpened: sensitivity profiles are tracked per predicate index, each level has its own parameters, and the target/gate index maps are general, over a grouped Hamming-ball base. The certificate inequality A^20391 ≤ B^10000 is decided exactly by the kernel. I agree 2.5 looks plausible, but this family seems to top out near 2.04. Getting further needs a new level design where one gate excludes more than one row.

.@zlatko_minev Excited to see the Measure Now, Mitigate Later / virtual error cancellation work, syndrome records as a post-processing resource is a great direction. We just released new weight-6 bivariate-bicycle codes that encode more logical qubits at distance 12: • [[336,20,12]] and [[360,24,12]] (25–50% more logicals than prior best at d=12)
• Exhaustive classification + certified exact distances (both sectors)
• Circuit-level d ≥ 6 under depth-8 syndrome cycle
• 1.1M-shot BP-OSD benchmarks: 3.6–6.2× lower block failure vs. gross code Certificates are laptop-replayable (DRAT / Lean-checked pruning). VEC-style dual-decoder post-processing should apply directly to these codes. Paper + verifiers: zenodo.org/records/23382175

Congrats to @GoogleQuantumAI on the magic state cultivation result on Willow, a major step for non-Clifford resources. Our new high-rate bivariate-bicycle codes (up to [[360,24,12]], with independently checkable distance certificates) pair naturally with surface-code MSC for lower-overhead hybrid distillation factories. Paper + certs: zenodo.org/records/23382175

Hey @OpenAI, @SimonsFdn, and @AnthropicAI Your $15M initiative to help mathematicians examine and rigorously build on AI/numerical results is timely. @SmartLedgerTech has certified the classic 4×4 Hubbard ground-state energy to ≥23 decimals (plus double occupancy, kinetic energy, and full spin correlations) via symmetry reduction, verified Cholesky, Temple enclosures, and Lean 4 formalization of the key inequalities. Separates untrusted numerics from exact checkers. Fully replayable in minutes on a laptop. Corrects a published benchmark. Paper + certificates: 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.

Building on the recent zero-free region work for the quasi-Riemann hypothesis, we give certified harmonic-measure bounds that improve the key logarithmic-control threshold (at a=7/8, e=10^{-3}, ε=1/10) from 10^{1778.3} down to ~10^{28.5}, with an optimal interval certified by obstruction witnesses. Explicit Littlewood bounds and Lean-checked certificates included. Paper + full release: zenodo.org/records/23400116 @ObhishekSaha

Empowering the energy transition with verifiable, transparent infrastructure. Explore how we are leveraging modern blockchain systems to bring efficiency, real-time tracking, and security to energy grids and sustainable projects: energy.smartledger.technolog…

👉zenodo.org/records/23382175

🚀 Excited to share our new work on bivariate-bicycle (BB) quantum error-correcting codes! We constructed three new weight-6 BB codes that encode more logical qubits at distance 12, and showed they are the only ones of their kind up to n = 360. We also built lightweight, independently checkable certificates for the exact distances of these and the IBM ladder codes - all on a single laptop. Key results: - Two [[336, 20, 12]] codes and one [[360, 24, 12]] code — 25% and 50% more logical qubits than the best prior distance-12 weight-6 code (k = 16) from evolutionary search. - Exhaustive classification: these are the only connected three-term weight-6 BB codes with n ≤ 360, k ≥ 20, and d ≥ 12 (up to presentation symmetries). - Certified exact distances (both sectors) for the @IBM ladder through the two-gross code [[288, 12, 18]], plus the [[360, 12]] code (exactly d = 24). - Circuit-level distance ≥ 6 (certified) for the new codes under the depth-8 syndrome cycle. - In 1.1 M shots under circuit-level depolarizing noise (p = 0.004, BP-OSD), block failure rates sit between the gross and two-gross codes: 3.6–6.2× lower than the gross code. - Physical overhead: 30–33.6 qubits per logical qubit (with ancillas) — 30–37.5% fewer than the two-gross code (at the cost of lower distance). The certificates are DRAT proofs (smaller codes) or proof trees (larger codes) whose key pruning lemma is checked in Lean 4. A reader can replay any of them in seconds to a minute on a laptop with standard tools, no proprietary search code or cluster required. Check out the full paper and certificate verifiers to replay the proofs yourself!👇

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