Tencent's Hyra Agent Cracks Four Unsolved Math Problems at Once

Tencent's Hunyuan team has posted a fresh batch of math results from Hyra, its recursive research agent, adding four new improvements to well-known open problems since its last math update. None of these are freshly opened problems, and none are being claimed as fully solved. What Hyra did is tighten the best-known numerical bounds on four classical questions that have sat on the frontier for years or decades, in some cases pushing within a few percent of the conjectured optimum.

The context here matters. Hyra is the Hunyuan Research Agent, a system Tencent describes as recursive and self-improving, built for performance-oriented research tasks. When it launched, it had beaten the historical best on 29 of 55 open math problems, improved qubit routing efficiency by 44.4% over classic SABRE, and designed an addition Transformer with just 15 trainable parameters, 58.3% fewer than the public record. The four new results extend that leaderboard rather than replacing it.

The four new bounds

Each advance is a numerical improvement on a constant or asymptotic rate in a well-studied problem. Here is what changed:

• 3D Blaschke-Lebesgue. This asks for the minimum-volume body of constant width w in three dimensions. The 2D version was settled a century ago (the Reuleaux triangle), but the 3D case is still open. Hyra raised the universal lower bound from 0.380799w³ to 0.411040w³, reaching 97.9% of the volume of the Meissner bodies, which are the conjectured optimum.
• Beurling-Ahlfors operator. A central object in complex analysis and quasiconformal mapping theory. Iwaniec conjectured that its L^p norm has a specific sharp value. Hyra improved the best known uniform coefficient from 1.575 down to 1.523958, moving measurably closer to that conjectured bound.
• Partial Hadamard matrices. These are rectangular sign matrices with orthogonal rows, and counting them accurately is a long-standing combinatorics problem. Hyra extended the asymptotic counting regime from the cubic scale down to the near-quadratic regime, meaning the count is now known accurately for much thinner matrices than before.
• Operator commutators. Approximating the identity using commutators is a problem where Terence Tao previously established an O(log^5(1/ε)) upper bound on the cost. Hyra reduced that to O(log^3(1/ε)), closing part of the gap toward the known logarithmic lower bound.

These are the kind of results that normally show up in single-problem papers. Posting four of them at once, from one agent, is what makes the update noteworthy.

Why the numbers matter

Two of these are strictly quantitative refinements. The Blaschke-Lebesgue bound is closer to a conjectured optimum, and the Beurling-Ahlfors coefficient is closer to Iwaniec's target. Those are the sort of decimals that experts in a subfield care about because they narrow the space where a proof of sharpness has to live.

The other two are structural. Moving Hadamard counting from cubic to near-quadratic changes the regime where you have provable asymptotics, which matters for coding theory and experimental design applications that rely on partial Hadamard structures. Dropping a commutator approximation from log^5 to log^3 is a two-power improvement on an operator-theory quantity that shows up in quantum information and functional analysis.

How Hyra actually produces these

Hyra is not a chatbot proving theorems in prose. It runs a search-and-execute loop over candidate constructions. The system uses a lightweight Harness framework, generating inspirational contexts by maintaining an experience bank through a Context Agent. Multiple Proposal Agents asynchronously consume queues, run and score solutions in independent sandboxes, and continuously iterate to optimize solutions.

Hyra supports a two-layer loop: an inner layer for optimizing solutions and an outer layer for evolutionary evaluators, covering more than ten scenarios including AI research and development, scientific discovery, and game design. In practice that means: propose a candidate construction (a body, a matrix family, an operator decomposition), evaluate it against the scoring function for the problem, keep what improves the bound, and let those winners seed the next round of proposals.

The design philosophy is deliberately minimal. The system follows the Bitter Lesson design philosophy, keeping the framework as lightweight as possible and expanding the agent's action space to a large extent, using a simple and general loop framework to convert intelligence and computing power into real returns. The heavy lifting is done by the underlying model, Hy3, a 295B-parameter open-weight mixture-of-experts released earlier this summer.

What is and is not being claimed

It is worth being precise about the scope. Hyra is not proving any of these problems in full. It is producing constructions, numerical solutions, and candidate configurations that beat prior published values on the specific metric each problem uses. In the earlier sum-vs-difference problem, the team went further with a complete, machine-checked resolution of the optimal exponent, where the construction at the heart of the matching lower bound was developed with Hyra. The four new results in this update are numerical improvements, not full resolutions.

That distinction matters for anyone trying to use this work. If you are building on a Hyra-improved constant, you get a better witness value but not a new theorem. If a subsequent human paper closes the remaining gap, Hyra's construction is likely to be cited as the state of the art on the constructive side.

Where to look and how to use it

Everything is on the Hyra-results repository, under an Apache 2.0 license. Each track has its own folder with the final artifact and, where relevant, scripts that reproduce the reported number. The results are current as of 2026-07-10, and several of these problems live on public, continuously-updated leaderboards where later entries may warm-start from Hyra's published solutions to reach still-better numbers.

The practical read for anyone working adjacent to these areas is straightforward. If you are in extremal geometry, harmonic analysis, combinatorial design, or operator theory, the new best-known values are now Hyra's, and the constructions are open. If you are building agentic research systems, the pattern of asynchronous proposal agents scoring candidates in sandboxes against evolving evaluators is worth studying regardless of whether you care about Blaschke-Lebesgue bodies. And if you are watching the general trajectory of research agents, this is another data point that iterative search over a strong base model, with tight verification loops, keeps compounding on problems that were previously human-only territory.