Hyra Results

Companion artifacts for Hyra: Hunyuan Research Agent.

This repository collects concrete solutions that Hyra produced across a range of open problems in science, mathematics, engineering, and creative design, released alongside the Hyra launch post. Each folder holds the final solution artifact and, where relevant, the self-contained scripts that reproduce it.

📝 Launch post: hy.tencent.com/research/hyra

News

• 2026-08-19: 🧾 Three new results, each with a Lean 4 formalization of its finite and numerical core.

  • Beurling–Ahlfors transform. Iwaniec's 1982 conjecture predicts the sharp Lᵖ operator norm p*−1; the best proven uniform coefficient drops from 1.575 (Bañuelos and Janakiraman, 2008) to 1.523958. Paper: AI4Science/beurling_ahlfors_bellman/.
  • Partial Hadamard matrices. Their asymptotic count is now known throughout every power-law range above n², not just the cubic range m ≫ n³, lowering the critical exponent from 3 (arXiv:2603.30013) to 2. Paper: AI4Science/partial_hadamard_counting/.
  • Commutators close to the identity. The identity is never a commutator, but comes within ε at a price: the least ‖D‖·‖X‖ needed falls from Tao's O(log⁵(1/ε)), since refined to O(log⁴), to O(log³(1/ε)), against Popa's log(1/ε) lower bound. Paper: AI4Science/commutator_log_cubed/.

• 2026-08-17: 📐 Blaschke–Lebesgue in three dimensions. The least volume of a convex body of constant width w is conjectured to be Meissner's ≈ 0.419860 w³; the best certified lower bound rises from 4π/33 · w³ ≈ 0.380799 w³ (Nishioka, arXiv:2606.01754) to > 0.411040 w³, closing 77.4% of the remaining gap. Paper: AI4Science/3d_blaschke_lebesgue/.

• 2026-07-29: 🎉 The sum-vs-difference problem is settled. For finite A ⊆ ℤ, the optimal exponent relating |A+A| to |A−A| has supremum exactly 2, approached arbitrarily closely but never attained: a complete, machine-checked resolution going beyond the sums_diffs record below. Proof: sum-diff-proof.

Results

Each row compares the best prior published result (Prev best, from the cited system or leaderboard) against Hyra. Arrows mark the better direction (↓ lower is better, ↑ higher is better); the Hyra-winning value is in bold.

Track	Task	Metric	Prev best	Hyra
AI4AI	nanochat_autoresearch	val BPB ↓	0.9109 e	0.9015
	nanogpt_speedrun	wall-clock ↓	77.5 s e	76.4 s (mean val loss: 3.280)
	sol_execbench	score ↑	0.754 e	0.771
AI4Science	autocorrelation_first	C₁ ↓	1.502870 a	1.502850
	autocorrelation_second	R ↑	0.962694 b	0.962901
	erdos_min_overlap	C₅ ↓	0.380868 b	0.380859
	sums_diffs	C(A) ↑	1.14489 b	1.21079
	packing_records	records broken	n/a f	100
	smallest_adder	params ↓	36 c	15
	parp1_docking	objective ↓	−9.77 d	−10.60
	qubit_routing	CNOTs added ↓	269,037 b	258,369
	sunspot_symbolic	forecast R² ↑	0.47 g	0.78
	3d_blaschke_lebesgue	Vol/w³ bound ↑	0.380799 h	0.411040
	beurling_ahlfors_bellman	C_BA ↓	1.575 i	1.523958
	partial_hadamard_counting	regime exponent ↓	3 j	2
	commutator_log_cubed	log exponent ↓	4 k	3

Prev-best sources.

• ^a TTT-Discover: Learning to Discover at Test Time (arXiv:2601.16175).
• ^b SimpleTES: Evaluation-driven Scaling for Scientific Discovery (arXiv:2604.19341).
• ^c AdderBoard trained-weights leaderboard (github.com/anadim/AdderBoard).
• ^d Olaparib, an approved PARP1 inhibitor (drug baseline).
• ^e Recursive: First Steps Toward Automated AI Research (github.com/recursive-org/first-steps-toward-automated-ai-research); AI4AI baselines: nanoGPT-speedrun, nanochat, and SOL-ExecBench.
• ^f Erich Friedman's Packing Center (erich-friedman.github.io/packing). Hyra's record-improving packings are credited there as "Found by Haowei Lin": 100 across 28 shape-in-shape families, each beating the previously listed best.
• ^g Baseline: a "copy last frame" (persistence) forecast. Hyra's score is the forecast R² on a fully-held-out, half-century-long segment of the record.
• ^h Nishioka: An improved lower bound for the three-dimensional Blaschke–Lebesgue problem from spectral and dual perspectives (arXiv:2606.01754), which gives 4π/33 ≈ 0.380799109526. Hyra's certified bound is (130838246407123/10¹⁵)·π > 0.411040473721188.
• ⁱ R. Bañuelos and P. Janakiraman, Lᵖ-bounds for the Beurling–Ahlfors transform (2008), which gives the uniform coefficient 1.575. Iwaniec's conjectured sharp value is 1.
• ^j D. Davis: Counting Partial Hadamard Matrices in the Cubic Regime (arXiv:2603.30013).
• ^k B. Bilich: An O(log⁴(1/ε)) refinement of Tao's construction of commutators close to the identity (github.com/bilichboris/TaoCommutators); the published exponent is Tao's 5, since refined to 4.

Metrics are as defined by each benchmark; comparisons are against the cited published results.

Metric notes.

• C₁: first autoconvolution/autocorrelation constant, max(f∗f)/(∫f)² (minimize).
• R: second autocorrelation ratio, ‖f∗f‖₂² / (‖f∗f‖₁·‖f∗f‖∞) (maximize).
• C₅: Erdős minimum-overlap constant (minimize).
• C(A): sum-vs-difference exponent, log(|A+A|/|A|) / log(|A−A|/|A|) (maximize).
• params: unique trainable parameters of a transformer that adds two 10-digit integers at ≥ 0.99 accuracy (minimize).
• objective: PARP1 docking objective, Vina score + 10·(1 − QED) (minimize).
• CNOTs added: extra CNOTs inserted by SWAP routing (minimize; 1 SWAP = 3 CNOTs).
• forecast R²: rolling-origin, free-running (24-month) forecast R² for monthly sunspot numbers (maximize).
• Vol/w³ bound: largest proven universal lower bound on Vol(K)/w³ over all convex bodies K ⊂ ℝ³ of constant width w (maximize; the conjectured optimum is ≈ 0.419860).
• C_BA: smallest proven uniform coefficient in ‖B‖_{Lᵖ→Lᵖ} ≤ C_BA·(p*−1) for the Beurling–Ahlfors transform, over all 1 < p < ∞ (minimize; the conjectured optimum is 1).
• regime exponent: infimum of the power-law exponents u for which m/nᵘ → ∞ is known to force the asymptotic formula for N(n,m) (minimize; the endpoint value itself is not claimed).
• log exponent: smallest proven k in m(ε) = O(logᵏ(1/ε)) for commutators within ε of the identity (minimize; the matching lower bound is k = 1).

Note. The results above were current as of 2026-07-10, except 3d_blaschke_lebesgue, added 2026-08-17, and the three entries added 2026-08-19. Several of these problems live on public, continuously-updated leaderboards; later entries there may warm-start from Hyra's published solutions to reach still-better numbers.

AI4Fun

Creative and game-playing demos (no leaderboard comparison):

• AI4Fun/reversi/: a AlphaZero-style Reversi (Othello) bot for the Botzone 8×8 arena (C++ pattern/n-tuple net + PUCT-MCTS + exact endgame solver).
• AI4Fun/music/: a five-part arrangement of 望春風 (Bāng-chhun-hong, 1933, 鄧雨賢).
• AI4Fun/3d_penguin/: a procedural 3-D QQ-penguin built by a single Blender bpy script.
• AI4Fun/3d_hunyuan/: a procedural 3-D Tencent Hunyuan (混元) logo orb.

Citation

If you use these results, please cite:

@misc{hyra2026,
  title        = {Hyra: Hunyuan Research Agent},
  author       = {{Hyra Team}},
  year         = {2026},
  howpublished = {\url{https://hy.tencent.com/research/hyra}},
}

License

This repository is licensed under the Apache License, Version 2.0; see LICENSE.