Theo Conjecture解决35年数学开放猜想，发现未预测的二阶项

AI系统Theo Conjecture近日破解了一个困扰数学界35年的图论难题。1这一猜想源于1987年Siemion Fajtlowicz的Graffiti程序提出的Conjecture 448，1涉及Havel-Hakimi残基的增长规律。1

Paul Erdős证明了残基增长速率至少为n / log n，其中常数为ζ(2) − 1 ≈ 0.644934。1随后William Staton假设这个下界就是精确答案，1但这一预测在过去40年间始终未获证明。1Theo Conjecture通过与人类数学家的协作循环，利用大语言模型、组合推理引擎和精确计算，1最终得出了完整的渐近展开式：R(Gₙ) = c₀ · n/log n + (c₀ − A) · n/log²n + O(n/log³n)。1其中A = 0.3201986326...，这一二阶项系数此前未被任何人预测。1该系数定义为求和公式Σ(k=2 to ∞) log k / [k²(k−1)]。1

在实际验证中，该系统在n ≤ 10,000的连续测试中发现，残基与向上舍入的Caro-Wei和的差值不超过2，1进一步验证了理论结果的准确性。

An AI system called Theo Conjecture has solved a longstanding mathematical problem originating from Paul Erdős's work, proving a hypothesis about graph residues that remained unproven for decades 1. The system discovered a previously unpredicted second-order term in the asymptotic expansion, revealing a formula that connects to the Riemann zeta function 1.

The conjecture traces back to 1987, when Siemion Fajtlowicz's Graffiti program generated Conjecture 448 1. Erdős established that the growth rate of Havel-Hakimi residues is at least n / log n with a constant of ζ(2) − 1 ≈ 0.644934 1. William Staton subsequently conjectured that this lower bound represented the exact answer, but the proof eluded mathematicians for 40 years 1.

Theo Conjecture's complete formula yields: R(Gₙ) = c₀ · n/log n + (c₀ − A) · n/log²n + O(n/log³n), where A = 0.3201986326... 1. The newly identified second-order coefficient is defined as A = Σ(k=2 to ∞) log k / [k²(k−1)] 1. Through collaboration between the AI system and human mathematicians, employing large language models, combinatorial reasoning engines, and precise computation, researchers validated their findings across consecutive tests up to n ≤ 10,000, where residues differed from the rounded Caro-Wei sum by no more than 2 1.