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The aim is to derive the exact-value formula for Ramsey numbers and explore the properties of K(d) and λ₀(m).

August 6, 2026Open Access

V5-拉姆齐数奇偶分离与λ₀(m)衰减速率的公理化——从偏元公理到精确值公式的理论支柱(V5 Axiomatization of K(d) Odd-Even Separation and λ₀(m) Decay Rate: The Theoretical Pillar from Partial-Element Axioms to the Exact Formula)

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The aim is to derive the exact-value formula for Ramsey numbers and explore the properties of K(d) and λ₀(m).
Derived the exact-value formulas within a partial-element mathematics framework.
Analyzed the odd-even separation of cumulative efficiency K(d) across recursion depths.
Extrapolated decay rates of λ₀(m) based on defined axioms and parameters.
Found K_odd=0.735 as a constant for odd d, indicating systematic separation.
Determined λ₀(2) as 9.77 with no free parameters based on angle and constraints.
Achieved a precise prediction of K(7)=0.329, matching with derived values from R(3,17)=95.

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Randomized trial explores odd-even separation and decay rate in Ramsey numbers, indicating novel computational insights.

Song Chen (2026) studied this question.

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