查看“︁HPrSSψ vs LPrSSψ分析”︁的源代码

上篇：[[LPrSSψ分析Part2]]

以下为超初等序列序数折叠函数（HPrSSψ）与LPrSSψ的分析。HPrSSψ与LPrSSψ在(0)(1,1,1)(2,2)(3,3,1)前完全一致，但HPrSSψ的强度大得多，可达TSSO以上。

== 分析1：(0)(1,1,1)(2,2)(3,3,1)~BGO ==
HPrSSψ与LPrSSψ在(0)(1,1,1)(2,2)(3,3,1)前完全一致，为：<math>\psi(\psi_2(\psi_3(\psi_4(\psi_5(\psi_6(...))))))</math>，分歧源自折叠方式不同。
{| class="wikitable"
|+分析1：(0)(1,1,1)(2,2)(3,3,1)~BGO
!HPrSSψ
!LPrSSψ
!BMS
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5)))</math>
|<math>\psi(\psi_2(\Omega_4))</math>
|(0)(1,1,1)(2,2)(3,3,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5))+\Omega)</math>
|<math>\psi(\psi_2(\Omega_4)+\Omega)</math>
|(0)(1,1,1)(2,2)(3,3,1)(1,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5))+\psi_1(\psi_3(\psi_4(\Omega_6)))</math>
|<math>\psi(\psi_2(\Omega_4)+\psi_1(\psi_3(\Omega_5)))</math>
|(0)(1,1,1)(2,2)(3,3,1)(1,1)(2,2,1)(3,3)(4,4,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5))+\Omega_2)</math>
|<math>\psi(\psi_2(\Omega_4)+\Omega_2)</math>
|(0)(1,1,1)(2,2)(3,3,1)(1,1,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5))+\psi_2(\Omega_3))</math>
|<math>\psi(\psi_2(\Omega_4)+\psi_2(\Omega_3))</math>
|(0)(1,1,1)(2,2)(3,3,1)(1,1,1)(2,2)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5))\times2)</math>
|<math>\psi(\psi_2(\Omega_4)\times2)</math>
|(0)(1,1,1)(2,2)(3,3,1)(1,1,1)(2,2)(3,3,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5)+1))</math>
|<math>\psi(\psi_2(\Omega_4+1))</math>
|(0)(1,1,1)(2,2)(3,3,1)(2)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5)+\Omega))</math>
|<math>\psi(\psi_2(\Omega_4+\Omega))</math>
|(0)(1,1,1)(2,2)(3,3,1)(2,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5)+\psi_1(\psi_3(\psi_4(\Omega_6))))</math>
|<math>\psi(\psi_2(\Omega_4+\psi_1(\psi_3(\Omega_5))))</math>
|(0)(1,1,1)(2,2)(3,3,1)(2,1)(3,2,1)(4,3)(5,4,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5)+\Omega_2))</math>
|<math>\psi(\psi_2(\Omega_4+\Omega_2))</math>
|(0)(1,1,1)(2,2)(3,3,1)(2,1,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5)+\psi_2(\psi_3(\Omega_5))))</math>
|<math>\psi(\psi_2(\Omega_4+\psi_2(\Omega_4)))</math>
|(0)(1,1,1)(2,2)(3,3,1)(2,1,1)(3,2)(4,3,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5)+\Omega_3))</math>
|<math>\psi(\psi_2(\Omega_4+\Omega_3))</math>
|(0)(1,1,1)(2,2)(3,3,1)(2,2)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5)+\Omega_3\omega))</math>
|<math>\psi(\psi_2(\Omega_4+\Omega_3\omega))</math>
|(0)(1,1,1)(2,2)(3,3,1)(2,2)(3)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5)+\Omega_3^2))</math>
|<math>\psi(\psi_2(\Omega_4+\Omega_3^2))</math>
|(0)(1,1,1)(2,2)(3,3,1)(2,2)(3,2)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5)+\psi_3(\Omega_4)))</math>
|<math>\psi(\psi_2(\Omega_4+\psi_3(\Omega_4)))</math>
|(0)(1,1,1)(2,2)(3,3,1)(2,2)(3,3)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5)\times2))</math>
|<math>\psi(\psi_2(\Omega_4+\psi_3(\Omega_5)))</math>
|(0)(1,1,1)(2,2)(3,3,1)(2,2)(3,3,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5+1)))</math>
|<math>\psi(\psi_2(\Omega_4+\psi_3(\Omega_5+1)))</math>
|(0)(1,1,1)(2,2)(3,3,1)(3)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5+\Omega)))</math>
|<math>\psi(\psi_2(\Omega_4+\psi_3(\Omega_5+\Omega)))</math>
|(0)(1,1,1)(2,2)(3,3,1)(3,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5+\Omega_2)))</math>
|<math>\psi(\psi_2(\Omega_4+\psi_3(\Omega_5+\Omega_2)))</math>
|(0)(1,1,1)(2,2)(3,3,1)(3,1,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5+\Omega_3)))</math>
|<math>\psi(\psi_2(\Omega_4+\psi_3(\Omega_5+\Omega_3)))</math>
|(0)(1,1,1)(2,2)(3,3,1)(3,2)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5+\psi_3(\Omega_5))))</math>
|<math>\psi(\psi_2(\Omega_4+\psi_3(\Omega_5+\psi_3(\Omega_5))))</math>
|(0)(1,1,1)(2,2)(3,3,1)(3,2)(4,3,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5+\Omega_4)))</math>
|<math>\psi(\psi_2(\Omega_4+\psi_3(\Omega_5+\Omega_4)))</math>
|(0)(1,1,1)(2,2)(3,3,1)(3,3)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5+\Omega_4\omega)))</math>
|<math>\psi(\psi_2(\Omega_4+\psi_3(\Omega_5+\Omega_4\omega)))</math>
|(0)(1,1,1)(2,2)(3,3,1)(3,3)(4)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5+\Omega_4^2)))</math>
|<math>\psi(\psi_2(\Omega_4+\psi_3(\Omega_5+\Omega_4^2)))</math>
|(0)(1,1,1)(2,2)(3,3,1)(3,3)(4,3)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5+\psi_4(\Omega_5))))</math>
|<math>\psi(\psi_2(\Omega_4+\psi_3(\Omega_5+\psi_4(\Omega_5))))</math>
|(0)(1,1,1)(2,2)(3,3,1)(3,3)(4,4)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5+\psi_4(\Omega_6))))</math>
|<math>\psi(\psi_2(\Omega_4+\psi_3(\Omega_5+\psi_4(\Omega_6))))</math>
|(0)(1,1,1)(2,2)(3,3,1)(3,3)(4,4,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_52)))</math>
|<math>\psi(\psi_2(\Omega_42))</math>
|(0)(1,1,1)(2,2)(3,3,1)(3,3,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_53)))</math>
|<math>\psi(\psi_2(\Omega_43))</math>
|(0)(1,1,1)(2,2)(3,3,1)(3,3,1)(3,3,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5\omega)))</math>
|<math>\psi(\psi_2(\Omega_4\omega))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5\Omega)))</math>
|<math>\psi(\psi_2(\Omega_4\Omega))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5\Omega_2)))</math>
|<math>\psi(\psi_2(\Omega_4\Omega_2))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,1,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5\Omega_3)))</math>
|<math>\psi(\psi_2(\Omega_4\Omega_3))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,2)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5\times\psi_3(\Omega_5))))</math>
|<math>\psi(\psi_2(\Omega_4\times\psi_3(\Omega_5)))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,2)(5,3,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5\Omega_4)))</math>
|<math>\psi(\psi_2(\Omega_4\times\psi_3(\Omega_5\Omega_4)))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,3)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5\times\psi_4(\Omega_6))))</math>
|<math>\psi(\psi_2(\Omega_4\times\psi_3(\Omega_5\times\psi_4(\Omega_6))))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,3)(5,4,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5^2)))</math>
|<math>\psi(\psi_2(\Omega_4^2))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,3,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5^3)))</math>
|<math>\psi(\psi_2(\Omega_4^3))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,3,1)(4,3,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5^\omega)))</math>
|<math>\psi(\psi_2(\Omega_4^\omega))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,3,1)(5)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5^\Omega)))</math>
|<math>\psi(\psi_2(\Omega_4^\Omega))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,3,1)(5,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5^{\Omega_2})))</math>
|<math>\psi(\psi_2(\Omega_4^{\Omega_2}))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,3,1)(5,1,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5^{\Omega_3})))</math>
|<math>\psi(\psi_2(\Omega_4^{\Omega_3}))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,3,1)(5,2)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5^{\psi_3(\Omega_5)})))</math>
|<math>\psi(\psi_2(\Omega_4^{\psi_3(\Omega_5)}))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,3,1)(5,2)(6,3,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5^{\Omega_4})))</math>
|<math>\psi(\psi_2(\Omega_4^{\psi_3(\Omega_5^{\Omega_4})}))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,3,1)(5,3)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5^{\psi_4(\Omega_6)})))</math>
|<math>\psi(\psi_2(\Omega_4^{\psi_3(\Omega_5^{\psi_4(\Omega_6)})}))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,3,1)(5,3)(6,4,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5^{\Omega_5})))</math>
|<math>\psi(\psi_2(\Omega_4^{\Omega_4}))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,3,1)(5,3,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5^{\Omega_5+1})))</math>
|<math>\psi(\psi_2(\Omega_4^{\Omega_4+1}))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,3,1)(5,3,1)(4,3,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5^{\Omega_52})))</math>
|<math>\psi(\psi_2(\Omega_4^{\Omega_42}))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,3,1)(5,3,1)(4,3,1)(5,3,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5^{\Omega_5^2})))</math>
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^2}))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,3,1)(5,3,1)(5,3,1)
|-
|<math>\psi(\psi_2(\psi_3(\Omega_5^{\Omega_5^{\Omega_5}})))</math>
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\Omega_4}}))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,3,1)(5,3,1)(6,3,1)
|-
|<math>\psi(\psi_2(\psi_3(\psi_5(\Omega_6))))</math>
|<math>\psi(\psi_2(\psi_4(\Omega_5)))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,4)
|-
|<math>\psi(\psi_2(\psi_3(\psi_5(\Omega_6)+\Omega_5)))</math>
|<math>\psi(\psi_2(\psi_4(\Omega_5)+\Omega_4))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,4)(3,3,1)
|-
|<math>\psi(\psi_2(\psi_3(\psi_5(\Omega_6)\times2)))</math>
|<math>\psi(\psi_2(\psi_4(\Omega_5)\times2))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,4)(3,3,1)(4,4)
|-
|<math>\psi(\psi_2(\psi_3(\psi_5(\Omega_6+1))))</math>
|<math>\psi(\psi_2(\psi_4(\Omega_5+1)))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,4)(4)
|-
|<math>\psi(\psi_2(\psi_3(\psi_5(\Omega_62))))</math>
|<math>\psi(\psi_2(\psi_4(\Omega_52)))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,4)(4,4)
|-
|<math>\psi(\psi_2(\psi_3(\psi_5(\Omega_6^2))))</math>
|<math>\psi(\psi_2(\psi_4(\Omega_5^2)))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,4)(5,4)
|-
|<math>\psi(\psi_2(\psi_3(\psi_5(\psi_6(\Omega_7)))))</math>
|<math>\psi(\psi_2(\psi_4(\psi_5(\Omega_6))))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,4)(5,5)
|-
|<math>\psi(\psi_2(\psi_3(\psi_5(\psi_6(\psi_7(\Omega_8))))))</math>
|<math>\psi(\psi_2(\psi_4(\psi_5(\psi_6(\Omega_7)))))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,4)(5,5)(6,6)
|-
|<math>\psi(\psi_2(\psi_3(\psi_5(\psi_6(\Omega_8)))))</math>
|<math>\psi(\psi_2(\psi_4(\Omega_6)))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,4)(5,5,1)
|-
|<math>\psi(\psi_2(\psi_3(\psi_5(\psi_6(\psi_8(\psi_9(\Omega_{11})))))))</math>
|<math>\psi(\psi_2(\psi_4(\psi_6(\Omega_8))))</math>
|(0)(1,1,1)(2,2)(3,3,1)(4,4)(5,5,1)(6,6)(7,7,1)
|-
|<math>\psi(\psi_2(\Omega_4))</math>
|<math>\psi(\Omega_3)</math>
|(0)(1,1,1)(2,2,1)
|}
未完待续
[[分类:分析]]