HPrSSψ vs LPrSSψ分析

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：$\psi ({\psi }_2({\psi }_3({\psi }_4({\psi }_5({\psi }_6(...))))))$，分歧源自折叠方式不同。

分析1：(0)(1,1,1)(2,2)(3,3,1)~BGO

HPrSSψ	LPrSSψ	BMS
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5)))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4))$	(0)(1,1,1)(2,2)(3,3,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5))+\mathrm{\Omega })$	$\psi ({\psi }_2({\mathrm{\Omega }}_4)+\mathrm{\Omega })$	(0)(1,1,1)(2,2)(3,3,1)(1,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5))+{\psi }_1({\psi }_3({\psi }_4({\mathrm{\Omega }}_6)))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4)+{\psi }_1({\psi }_3({\mathrm{\Omega }}_5)))$	(0)(1,1,1)(2,2)(3,3,1)(1,1)(2,2,1)(3,3)(4,4,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5))+{\mathrm{\Omega }}_2)$	$\psi ({\psi }_2({\mathrm{\Omega }}_4)+{\mathrm{\Omega }}_2)$	(0)(1,1,1)(2,2)(3,3,1)(1,1,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5))+{\psi }_2({\mathrm{\Omega }}_3))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4)+{\psi }_2({\mathrm{\Omega }}_3))$	(0)(1,1,1)(2,2)(3,3,1)(1,1,1)(2,2)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5))\times 2)$	$\psi ({\psi }_2({\mathrm{\Omega }}_4)\times 2)$	(0)(1,1,1)(2,2)(3,3,1)(1,1,1)(2,2)(3,3,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5)+1))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4+1))$	(0)(1,1,1)(2,2)(3,3,1)(2)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5)+\mathrm{\Omega }))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4+\mathrm{\Omega }))$	(0)(1,1,1)(2,2)(3,3,1)(2,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5)+{\psi }_1({\psi }_3({\psi }_4({\mathrm{\Omega }}_6))))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4+{\psi }_1({\psi }_3({\mathrm{\Omega }}_5))))$	(0)(1,1,1)(2,2)(3,3,1)(2,1)(3,2,1)(4,3)(5,4,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5)+{\mathrm{\Omega }}_2))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4+{\mathrm{\Omega }}_2))$	(0)(1,1,1)(2,2)(3,3,1)(2,1,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5)+{\psi }_2({\psi }_3({\mathrm{\Omega }}_5))))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4+{\psi }_2({\mathrm{\Omega }}_4)))$	(0)(1,1,1)(2,2)(3,3,1)(2,1,1)(3,2)(4,3,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5)+{\mathrm{\Omega }}_3))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4+{\mathrm{\Omega }}_3))$	(0)(1,1,1)(2,2)(3,3,1)(2,2)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5)+{\mathrm{\Omega }}_3\omega ))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4+{\mathrm{\Omega }}_3\omega ))$	(0)(1,1,1)(2,2)(3,3,1)(2,2)(3)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5)+{\mathrm{\Omega }}_3^2))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4+{\mathrm{\Omega }}_3^2))$	(0)(1,1,1)(2,2)(3,3,1)(2,2)(3,2)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5)+{\psi }_3({\mathrm{\Omega }}_4)))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4+{\psi }_3({\mathrm{\Omega }}_4)))$	(0)(1,1,1)(2,2)(3,3,1)(2,2)(3,3)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5)\times 2))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4+{\psi }_3({\mathrm{\Omega }}_5)))$	(0)(1,1,1)(2,2)(3,3,1)(2,2)(3,3,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5+1)))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4+{\psi }_3({\mathrm{\Omega }}_5+1)))$	(0)(1,1,1)(2,2)(3,3,1)(3)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5+\mathrm{\Omega })))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4+{\psi }_3({\mathrm{\Omega }}_5+\mathrm{\Omega })))$	(0)(1,1,1)(2,2)(3,3,1)(3,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5+{\mathrm{\Omega }}_2)))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4+{\psi }_3({\mathrm{\Omega }}_5+{\mathrm{\Omega }}_2)))$	(0)(1,1,1)(2,2)(3,3,1)(3,1,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5+{\mathrm{\Omega }}_3)))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4+{\psi }_3({\mathrm{\Omega }}_5+{\mathrm{\Omega }}_3)))$	(0)(1,1,1)(2,2)(3,3,1)(3,2)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5+{\psi }_3({\mathrm{\Omega }}_5))))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4+{\psi }_3({\mathrm{\Omega }}_5+{\psi }_3({\mathrm{\Omega }}_5))))$	(0)(1,1,1)(2,2)(3,3,1)(3,2)(4,3,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5+{\mathrm{\Omega }}_4)))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4+{\psi }_3({\mathrm{\Omega }}_5+{\mathrm{\Omega }}_4)))$	(0)(1,1,1)(2,2)(3,3,1)(3,3)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5+{\mathrm{\Omega }}_4\omega )))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4+{\psi }_3({\mathrm{\Omega }}_5+{\mathrm{\Omega }}_4\omega )))$	(0)(1,1,1)(2,2)(3,3,1)(3,3)(4)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5+{\mathrm{\Omega }}_4^2)))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4+{\psi }_3({\mathrm{\Omega }}_5+{\mathrm{\Omega }}_4^2)))$	(0)(1,1,1)(2,2)(3,3,1)(3,3)(4,3)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5+{\psi }_4({\mathrm{\Omega }}_5))))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4+{\psi }_3({\mathrm{\Omega }}_5+{\psi }_4({\mathrm{\Omega }}_5))))$	(0)(1,1,1)(2,2)(3,3,1)(3,3)(4,4)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5+{\psi }_4({\mathrm{\Omega }}_6))))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4+{\psi }_3({\mathrm{\Omega }}_5+{\psi }_4({\mathrm{\Omega }}_6))))$	(0)(1,1,1)(2,2)(3,3,1)(3,3)(4,4,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_{5}2)))$	$\psi ({\psi }_2({\mathrm{\Omega }}_{4}2))$	(0)(1,1,1)(2,2)(3,3,1)(3,3,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_{5}3)))$	$\psi ({\psi }_2({\mathrm{\Omega }}_{4}3))$	(0)(1,1,1)(2,2)(3,3,1)(3,3,1)(3,3,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5\omega )))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4\omega ))$	(0)(1,1,1)(2,2)(3,3,1)(4)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5\mathrm{\Omega })))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4\mathrm{\Omega }))$	(0)(1,1,1)(2,2)(3,3,1)(4,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5{\mathrm{\Omega }}_2)))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4{\mathrm{\Omega }}_2))$	(0)(1,1,1)(2,2)(3,3,1)(4,1,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5{\mathrm{\Omega }}_3)))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4{\mathrm{\Omega }}_3))$	(0)(1,1,1)(2,2)(3,3,1)(4,2)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5\times {\psi }_3({\mathrm{\Omega }}_5))))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4\times {\psi }_3({\mathrm{\Omega }}_5)))$	(0)(1,1,1)(2,2)(3,3,1)(4,2)(5,3,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5{\mathrm{\Omega }}_4)))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4\times {\psi }_3({\mathrm{\Omega }}_5{\mathrm{\Omega }}_4)))$	(0)(1,1,1)(2,2)(3,3,1)(4,3)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5\times {\psi }_4({\mathrm{\Omega }}_6))))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4\times {\psi }_3({\mathrm{\Omega }}_5\times {\psi }_4({\mathrm{\Omega }}_6))))$	(0)(1,1,1)(2,2)(3,3,1)(4,3)(5,4,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5^2)))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4^2))$	(0)(1,1,1)(2,2)(3,3,1)(4,3,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5^3)))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4^3))$	(0)(1,1,1)(2,2)(3,3,1)(4,3,1)(4,3,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5^{\omega })))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4^{\omega }))$	(0)(1,1,1)(2,2)(3,3,1)(4,3,1)(5)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5^{\mathrm{\Omega }})))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4^{\mathrm{\Omega }}))$	(0)(1,1,1)(2,2)(3,3,1)(4,3,1)(5,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5^{{\mathrm{\Omega }}_2})))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4^{{\mathrm{\Omega }}_2}))$	(0)(1,1,1)(2,2)(3,3,1)(4,3,1)(5,1,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5^{{\mathrm{\Omega }}_3})))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4^{{\mathrm{\Omega }}_3}))$	(0)(1,1,1)(2,2)(3,3,1)(4,3,1)(5,2)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5^{{\psi }_3({\mathrm{\Omega }}_5)})))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4^{{\psi }_3({\mathrm{\Omega }}_5)}))$	(0)(1,1,1)(2,2)(3,3,1)(4,3,1)(5,2)(6,3,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5^{{\mathrm{\Omega }}_4})))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4^{{\psi }_3({\mathrm{\Omega }}_5^{{\mathrm{\Omega }}_4})}))$	(0)(1,1,1)(2,2)(3,3,1)(4,3,1)(5,3)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5^{{\psi }_4({\mathrm{\Omega }}_6)})))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4^{{\psi }_3({\mathrm{\Omega }}_5^{{\psi }_4({\mathrm{\Omega }}_6)})}))$	(0)(1,1,1)(2,2)(3,3,1)(4,3,1)(5,3)(6,4,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5^{{\mathrm{\Omega }}_5})))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4^{{\mathrm{\Omega }}_4}))$	(0)(1,1,1)(2,2)(3,3,1)(4,3,1)(5,3,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5^{{\mathrm{\Omega }}_5+1})))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4^{{\mathrm{\Omega }}_4+1}))$	(0)(1,1,1)(2,2)(3,3,1)(4,3,1)(5,3,1)(4,3,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5^{{\mathrm{\Omega }}_{5}2})))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4^{{\mathrm{\Omega }}_{4}2}))$	(0)(1,1,1)(2,2)(3,3,1)(4,3,1)(5,3,1)(4,3,1)(5,3,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5^{{\mathrm{\Omega }}_5^2})))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4^{{\mathrm{\Omega }}_4^2}))$	(0)(1,1,1)(2,2)(3,3,1)(4,3,1)(5,3,1)(5,3,1)
$\psi ({\psi }_2({\psi }_3({\mathrm{\Omega }}_5^{{\mathrm{\Omega }}_5^{{\mathrm{\Omega }}_5}})))$	$\psi ({\psi }_2({\mathrm{\Omega }}_4^{{\mathrm{\Omega }}_4^{{\mathrm{\Omega }}_4}}))$	(0)(1,1,1)(2,2)(3,3,1)(4,3,1)(5,3,1)(6,3,1)
$\psi ({\psi }_2({\psi }_3({\psi }_5({\mathrm{\Omega }}_6))))$	$\psi ({\psi }_2({\psi }_4({\mathrm{\Omega }}_5)))$	(0)(1,1,1)(2,2)(3,3,1)(4,4)
$\psi ({\psi }_2({\psi }_3({\psi }_5({\mathrm{\Omega }}_6)+{\mathrm{\Omega }}_5)))$	$\psi ({\psi }_2({\psi }_4({\mathrm{\Omega }}_5)+{\mathrm{\Omega }}_4))$	(0)(1,1,1)(2,2)(3,3,1)(4,4)(3,3,1)
$\psi ({\psi }_2({\psi }_3({\psi }_5({\mathrm{\Omega }}_6)\times 2)))$	$\psi ({\psi }_2({\psi }_4({\mathrm{\Omega }}_5)\times 2))$	(0)(1,1,1)(2,2)(3,3,1)(4,4)(3,3,1)(4,4)
$\psi ({\psi }_2({\psi }_3({\psi }_5({\mathrm{\Omega }}_6+1))))$	$\psi ({\psi }_2({\psi }_4({\mathrm{\Omega }}_5+1)))$	(0)(1,1,1)(2,2)(3,3,1)(4,4)(4)
$\psi ({\psi }_2({\psi }_3({\psi }_5({\mathrm{\Omega }}_{6}2))))$	$\psi ({\psi }_2({\psi }_4({\mathrm{\Omega }}_{5}2)))$	(0)(1,1,1)(2,2)(3,3,1)(4,4)(4,4)
$\psi ({\psi }_2({\psi }_3({\psi }_5({\mathrm{\Omega }}_6^2))))$	$\psi ({\psi }_2({\psi }_4({\mathrm{\Omega }}_5^2)))$	(0)(1,1,1)(2,2)(3,3,1)(4,4)(5,4)
$\psi ({\psi }_2({\psi }_3({\psi }_5({\psi }_6({\mathrm{\Omega }}_7)))))$	$\psi ({\psi }_2({\psi }_4({\psi }_5({\mathrm{\Omega }}_6))))$	(0)(1,1,1)(2,2)(3,3,1)(4,4)(5,5)
$\psi ({\psi }_2({\psi }_3({\psi }_5({\psi }_6({\psi }_7({\mathrm{\Omega }}_8))))))$	$\psi ({\psi }_2({\psi }_4({\psi }_5({\psi }_6({\mathrm{\Omega }}_7)))))$	(0)(1,1,1)(2,2)(3,3,1)(4,4)(5,5)(6,6)
$\psi ({\psi }_2({\psi }_3({\psi }_5({\psi }_6({\mathrm{\Omega }}_8)))))$	$\psi ({\psi }_2({\psi }_4({\mathrm{\Omega }}_6)))$	(0)(1,1,1)(2,2)(3,3,1)(4,4)(5,5,1)
$\psi ({\psi }_2({\psi }_3({\psi }_5({\psi }_6({\psi }_8({\psi }_9({\mathrm{\Omega }}_{11})))))))$	$\psi ({\psi }_2({\psi }_4({\psi }_6({\mathrm{\Omega }}_8))))$	(0)(1,1,1)(2,2)(3,3,1)(4,4)(5,5,1)(6,6)(7,7,1)
$\psi ({\psi }_2({\mathrm{\Omega }}_4))$	$\psi ({\mathrm{\Omega }}_3)$	(0)(1,1,1)(2,2,1)

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