11,329
pages

This is my analysis of BM3.1/3.2. For BM2/2.3 analysis, go here

## $$\psi(\Omega_\omega)$$ to TFB

(0,0,0)(1,1,1) has level $$\psi(\Omega_\omega)$$

(0,0,0)(1,1,1)(1,1,0) has level $$\psi(\Omega_\omega+1)$$

(0,0,0)(1,1,1)(1,1,0)(2,1,0) has level $$\psi(\Omega_\omega+\Omega)$$

(0,0,0)(1,1,1)(1,1,0)(2,2,0) has level $$\psi(\Omega_\omega+\psi_1(\Omega_2))$$

(0,0,0)(1,1,1)(1,1,0)(2,2,1) has level $$\psi(\Omega_\omega+\psi_1(\Omega_\omega))$$

(0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,2,0) has level $$\psi(\Omega_\omega+\Omega_2)$$

(0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)(3,3,1)(3,3,0) has level $$\psi(\Omega_\omega+\Omega_3)$$

(0,0,0)(1,1,1)(1,1,1) has level $$\psi(\Omega_\omega 2)$$

(0,0,0)(1,1,1)(2,0,0) has level $$\psi(\Omega_\omega \omega)$$

(0,0,0)(1,1,1)(2,1,0) has level $$\psi(\Omega_\omega \Omega)$$

(0,0,0)(1,1,1)(2,1,0)(1,1,1) has level $$\psi(\Omega_\omega \Omega + \Omega_\omega)$$

(0,0,0)(1,1,1)(2,1,0)(2,1,0) has level $$\psi(\Omega_\omega \Omega^2)$$

(0,0,0)(1,1,1)(2,1,0)(3,2,1) has level $$\psi(\Omega_\omega \psi_1(\Omega_\omega))$$

(0,0,0)(1,1,1)(2,1,0)(3,2,1)(3,2,1) has level $$\psi(\Omega_\omega \psi_1(\Omega_\omega 2))$$

(0,0,0)(1,1,1)(2,1,0)(3,2,1)(4,2,0) has level $$\psi(\Omega_\omega \Omega_2)$$

(0,0,0)(1,1,1)(2,1,1) has level $$\psi(\Omega_\omega^2)$$

(0,0,0)(1,1,1)(2,1,1)(1,1,1) has level $$\psi(\Omega_\omega^2 + \Omega_\omega)$$

(0,0,0)(1,1,1)(2,1,1)(1,1,1)(2,1,0) has level $$\psi(\Omega_\omega^2 + \Omega_\omega \Omega)$$

(0,0,0)(1,1,1)(2,1,1)(1,1,1)(2,1,0)(3,2,1)(4,2,1) has level $$\psi(\Omega_\omega^2 + \Omega_\omega \psi_1(\Omega_\omega^2))$$

(0,0,0)(1,1,1)(2,1,1)(1,1,1)(2,1,0)(3,2,1)(4,2,1)(3,2,1) has level $$\psi(\Omega_\omega^2 + \Omega_\omega \psi_1(\Omega_\omega^2 + \Omega_\omega))$$

(0,0,0)(1,1,1)(2,1,1)(1,1,1)(2,1,0)(3,2,1)(4,2,1)(3,2,1)(4,2,0) has level $$\psi(\Omega_\omega^2 + \Omega_\omega \Omega_2))$$

(0,0,0)(1,1,1)(2,1,1)(1,1,1)(2,1,1) has level $$\psi(\Omega_\omega^2 2))$$

(0,0,0)(1,1,1)(2,1,1)(2,1,1) has level $$\psi(\Omega_\omega^3)$$

(0,0,0)(1,1,1)(2,1,1)(3,0,0) has level $$\psi(\Omega_\omega^\omega)$$

(0,0,0)(1,1,1)(2,1,1)(3,1,1) has level $$\psi(\Omega_\omega^{\Omega_\omega})$$

(0,0,0)(1,1,1)(2,1,1)(3,1,1)(4,1,1) has level $$\psi(\Omega_\omega^{\Omega_\omega^2})$$

(0,0,0)(1,1,1)(2,1,1)(3,1,1)(4,1,1)(5,1,1) has level $$\psi(\Omega_\omega^{\Omega_\omega^{\Omega_\omega}})$$

## TFB to  $$\psi(\psi_I(0))$$

(0,0,0)(1,1,1)(2,2,0) has level TFB = $$\psi(\Omega_{\omega+1})$$

(0,0,0)(1,1,1)(2,2,0)(2,2,0) has level $$\psi(\Omega_{\omega+1} 2)$$

(0,0,0)(1,1,1)(2,2,0)(3,1,0) has level $$\psi(\Omega_{\omega+1} \Omega)$$

(0,0,0)(1,1,1)(2,2,0)(3,1,1) has level $$\psi(\Omega_{\omega+1} \Omega_\omega)$$

(0,0,0)(1,1,1)(2,2,0)(3,2,0) has level $$\psi(\Omega_{\omega+1}^2)$$

(0,0,0)(1,1,1)(2,2,0)(3,2,0)(4,2,0) has level $$\psi(\Omega_{\omega+1}^{\Omega_{\omega+1}})$$

(0,0,0)(1,1,1)(2,2,0)(3,3,0) has level $$\psi(\Omega_{\omega+2})$$

(0,0,0)(1,1,1)(2,2,0)(3,3,1) has level $$\psi(\Omega_{\omega*2})$$

(0,0,0)(1,1,1)(2,2,0)(3,3,1)(4,4,0)(5,5,1) has level $$\psi(\Omega_{\omega*3})$$

(0,0,0)(1,1,1)(2,2,1) has level $$\psi(\Omega_{\omega^2})$$

(0,0,0)(1,1,1)(2,2,1)(1,1,1)(2,2,0) has level $$\psi(\Omega_{\omega^2} + \psi_\omega(\Omega_{\omega+1}))$$

(0,0,0)(1,1,1)(2,2,1)(1,1,1)(2,2,0)(3,3,1)(4,4,1) has level $$\psi(\Omega_{\omega^2} + \psi_\omega(\Omega_{\omega^2}))$$

(0,0,0)(1,1,1)(2,2,1)(1,1,1)(2,2,0)(3,3,1)(4,4,1)(2,2,0) has level $$\psi(\Omega_{\omega^2} + \Omega_{\Omega+1})$$

(0,0,0)(1,1,1)(2,2,1)(1,1,1)(2,2,0)(3,3,1)(4,4,1)(3,3,1) has level $$\psi(\Omega_{\omega^2} + \Omega_{\Omega 2})$$

(0,0,0)(1,1,1)(2,2,1)(1,1,1)(2,2,1) has level $$\psi(\Omega_{\omega^2} 2)$$

(0,0,0)(1,1,1)(2,2,1)(2,1,1)(3,2,1) has level $$\psi(\Omega_{\omega^2}^2)$$

(0,0,0)(1,1,1)(2,2,1)(2,2,0) has level $$\psi(\Omega_{\omega^2 + 1})$$

(0,0,0)(1,1,1)(2,2,1)(2,2,0)(3,3,1) has level $$\psi(\Omega_{\omega^2 + \omega})$$

(0,0,0)(1,1,1)(2,2,1)(2,2,0)(3,3,1)(4,4,1) has level $$\psi(\Omega_{\omega^2 2})$$

(0,0,0)(1,1,1)(2,2,1)(2,2,1) has level $$\psi(\Omega_{\omega^3})$$

(0,0,0)(1,1,1)(2,2,1)(3,0,0) has level $$\psi(\Omega_{\omega^\omega})$$

(0,0,0)(1,1,1)(2,2,1)(3,1,0) has level $$\psi(\Omega_{\Omega})$$

(0,0,0)(1,1,1)(2,2,1)(3,1,1) has level $$\psi(\Omega_{\Omega_\omega})$$

(0,0,0)(1,1,1)(2,2,1)(3,1,1)(4,2,1) has level $$\psi(\Omega_{\Omega_{\omega^2}})$$

(0,0,0)(1,1,1)(2,2,1)(3,1,1)(4,2,1)(5,1,1)(6,2,1) has level $$\psi(\Omega_{\Omega_{\Omega_{\omega^2}}})$$

## $$\psi(\psi_I(0))$$ to $$\psi_{I(\omega,0)}(0)$$

(0,0,0)(1,1,1)(2,2,1)(3,2,0) has level $$\psi(\psi_I(0))$$

(0,0,0)(1,1,1)(2,2,1)(3,2,0)(1,1,1)(2,2,1)(3,2,0) has level $$\psi(\psi_I(0) 2)$$

(0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,0) has level $$\psi(\Omega_{\psi_I(0) + 1})$$

(0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,0)(3,3,0) has level $$\psi(\Omega_{\psi_I(0) + 2})$$

(0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,0)(3,3,1) has level $$\psi(\Omega_{\psi_I(0) + \omega})$$

(0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,0)(3,3,1)(4,4,1)(5,1,1)(6,2,1)(7,2,0) has level $$\psi(\Omega_{\psi_I(0) 2})$$

(0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,0)(3,3,1)(4,4,1)(5,1,1)(6,2,1)(7,2,0)(4,4,1) has level $$\psi(\Omega_{\psi_I(0) \omega})$$

(0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,0)(3,3,1)(4,4,1)(5,1,1)(6,2,1)(7,2,0)(4,4,1)(5,1,1)(6,2,1)(7,2,0) has level $$\psi(\Omega_{\psi_I(0)^2})$$

(0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,0)(3,3,1)(4,4,1)(5,1,1)(6,2,1)(7,2,0)(5,1,1) has level $$\psi(\Omega_{\psi_I(0)^{\Omega_{\omega}}})$$

(0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,0)(3,3,1)(4,4,1)(5,1,1)(6,2,1)(7,2,0)(5,1,1)(6,2,1)(7,2,0) has level $$\psi(\Omega_{\psi_I(0)^{\psi_I(0)}})$$

(0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,0)(3,3,1)(4,4,1)(5,1,1)(6,2,1)(7,2,0)(5,1,1)(6,2,1)(7,2,0) has level $$\psi(\Omega_{\psi_I(0)^{\psi_I(0)}})$$