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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 \(\psi(\Omega_{\psi_I(0)^{\psi_I(0)}})\)

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