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\(\square\) is rest of array

\(\circ\) is row of zeroes

7. \(a$\circ [0]_{[\diamond 0,n+1]\bullet} \bullet\circ = a$\underbrace{\circ [0]_{[\diamond ... \circ [0]_{[\diamond 0,n]\bullet} \bullet\circ ...,n]\bullet} \bullet\circ}_{a}\)

S3. If array have 0 in the end, last entry never show up.

\([0]_{[0,1]}\) has level \(I\)

\([0]_{1[0,1]}\) has level \(\Omega_{I + 1}\)

\([0]_{[0]_{[0,1]}[0,1]}\) has level \(\Omega_{I*2}\)

\([0]_{[0,1][0,1]}\) has level \(I_2\)

\([0]_{[1,1]}\) has level \(I_w\)

\([0]_{[[0]_{[0,1]},1]}\) has level \(I_I\)

\([0]_{[[0,1],1]}\) has level \(I(1,0)\)

\([0]_{[0,1][[0,1],1]}\) has level \(I_{I(1,0) + 1}\)

\([0]_{[[0,1],1][[0,1],1]}\) has level \(I(1,1)\)

\([0]_{[[0,1][0,1],1]}\) has level \(I(2,0)\)

\([0]_{[[[0,1],1],1]}\) has level \(I(1,0,0)\)

\([0]_{[[0,1]_2,1]}\) has level \(\chi(\varepsilon_{M+1})\)

\([0]_{[[0,1]_3,1]}\) has level \(\chi(\varepsilon_{\Omega_{M+1}+1})\)

\([0]_{[[0,1]_{[0,1]},1]}\) has level \(\chi(\Omega_{M*2})\)

\([0]_{[0,2]}\) has level \(\chi(I_{M+1})\)

\([0]_{[0,3]}\) has level \(\chi(I_{M_2+1})\)

\([0]_{[0,[0,1]]}\) has level \(\chi(M_M)\)

\([0]_{[0,[0,1]_2]}\) has level \(\chi(M(1,0))\)

\([0]_{[0,[[0,1]_2,1]_2]}\) has level \(\chi(M(2,0))\)

\([0]_{[0,[[0,1]_3,1]_2]}\) has level \(\chi(\varepsilon_{M\{2\} + 1})\), where \(M\{n\}\) is n-ex-mahlo cardinal.

\([0]_{[0,[0,2]_2]}\) has level \(\chi(I_{M\{2\} + 1})\)

\([0]_{[0,[0,[0,1]]_2]}\) has level \(\chi(I_{M\{2\} + M})\)

\([0]_{[0,[0,[0,1]_2]_2]}\) has level \(\chi(I_{M\{2\}*2})\)

\([0]_{[0,[0,1]_3]}\) has level \(\chi(I(1,M\{2\}+1))\)

\([0]_{[0,[0,1]_{[0,1]}]}\) has level \(\chi(M_M\{2\})\)

\([0]_{[0,0,1]}\) has level \(\chi(M(1,0)\{2\})\)

More coming soon.

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