Optimized first-order dimensional array notation

When it encounters a first-order comma, hit should search for a 0th order separator (a separator without a subscript). This should give the ordinal strength Bachmann-Howard ordinal instead of Feferman-Schutte Ordinal. For example, in {0{0,11}11}, which has the strength of your system, S1 would be {0,11} and Sn+1 would be {0,{0 Sn 1}11}.

Higher-order array notation

We now introduce nth order separators ({}n) and nth order commas (,n). An nth order comma would search for an n-1th order separator, and if doesn't find one, it adds one. right inside the highest nested lower level separator For example, {0,22} becomes {0{0,22}11}. This has level psi(psi(0))

Double-comma array notation

,n should be shorthand for {0,,n} and {m}n should be shorthand for {m,,n}. Each double-comma containing separator searches or another separator. For example {0,,0,,1} searches for {0,,0__1} If if finds a lower level separator, adds the separator it is searching for. For example, {0{0,,0,,1}1} becomes {0{0,,0{0,,0,,1}1}1} 

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