User:TGReddy

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I'm TGR

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TAN
 * 1) Base TAN
 * 2) *Base arrays reach \( \varphi(\omega,0) \).
 * 3) *Regular separators reach \( \Gamma_{0} = \varphi(1,0,0) \).
 * 4) *Nested separators reach \( \psi(\Omega_{2}) \).
 * 5) Extension 1: n-ticks
 * 6) *Definition 1: an n-tick has strength of \( \Omega_{n} \), the limit of (...)-ticks is \( \psi(\psi_{I}(0)) \), the OFP.
 * 7) *Definition 2: n-ticks have strength around \( I(\omega,0) \).
 * 8) *Original Intended Behavior: an n-tick has strength \( \psi(C(n;0)) \) in UNOCF, the limit of (...)-ticks is \( \psi(K) \) in UNOCF. (this is not a feasible extension and I am 99% sure it cannot be defined)
 * 9) Extension 1.5: tick-on-tick
 * 10) *This is such a terribly defined extension that I only have around 10 examples for where it's analysis should reach and they're almost all wrong. However, if this extension somehow managed to work as intended (not even I know what 'intended' is) then it's limit could range between \( \psi(C(1;;0)) \) and \( \psi(C(1\{w\}0)) \) in UNOCF. Terrifying!
 * 11) Extension 2: TBA

TGRx
 * 1) Symbol 1: xT
 * 2) *This symbol caps out at \( \omega \), as it is functionally equivalent to the Successor function
 * 3) Symbol 2: xxG
 * 4) *This symbol has limit \( \psi(\Omega) = \varepsilon_{0} \)
 * 5) Symbol 3: xR
 * 6) *This symbol has not been fully analyzed, but the current analysis goes up to \( \psi(\Omega^{2} \cdot 2) \), with a tentative estimation for \( \psi(\Omega^{\omega}) \). It likely goes decently far beyond this, but there are also weird spots involving empty atoms that may break the notation entirely.

rTAN EasyBMS
 * This was a failed attempt to add n-shifting to TAN, but it only has 2-shifting. It has strength \( \Omega+{\omega} \).
 * This isn't a notation, but an easy way to expand BMS expressions, although right now it can only accurately expand PrSS and PSS expressions (it doesn't account for ascension matrix). I accidentally invented it while trying to define TLAN (failed TAN extension that just accidentally turned it into BMS).