Toppolt
Creator: ØP Duh(youtube)
Date of creation: 11/2/2026
Systems used: Sbiis Saibian's Solidus-Extended Cascading-E notation, Chris Bird' Array notation
Defined as:
E1e+100(E1e+100{##100##, #^^##^^####^^####, ##100##, #^^##^^####^^####, #1e+6#^#/#^#1e+6#}[#/#]####1e+24^^1e+24^^1e+24^^1e+24)##100##^^##100##, ##100##^^##100##, #100#^#/#^#100#
Toppoltiduotop = Toppolt(Toppolt)
Toppoltritop = Toppolt(Toppolt(Toppolt))
Toppoltiquadritop = Toppolt(Toppolt(Toppolt(Toppolt)))
Toppoltitoppolt = Toppolt
Toppoltiduotoppolt = Toppoltiduotop
Toppoltiduotoppoltiduotop = Toppoltiduotop(Toppoltiduotop)
Toppoltritoppoltiduotop = Toppoltritop(Toppoltritop)
Toppoltiduotoppoltritop = Toppoltiduotop(Toppoltiduotop(Toppoltiduotop))
Toppoolt = Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt))))))))))
Toppol = Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt(Toppolt))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
Toopool = 1 Toppolt layers of Toppolt
Toppot = 1 Toppolt layers of 1 Toppolt layers of Toppolt layers... and so on REPEATED 1 TOPPOLT TIMES
TOP = 1 Toppot layers of 1 Toppot layers of 1 Toppot layers repeated E...(amount of 1 Toppot Es)(1 Toppot)(1 Toppot of #s connected to 1 Toppot)(1 Toppot arrows)(1 Toppot of #s connected to 1 Toppot)(1 Toppot arrows)...(repeating 1 Toppot times) times and a final Toppolt at the end, if placed inside a function that contains another number, it will clone itself for a (current value) amount of times and connect all of it together, and does that indefinitely until it's value is (original value) times bigger or more than the other number value that's inside the function, it being alone in the function does nothing, TOP will always be the first one to activate inside any function, activating only once, then let the others do their things, parentheses doesn't matter, 2 or more TOPs in the function causes an endless loop of growth that never ends, scretching out indefinitely, placing Infinity alongside TOP in a function would cause it to grow to Infinity.(disclaimer: TOP isn't a function, it's a value that grows by itself, can be used in functions but cannot be used as hyper operators)
Self-Operating Growth Toppolt(Re-topped Toppolt): Rᵀᵒᵖ(Toppolt)
Rᵀᵒᵖ is a function in which tops up a number inside it with the number itself for as many times as the actual value of the number in Cascading-E notation as in E(E(E...[amount of Es depends on the value of the number][number here][hash here(how many hashes depends on the actual value of the number and each STACK of hashes is strictly raised to the power by another STACK of hashes as many times as the value of the number and each stack of hash ends in the actual value of the number before being raised to the power of another stack)], for example, Rᵀᵒᵖ(Septuagintillion) is E(septuagintillion)(septuagintillion of #s connected to septuagintillion)(septuagintillion arrows)(septuagintillion of #s connected to septuagintillion)(septuagintillion arrows)...(repeating a septuagintillion times), but then the result is then calculated with every single function that exists in mathematics individually, and all the results with all of the functions is then used as power towers on top of the resulted number, the biggest being at the top and the smallest at the bottom, with the amount of arrows raised each time equivalent to all of the values of the whole power tower including the base combined, the Rᵀᵒᵖ function loops itself indefinitely until the number's resulting value is [E...(number value)(stack of hashes raised with (number value) amount of arrows of more stacks of hashes in many times as the value of the number with each hash ending in the number's value) and process repeated (new resulted number value raised by new number value amount of arrows to the same new resulted number by new resulted number amount of times) times with each replacing all the amount of number values, hashes and arrows with the resulted number value amount raised by the (new number value) amount of arrows to the entire expression a (new number value) amount of times] times bigger or more than it's original self, the resulting number is the "Top" value of the number in the function, if the Rᵀᵒᵖ function has 2 numbers or more inside of it instead, like Rᵀᵒᵖ(septuagintillion | quadrillion | sextillion), it turns the septuagintillion into their Rᵀᵒᵖ form, and quadrillion into their Rᵀᵒᵖ form, and sextillion into their Rᵀᵒᵖ form seperately, then it checks how many possible orders there are for the numbers, then raises the 3 numbers to all of the rest except the number that is the base itself with all of the raised and base number's value equivalent to how many arrows they are raised to EVERY SINGLE TIME and checks how many different orders there are, and then raises the final number's value to every single different order possible that all the numbers can be arranged in.(the orders also includes the base number itself) with the amount of arrows equivalent to the value of the entire order(except the number that is being raised to the power by the entire order) and the same with the rest of the other numbers, then finally raising the smallest number result in the entire function to the next bigger number until the biggest number with the amount of arrows each time equivalent to the value of all the numbers inside the function combined together, then calculates the same thing over and over with every singular function that has ever existed and then raises all of the numbers to ALL of the results for each number from smallest at the bottom to the biggest being the top, the amount of arrows depends on what the value of the entire thing combined is in normal addition, finally coming to the final result, and TOP can only become bigger when it's not in it's Rᵀᵒᵖ form yet, once all numbers has reached their Rᵀᵒᵖ forms, TOP cannot increase it's size because it's now in Cascading-E notation form, but having a Rᵀᵒᵖ function with 2 or more TOPs causes a paradox and causes them to grow indefinitely, the Rᵀᵒᵖ function can only initiate when all numbers are stable inside it, Rᵀᵒᵖ function will always be the last one to initiate no matter what.(also, every function except Rayo's function, Busy Beaver, FOOT, Oracle extensions and other functions whose only purpose is to scale up numbers)
Reminder: Toppolts that are used as hyper operators means they connect with the one inside them, like literally, as in million-million to millillion.
THE HYPER SYSTEM
Hyper Toppolt
E1e+240(E1e+240(E1e+100(E1e+100{##100##, #^^##^^####^^####, ##100##, #^^##^^####^^####, #1e+7#^#/#^#1e+7#}[#/#]####1e+24^^1e+24^^1e+24^^1e+24)##100##^^##100##, ##100##^^##100##, #1e+7#^#/#^#1e+7#)#^#1000##^^##1000#^#, #^#1000##^^##1000#^#)#^^##1000##^^#^^#^^##1000##^#, #^^#24##^^#1000#^^##24#^^#
Everything else is the same but uses Hyper Toppolt here, call them by their normal names with "Hyper" at the start, Rᵀᵒᵖ & TOP has no HYPER variations as they are already the tops.
Commenters' ideas:
Benjiman125125125:
Quaddutto: defined as: E(4^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^................{E^^^^^^^^^^^^^^^^^^^^^^^...........................4{################################....................... Reapeted g44444^^^^^^^^^^^^^^^^^^^^..444444^^^^^^^^^^^^^^^^^..(g44444^^^^^^^^^^^^^^^^^^^^^^^^^^^..44444^^^^^^^^^^^^^^^^^...4............ times Repeated TOP ^^^^^^^....... TREE(4^^^^4^^^^...) TREE(3) times and that is the amount that you put in the hyper E notation it's near bigger than TREE(10^10^10^100) ^2Â
Quaddutto's tag: illegal(too many symbols stacks), highly ill defined(lack of specific values and amount of systems and their names that were used to combine are unknown) & computable(theoretically possible to calculate using a mathematical algorithm) extremely large finite number.