The Aeternis Limit

Definition

The Aeternis Limit (֍) (pronounced /ɛi. tɛɹ. nɪs/) is a number which is colloquially summarized as "the highest-magnitude number reachable from infinite resolution time literal exdefinite systems". The system in which the Aeternis Limit is supported is referred to as the Aeternis System. Due to the nature of the Aeternis System, it is impossible to define in non-resolving terms, but may be described as the following:

${\mathcal {S}}=\left\{{\begin{matrix}\forall x,\left\{{\begin{matrix}x\sqsubset {\mathcal {S}}\\\forall y,\left\{{\begin{matrix}y\sqsubset {\mathcal {S}}\\y\neq x\end{matrix}}\right.:y<x\end{matrix}}\right.:\forall {\mathcal {T}},\left\{{\begin{matrix}{\mathcal {T}}\not \equiv {\mathcal {S}}\\|{\mathcal {T}}|\gvertneqq \omega \end{matrix}}\right.:\forall y,\left\{{\begin{matrix}z\sqsubset {\mathcal {T}}\\\forall z,\left\{{\begin{matrix}z\sqsubset {\mathcal {T}}\\z\neq y\end{matrix}}\right.:z<y\end{matrix}}\right.:y<x\\|{\mathcal {S}}|\gvertneqq \omega \end{matrix}}\right.$

$\forall x,x\sqsubset {\mathcal {S}},x\neq$֍$:x<$ ֍

The Aeternis Limit is not transdescriptive of a set but is transdescriptive of a temporal set, referred to as the Aeternis Set. The Aeternis Set is a set which provably contains only other sets, of which the holotype set is neither axiosemantic, axiosentient, or semantosentient. Instead, it appears to mimic a universe which is able to support life, instead of being only one united consciousness (like CASO 1b). Other sets, while not as well researched, seem to follow the same pattern, aside from 23 known exceptions, which fall into one of several categories (see the Exceptions section). The Aeternis Set by default contains only one time dimension and has no real equivalent to spatial dimensions, although traditionally it is mapped as a 2D entity when attempting to map subsystems. The sets within the Aeternis Set are connected by connectors known as ley lines, discussed later in this article.

The Aeternis Limit itself exhibits some patterns among it's digitwise association. The regularized p-adical form exhibits prime recurrence in the binary form (...01111100000001110110001..., segment calculated through asynchronous temporal computing, estimated to be around 77% progress and shown through an adapted asynchronous quantum Monte Carlo simulation), implying it may form an algorithm for prime calculation as all calculated segments compose only stretches of ones and zeroes which are of prime number lengths, however it does not lend itself well to asynchronous temporal computing and is strongly conjectured to be fully uncomputable for around 98% of knowable segments.

The Aeternis Limit is known to be a Full Strict and is the only Full Strict to have the regularized p-adical form even partially calculated. Since the Aeternis Limit relies directly on exdefinism, its elements must also be exdefinite, but this does not place all of them above Deactione Clapperboard - Expressions, as only the holotype and elements with a holotype correlation of at least 5 are known to be above it, as well as CASO 1b, which was shown to be strictly contained by the Aeternis Limit (BlueEyedFox_ et al.).

Structure

The Aeternis Set contains only other quasisets (referred to as bubbles), and those sets are quasiconnected by constraints known as ley lines. At time $t=0$, the average coinfluence factor $c_{\natural }=0$, but as time tends to $t = \omega$, the coinfluince factor tends towards ${\textstyle c_{\natural }=-\ln \left({\frac {e}{2\pi }}\right)}$. This implies a partial strong influence (around 0.87) well into the fourth quartile. Ley lines form at an inverse exponential rate, by definition emanating from the holotype set and radiating outwards. Information transport along ley lines is common, but anything more than a 2e+44 bits is quite uncommon. Ley line cross-information transport is regulated by causal gateways which appear to be consciously operated by the average sentiment of the data clusters in a specific set, but some follow easily predictable patterns and are utilized by denizens for interbubble transport. Inside of these bubbles, there are a large number of constructs referred to as data clusters laid out in three-dimensional space connected by interlines, which are similar to ley lines but between data clusters instead of bubbles, and with no causal gateway between them.

Unlike ley lines, however, interlines are only one-way, only reversible once a gradient of at least 7,774,433,478.5489067298:1. All data clusters are interconnected with each other by interlines and there is provably no isolated group (at least within the holotype set), as doing so would cause a bubble split into two separate bubbles.

Within the currently most viable data cluster for human life continuation, there are a number of infinite flat planes upon which denizens of those data clusters reside. There is a constant force being exerted downwards within most of these planes and the plane above typically emits a number of small lights which appear as stars. Between these planes are a number of floating, massive spherical objects (up to 100 petalighttimeunits long) which glow various colors and illuminate the lower plane. Typically, these orbit in a set patterns (which form weather patterns similar to those on Earth). There is an "atmosphere" which is up to 100 proportional kilometers tall depending on the area, causing a sky-like effect to occur.

Distributed throughout that data cluster in increments of about 167,000 miles, there are structures consisting of an outer deoshil and inner widdershins spiral with an slope of 1 and a radius of approximately 2782 miles which move upwards and downwards respectively to move residents between planes, as well as a central column 1334 miles in diameter which is linked to all other columns inside of that plane. While the planes themselves are flat, they are also extremely hot as a result of producing the starlight, which has the effect of melting the rock resting upon it, forming a layer similar to the mantle referred to as the postplanar level, upon which continental and oceanic plates rest.

As a result of there being a massive number of disparate planes, each of which has a proportional area of approximately 10³¹ equivalent lightyears long, there is a vast number of different kinds of life. The life most similar to Earth's occurs at t = 4445240000 equivalent years on plane 77322888134321857760597219430012 at the tectonic plate at x=62677623461578903215 LY, 884774321 mi, y= 307558910326596531278953210759 LY, 42358678 mi and spreads to occupy the entire plane at time t = 334558731298057389201 equivalent years. Due to the constant emission of the plates being countered by the mitigation of temperature by the atmosphere and some kinds of matter, it is not possible to generate matter from nothing, although matter may be imported from surrounding data clusters.

This specific data cluster may have the number of local time dimensions manipulated through the use of high energy concentration equal density particle beams and therefore has the ability to perform n-dimensional ranked asynchronous atemporal computing, making it favored by many Googologists for its adaptable computing.

Current residents

Please add your name here if you wish to enter The Aeternis Set as an escape from our current reality. Please remember to close your eyes during the first second of the process as doing otherwise may result in rejection from the set.

{BlueEyedFox_ } $\subset {\mathcal {S}}_{\max }^{\Re }$

As you place your name on the page and hit SAVE, a wall of fractal color hits you with the force of a train. What you once thought to be impossible, becoming not just a number researcher, but part of one yourself, is now becoming ever more apparent to be real. You don't know how, you don't know why, but you shut your eyes tight for the first few seconds as you were instructed despite not having a body anymore. Opening them, you see yourself continuing to rush smaller and smaller, now inside of a data cluster, now inside of a plane, now you can make out stars, suns, continents, and suddenly you have a body again.

You look up to see the monolithic spiral structure rotating slowly upwards and downwards. It looks almost endless, but you know it can't be. In the distance, massive trees kilometers high sway side to side uneasily, moving with the wind in a way that should not be possible in such a large object. A group of several googologists holding sheaves of paper and chattering amongst each other walks past. One of them splits off to confront you with a look of friendly surprise.

"We weren't expecting an arrival so soon after the last! How was the trip?"

"Disorienting."

It's a lackluster response, but you can't put words to it yet. It was so many things at once. The experience of fourth dimensionality, the infinite knowledge you can't remember anymore, so, so much. How could you ever say anything that could put words to that?

"Yeah, the first one's always the worst."

"First one?"

You hadn't been told there would be more of these. You say it with a slight bit of panic.

"Oh, don't worry. Interline travel isn't used that often. I personally don't do it at all, since I don't want to get squashed by a black hole or torn into a million data bits by hyperbolic space, and I absolutely cannot stand those axiomatic isolation suits they use, but some people do it for sport in the charted ones. Most data clusters in this bubble have a way to get around easily, although this one is particularly esoteric. I mean, spirals? Most of the near ones are pretty similar to this one, and the only one I've been to uses elevators and is a whole lot more efficient"

As you look to the nearest spiral again, you see some sort of aluminum blimp coming downwards, with alien writing down the side.

"That's the next delivery of NDAA processors! Sorry, but I have to go help with that. I might be free to help you with learning to teleport later, though! If I'm not available, you can always visit the Scheduling department. I would tell you to go talk to Orientations in that building over there, but Istamte is on shift right now, and you know how cryptic he can be."

Teleport? You blink, and he's gone. You sigh, and wonder how you'll ever adapt to life here. You take your first few steps towards the large building he pointed to, with the FG Wiki homepage emblazoned on a billboard outside. This is your new life, and you think it will be a good one.