## Existence of a loop in a Turing machine?

Consider a Turing Machine which (1) reads all its input and (2) accepts inputs arbitrarily large. Can we conclude that there must be a loop in the finite-state control as its inputs get larger?

## Is there any decentralized, “serverless” network of any kind in existence with more than a handful of users?

I’m trying to verify that the findings of my own private "research", spanning over 10 years are accurate.

Basically, I’ve been actively hunting for any signs of any kind of "Internet alternative", decentralized network running "inside" the Internet, or even just individual applications for a specific task, which have more than a nominal group of hardcore fans who don’t actually use it meaningfully because they are just to few.

I first attempted to make a list of all the services I’ve already concluded are dead or won’t ever get ready, but I soon gave up and removed that part from the post. Whether I have such a list or not, I know that there will be tongue-in-cheek suggestions such as "Tor" or "Freenet" or "Zeronet", but please try to take this seriously.

I have so many times got excited (Dat, SAFE Network, IPFS, etc.) only to fall back into my chair, depressed from the total lack of activity inside each network. It’s not meaningful to sit and create things that nobody will ever be able to access, and which stands an even lesser chance of being profitable.

(No, I’m not greedy, but I need to make money somehow in order to survive and the old Internet has been utterly destroyed in every way. However, I’m not going to elaborate on that since, if you don’t already agree with me at this point, there isn’t really anything I can ever say to convince you otherwise.)

My sad conclusion is that there just is no such network/protocol/service as I’m looking for. Nobody has managed to market their solution in any meaningful way, perpetually working on code while ignoring the world which has never heard of their fantastic thing which is just a directory tree on GitHub, year after year…

The only non-fake, semi-useful individual applications I’ve been able to find are Bitcoin Core and Bisq. However, neither of those help me reach out to people or communicate in any way. The first is just a "digital wallet" and the second enables me to buy Bitcoin for fiat money via bank transfers with individuals without having to send in a photo id to some centralized site (which is one of the reasons why the old Internet is destroyed).

So, could it actually be that, in spite of actively searching everywhere for this, I’ve somehow missed something which is huge and decentralized? Another huge problem is that there’s a million sites/projects/whitepapers which lie about being dencentralized/privacy-respecting/secure, which further complicates things. I’ve seen countless websites which appear to have been mass produced just to "muddle the waters".

I’m looking for some way to reach out to people and not be harassed with "phone verification" or "sorry, we cannot grant access at this time" fake error messages for VPN/Tor users. "SAFE Network" has been working for over a decade and are forever and always "just a few months away" from release…

PS: Please don’t reply something about how "the Internet is already decentralized". No. It isn’t. It’s the most centralized network imaginable in its current form.

## Are there different planes of existence in Dragonlance?

Throughout editions, there has been the astral plane as well as other planes. Which planes are in the Dragonlance setting?

## What planes of existence does everyone visit while sleeping according to the Great Wheel cosmology?

When someone is sleeping what planes of existence do they visit according to the Great Wheel cosmology in D&D 5e?

As far as I remember, in one of the previous editions there was a separate plane you went to while dreaming, but what about for D&D 5e?

Is there a mechanic, for example, describing a transition during sleep, a possible death during sleep, or a transition to another person’s sleep that would shed light on this issue?

Maybe there is information compatible with D&D 5th edition in the books about Planescape (since we are dealing with the Great Wheel)?

Please provide references to the sources.

## Why does the Amulet of the Black Skull specify that you cannot use it to teleport to another plane of existence?

The Amulet of the Black Skull from Tomb of Annihilation says:

You can use an action to expend 1 of its charges to transport yourself and anything you are wearing or carrying to a location within 100 feet of you. The destination you choose doesn’t need to be in your line of sight, but it must be familiar to you (in other words, a place you have seen or visited), and it must be on the same plane of existence as you.

Why does the description specifically prohibit intraplanar travel when it already specified that the location must be within 100 feet of you?

Are there any situations when this is definitively not a redundancy?

I’ve never played Tomb of Annihilation, is there an adventure specific circumstance I’m not aware of that makes both restrictions necessary in the descriptions?

## Is this Correct, the existence of cryptography requires $UP \cap Co-UP \not\subseteq BPP$

Is this Correct, the existence of cryptography requires $$UP \cap Co-UP \not\subseteq BPP$$? Or does it require $$UP \not\subseteq BPP$$?

## Can a gargantuan creature be shoved into a demiplane using polymorph and released into a different plane of existence

For context, my party is going to face a gargantuan (20 by 20 ft. or larger) creature with obscene levels of health, so would it be possible to make a demiplane and polymorph the gargantuan creature down to size and then shove it into the demiplane, trapping it there.

This spell transforms a creature that you can see within range into a new form. An unwilling creature must make a Wisdom saving throw to avoid the effect. The spell has no effect on a shapechanger or a creature with 0 hit points. The transformation lasts for the duration, or until the target drops to 0 hit points or dies. The new form can be any beast whose challenge rating is equal to or less than the target’s (or the target’s level, if it doesn’t have a challenge rating).

After trapping it there, would it be possible to release it in, let’s say, Hell or just a ‘void’? This is saying that the creature has utilised everything it can to resist magic and it is shoved into the demiplane.

This is saying that the creature has utilised everything it can to resist magic and it is shoved into the demiplane.

## Can there be more than 67 kalashtar in existence at once?

Kalashtar were originally formed when 67 adaran monks fused their being with quori spirits from Dal Quor. All descriptions of the race, as well as their naming convention suggests a 1:1 ratio of human:quori, ie. that in one kalashtar there is exactly one quori and one human.

Combining these two statements could lead one to believe that the number of kalashtar is limited by the number of quori that escaped Dal Quor at that time. Is this so? I see no mention of such a cap.

If there can be more than 67 kalashtar at a time, where do the quori come from? Do they also reproduce? Do new ones escape Dal Quor?

## Can the Host Header be used to hide the existence of a service?

Imagine a web server running on 93.184.216.34, usually reachable via the public DNS entry example.com. Web servers usually allow the distinction of multiple “virtual” servers, based on the Host header received via the HTTP request.

Now imagine the same web server would offer a different service when requested via cx6wdffpuik997eljf6d878i6f3np4207ne30vyjsvhpra69, which was not a public DNS entry, but rather done via a local DNS server or a modified hosts file.

Would this effectively hide the existence of the hidden service? Is this done in practice?

Note: I am aware that this alone should not be used to secure the service. Authentication via client-certificates would be done in addition.

## The existence of a cycle in a directed graph is a NL-complete?

Show that the problem of the existence of a cycle in a directed graph is a $$NL-complete$$ problem.

I have already successfully demonstrated that this problem $$\in NL$$. But I’m stuck on how to take it apart that it’s $$NL-hard$$.

To show that the problem is $$NL-hard$$, we can start from problem $$s; t-connectivity$$ and as an intermediate step, create a acyclic graph $$G^a$$ which is $$s’; t’- connected$$ if and only if the original graph $$G$$ is $$s; t- connected$$. Using the length of the paths of a vertex $$x$$ at a vertex $$y$$.