Which class has access to the best ‘stay at home’ adventuring methods?

Assuming a 20th level character, which class would allow them to remotely assist a party of adventurers without ever leaving a well-warded personal sanctum? In 3.5e/PF, there existed a plethora of spells mostly based around the Wizard to support this kind of ‘off-site meddling’ but I know less about 5E and what Wizards and their ilk can accomplish there (especially at higher levels).

For the purposes of this question, assume the following;

  • The character is completely unwilling to leave their sanctum unless they have some inherent way to cheat death that is 100% reliable (paying a powerful cleric to resurrect you after X time doesn’t count for our paranoid and suspicious protagonist).
  • Class features that are mobile (such as Familiars or Animal Companions) can leave the sanctum, as can summoned or bound creatures.
  • They have intentionally chosen their class and even found some way of acquiring reasonable magic items towards this goal – they are a purpose-built ‘remote assistance’ character.

‘Best’ is not simply damage-per-round but overall quality of assistance – a battery of divinations doesn’t directly do damage but does allow the party to bypass encounters, effectively doing all the damage of the enemy hp of that encounter. Remote healing is not damage but can keep party members alive to do more damage, so on. In this case I am not looking at any specific character level for the party being assisted, but rather at spells, techniques, or class features that would apply to the widest range of parties successfully. Consider this less ‘bob stays at home and still helps the party’ but more ‘Mordenkainen’s Magical Assist (MMA) Incorporated’.

Are communication methods for Intelligent Items cumulative?

So I’ve been looking at the rules for Intelligent Magic Items because I have a Bladebound magus in my group, and it looks as though Empathy -> Speech -> Telepathy is almost like an upgrade path of communication methods for intelligent items.

My question is, does a magic item that can communicate via telepathy also have the ability to speak and communicate empathically, or is each type of communication a separate ability and it would have to have BOTH telepathy and speech in order to speak?

Methods to Prove Data Authenticity from Potentially Compromised Sources?

I’ve been thinking about this problem for some time and I wanted to ask if there are any known methods, or research papers, about how to prove "authenticity" or correctness of data originating from a potentially compromised source (remote server, process, etc). Specifically what I’ve been imagining is say you have service A and service B, service B sources data from A but is worried that A has been compromised such that even if data is signed by A, B can’t trust that it was generated by code written by A‘s developers. Is it possible for B to prove to itself that data from A is authentic, that it was indeed generated by the expected code and not injected or generated by an attacker who has compromised A?

One solution I’ve been thinking about is using a sort of distributed ledger or blockchain so that multiple nodes compute the same data, and in doing so raises the bar such that an attacker would have to compromise N% of the services producing the needed data, this provides naturally replication and I can use an appropriate consensus protocol, but ofc introduces some overhead, efficiency concerns, and I would need to think hard about side-effects being performed more than once.

If there is only one node possible of generating data, such as a sensor node, and it is compromised, I’d imagine all hope is lost, but I also wouldn’t be surprised if there is some clever crypto scheme that attempts to solve this problem as well.

I hope it’s clear as to what the question is, thank you.

Destroying data on storage drives via overwrite methods really doesn’t work?

I’m going to sell a computer hard drive on the Internet, it’s a 500GB SATA hard drive, I really used it 3 or 2 years ago, I never used it again, I used about 20 or 40% of the space.

I have read about various tools and used Hardwipe, first I deleted the volume and recreated it, then with the program (option to clean free space) I used the GOST R 50739-95 method, when it finished then I did it again with the random method (both It took about 6 hours, in total I spent 2 days on this task, and I had several interruptions so I had to disconnect and continue the overwrite).

I have read an article on the internet (I shouldn’t believe everything I read on the internet, but that’s why I am asking this question), where it mentions that overwriting these random bytes is not enough and even if I used the DoD 5220.22-M method the data could To be recoverable, it mentions that a good method is degaussing (but this is really crazy, that is, a disk that used so little space), is this information really true? Should I use a Gutmann method?

Thanks

Did I understand how thin-blood alchemy distilation methods work right?

Long ago, I prepared a Vampire the Masquerade 5e and ask a lot of questions about thin-blood. After a short time, my players decide to play non thin-blood characters. Now, I want to play a campaign with only thin-blood characters.

Thin-blood alchemy have three distilation methods. Athanor corporis, Calcinatio and Fixatio. I understand them in a way that look strange for me (mostly Athanor corporis and Calcinatio):

  • Athanor corporis: You make your formulas with your own body, and you can keep them indefinitely. But you can use only one at a time, and you have to concentrate for 3 turn to switch formulas. But something that I don’t understand is "does you keep the previous formula in your body, and just have to switch to have it again, or did you need to re-distill it later to have it again?"
  • Calcinatio: You make your formulas with kine. They have the formula in them until they have an emotional shift. If you drink there blood, you have the power. But what I don’t understand is "Is the formula is still in the human after drinking?" and "What happend if someone else drink the formula?"
  • Fixatio: Classic rpg alchemy. You make a potion, it give you powers for a short time if you drink it. The only question that I have is "can you share your formula with another thin-blood, so they can use the power too?"

related: How do thin-bloods and thin-blood alchemy work?

Discrepancy between the results of NIntegrate with different methods and options

I am trying to perform a numerical integration on a function defined through a sum of exponential terms. The summation is given by:

sum[z_, z0_, t_, nmax_] :=   1/Sqrt[4 t]*Sum[ Exp[-(z - z0 - 2 n)^2/(4 t)] + Exp[-(z + z0 - 2 n)^2/(4 t) ], {n, -nmax, nmax}]; 

and we define

f[z_, zp_, y_, yp_, z0_, t_] =    ( Exp[-(y - yp)^2/(8t)]/Sqrt[8t] )*D[sum[z, z0, t, 20]*sum[zp, z0, t, 20], t, z, zp]; 

where I have chosen nmax=20.

I wish to perform numerical integration on f. I define

int1[a_] :=   NIntegrate[ f[zp, zpp, 0, ypp, z0, t]*( ypp (zp - zpp) )/( a (zp - zpp)^2 + ypp^2 )^(3/2),  {z0, 0., 1.}, {t, 0., 10.}, {zp, 0., 1.}, {zpp, 0., 1.}, {ypp, 0., Infinity}] 

Based on which I get the following table (no errors generated)

tab1 = Table[{a, int[a]}, {a, 1., 5., .5}]  (* {{1., 0.00135643}, {1.5, 0.000734155}, {2., -0.000611633},  {2.5, 0.0000596739}, {3.,0.0359735}, {3.5, 0.0292143},  {4., 0.01122}, {4.5, 0.00889722}, {5., 0.00649666}} *) 

To check, I tried AccuracyGoal-> 30 and PrecisionGoal -> 30 and got the same results. However, as soon as I include WorkingPrecision, the integrated gives 0 all the time. For example:

intwrk[a_] :=   NIntegrate[ f[zp, zpp, 0, ypp, z0, t]*(ypp (zp - zpp))/(a (zp - zpp)^2 + ypp^2)^(3/2),  {z0, 0, 1}, {t, 0, 10}, {zp, 0, 1}, {zpp, 0, 1}, {ypp, 0, Infinity},  AccuracyGoal -> 30, PrecisionGoal -> 30, WorkingPrecision -> 100] 

Gives all zeros – which I can’t seem to understand. Am I doing something wrong here?

Then I also performed the calculation using LocalAdaptive method:

int2[a_] :=   NIntegrate[ f[zp, zpp, 0, ypp, z0, t]*(ypp (zp - zpp))/(a (zp - zpp)^2 + ypp^2)^(3/2), {z0, 0., 1.}, {t,0., 10.}, {zp, 0, 1}, {zpp, 0., 1.}, {ypp, 0., Infinity }, Method -> "LocalAdaptive"] 

which gives

tab2 = Table[{a, int2[a]}, {a, 1., 5., .5}]  (*  {{1., 1.75934*10^-29}, {1.5, -8.79671*10^-30}, {2., 8.7967*10^-30},  {2.5, -8.7967*10^-30}, {3., 8.7967*10^-30}, {3.5, -2.80635*10^-51},  {4., -8.79671*10^-30}, {4.5, -9.78474*10^-37}, {5., -9.78474*10^-37}} *) 

which is a very different result. This one also runs much faster than the int1. I guess these numbers here are not reliable, but how can I check them?

PS: based on the answer to my previous post, I tried Method -> "GaussKronrodRule" and Method -> {"MultidimensionalRule", "Generators" -> 9}, but they run forever and I couldn’t get any outcome.

Are these two methods of handling Elven Accuracy “Double Advantage” mathematically equivalent?

For context, part of the Elven Accuracy feat (Xanathar’s Guide to Everything, p. 74) states:

Whenever you have advantage on an attack roll using Dexterity, Intelligence, Wisdom, or Charisma, you can reroll one of the dice once.

So the obvious way to handle this, mechanically, is to roll two dice, pick the lowest, and roll it again. But as an effort to save time, I’ve proposed instead simply rolling three dice simultaneously, and picking the highest rolled value.

The problem is that I’m not certain that this is mathematically correct.

I created a code simulation that was intended to model the probability curve of both methods, and it suggests that the two methods are mathematically equivalent, but the simulation only performs direct sampling of random numbers and their results; it has unavoidable error in the results, and it doesn’t attempt to solve the underlying mathematical principles involved.

//Roll 3, pick highest ResultSet: Double Advantage      Average: 15.48246                                                                                                      Variance: 14.94721234837884                                                                                            Std. Deviation: 3.8661624834425727                                                                                     95% range: [6, 20]                                                                                                     Mode: 20                                                                                                               Median: 16         //Roll 2, reroll lowest, pick highest ResultSet: Alternate Double Advantage                                                                                      Average: 15.488486                                                                                                     Variance: 14.944649427739675                                                                                           Std. Deviation: 3.8658310138623073                                                                                     95% range: [6, 20]                                                                                                     Mode: 20                                                                                                               Median: 16             

Is it correct to say that these two dice-rolling methods are equivalent, or should I stick to the RAW interpretation of how these dice should be rolled?


For full context, I’m planning out a build for a Shadow Sorcerer that fights only in melee combat, and if this character has the ability to nearly-permanently shroud themselves in Darkness (which is one of their class features), it’ll give them nearly permanent Advantage against creatures that don’t have Devil’s Sight or Truesight (or a reliable, spammable Counterspell/Dispel Magic). So simplifying this roll can matter in terms of time saved.

Are there any non-epic methods of time travel (years/decades/centuries) in third edition?

Are there any non-epic methods of time travel (years/decades/centuries, not smaller than a year) in third edition?

I’m not looking at short duration tricks, nor am I looking for anything that is a one-way trip. Please exclude theoretical optimization tricks.

I am looking for a way to travel a large temporal distance, and back again, preferably affecting the destination in question. Forwards or backwards in time is fine.

Which methods are available for NDEigensystem?

I am trying to find out what methods/options are available for NDEigensystem and descriptions of their use. Perusing the help, online Q&As, Mathematica’s in-line autofill, etc., I’ve found a few, but it’s unclear what they do. For example, what is the a difference between Method -> {"PDEDiscretization" -> {"FiniteElement", "MeshOptions" -> {"MaxCellMeasure" -> Automatic}}} and Method -> {"SpatialDiscretization" -> {"FiniteElement", {"MeshOptions" -> {MaxCellMeasure -> Automatic}}}}. To confuse things further, some Methods seem have additional options (e.g., "Eigensystem").

Is there a way to uncover all the available Methods available to NDEigensystem, including a description and their options?