Does hidden just mean unseen and unheard?

Exactly what “hidden” means in game is not completely obvious.

Hiding When you try to hide, make a Dexterity (Stealth) check. Until you are discovered or you stop hiding, that check’s total is contested by the Wisdom (Perception) check of any creature that actively searches for signs of your presence.

You can’t hide from a creature that can see you, and if you make noise (such as shouting a warning or knocking over a vase), you give away your position. An invisible creature can’t be seen, so it can always try to hide. Signs of its passage might still be noticed, however, and it still has to stay quiet. (PHB p. 177)

So we know you can take an action do do it, and that when you are hidden from a creature they don’t know (exactly) where you are.

One further hint comes from the Unseen Attackers and Targets section:

If you are hidden–both unseen and unheard–when you make an attack, you give away your location when the attack hits or misses. (PHB p. 195)

Does “hidden” just mean unseen and unheard, like that section suggests? (also unsmelt, unfelt, untasted – generally unsensed) Or does it mean something else?

Some implications if this were the case:

  • There would be some extra niche cases that allowed easier access to being hidden.
  • creatures out of sight of a PC that had the Deafened condition would effectively be hidden from the PC
  • The Silence spell could be used to stop enemies without line of sight to a PC from knowing exactly where they/their party are in its radius (effectively “Mass Hide” as long as they have a line of sight blocker and stay in the radius)

what does this connection failure message mean?

$ psql -h host db_name

psql: could not fork new process for connection: Cannot allocate memory

I think I have enough free RAM?

Other conditions, when using jdbc:

Caused by: java.lang.IllegalStateException: Received resultset tuples, but no field structure for them     at org.postgresql.core.v3.QueryExecutorImpl.processResults(QueryExecutorImpl.java:2086)     at org.postgresql.core.v3.QueryExecutorImpl.execute(QueryExecutorImpl.java:288)     at org.postgresql.jdbc.PgStatement.executeInternal(PgStatement.java:430)     at org.postgresql.jdbc.PgStatement.execute(PgStatement.java:356)     at org.postgresql.jdbc.PgPreparedStatement.executeWithFlags(PgPreparedStatement.java:168)     at org.postgresql.jdbc.PgPreparedStatement.executeQuery(PgPreparedStatement.java:116)  org.postgresql.util.PSQLException: A connection could not be made using the requested protocol null.         at org.postgresql.core.ConnectionFactory.openConnection(ConnectionFactory.java:59)         at org.postgresql.jdbc.PgConnection.<init>(PgConnection.java:216)         at org.postgresql.Driver.makeConnection(Driver.java:404)         at org.postgresql.Driver.connect(Driver.java:272)         at java.sql.DriverManager.getConnection(DriverManager.java:664)         at java.sql.DriverManager.getConnection(DriverManager.java:247)    Detail: Failed on request of size 81160 in memory context "MessageContext". java.lang.RuntimeException: org.postgresql.util.PSQLException: ERROR: out of memory   Detail: Failed on request of size 81160 in memory context "MessageContext". 

Relabel to front, what does topological sort according to admissible network mean?

In the CLRS book it says that “relabel to front” algorithm, which solves the maximum-flow problem, maintains a list of topologically sorted vertices in the admissible network and that vertices with zero excess flow are moved to the front of the list.

I do not fully understand what is the meaning of it. I would imagine that the vertices are sorted according to the number of admissible edges incident on it. But then how would moving vertices with no excess flow to front affects the sorting order in this case. Also how come the list is already sorted when it is initialized with random order of the vertices?

Edit:

Just realized that topological sorting of vertices in the admissible network means that for every admissible edge (u,v) in the admissible network the vertex u appears before v in the list.

This does not answer my last two parts of my question though, how is that the list is already sorted when initialized and what effect does moving zero-excess-flow vertices to front affect the order. Thanks.

What does it mean by “not recursively enumerable”?

I came across following therem:

There exists a recursively enumerable language whose complement is not recursively enumerable.

Now, I know following definitions:

  • Recognizable language is one which have one-to-one correspondence with the natural number with the additional property that we could specify an algorithm to enumerate the language elements.
  • Given the string not in the co-recognizable language, we can give Turing machine which can eventually confirm that the string indeed does not belong to the language.

Then what does the above theorem mean?:

  1. $ L’$ does not have one-to-one correspondence with the natural numbers?
  2. We cannot give an algorithm to enumerate the $ L’$ s elements?
  3. $ L’$ is co-recognizable.

In Pathfinder 2e does the Craft Anything Feat mean you do not need a formula?

In Pathfinder 2e we have the Feat called Craft Anything. Which states, in part, that

As long as you have the appropriate Crafting skill feat (such as Magical Crafting for magic items) and meet the item’s level and proficiency requirement, you ignore just about any other requirement, such as being of a specific ancestry or providing spells. The only exceptions are requirements that add to the item’s cost, castings of spells that themselves have a cost, and requirements of special items such as the philosopher’s stone that have exclusive means of access and Crafting. The GM decides whether you can ignore a requirement.

The description of the Crafting Skill under the subheading Crafting Trained Actions states, in part, that

To Craft an item, you must meet the following requirements:

..

  • You have the formula for the item

..

Craft Anything is a legendary feat, but does it override the need for a formula? Is the formula a

requirement[s] that add to the item’s cost

What does “a spellcaster level” mean applying to monsters?

There is “a spellcaster level” mentioned in the MM:

A monster with the Spellcasting class feature has a spellcaster level and spell slots

Does “a spellcaster level” means basically “a sorcerer level” or “a wizard level” or any particular class level from the PHB, with all its features and restrictions (like spellbooks)? In this case, how do we define the exact class?

Or does that mean something different applying to monsters, which are not based on player classes? In this case, what does it mean exactly?

A relevant question: Where are the NPC mages' spellbooks in the Lost Mine of Phandelver adventure?

What does “a spellcaster level” mean applying to monsters?

There is “a spellcaster level” mentioned in the MM:

A monster with the Spellcasting class feature has a spellcaster level and spell slots

Does “a spellcaster level” means basically “a sorcerer level” or “a wizard level” or any particular class level from the PHB, with all its features and restrictions (like spellbooks)? In this case, how do we define the exact class?

Or does that mean something different applying to monsters, which are not based on player classes? In this case, what does it mean exactly?

A relevant question: Where are the NPC mages' spellbooks in the Lost Mine of Phandelver adventure?

What does elite mean?

In many Adventure Paths or specific books I find this “Elite” sorta template on creatures, but if memory serves me I’ve never actually found descriptions about what’s the difference between a standard creature and an elite one. So that’s the question, what is the difference between a standard creature and an elite one?

What does “Summoned creature has maximum hit points” actually mean?

So, I’m running Princes of the Apocalypse for my group, they’re about to encounter their first elemental prince, Yan-C-Bin, and I see that he has the following ability:

The part I’m confused about is “maximum hit points.” Air elementals have their hit points listed as “90 (12d10+24)” in their stat block. Is this line meant to make sure people are deploying a fully-healed air elemental as opposed to one with 30 HP (regardless of whether they use the average hit points or they actually roll their hit dice), or is it meant to convey that these are extremely robust air elementals and each should have the maximum possible hit points as decided by the hit dice, 144 (120+24), and the fully-healed part is implied?