Perhaps just leave the try variant out of the first sentence, and if necessary describe it in a separate sentence? Something like:

When a locking request cannot be immediately satisfied the thread is typically put to sleep, which is a non-runnable state terminated by the wake operation.

(Most?) Lock operations include a _try variant which returns an error rather than sleeping if the lock cannot be obtained.

A sleep queue

can omit the , here

enables the construction of process-shared locks.

A related

creating sleep queues

allowing the lock scope to be limited regardless

I'm not sure "start of" is necessary, it should be clear from context (and there is an example below).

on a little-endian

The sleep queue to which a sleeping thread is assigned is individual
or even is an individual one

up a limited number of threads from a given sleep queue

I reformulated this by adding 'byte', i.e. ... the address of the start byte ...'.
I can write a perverse example where e.g. the first 4 bytes are shared and the rest is not. In this case the lock is shareable.

Oh, I see. OK.

Might be more clear as:

user's duty ...
ensure lock acquire and release memory semantics, if the

a simple lock

missed this one

oops correction to my earlier comment. If the timeout expired

Does you comment refers to the 'why not adhere' request ? Please see the expanded sentence with a reference to POSIX requirements for pthread_mutex_setprioceiling(3).

Sorry, not enough context I guess.

After the lock is obtained the new ceiling value

request obtains a write lock on the specified
(It's hard for me to explain article choice here, but "a lock" just sounds right to me in this context)

indicated by the URWLOCK_WRITE_OWNER bit being set,

strip this "already": there are read lock owners

already makes sense in the case of a write lock owner, since we're trying to get the write lock ourselves

obtain the write-lock.

Instead

(I'm puzzling over article choice here because I think it should be a at line 810. It makes sense to me because the "struct rwlock" above suggests "a lock".)

The unlock type (read or write)

about the identity of the thread

How is the one chosen?

or, in the case that the URWLOCK_PREFER_READER flag...

the process-private

the process-pirvate

Maybe:
indicate that there is a waiter

Wake up multiple sleeping threads
or
Wake up a batch of sleeping threads

I think the "where the waiter" is implicit and makes it harder for me to follow. Perhaps:

Only normal mutexes are supported by the request.
The sleep queue is always one for a normal mutex type.

is more than one

only one l, successful

A request ... not restartable.

An unblocked

sleeping

specifies the sub-request

creating a new object

object's size

the last open file descriptor is closed and the last mapping for it is destroyed ?

Maybe is a live shared object? I think "an alive shared object" is acceptable but unconventional English.
Perhaps "an alive" is in fact better to match UMTX_SHM_ALIVE though. Keep it if you think it'll be more clear to readers.

when only the liveness ... since the file descriptor

return a POSIX

the errno variable

(or just "and errno is set")

points to invalid memory

in the c_clockid

has changed the lock owner thread identifier during unlock.

member of

either "or the timeout.tv_nsec member..."
or just "or timeout.tv_nsec is greater" (no need to repeat member again here I'd say)

maybe "one of the values read from" or "one or more of the values read from"

the m_ceilings

is greater than

Unlock attempted on an object not owned by the current thread
(or "owned by another thread", as you see fit)

no , after address

The maximum number of

granted ownership of (no the)

specified a timeout in the uaddr1 or uaddr2 argument, and timed out...

(assuming "or" instead of "and" is desired)

for a non-restartable

for a restartable

without a timeout

It is explained in the last paragraph of the SLEEP QUEUES subsection. I do not see it useful to repeat the formulation several times, it was the reason for the subsection writing.

It may be not owned by any thread, for this error, as well.

Both uaddr1 and uaddr2 are needed to specify the timeout, uaddr1 is size, uaddr2 is the pointer to a structure sized by uaddr1. This was explained in 'structures'.

Yeah, definitely not useful to repeat it again.
Do you think it's valuable to write something like "one writer is woken up, as described in the SLEEP QUEUES subsection"?

a timeout in the uaddr1 and uaddr2 arguments, and timed