Message ordering in distributed system

Message ordering in distributed system

I want to build a distributed system where I have "threads" (a collection
of messages with it's own ID, not a system process) that are distributed
across many servers. These threads must have two critical properties:
Each message in thread must have an order number that reflects it's
position in thread based on time. For example by saying
"thread1/message10" I can get to message #10 in thread #1
Once new message gets added to thread a system must be able to assign it
an order number that is consistent for all instances of thread on all
servers and this number must never change.
I want to know if there's any known solution, library or algorithm that
can help me implement a second option because now I see it as a big
problem because due to many factors different servers can get the same
message at different times and that might affect it's order number.
Just to outline my thoughts on a problem so far say I have 3 servers with
my distributed thread which already contains 5 messages and each server
sends a new message to it's own thread and to remaining two.
Naive ordering. Each server think it's own message number is 6 and the
remaining two messages from other servers will get their numbers on
arrival depending on network latency and many other random factors so
order numbers are not consistent across servers. This is unacceptable
right away.
UTC timestamp based ordering. When each thread gets a new message I take
say 10 preceding messages that already have correct order numbers, extract
their timestamps and determine a new message's order number by finding
it's timestamp place in a list of last 10 timestamps. This might work I
guess but it does require that some message's order number can be assigned
and then changed at some point which is unacceptable. Also I'm not sure if
this will work right when a number of incoming messages is huge.
Thanks for all the help.