Nope.  We parse everything as string values.

It was an issue with PHP's array_merge().  It automatically reindexes 
array keys that are *numeric* ... meaning it disregards the current 
variable type.  The documentation is not clear about this (it uses the 
term "numeric" without defining it).  So we need to use the '+' 
operator instead to avoid this behavior.

Changes have been made in Git (master):

commit 321b79fa90a12d777477a8ec1f14b08102c3624a
Author: Michael M Slusarz <slusarz@horde.org>
Date:   Thu May 29 17:29:37 2014 -0600

     [mms] Fix working with mailboxes containing entirely integers 
(Bug #13157).

  .../Imap_Client/lib/Horde/Imap/Client/Socket.php   |    2 +-
  framework/Imap_Client/package.xml                  |    2 ++
  2 files changed, 3 insertions(+), 1 deletions(-)

http://github.com/horde/horde/commit/321b79fa90a12d777477a8ec1f14b08102c3624a

I did not include it in my previous update, but I really think that it has to
do with the parsing. Even though Dovecot uses an empty namespace
from the test logs, it returns the folder name as (2011) and cyrus without
the altnamespace has a folder name of INBOX.2011. It is definitely the
case, that as long as there is a single non-digit character the problem
does not occur. It looks like a problem parsing the IMAP server response.

Regards,
Ken

Except the altnamespace you have (empty) is exactly what Dovecot uses. 
  And Dovecot not only works for you, but is what I develop on myself.

I will go back and configure Cyrus on my test VM to use this 
altnamespace, but I am doubtful that will change anything.

We use the altnamespace:

        altnamespace: 0
             Use  the  alternate  IMAP  namespace, where personal 
folders reside at the same level in the
             hierarchy as INBOX.

        This option ONLY applies where interaction takes place with 
the client/user.  Currently  this  is
        limited  to  the  IMAP protocol (imapd) and Sieve scripts 
(lmtpd).  This option does NOT apply to
        admin tools such as cyradm (admins ONLY), reconstruct, quota,   
etc.,  NOR  does  it  affect  LMTP
        delivery of messages directly to mailboxes via plus-addressing.

This definitely shows the bug. It works for you with Cyrus because the 
folder name has non-digits in it, ie. INBOX.123. If you enable 
altnamespace, you should definitely be able to reproduce it.

Regards,
Ken

Looking at this... what is your namespace on the Cyrus server?  These 
mailboxes are being created in the empty namespace... which may not be 
in the personal namespace (at least in the default Cyrus config).

Can't reproduce on CentOS 6.5 with Cyrus 2.3.16 (IMP 6.2):
S: * OK [CAPABILITY IMAP4 IMAP4rev1 LITERAL+ ID STARTTLS 
COMPRESS=DEFLATE] centos.curecanti.org Cyrus IMAP 
v2.3.16-Fedora-RPM-2.3.16-6.el6_2.5 server ready
1 [LOGIN Command - username: slusarz]
S: 1 OK [CAPABILITY IMAP4 IMAP4rev1 LITERAL+ ID LOGINDISABLED 
COMPRESS=DEFLATE ACL RIGHTS=kxte QUOTA MAILBOX-REFERRALS NAMESPACE 
UIDPLUS NO_ATOMIC_RENAME UNSELECT CHILDREN MULTIAPPEND BINARY SORT 
SORT=MODSEQ THREAD=ORDEREDSUBJECT THREAD=REFERENCES ANNOTATEMORE 
CATENATE CONDSTORE SCAN IDLE LISTEXT LIST-SUBSCRIBED X-NETSCAPE 
URLAUTH] User logged in
C: 2 LSUB "" INBOX.123
S: 2 OK Completed (0.000 secs 1 calls)
C: 3 LIST "" INBOX.123
S: 3 OK Completed (0.000 secs 1 calls)
C: 4 CREATE INBOX.123
S: 4 OK Completed
C: 5 SUBSCRIBE INBOX.123
S: 5 OK Completed
C: 6 LSUB "" INBOX.123
S: * LSUB () "." "INBOX.123"
S: 6 OK Completed (0.000 secs 2 calls)
C: 7 LIST "" INBOX.123
S: * LIST (\HasNoChildren) "." "INBOX.123"
S: 7 OK Completed (0.000 secs 2 calls)
C: 8 LOGOUT
S: * BYE LOGOUT received
S: 8 OK Completed
For the record: there is nothing off about the server responses in 
your IMAP log (other than the fact I am assuming you cut out some 
responses, since it is missing a bunch of stuff in there).

Okay, sorry for the delay. I set up a test Dovecot 2.2 server and sure 
enough the problem is not seen with that backend. We see it on our 
Cyrus IMAPD 2.3.14 from EPEL. Here is a transcript of the IMAP logs 
for creating a top-level folder with only digits in both Dovecot and 
Cyrus:

Cyrus 2.3.x:
C: 2 LSUB "" 2011
C: 3 LIST "" 2011
C: 4 LSUB "" 2011
C: 5 LIST "" 2011
C: 6 CREATE 2011
C: 7 SUBSCRIBE 2011
C: 8 LIST "" 2011
S: * LIST (\HasNoChildren) "/" "2011"
S: * LSUB () "/" "2011"
S: * LIST (\HasNoChildren) "/" "2011"

Dovecot 2.2:
C: 3 LIST () "" (2011)
C: 4 LIST () "" (2011)
C: 5 CREATE 2011
C: 6 SUBSCRIBE 2011
C: 7 LIST () "" (2011)
S: * LIST (\NoInferiors \UnMarked) "/" "2011"
S: * LIST (\Subscribed \NoInferiors \UnMarked) "/" "2011"

Hopefully, you can see why this causes a problem with a Cyrus backend. 
If there are any characters other than numbers in the top-level folder 
name, it works for Cyrus too.

Regards,
Ken

Dovecot 2.2.

Thank you for the response. I will try to dig into it further. What 
IMAP backend are you using for your testing? Maybe the problem relates 
to an interaction there which is why you cannot reproduce it.

Regards,
Ken

Can't reproduce on either IMP 6.1.8 or IMP 6.2.

See, e.g.: 
https://github.com/horde/horde/commit/ff633998cb0c30f271316de26e707ac6e56a0688

When a folder is created with a name that is composed ONLY of digits 
(0-9), it does not show properly on the subscribed folders after a 
logout/login. If any non-digit is added to the folder name (i.e. space 
or other alpha) using rename, the folder shows up properly as 
subscribed. I noticed this when helping a user archive their Email by 
year to clear their INBOX. Any assistance would be appreciated.

Regards,
Ken