MacOS – Tried to fix filesystem type: FFFFFFFF-FFFF-FFFF-FFFF-FFFFFFFFFFFF and probably made it worse

disk-utilitydiskutilmacospartitionrecovery

I have a MacBook Air 11 inch which I recently tried to install Linux on with a swap partition and a root partition. In my stupidity I used the “disks” program under “try ubuntu now” to delete the Linux partitions and then extend the Mac partition. As a result the partition ended up having the filetype “FFFFFFFF-FFFF-FFFF-FFFF-FFFFFFFFFFFF”. I searched around on Google and came across this:

macOS partition startup Volume type FFFFFFFF-FFFF-FFFF-FFFF-FFFFFFFFFFFF

I tried to use this to fix the error but have not been able to. This is what I’ve done:

diskutil umountDisk disk0
gpt remove -i 2 disk0
diskutil umountDisk disk0
gpt add -i 2 -b 409640 -s 372637568 -t 7C3457EF-0000-11AA-AA11-00306543ECAC disk0

From here it flagged up the error: “gpt add: disk0: error: no space available on device” but I moved on to the second section because the guy in that post said that it solved his problem.

diskutil list
gpt -r show disk1

(I do no have the pictures for these)

diskutil umountDisk disk0
gpt destroy disk0
gpt create -f disk0

gpt add -i 1 -b 40 -s 409600 -t C12A7328-F81F-11D2-BA4B-00A0C93EC93B disk0
gpt add -i 2 -b 409640 -s 372637568 -t 7C3457EF-0000-11AA-AA11-00306543ECAC disk0

I only did the first two as the diskutil list only showed two.The first was created fine but the second flagged up the error: “gpt add: disk0: error: no space available on device”. Even still I went ahead and rebooted to see if anything happened and obviously nothing did.

From here I am apprenhensive to go on with the things I have seen from searches. Here is what ”diskutil list” shows now:

Strangely the internet recovery seems to have flipped to disk0 while the mac drive is now on disk1. Here’s what “gpt -r show disk1” returns:

I am not very terminal-savvy and I would hate to lose this data as it isn’t backed up and is important. Is it still viable to try to make this bootable or is it time to hand it to professional data recovery for estimates and just get the files that might be left over at this point?

Update 1

So this is the hexdump which was retrieved using the other computer below:

hexdump -Cv /Volumes/MYFAT/disk0.bin
00000000  67 09 20 65 04 d9 06 58  01 00 00 00 00 00 00 00  |g. e...X........|
00000010  fb d8 02 00 00 00 00 00  01 00 00 80 00 00 00 00  |................|
00000020  4e 58 53 42 00 10 00 00  c8 d1 5a 01 00 00 00 00  |NXSB......Z.....|
00000030  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000040  02 00 00 00 00 00 00 00  10 11 96 f5 cf 27 4a 3c  |.............'J<|
00000050  a8 30 3e 64 32 d4 08 e6  c7 a6 04 00 00 00 00 00  |.0>d2...........|
00000060  fc d8 02 00 00 00 00 00  18 01 00 00 18 6c 00 00  |.............l..|
00000070  44 f8 01 00 00 00 00 00  f8 83 01 00 00 00 00 00  |D...............|
00000080  32 00 00 00 85 10 00 00  30 00 00 00 02 00 00 00  |2.......0.......|
00000090  73 10 00 00 12 00 00 00  39 a5 04 00 00 00 00 00  |s.......9.......|
000000a0  3e 6c 05 00 00 00 00 00  01 04 00 00 00 00 00 00  |>l..............|
000000b0  00 00 00 00 64 00 00 00  03 04 00 00 00 00 00 00  |....d...........|
000000c0  20 04 00 00 00 00 00 00  22 04 00 00 00 00 00 00  | .......".......|
000000d0  45 a5 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |E...............|
000000e0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000000f0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000100  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000110  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000120  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000130  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000140  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000150  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000160  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000170  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000180  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000190  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000001a0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000001b0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000001c0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000001d0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000001e0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000001f0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000200  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000210  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000220  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000230  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000240  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000250  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000260  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000270  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000280  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000290  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000002a0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000002b0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000002c0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000002d0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000002e0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000002f0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000300  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000310  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000320  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000330  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000340  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000350  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000360  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000370  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000380  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000390  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000003a0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000003b0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000003c0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000003d0  00 00 00 00 00 00 00 00  ff f5 a4 00 00 00 00 00  |................|
000003e0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000003f0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000400  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000410  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000420  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000430  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000440  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000450  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000460  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000470  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000480  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000490  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000004a0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000004b0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000004c0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000004d0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000004e0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000004f0  00 00 00 00 00 00 00 00  23 c2 20 01 00 00 00 00  |........#. .....|
00000500  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000510  94 c2 20 01 00 00 00 00  01 00 00 00 00 00 00 00  |.. .............|
00000520  01 00 04 00 08 00 00 00  00 00 00 00 00 00 00 00  |................|
00000530  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000540  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000550  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000560  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000570  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000580  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000590  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000005a0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000005b0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000005c0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000005d0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000005e0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000005f0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000600

Best Answer

You need to post a hexadecimal dump of a few sectors of the internal drive. I need to see this before determining if a fix can be found. Unfortunately, Internet Recovery does not provide a hexadecimal dump utility. Therefore, I propose you do the following. Let me know if you have any problems.

The next step would be for you to post a hexdump of the first 3 sectors following the first partition. Below are the steps I would use to accomplish this task. These steps will not change the internal drive.

Using the working Mac, format a flash drive for a single FAT32 volume labeled MyFat. The flash drive probably should be MBR partitioned, but I believe GPT partitioning will also work.
Boot the broken Mac to Recovery Mode.
Open a Terminal application window.
Insert the flash drive into a USB port on the Mac.
Enter the command given below. This will write out a binary copy of the first three 512 bytes sectors following disk0s1.

Note: I assume the internal drive is disk0. If not, make the appropriate substitutions.
```
dd if=/dev/disk0 count=3 skip=409640 of=/Volumes/MyFat/disk0.bin
```
Shutdown the Mac.
Insert the flash drive in the working Mac.
Enter the command given below in a Terminal application window.
```
hexdump -Cv /Volumes/MyFat/disk0.bin
```
Post the output to your question. I would prefer you copy and paste the text to your question. An image (picture) is very inconvenient.

Once you have provided this dump, I will be able to determine how to proceed.

Update #1

The third line, in the output you posted, shows the letters NXSB. This is a good indication that a APFS partition once resided at offset 409640. The hexadecimal sequence c8 d1 5a 01 00 00 00 00 appears on the same line. One can enter, into the Calculator application, these hexadecimal pairs in reverse order, as shown below.

This value can be converted to decimal by clicking on the 10 button. The result is shown below.

Next, one can click on the x8= buttons to multiply by 8. The result is shown below. This is the value you should have used for the partition size instead of 372637568.

Note: This step was required because your sector size is 512 bytes. This step can be skipped when the sector size is 4096 bytes.

This what you entered:

diskutil umountDisk disk0
gpt add -i 2 -b 409640 -s 372637568 -t 7C3457EF-0000-11AA-AA11-00306543ECAC disk0

This is what you should have entered:

diskutil umountDisk disk0
gpt add -i 2 -b 409640 -s 181833280 -t 7C3457EF-0000-11AA-AA11-00306543ECAC disk0

References

Apple File System Reference, dated 2019-02-07, page 25.

Related Solutions

I think I messed up the Fusion Drive on the 1TB iMac (with BootCamp)

Theoretically everything is fine with your Fusion Drive. Fusion Drives look like this. Disk0 is your SSD with 121 GB and disk1 is your HDD with ~1 TB (~1.121 TB summed up).

The larger parts of your SSD (disk0s2) and your HDD (disk1s2) are pooled to a CoreStorage LVG (Fusion Drive: disk3) with a size of 967.8 GB. The rest is reserved for EFIs, a Recovery HD (alltogether ~1.3 GB) and your old Windows partition - now probably free space (~152 GB).

The logical volume 'Macintosh HD' (967.8 GB) spans disk0s2 and disk1s2. This is the first 'Macintosh HD' in picture 1. The volume 'Macintosh HD' - it's the one visible on the desktop - should ideally also have about 967.8 GB. This is the second 'Macintosh HD' in picture 1.
In fact it has only 852.67 GB (see picture 3).

In the second picture the logical volume 'Macintosh HD' is the first listed in black, the volume 'Macintosh HD' is the second listed in black, the other two 'Macintosh HD's listed in grey are the parts of your SSD and HDD dedicated to the logical volume 'Macintosh HD'.

In my opinion something went wrong after deleting various partitions with the Bootcamp Assistant/Disk Utility or in Windows.

Preparation:

Detach any external drive (especially your external Time Machine backup drive)
Restart to Internet Recovery Mode by pressing alt cmd R at startup.
The prerequisites are the latest firmware update installed, either ethernet or WLAN (WPA/WPA2) and a router with DHCP activated.
On a 50 Mbps-line it takes about 4 min (presenting a small animated globe) to boot into a recovery netboot image which usually is loaded from an apple/akamai server.

I recommend ethernet because it's more reliable. If you are restricted to WIFI and the boot process fails, just restart your Mac until you succeed booting.

Alternatively you may start from a bootable installer thumb drive (preferably Mavericks or Yosemite) or a thumb drive containing a full system (preferably Mavericks or Yosemite).

Now you may either repair CoreStorage or rebuild your Fusion Drive:

'Repair CoreStorage' (not recommended):

First i would try to check the volume 'Macintosh HD' with Disk Utility. If the volume is corrupted consider a reinstall of Mac OS X.
If the volume is ok quit Disk Utility
Open Terminal and enter diskutil unmountDisk /dev/LVIdentifier and both diskutil unmountDisk /dev/DiskContainingApple_CoreStorageIdentifier
In your case: first diskutil unmountDisk /dev/disk3 then diskutil unmountDisk /dev/disk0 and diskutil unmountDisk /dev/disk1
remove the EFI NO NAME partition with gpt remove -i IndexNumberOfEFINoName DiskIdentifier:
gpt remove -i 4 disk1
Remount the CoreStorage disks and then the Logical Volume:
In your case: first diskutil mountDisk /dev/disk0 and diskutil mountDisk /dev/disk1 and then diskutil mount /dev/disk3.

enter gpt -r -vvv show /dev/diskIdentfierOfApple_CoreStorage to get infos of your HDD CoreStorage disk.
In your case: gpt -r -vvv show /dev/disk1
It should look like this:

-bash-3.2# gpt -r -vvv show /dev/disk1
gpt show: /dev/disk1: mediasize=1000204886016; sectorsize=512;         blocks=1953525168
gpt show: /dev/disk1: PMBR at sector 0
gpt show: /dev/disk1: Pri GPT at sector 1
gpt show: /dev/disk1: GPT partition: type=C12A7328-F81F-11D2-BA4B-00A0C93EC93B, start=40, size=409600
gpt show: /dev/disk1: GPT partition: type=53746F72-6167-11AA-AA11-00306543ECAC, start=409640, size=1671210848
gpt show: /dev/disk1: GPT partition: type=426F6F74-0000-11AA-AA11-00306543ECAC, start=1671620488, size=1269760
gpt show: /dev/disk1: Sec GPT at sector 1953525167                               
     start          size  index contents                                        
         0             1        PMBR                                            
         1             1        Pri GPT header                                  
         2            32        Pri GPT table                                   
        34             6
        40        409600      1 GPT part - C12A7328-F81F-11D2-BA4B-00A0C93EC93B
    409640    1671210848      2 GPT part - 53746F72-6167-11AA-AA11-00306543ECAC
1671620488       1269760      3 GPT part - 426F6F74-0000-11AA-AA11-00306543ECAC
1672890248     280634887
1953525135            32        Sec GPT table
1953525167             1        Sec GPT header

The free space on your HDD has 280634887 blocks. Please calculate the biggest block number dividable through 8. That's 280634880 blocks (á 512 bytes) which equals 143685058560 B or ~143.7 GB. Add the size of your HDD CoreStorage Physical Volume (852666400768 B) The result is 143685058560 B + 852666400768 B = 996351459328 B
Resize your HDD CoreStorage physical volume with diskutil cs resizeDisk HDDPVUUID newsize
In your case: diskutil cs resizeDisk 93892BE8-2B7F-4ABD-A4C3-984495DCD98D 996351459328b
Calculate the maximal size of your CoreStorage Logical Volume in diskutil cs list: (size disk0s2) + (size disk1s2) In your case that's 120988852224 B + 996351459328 B = 1117340311552 B. That should be the size of your refreshed Logical Volume Group.
Resize your Logical Volume with diskutil cs resizeVolume LVUUID LVGSize-128 MB In your case that's diskutil cs resizeVolume D237FFDC-7DA4-41D7-AC13-4CC7E5E8C0A0 1117212311552b. If you get an error (There is not enough free space...) choose a smaller size like 1117148311552b.
Quit Terminal and open Disk Utility.
Check your expanded CoreStorage Volume for errors.
Quit Disk Utility, choose your CS volume as startup disk and restart your Mac

'Rebuild Fusion Drive' (recommended if you have a Time Machine backup)

Booted to Internet Recovery Mode open Utilities → Terminal in the menubar and enter:
diskutil cs list to get the CoreStorage listing.
Copy the Logical Volume UUID, it's the fifth listed.
Now delete the Logical Volume with diskutil cs deleteVolume LVUUID.
In your case: diskutil cs deleteVolume D237FFDC-7DA4-41D7-AC13-4CC7E5E8C0A0.
Copy the Logical Volume Group UUID, it's the first listed in the listing of diskutil cs list.
Then delete the Logical Volume Group with diskutil cs delete LVGUUID.
In your case: diskutil cs delete 1EFE58BC-3613-44C4-86EE-D816F3B66E3E
Enter exit and quit 'Terminal'
Open 'Disk Utility'. Enter 'Ignore' if you are asked to fix the drives.
Choose your SSD and partition it: 1 Partition Mac OS X Extended (Journaled), hit the Options button and choose GUID Partiton table and hit OK and Apply.
Please check that the size is ~121 GB

Example:
Choose your HDD and partition it: 1 Partition Mac OS X Extended (Journaled), hit the Options button and choose GUID Partiton table and hit OK and Apply.
Please check that the size is ~1 TB

Example:
Quit Disk Utility and open Terminal
Enter diskutil list

Example (your disk identifiers and sizes are different of course: Your volume SSD probably has the Identifier disk0s2 and the size 121 GB and your volume HDD probably has the Identifier disk1s2 and the size 1.0 TB):
Enter diskutil cs create "Name" IdentifierSSD IdentifierHDD
In your case probably diskutil cs create "Macintosh HD" disk0s2 disk1s2.

Copy the resulting LVGUUID

Example:
Enter diskutil cs CreateVolume LVGUUID jhfs+ "Macintosh HD" 100%.

Example:
Enter diskutil cs list
Check the size of your Logical Volume. It should have the size ~1.121 TB

Example:
Quit Terminal
Open 'Disk Utility' and check your newly created volume for errors
Quit 'Disk Utility'
Attach your external Time Machine backup drive or check this answer if you use NAS or another network share.
Open 'Restore from Time Machine Backup'
Choose the appropriate Time Machine backup and restore your system
Reboot to your restored system.
Unmount and detach your Time Machine backup drive
Open 'Terminal' and enter 'diskutil list'
Check if your 'Recovery HD' is listed.
If your 'Recovery HD' is missing, usually reinstalling your current system with the latest available system installer (e.g. 'Install OS X Mavericks (10.9.5)' if Mavericks is currently installed) will recreate it without loosing any data. AFAIK Recovery Partition Creator 3.8 will NOT create a Recovery HD on CoreStorage volumes.
After reinstalling the system with the latest available system installer open App Store and install the latest security fixes.

Partition type FFFFFFFF-FFFF-FFFF-FFFF-FFFFFFFFFFFF, drive unmountable

The volumes could be recovered in a TeamViewer session by searching for special strings similar to the method outlined in this answer: My SATA hardrive was ejected, and is unable to be remounted due to issues.

The assumptions made:

disk3s4 (24.6 GB) and disk3s5 (650 MB) are located at the end of the disk (see diskutil list screenshot of the question - both vanished after destroying the old partition table with sudo gpt destroy /dev/disk3)
disk3s2 (Macintosh) occupies/occupied the whole unallocated disk space (except the 1st Recovery HD) of ~294 GB and is encrypted.

To get the starting block of the first Recovery HD enter (which has to be in the 271 GiB - 274 GiB or ~291 GB - ~295 GB range of the disk)

sudo hexdump -s 271g /dev/disk3 | grep "48 46 53 4a"

(hexdump uses GibiBytes instead of GigaBytes!) which revealed:

447f801400 48 2b 00 04 80 00 21 00 48 46 53 4a 00 00 00 06
447f828a00 48 2b 00 04 80 00 21 00 48 46 53 4a 00 00 00 06
447f840c00 48 2b 00 04 80 00 20 00 48 46 53 4a 00 00 00 06
447f871e00 48 2b 00 04 80 00 21 00 48 46 53 4a 00 00 00 06
...

0x447f801400 is Byte 294196876288 (or block 574603274) of the disk. Since the string HFSJ resides in the third block of a volume, the Recovery HD starts with block 574603272.

The typical output if the previous volume wasn't a FileVault but a normal HFSJ volume would look like this instead:

447f800c00 48 2b 00 04 80 00 20 00 48 46 53 4a 00 00 01 ff
447f801400 48 2b 00 04 80 00 21 00 48 46 53 4a 00 00 00 06
447f828a00 48 2b 00 04 80 00 21 00 48 46 53 4a 00 00 00 06
447f840c00 48 2b 00 04 80 00 20 00 48 46 53 4a 00 00 00 06
447f871e00 48 2b 00 04 80 00 21 00 48 46 53 4a 00 00 00 06
...

The first and second byte number show a difference of 0xc00-0x1400=0x800 or 2048 Bytes because the preceding OS X volume has an alternative volume header in the second last block while FileVault volumes don't have one.

The Recovery HD has a fixed size of 1269536 blocks and it can be added with gpt to the partition table.

sudo gpt add -i 3 -b 574603272 -s 1269536 -t 426F6F74-0000-11AA-AA11-00306543ECAC disk3

Now verify the volume with

diskutil verifyVolume disk3s3

If the partition boundaries and the volume are/is OK you'll get an exit code 0.

In the unallocated disk space between EFI and Recovery HD a CoreStorage partition was added:

sudo gpt add -i 2 -b 409640 -s 574193632 -t 53746F72-6167-11AA-AA11-00306543ECAC disk3

The FileVault password window popped up and the password was entered - so it was added successful probably.

The disk and the volume were verified with:

diskutil verifyDisk disk3
diskutil verifyVolume disk3s2

which both exited with code 0 and all was fine.

Later the FileVault volume was extended to the full size of the disk with:

diskutil cs lvUUID resizeStack 318g #with lvUUID: the Logical Volume UUID of the second CoreStorage container