A partial transcript of the photograph of a failed attempt:
… a recovery system can't be created. …
http://www.apple.com/support/no-recovery redirects to
Did you attempt a
non-clean installation of Mavericks over an installation of pre-release Yosemite – without erasing the Yosemite startup volume?
Pre-release or not, I should
never recommend that; and in some environments it may be difficult to achieve.
(Maybe too early to tell whether firmware for Yosemite will allow installation of Mavericks on every supported Mac, and so on. Consider at least
How can I downgrade the OS on a Mac to the original one it came with? – Snow Leopard desired there, but hopefully you get the idea (side note, terminology: Apple does not provide an option to downgrade the OS). There's an unanswered question from me:
Amongst Macs that can be upgraded to support OS X Recovery, can any model *not* accept a firmware downgrade?)
What's the firmware of the affected Mac?
Was yesterday's backup of Mavericks, or of Yosemite?
What version, what build is the Recovery OS? (Use sw_vers in Terminal.)
When did Disk Utility last report that the HFS Plus file system of the Time Machine backup was
apparently OK?
Have you tried erasing the volume to which you're attempting installation, to which you're attempting restoration, before making those attempts?
Have you tried partitioning the disk on which you're making those attempts, before making them?
Last but not least, refocusing on the opening post and my first responses, please: what did iDefrag show about the catalog and attributes files?