Seems to be a problem with iOS 7 and memory management. Tons of low memory diagnostic errors have been reported for iOS 7 users on these forums. Do a search for Safari Crashes and you'll see countless others dealing with the same kind of memory dump crashes. Apple should be able to resolve the majority of these crashes with an update.. But in the future they may also be faced with having to increase the available RAM to assist in avoiding crashes caused by bad memory management. Call Apple and let hem know your a victim as others are doing.
I had an Air and noticed twice as many memory dump crashes than my previous 4th Gen.. After iOS 7.0.4.. I returned the Air and picked up another 4 and have had far less crashes. This experience also lends to AnAndTech's review and assessment that the 64bit A7 may become an issue with browser based applications due to 64bit memory architecture.
http://www.anandtech.com/show/7460/apple-ipad-air-review
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The move to a 64-bit platform however does complicate things a bit. Moving to a larger memory address space increases the size of pointers, which in turn can increase the footprint of 64-bit applications compared to their 32-bit counterparts. So although there’s clearly a performance uplift from app developers recompiling in 64-bit mode (more registers, access to new instructions), there’s also an associated memory footprint penalty. Since the iPad Air and iPhone 5s don’t feature a corresponding increase in memory capacity, I wondered if this might be a problem going forward.
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Based on my experience with the Air vs. the 4, I would said it does. Apple really needs to fine tune iOS 7 to be suitable for the 64bit+1gb Ram combo'd Air.. The 32bit cpu's are more memory friendly... still crash, just not as often.