The app has been modified or damaged

The app has been modified, and it’s code does not match the original signed code. The app may be broken or corrupted, or it may have been tampered with. If you feel that an app has been damaged or tampered with, you should delete it by dragging it to the Trash.

Some apps and tools, such as AppleScript applications and some legacy tools, modify themselves after signing. These types of apps cannot be opened unless the Gatekeeper setting in Security & Privacy preferences is set to Anywhere.

Open the General pane of Security & Privacy preferences

For more information about protecting your Mac from harmful software, see:

Protect your Mac from malware

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I attempted to open by right clicking and selecting open. This results in the same message.

I modified my Security and Privacy preferences, changing "Allow apps downloaded from" from "Mac App Store and identified developers" to "Anywhere".

Upon doing that, the resulting dialog says:

"BaseX" is an application downloaded from the Internet. Are you sure you want to open it?

If I click yes, it opens.

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I distinctly recall in the recent past that if an app was unsigned, it would prevent me from opening it the first time by double-clicking. If I right clicked and selected open, it would say something about an unidentified developer and I could open it. 

I'm not sure if your app is signed or not - but the behavior is unlike any other app I've encountered previously. Now, it could be that a recent update to OS X changed the general behavior (OS X 10.9.1, Build 13B42), and I just haven't experienced this before.

If you have any further questions, let me know.

Best,

Charles