Here's a topic likely to get folks going or at least provide amusement over the question my mental integrity
A little over a year ago I acquired a Burnand of Newcastle hammergun with the intent of eventually having it sleeved, as it had been cut per UK law due to being been sold out of proof. Sadly, on receiving the gun, it was obvious that there was sufficient metal left in the barrels that it almost certainly would have passed proof if someone had bothered to go to the expense. What makes this particularly vexing is I hate to see decent Damascus barrels needlessly destroyed or sleeved. Oh well.
As shown in the photographic links below, the barrels were originally 13 bore black powder and both bores currently measure 0.720. However, the barrels are a whopping 0.75 thou at the cuts! Such a shame. Now, interestingly, the barrels were not cut in the standard manner with a rectangle being removed from each side. Instead, as shown in the attached photographs, they were merely cut in notches. This is what eventually got me thinking - yes, this is sometimes a dangerous thing! The wild train of thought occurred to me... Damascus is welded together…so…. might it be feasible with the right weld material to repair such a cut?
Now, I admit first off I'm not a metallurgist or anything approaching a professional welder and I know there are issues with variations in steel composition, annealing, work hardening etc. I’m also aware that one of the most stupid things I’ve seen are large patches welded across cutouts of barrels. But nevertheless I wonder if it is technically feasible. Now before you jump to the conclusion that I'm a complete cretin let me be clear that IF such a thing is possible then, as it were, 'the proof of the barrels would be in the testing' and they'd be submitted to the proof house as a final test. But back to my lunatic fringe idea, does anyone know if there might be an approach to weld repairing such cuts that might be deemed theoretically safe enough to warrant an experiment performing the work and submitting them for proof after clean up? I'd have to check as well that such a thing would be accepted for test.
Of course, apart from the probable impracticality of this admittedly hare brained scheme, even if successful it would leave a cosmetic scar on the Damascus and would doubtless be devalued compared to a straightforward sleeving . Nevertheless, despite such drawbacks the idea of such a test intrigues me. Worst case it could be sleeved subsequent to experimentation.
I’ve included a few other photographs of the gun to give a sense of it and the shame of having the Damascus destroyed. It is an early enough gun that it was produced when Purdey’s patent was still in force for his has new double bite bolt as shown by the patent markings on the “table”.
An interesting piece which realistically I shall probably have sleeved via the normal process with blacked barrels but it would a shame to see the Damascus barrels go quietly into the night without one last desperate grasp at existence. 
Well then... have at it

Jeremy
https://www.dropbox.com/s/f8m8ac6pzl6xpnu/burnand-cut-web.jpg?dl=0https://www.dropbox.com/s/hlusrdl4lmsmkb3/burnand-cut-2-web.jpg?dl=0https://www.dropbox.com/s/2jgg265yuo4y9dy/Burnand-Measures-web.jpg?dl=0https://www.dropbox.com/s/e9bgmrplbt502ws/Burnand-proofs-web.jpg?dl=0https://www.dropbox.com/s/oflzagj5pry39x9/Burnand-Pat-web.jpg?dl=0https://www.dropbox.com/s/2kht77it753jx3b/Burnand-side-web.jpg?dl=0