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Ozsvath and Stipsicz showed that the LOSS invariant is natural under +1contact surgery. We extend their result and prove the naturality of LOSSinvariant under all positive integer contact surgeries. The additionalgenerality provided by this result allows construction of new infinite familiesof examples of Legendrian (or transverse) non-simple knots that aredistinguished by their LOSS invariants.

Naturality of Legendrian LOSS invariant under positive contact surgery