Pat the salmon fillets dry with paper towels. Lightly season with salt and pepper.
Whisk together the soy sauce, rice vinegar, erythritol, brown sugar substitute, garlic powder, ginger, arrowroot, and water in a large measuring cup with a spout.
Add the sesame oil to a large skillet over medium high heat. When the oil is hot add the salmon, skin side down, to the skillet. Leave it undisturbed for 3 to 4 minutes to allow the skin to crisp.
Cover the skillet and allow the salmon to continue cooking 2 to 3 minutes or until the fillets are light pink. You may notice little bits of white fat come up around the fillet when it is cooking, this is okay.
Pour the sauce around the fish and allow it cook 2 to 3 mintues until thickened. You may use a fork or whisk to stir the sauce as it cooks. Use a spoon to ladle some of the sauce on top of the fish.