JPEG Logo Vectorization Needed

I have a company logo saved only as a JPEG and I need it converted into a clean, fully-scalable vector file. No edits or creative tweaks are required—I’m happy with the design exactly as it is. The sole goal is to recreate the artwork in Illustrator (AI/EPS/SVG) so it prints flawlessly on merchandise of all sizes, from small promo items to large banners.

Please recreate every curve, color, and alignment precisely, deliver the final files in AI, EPS, and transparent-background SVG, and include an outlined-fonts PDF proof so I can verify accuracy before approving.