Permanent establishment rules define fixed business presence, equipment and agent tests determining cross-border taxable presence. Article 5 defines permanent establishment as a fixed place of business including management, branches, offices, factories, workshops, extraction sites and construction or assembly projects exceeding six months; it treats seabed exploration and natural resource exploitation and related activities as exercised through a permanent establishment. Substantial equipment in the other State and supervisory activities in connection with such equipment create a permanent establishment. Exclusions include facilities or stock held solely for storage, display, delivery or processing, fixed places for purchasing or information collection, and preparatory or auxiliary activities. Dependent agents with authority to conclude contracts create a permanent establishment, while independent agents acting in the ordinary course do not, and corporate control alone is not determinative.