Permanent establishment: fixed place and agency rules determine taxable presence where activities exceed specified duration or bind the enterprise. The permanent establishment concept treats a fixed place of business-such as management, branch, office, factory, workshop, extraction site, construction project beyond a specified duration, or sustained service provision through personnel-as creating taxable presence. Routine uses of facilities, stockholding for storage or display, stock for processing by another enterprise, purchasing or information collection, and preparatory or auxiliary activities are excluded. An agent with habitual authority to conclude contracts for the enterprise creates a permanent establishment unless limited to purchasing, while independent agents in the ordinary course of business do not, and corporate control alone is insufficient to create a permanent establishment.