I think everyone's ideas of the base principles is great! It's always helpful to hear other people describe the same simple idea in their own words.
I would describe the fundamentals in two frameworks.
1- Like the OP had said, zones and sectors. What I would call myself " observations, effort, and using natural energies (sun/wind/slope)" Permaculture design usually deals with a dwelling as the focal point of the design. Daily effort to maintain the property is most intense closest to the house (generally), and decreases in quality and quantity as you increase distance from the home. While working or moving through any part of the yard, it is important to constantly be letting your eyes wander and be curious as to what is going on big and small. Daydreaming and thinking about the property, having lots of observational data to guide and inspire design is crucial. With a grasp of the effort flow and the data to describe its needs, designing to use the available solar heat, or wind drying alley, or wet low area etc . . . will be almost as self directing as a math equation calculating a result.
2 - Use knowledge of biology/ecology/geology/other experiences to tap into nature's already functioning workflow. This second permaculture principle is the mindset of a personal competition to tap into as many free natural workforces and resources as possible. Don't dig and turn and amend soil with shovels and chemicals. Disturb the top inch or two of soil and plant with deep taprooted annuals to dig and
compost the area for you. Worms and other underground dwellers will burrow around eating and dropping their own packets of bio activated fertilizers. Or for another example, use sacrificial plants as living traps to concentrate pests for easy removal. Use yard cuttings and treefall debris as mulch rather than purchase it. Propagate plants from cuttings around the local area.
I think that with these two principles a person can attain the tools and mindset needed to apply permaculture to anything they want.