Leaky faucet due to a 'broken' spout? I have a leaky compression faucet and I'm having difficulties pinpointing the...

I have a leaky compression faucet and I'm having difficulties pinpointing the source of the problem.
At first, my instincts told me that the problem be at the stem assembly, but upon further observations, I realized that when I closed the shutoff valve lower than the sink the drips were still continuous. Not to isolate that problem alone, I also continued my investigation by diagnosing the stem assembly. Thereafter dissembling the handle, I notice some calcium deposited embedded in the retaining nut but no corrosions (unfortunately my inspection stopped short at the retaining nut because the calcium buildup around it made it impossible for it to budge).

I want to invest my repairs contained by the valve seat because that's where on earth I believe the problem lies but what do you guys think? And if you have any suggestions on how to fix the spigot, I would be delighted to hear it.
Moisture by fireplace door - brick chimney?
Here are tips on fixing a leaky faucet

Number of posts needed to support porch roof?
It sounds like the form on the disc for your angle stop is leaking. Do youself a favor. Take the angle stop out completely and install a 1/4 turn valve surrounded by its place. It's like an angle stop, but uses a ball spout assembly instead of the disc. You shouldn't have any problem with leak after that.
What is the heat difference suppose to be...
I would say the valve form. Replaced mine and everything was fine. Why when you close the shut off tap did the drip not stop?? Calcium may have corroded the shut off spout and it may not be working. I think I would look into that.
I own an elder Jacuzzi hot tub, and...
Answers:    well you other should change the valve form. you will need a seat tool and unsullied seats. try this. it also sounds like you have need of some new angle stops.