Same issue on macOS sierra today. After 3 hours of hair pulling I found this out:
1. Shut down Mac (completely power down, hold the button if need be). Get all peripherals out (disconnect all stuff). Charger stays in.
OPTIONAL: If you have an ethernet cable and a compatible Mac it will likely be quicker on that.
2. Hold Option (ALT) + CMD + R and press the power button. Do not let go of the keys yet.
3. Internet recovery should show up on-screen. Wait it out.
4. Type in WiFi password. WPA2-PSK wifi preferred. If wifi doesn't work, try another. You get a -1006f error: it's your wifi. Try a cable. You get that error if certain ports, protocols and endpoints are inaccessible from your network. It can be on a cable too!
5. Wait until internet recovery downloads the image. Takes ages, be patient. You will get a -5XXXsomething error if your connection is borked during download. (I've seen it all...)
6. The recovery menu should come up.
7. Open Disk Util. Select the disk you want to install to. Press Erase, select OS X Journaled (NOT ENCRYPTED or CASE SENSITIVE!). Type in a name WITHOUT whitespace, e.g. OSX. Run the erase. Wait until done.
8. Close Disk Util, open Terminal (on the top bar, under tools or whatever, select Terminal).
9. THIS IS IT!!! Get an accurate watch or make sure the clock on your phone is correct. Type in the following to the terminal and replace mmddHHMMyy with mm=two digits of month; dd=two digits of day; HH=two digits of hour (24 hours); MM=two digits of minutes; yy=last two digits of current year. Example: date 1110220016 would be Nov. 10 2016, 22:00
date mmddHHMMyy
10. Type in date again and press enter (no need to give it values this time). It should tell you what the time is. Is it what you wanted? Then cool. If not, fix again. You can do date -h to look at the help.
11. Type in:
csrutil enable
csrutil clear
12. No need to restart. On the top bar, select Terminal and press Quit Terminal.
13. You get back to the install screen. Install that **** OS - you deserve it!
My theory:
For the appstore logins are likely token-based. I assume whatever disaster of a technology they are using it cannot account for client-side timestamps (which it should, but whatever). This leaves you with an immediately expired token for downloading the required components (hence the login screen) if your time drift is outside an accepted threshold (likely a couple minutes, -+2 min or so, unsure what is the most you can get), you will get the mentioned error: AMD-Action:authenticate:SP and the install will fail.
Why? That's cause most of the time if battery is drained and your CMOS battery dies too or you do a PRAM reset, you'll get reverted back to the Mac's original timestamp (likely date of manufacture). That's why. FML.
Hope this helps.
--P.S.: Oh yeah, you can try USB recovery, not sure if that helps. Create a bootable installer for macOS - Apple Support