Well I'll try pushing the limits to how far you can go without becoming transient or omnipotent in your world theory, not sure if your going for a storyboard or a few ideas so will just go with it since it seems interesting enough for a story.
Feel free to use any or none of these ideas.
Cellphones can use P2P and mining to pay for cellphone calls.
Healthcare systems can use P2P to cross consult with doctors worldwide to find solutions and in warzones online communication sometimes is the only way to access doctors.
Bitmessage can be used to send encrypted messages with namecoin becoming a decentralized domain system.
Ancient users will remember the days when Prism-break and projects like Illusion were used due to a privacy war.
Similar to the Statement on Intellectual Freedom in Libraries can be the inital setting.
It is the most important responsibility of libraries to offer collected materials and library facilities to the people who have the Right to Know as one of their fundamental human rights. In order to fulfill their mission, libraries shall recognize the following matters as their proper duties, and shall put them into practice.
1.Libraries have freedom in collecting their materials.
2.Libraries secure the freedom of offering their materials.
3.Libraries guarantee the privacy of users.
4.Libraries oppose any type of censorship categorically.
When the freedom of libraries is imperiled, we librarians will work together and devote ourselves to secure the freedom
Schooling will be affected but not by P2P but the greater effect of online education
edX is only the beginning in Present Time by then the developments are at far larger scales that provide knowledge from multiple locations.
http://www.ctvnews.ca/harvard-mit-joining-forces-in-online-partnership-1.804095Transit I can only ponder upon I would imagine that it would look cool or mix art with precision such as rideback with fully integrated tech some basic engineering such as collision detection artistic design etc.
http://caetanosilva.com/Akira-Bikehttp://www.youtube.com/watch?v=KB6h7snP8O8Just one example of the possibilities haven't even mentioned cars I presume they will not be flying yet.
Floating perhaps using engine power from concentrated energy but not up to hard light yet.
Powered by atomic concentration of atoms, p2p somewhere in there.
AI WISE: Imagine something similar to Summer Wars
Land of Oz where we have virtual intelligence and people running the systems through visual communications screens but with wireless transmission of the bitcoins we could have Virtual Admins in an interactive system the blockchain can be the middle basically super p2p
Food Distribution: Depends on how you view it if the technology is sufficient enough automated food delivery systems could be launched at larger scales and they might work more efficiently decentralized but that is beyond our tech but who knows with the increases in processing power and the movements of robotics if you watch Daily Planet we might see that in higher frequencies in the not so distant future. The application of p2p technology to food distribution may be just as significant as the application of the Green revolution by reducing waste by-products in manufacturing and improving processing efficiencies.
Energy: Well that one is fascinating I can see applications of a decentralized power network spread through independant power generation but at scales large enough to create mesh networks the technicals would be interesting.
I wish it was as simple as saying microwaves but if you know your history microwaves fry cows over longer distances and power cannot be transmitted to satellites and resent back to recievers yet, unfortunately we are not in Halo and do not have the Orbital Defense platforms being powered from ground based power stations.
That said applications of decentralization to energy would prevent a single point of failure if the powers are not spread through wired transmission but through wireless instead.
The issue of soft energy is not yet settled but geothermal provides a base for heating energy, applications of it to a larger power generation becomes interesting could be moving parts example wheel rotation powering your car battery or something rarely considered such as the energy produced by friction in a number of different technologies applying it to some ideas.
Anyways went a bit long, best of luck with your book.