Yes and no.
In a general sense... you will ALWAYS be in competition and potential conflict with other players.
If you harvest resources before someone else can harvest them, you deny other players that potential wealth.
If you explore and find salvage/relics/modules before someone else can, you deny other players that potential wealth.
If you destroy lots more NPCs than others, you make more ISK from those bounties, which in turn devalues the ISK of everyone else.
If you build more then anyone else, you are crowding out others on market and stepping on their potential income.
And anyone in the game can use any of the above as a pretext for blowing you up in a direct ship engagements (fair or not). Or sometimes they don't even need the pretext at all and will do it for giggles.
And all of the above does not require consent to be done.
However...
you are not mechanically obligated to engage back in a direct ship-to-ship confrontation. There is always a way around everything else in the game if you do enough research and understand the mechanics well enough.
And you can engage in "PvP" without ever having to fire a shot at another player.
What EVE is, is a
multi-faceted PvP game.
Ship-on-ship violence is often the easiest to see form of PvP... but it isn't the only way to be in conflict with others.
Conflict with others.That is the key phrase.
edit: as for where this is all written... take a look at the Official Newbie FAQ:
http://web.ccpgamescdn.com/communityassets/pdf/EVE-Online-New-Pilot-FAQ.pdf
CCP wrote:In EVE Online, any player may attack any other player if they choose to, no
matter where they happen to be. This is because EVE Online is essentially
a PvP (Player versus Player) game at its core.
-Part 1, Section 5-3
CCP wrote:once you
enter New Eden you must consider every action you take as a form
of PvP since this is the core game concept.
-Part 2, Intro
CCP wrote:The essential core concept of EVE Online is that it is full time PvP in a sandbox
environment. As has been mentioned in previous sections any player can
engage another player at any time in any place.
- Part 2, Section 7-Intro
And if you read the DEV blogs, forums posts, and tweets for long enough... the Developers' intent are pretty clear; to bring everything into a reasonable balance between "tears and laughter" (their words, not mine).