if you play a unit to an open battlefield do you control it if its empty on the stack this interaction is specific towards Riven legend when you play to a battlefield you control the key word here is the control aspect cause when these cards hit and the stack resolves allowing the conquer to be successful would it restand to rivens ability? card ex is Sai Scout it states it can be played to an open battlefield or the Sneaky Deckhand

Short answer: No — playing a unit to an open battlefield doesn't make you its controller at the moment of the play, so a "when you play a unit to a battlefield you control" trigger won't see it there.

"Open" is defined as unoccupied and uncontrolled (Rule 170.11.c), so a battlefield you can legally play Sai Scout or Sneaky Deckhand to is by definition one you don't control. Playing the unit there applies Contested (Rule 190.3.a.1) and stages a Non-Combat Showdown; Control is only established when that Showdown closes with only your units remaining (Rule 348.2.a) — which is a Conquer, scoring you a point (FAQ #1585, #5632). So the control does eventually happen, but it happens on the Conquer, not on the play — the conquer triggers would fire, a "you control this battlefield" condition checked at the time of the play would not.

Two caveats worth planning around. If Riven's trigger is checked on play, the battlefield must already be yours before you play there (a battlefield you already control doesn't become Contested, FAQ #9705), and if an enemy unit is present the field isn't open at all, so Sai Scout isn't playable there. Also, whether the ability "rests/readies" on the Conquer or on the play is a wording question — I could not retrieve a Riven legend card from the database (only Riven, Shattered and Riven, Broken Blade units and Blade of the Exile), so if you paste the legend's exact printed text I can pin the timing down precisely rather than answering from the generic control rules. This is my interpretation based on Rules 170.11.c, 190.3.a.1 and 348.2.a; no official FAQ exists for this specific interaction.