A topic from AEG's L5R CCG Rules forum, copied for Oracle of the Void from a copy of the forum saved in October 2015, so pages it didn't save are missing. Players' names are left out; the rules officials are named. Rulings are as they stood on these dates; later rulings, the rulebooks and the Rules Archive may differ.
A player, 12 February 2008
Sincerity Bushido Virtue Political Limited: Bow one of your target Samurai: Target a card in your hand and another player. That player guesses whether the card’s base Focus Value is “high” (3 or more) or “low” (2 or less). Show the card. If the guess is right, the player draws a card; otherwise gain 3 Honor.
Kyuden Kyotei Your Market holdings in and out of play have the Legacy keyword. Political Reaction: Even if this Stronghold is bowed, if you control the Imperial Favor, before a Fate card out of play turns face-up: Give the card +1 Focus Value when it turns face-up.
Can I use Kyuden Kyotei to bump the FV of the card targeted by Sincerity when I show it to my opponent?
Martin Lund (rules official), 12 February 2008
Sincerity Bushido Virtue Political Limited: Bow one of your target Samurai: Target a card in your hand and another player. That player guesses whether the card’s base Focus Value is “high” (3 or more) or “low” (2 or less). Show the card. If the guess is right, the player draws a card; otherwise gain 3 Honor.
Kyuden Kyotei Your Market holdings in and out of play have the Legacy keyword. Political Reaction: Even if this Stronghold is bowed, if you control the Imperial Favor, before a Fate card out of play turns face-up: Give the card +1 Focus Value when it turns face-up.
Can I use Kyuden Kyotei to bump the FV of the card targeted by Sincerity when I show it to my opponent?
You can, but Sincerity's card text is very clear about referring to the "base" focus value of the card you reveal. The base value is the printed value, not the modified value.
Ergo, boosting the Focus Value of the card from 2 to 3 won't change the fact that it is "low" for Sincerity because its Base focus value is 2.