What brings a faction's army to you in Kenshi

A faction sends its army after you when a ruler or a named champion falls and your squad had a hand in it. Killing or capturing Holy Lord Phoenix brings The Holy Nation's campaign. Killing or capturing Esata the Stone Golem brings the Shek Kingdom's. Taking down Emperor Tengu or Longen sets Eyegore hunting you for the United Cities. Each campaign also lists the states under which it does not start.
When a ruler falls
- Holy phoenix is deadmust be trueHoly Lord Phoenix: deadOnly when your squad had a hand in it
- Player kidnapped Phoenixmust be trueHoly Lord Phoenix: imprisonedOnly when your squad had a hand in it
Both campaigns go by the same name in the game. One needs Holy Lord Phoenix dead, the other needs him held prisoner, and each needs your squad to have been involved. A Lord who dies without you does not send the army to your door.
When a champion or her captains fall
- Player killed/napped esatamust be trueEsata the Stone Golem: alive (must be false)Only when your squad had a hand in it
- Bayan is not alivemust be trueBayan: alive (must be false)Only when your squad had a hand in it
- Player is ally of Shek Kingdommust be false
- Player killed/napped esatamust be falseEsata the Stone Golem: alive (must be false)Only when your squad had a hand in it
Killing or capturing Esata the Stone Golem starts the first campaign. The second is her own revenge for Bayan, and it holds back in two states: when your squad is an ally of the Shek Kingdom, and when you have already dealt with Esata the Stone Golem herself. A matching campaign answers the death of Seto.
When an emperor or a lord falls
- All nobles are not alivemust be falseLady Tsugi: alive (must be false), Lady Sanda: alive (must be false), Lord Yoshinaga: alive (must be false), Lord Inaba: alive (must be false), Lord Nagata: alive (must be false), Emperor Tengu: alive (must be false)
- Player killed/knapped Tengumust be trueEmperor Tengu: alive (must be false)Only when your squad had a hand in it
- Player killed/knapped Eyegoremust be falseEyegore: alive (must be false)Only when your squad had a hand in it
- All nobles are not alivemust be falseLady Tsugi: alive (must be false), Lady Sanda: alive (must be false), Lord Yoshinaga: alive (must be false), Lord Inaba: alive (must be false), Lord Nagata: alive (must be false), Emperor Tengu: alive (must be false)
- Longen is alivemust be falseLongen: aliveOnly when your squad had a hand in it
- Player killed/knapped Eyegoremust be falseEyegore: alive (must be false)Only when your squad had a hand in it
Eyegore comes after you once Emperor Tengu or Longen falls with your squad involved. Neither hunt starts once every noble on that list is gone, and neither runs once Eyegore himself is dead or taken.