Solomon seals the fate of Adonijah with a severe oath, grounding his decision in the divine destiny of his kingdom. He draws a direct line between God's promise to secure his reign and the immediate need to eliminate anyone who threatens that stability.
God alone established and secured the kingdom [מצודת ציון, ביאור שטיינזלץ]. The primary approach among commentators is that the founding of this royal dynasty serves as a reinforcing parallel to the reality that Solomon now sits securely on the throne of David [מצודת דוד]. This establishment of the royal house unfolded exactly as God had spoken and promised through Nathan the prophet [רש״י, ביאור שטיינזלץ].
It is precisely from these divine promises that Solomon derives Adonijah's sentence. God had assured Solomon that he would be a man of peace and that his descendants would continue to rule. To guarantee and protect this promised peace, Solomon realizes he must remove any rebel or adversary who might disrupt the kingdom's stability. Consequently, to uphold God's vision for a secure reign, Adonijah must be put to death that very day [מלבי״ם].