In accordance with fact or reality

• Factually correct or accurate
• Not false

Accurate; exact; within tolerance

• Properly aligned or calibrated; straight
• Following a path directly toward the target

Loyal and faithful

• Steadfast in allegiance or affection

Genuine or authentic; not fake

• In the strict or proper sense

In logic or computing, the affirmative state

• One of two Boolean values; logic 1

Accurately or exactly

• In a straight or properly aligned manner
• Truthfully

To straighten or make level

• To adjust for accuracy or alignment
• To true up a surface or wheel

Truth

• The quality of being exactly aligned or accurate
• A pledge or truce (archaic)