Game concept
Personal Artifact Claim
The game also links it as Personal Artifact Claims.
From the game's encyclopedia
A Personal Artifact Claim is an Artifact Claim that is personal to you, as opposed to a House Artifact Claim.
When you die, your children get Claims on all your Artifacts.
You also get a Claim on an Artifact if it's stolen during a Siege or Raid.
Artifact Claims are never inherited.
The game's text for patch 1.20.1.2. Words in blue are entries of the encyclopedia: hover one to read it, as in the game.
Personal Artifact Claim is an entry of Crusader Kings III's in-game encyclopedia. The game explains it: "A Personal Artifact Claim is an Artifact Claim that is personal to you, as opposed to a House Artifact Claim." It is part of Artifact Claim. The game also links it as Personal Artifact Claims. Patch 1.20.1.2, from game/common/game_concepts/00_game_concepts.txt and game/localization/english/game_concepts_l_english.yml.
Source: game/common/game_concepts/00_game_concepts.txt, game/localization/english/game_concepts_l_english.yml and the English localisation, Crusader Kings III 1.20.1.2.