Game concept
House Artifact Claim
The game also links it as House Artifact Claims.
From the game's encyclopedia
If you hold an Artifact for long enough, your whole House will get an Artifact Claim on it – a House Artifact Claim.
You can only act on a House Artifact Claim if the Artifact is not held by a member of your house.
When a Cadet Branch is formed, any existing House Claims on Artifacts held by the members of the new House are transferred to the new House.
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.
House Artifact Claim is an entry of Crusader Kings III's in-game encyclopedia. The game explains it: "If you hold an Artifact for long enough, your whole House will get an Artifact Claim on it – a House Artifact Claim." It is part of Artifact Claim. The game also links it as House 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.