Game concept
Siege Progress
From the game's encyclopedia
The Siege Progress indicates how close a Siege is to being completed and how long the Siege is expected to last. When Progress is full, the Holding will become Occupied.
The amount of Siege Progress required is affected by Fort Level and the manning of the Garrison.
Progress is gained daily and is affected by Siege Events. It can also be increased by having Siege Weapons, or an Army that vastly outnumbers the Garrison.
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.
Siege Progress is an entry of Crusader Kings III's in-game encyclopedia. The game explains it: "The Siege Progress indicates how close a Siege is to being completed and how long the Siege is expected to last." 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.