Outside Fortress Sudoku by clover!

(This post is part of the Genuinely Approachable Sudoku (GAS) series.)
What happens when you try to build a fortress outside the grid? Find out in this puzzle where the gray cells must exceed the respective numbers to the top and left.

Outside Fortress Sudoku by clover!

PDF

or solve online (using SudokuPad)

Theme: Out in the Cold

Author/Opus: This is the 119th puzzle from Clover, part of the Genuinely Approachable Sudoku (GAS) team.

Rules: Standard Sudoku rules (insert a number from 1 to 9 into each cell so that no number repeats in any row, column, or bold region). Also, when a number appears in a gray cell, it must be greater than the clue number above its column and the clue number to the left of its row.

GAS Time Standards (highlight to view): Two party hats (🎩🥳): 6:30; One party hat (🥳): 12:00. All other solvers earn a 🦕: chilly Chilantaisaurus.

Thomas Hits the GAS (highlight to view): 1:50, with SudokuPad replay file shared as a download for now (requires loading via settings menu with improvements expected before people should use this regularly).

Solution: PDF; solving video with explanation to be added later from GAS team.

Note: Follow this link for other less common variations of Sudoku.

Note 2: Comments on the blog are great! For a more interactive discussion, please also consider using our Daily GAS discussion post on the GMPuzzles Discord. Not a member of the Discord? Click this link for basic access.

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