(This post is part of the Genuinely Approachable Sudoku (GAS) series.)
In this twist on the typical Kropki formula, it is the sums of the values in each cage that are being compared when considering the black and white dots.

PDF

or solve online (using SudokuPad)

Author/Opus: This is the 107th puzzle from Bill Murphy, 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). If a white circle is given between two cages, then the sums of the numbers in those cages must differ by 1. If a black circle is given between two cages, then the sums of the numbers in those cages must have a ratio of 2. Numbers cannot repeat in a cage, and not all circles are given.

GAS Time Standards (highlight to view): Two party hats (🎩🥳): 8:00; One party hat (🥳): 15:00. All other solvers earn a 🦕: C-Saurophaganax.

Thomas Hits the GAS (highlight to view): 2:50, 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.