The following statements describes the most up-to-date findings utilising the BUG principle:

Definition:

- A Bivalue Universal Grave (BUG) is any grid in which all the unsolved cells have two candidates, and if a candidate exists in a row, column, or box, it shows up exactly twice. (example)

A BUG-Lite is a partial BUG pattern that exhibits similar properties of a BUG where all nodes in the pattern are bivalue and if a candidate exists in a row, column, or box, it shows up exactly twice. (example)

A poly-valued cell for the purposes of this thread is a cell having more than two candidates.

A Local Bivalue Move or Localized BUG Move (LBM) is the selection of one or 2 candidates from a cell that causes each candidate in the 2-candidate selections in that row, column, or box show up exactly twice. (example, example)

A non-BUG candidate is a candidate that is excluded during a LBM from a cell. All non-BUG candidates are not part of a BUG.

A BUG+n is a BUG that has exactly n number of poly-valued cells. A BUG+1 is a BUG that has exactly one poly-valued cell left.

- BUG grids can have either zero or more than one solution, and so are incompatible with a unique solution puzzle. Hence the puzzle solution must come from the non-BUG candidates. (proof)

Corollary 2: Any deductions implied by all non-BUG candidates in the grid must be valid. (example)

Corollary 3: Any placement of a candidate which removes all non-BUG candidates is an invalid move. (example, example)

Corollary 4: Any placement of a candidate which forces a grid into a BUG+1 is a valid move. (example)

Corollary 5: Corollaries 1, 2 and 3 can be applied to a BUG-Lite.