[AkiyamaKunka]

What

Three window calculations floor the window's origin but compute its size with a raw / 3.0:

// CenterThirdCalculation.landscapeRect
rect.origin.x   = visibleFrameOfScreen.minX + floor(visibleFrameOfScreen.width / 3.0)
rect.size.width = visibleFrameOfScreen.width / 3.0      // not floored

So on any screen whose width or height isn't a multiple of 3, they place windows on fractional pixels. On a 1000pt-wide frame the center third comes out 333.33pt wide — a non-integer window frame, and 0.67pt short of meeting the last third, which floors to 333. Every other calculation (first/last thirds, quarters, sixths, ninths, …) floors its size, so these three are the exception:

• CenterThirdCalculation — width / height
• CenterTwoThirdsCalculation — origin and size
• MiddleVerticalThirdCalculation — height

The fix

Floor the sizes like the sibling calculations. The single center third now takes the remainder between the first and last thirds (width - 2 * floor(width / 3)), so the three thirds tile the screen with whole-pixel, gap-free geometry; the center two-thirds becomes 2 * floor(width / 3) centered with an integer margin.

Example on a 1000×800 frame:

action	before	after
center third	(333, 0, 333.33, 800)	(333, 0, 334, 800)
center two-thirds	(166.5, 0, 666.67, 800)	(167, 0, 666, 800)
middle vertical third	y 266, h 266.67	y 266, h 268

Tests

Added CenterThirdsRectTests: whole-pixel geometry, the center third tiles contiguously with the first and last thirds, and the centered actions have equal margins on both sides. They fail on main and pass with the fix. The full test suite passes (729 tests).