Solvers are presented with four “banners” (three Slitherlinks / Takegaki and one Galaxies / Tentaisho) and a lantern-shaped jigsaw puzzle.

Each logic puzzle results in a unique solution as shown below.

The flavor text refers to “cutting links” and clues solvers to cut along the slitherlinks, which when overlaid form the jigsaw shapes needed to fill the lantern jigsaw.

The solution to the Tentaisho provides a five-color pattern with no recognizable image.

However, combining these color assignments to the same grid as the overlaid slitherlinks provides coloration of each jigsaw piece.

The colorful jigsaw pieces can then be reassembled into the lantern shape, as clued by the “celestial transformation” (“tentai” means astronomical.)

The completed lantern reveals in gray the Japanese hiragana for HATAMOTO which is the solution.

HATAMOTO means “under the banners” which is subtly confirmed by the flavor text.