Heap's conjecture on space-efficient knot-mosaic layouts

A space-efficient layout is a knot-mosaic layout with a fixed mosaic size and a fixed number of non-blank tiles. Consider layouts having the same mosaic size and the same number of non-blank tiles.

Heap's conjecture. Such space-efficient layouts produce the same set of prime knots.

The conjecture is motivated by prior observations for several 6-mosaic and 7-mosaic layouts, which produce identical sets of knots. The supplied text presents these observations as evidence supporting a conjecture first proposed in the cited work; no resolution is given here.