The thread would have to be made rigid, too. Another possibility is that they can be fused together (reversibly), and are layered like paper mache.
The only thing we really know is that the process involves some degree of heat (assuming I'm not misremembering it needing fuel,) but not just that alone. Maybe saliva+heat, and any wafers lost on reforging is Urist accidentally eating the candy.
It has a [FUEL] token just like every other smelter reaction, even though no fire that could possibly melt or even soften the candy could possibly be produced with a single lump of coal, and any fire hot enough would melt the furnace before the candy.
Again, I would suspect there to be some sort of catalyst causing some chemical change (found solely in dwarven picks, craftsdwarf workshops, and dwarven smelters,) similar to the way that flux brings the melting point of iron down low enough to make steel. Strands of candy are in some alternate state that leaves them flexible, which can be shaped and molded, then a chemical reaction hardens it like concrete is hardened.
Urist McPhysicist Posits Adamantine Strands as Subatomic, One-dimensional "Threads"; Mountainhome Scholars Balk!
Layering one-dimensional objects on top of one another still creates a one-dimensional object. Zero times any number still equals zero.
Rather, I've seen the ludicrously low density explained as an extremely unusual molecular structure, in much the same way that charcoal and diamonds are both carbon, but one is far denser and shows far different properties than the other.
That said, especially if we are to believe that sub-atomic edges are literal, and not a stand-in for some sort of odd effect like a continuous electromagnetic field generated by "inert" metal, it may even be some sort of exotic particle arranged in molecule-like formation.