Technically, my hardest “soap” was when I dissolved finely grated stearin candle wax (FFA-type palm stearin) into excess lye (for titration = SAP determination). Essentially pure palmitic/stearic acid. It's not a saponification (ester cleavage) reaction, but neutralisation, so it would react within seconds.
The lye was boiling, still I didn't get more than a few % of the stearin dissolved before the solution turned into a gooey mess. I diluted with (cold) water, just to watch how the gel would solidify, and it nearly burned upon reheating. In the end I managed to salvage something that I could barely scoop into a mould.
After cooling, it was literally rock hard, no exaggeration. It felt like a piece of plaster and shattered into pieces when I hit it with a hammer. While technically soap, it was extremely lye-heavy (on purpose) and still had an absurdly high water content. I let it carefully dry – it shrank by an unbelievable amount (to about half its original size, while retaining its shape), and became even harder, like pumice or heavy-duty styrofoam. I filed off the amount I needed for the titration – which was no less of a pain, since this stuff is soap, yes, still incredibly badly soluble in cold water, so I had to heat it up to near boiling, and keep it hot for the whole titration, otherwise it would gel.
I was so glad when this project was over (and doubly so that it was worth the hassle – I got a reasonable SAP of 0.158, close to the value of pure palmitic acid). The freshly identified sodium palmitate, after neutralisation of excess lye with more candle filings, proved as a valuable ingredient to harden up M&P soap.
For such a soap made from 100% palmitic acid,
soap calculators spit out a soap that is maxing out the “hardness”/“longevity” scales, which can't be more true. The “creamy [lather]” number is high as well, yet I didn't manage to get this soap lather at all (it was just too insoluble), so I had no chance at all to judge the qualities of lather.
I don't know if this is valuable for you in the sense of your original question. If you want to make a maximally hard-by-the-numbers soap that is still usable as soap, better go the 100% coconut oil way. It comes out hard and scratchy too, but at least it dissolves reasonably and gives of lather happily. Offset the irritiating properties of high-CO soap with as high as 20% lye discount, and/or make a bar with hardly any superfat to compare it with.
I thought it might be just me, but I'm impressed by how long lasting 
