Dev here, thanks for your comment! The header section is statically divided into 15 equal-sized "slots", each one containing an encrypted volume header (or random noise if unused). So, when opening the third volume, the tool statically knows where to find the header. The header then contains pointers into the data section for where to find the data of the third volume. Also, it contains the password to the second volume. The most secret volume is the highest-order one.

Dev here, thanks for your comment! The block allocations are mathematically proven to be secure, you can find the proof in the Thesis linked on shufflecake.net. In a nutshell, the disk snapshot (assuming the adversary only has one) always looks like randomly-scattered decryptable data + random noise, whether or not you have surrendered all passwords.

Dev here, thanks for your comment! There's no way to prove that you don't have further data, if you do have it. You cannot mathematically convince someone of a false statement. Shufflecake is mainly aimed at people that have something to hide.

Dev here. The aim of Shufflecake is not to hide the fact that you have something to hide (because that can't be done), but to give you the necessary "infrastructure" for you to cook up a plausible lie about the disk contents. You still need to be good at lying, but with previous software that's not enough: with TrueCrypt, for example, you cannot _plausibly_ claim that you're only using one volume, no matter how plausible that is, because _everybody_ uses the second volume. Shufflecake supports more than two volumes, so that solves the problem (omitting some details). A more rigorous and thorough discussion is available in the Master's Thesis linked on shufflecake.net, and will soon be summarised in a research paper.