Burst has many traits from many different “fathers”, so it's not possible to list just one white paper. Below you will find a list of related white papers.
The most recent and most constituent white paper on Burst is The Burst Dymaxion, describing the concept and implementation of a layer to the Burst blockchain which will be capable of sustaining the total global load of non-cash transactions.
Nxt White Paper
Burst started as a fork of Nxt. Below you will find the Nxt community white paper.
There was a substantial modification to the fork by carving out Proof-of-Stake (PoS) completely and replacing it with PoC (Proof-of-Capacity).
Other Proof of Capacity White Papers
A similar concept to Proof of Capacity is called Proof of Space and was described 2013 in the Proofs of Space paper  by Dziembowski, Faust, Kolmogorov and Pietrzak.
Based on this paper, a Proof-of-Space cryptocurrency “SpaceMint” was proposed in a paper by Sunoo Park, Kwon, Fuchsbauer, Pietrzak et al.
Both of these papers (“Proof of Space” and “SpaceMint”) are only mentioned as a loose reference and because the SpaceMint paper refers to BURST.