Short answers, pulled from the story.
Fred Hoyle first proposed the theory in 1946, arguing that very hot nuclei would assemble thermodynamically into iron. He refined the theory in 1954 with a paper describing how advanced fusion stages in massive stars synthesize elements from carbon to iron.
The B2FH paper is the 1957 review paper "Synthesis of the Elements in Stars" by Margaret Burbidge, Geoffrey Burbidge, William Alfred Fowler, and Fred Hoyle. It synthesized nuclear physics, stellar evolution, and observed element abundances to create the foundation of stellar nucleosynthesis theory, and became one of the most heavily cited papers in astrophysics history.
The proton-proton chain dominates in stars up to about the mass of the Sun, releasing about 26.2 MeV per cycle, while the carbon-nitrogen-oxygen cycle dominates in more massive stars, releasing 25.0 MeV per cycle. The CNO cycle is far more temperature-sensitive, with a 10% temperature increase producing a 350% jump in energy output compared to 46% for the proton-proton chain.
Elements heavier than iron cannot be built by fusion alone and are instead created by neutron capture processes called the r-process and the s-process. These processes were a central focus of the 1957 B2FH paper. The r-process and s-process account for elements including silver, gold, and uranium.
Supernova nucleosynthesis is the creation of elements during the explosion of a massive star or white dwarf. The upper layers of a massive star collapse onto the core, generating a compressional shock wave that briefly raises temperatures by roughly 50% and triggers furious nuclear burning lasting about one second. This explosive process is the final epoch of stellar nucleosynthesis.
In 1920, Arthur Eddington proposed that stars obtain their energy from nuclear fusion of hydrogen to form helium, drawing on precise atomic mass measurements by F. W. Aston and a suggestion by Jean Perrin. He also raised the possibility that heavier elements are produced inside stars, making this proposal a preliminary step toward the full theory of stellar nucleosynthesis.