We revisit the problem of designing light-client blockchain protocols from the perspective of classical proof-system theory. This results in a framework that allows quantifying the security guarantees provided to a light-client verifier even when interacting only with a single dishonest (full-node) prover. We define a new primitive called succinct non-interactive argument of chain knowledge (SNACK) capturing this intuition and show how augmenting any blockchain with a graph-labeling proof of sequential work (GL-PoSW) enables SNACK proofs for this blockchain. We also provide a unified and extended definition of GL-PoSW covering all existing constructions and describe a new variant. We then show how SNACKs can be used to construct light-client protocols, and highlight some deficiencies of existing solutions. (Joint work with: Georg Fuchsbauer, Peter Gazi, and Karen Klein)