  Intuitively there is a drastic distinction between the pure decentralized
block-chain systems like Defis and those that only utilize block-chain as an
enhancing technology but remain centralized with real-world business model and
conventional technologies like database, application server, etc. Our study
explores extensively this distinction from a methodological point of view,
classifies them into blockchain-complete and blockchain-partial, analyzes key
features of the two types, and reveals the root cause of this distinction. We
analyze the function or, in more strong words, the "ultimate purpose" of
blockchain in the blockchain-partial systems, and present a conceptual model we
named proof-chain that quite satisfactorily represented the general paradigm of
blockchain in blockchain-partial systems. A universal tension between strength
of proof-chain and privacy is then revealed and the zero-knowledge based
proof-chain takes shape. Several case studies demonstrate the explaining power
of our proof-chain methodology. We then apply proof-chain methodology to the
analysis of the ecosystem of a collaborating group of blockchain-partial
systems, representing the paradigm of public and private data domain whose
border the proof-chain crosses. Finally, some derived guidelines from this
methodology speak usefulness of our methodology.
