This paper reconstructs zero-knowledge extensions on Solana as an architecture theory. Drawing on the existing ecosystem and on the author's prior papers and implementations as reference material, we propose a two-axis model that normalizes zero-knowledge (ZK) use by purpose (scalability vs. privacy) and by placement (on-chain vs. off-chain). On this grid we define five layer-crossing invariants: origin authenticity, replay-safety, finality alignment, parameter binding, and private consumption, which serve as a common vocabulary for reasoning about correctness across modules and chains. The framework covers the Solana Foundation's three pillars (ZK Compression, Confidential Transfer, light clients/bridges) together with surrounding components (Light Protocol/Helius, Succinct SP1, RISC Zero, Wormhole, Tinydancer, Arcium). From the theory we derive two design abstractions - Proof-Carrying Message (PCM) and a Verifier Router Interface - and a cross-chain counterpart, Proof-Carrying Interchain Message (PCIM), indicating concrete avenues for extending the three pillars.