Assuming the Math Guide’s probability foundations and the hash and
commitment foundations of the Crypto Guide, this volume of The
Zcash Arboretum constructs Nakamoto consensus from first principles and
quantifies the security it buys. It states the
block tree and the most-work rule as the protocol specification defines
them and as the deployed zebra implements them; builds, on the
Math Guide’s foundations, the race-specific probability the
analysis needs (memoryless clocks, the biased random walk, the negative
binomial law); develops the exact first-seen-model
double-spending analysis of Rosenfeld’s Analysis of hashrate-based
double-spending — the catch-up theorem, the confirmation formula, and
the economics of the attack — with every derived number recomputed by script
and the results instantiated for Zcash’s proposed 25-second blocks; explains the
draft NU7 transition to 25-second blocks and halving-preserving reissuance;
and explains the protocol and implementation safety rails (difficulty
adjustment, reorg windows, coinbase maturity, wallet confirmation policy)
that frame the model’s assumptions. Where the specification, the paper, and the
deployed nodes disagree, the divergence is stated.