The "Fencepost Error" (Ueki-zan) at the Root of Proof-of-Work Consensus: From Adam Back's Hashcash and the 2015/2016 Retargeting Off-by-One Bug to Hawkes Burst Cascades, Cross-Pacific Heritage Liquidity, and QFS-zkVM Exact Boundary Arithmetic

In elementary school arithmetic, the Fencepost Theorem (Ueki-zan) states that N discrete posts planted along a line define exactly N - 1 intervals between them. Remarkably, one of the most consequential vulnerabilities in modern decentralized finance and distributed consensus traces directly to a failure of elementary fencepost arithmetic in Proof-of-Work (PoW) difficulty retargeting—originating in the Hashcash cost-function paradigm pioneered by Adam Back (1997/2002) and codified in Bitcoin's CalculateNextWorkRequired (pow.cpp). By dividing the elapsed time across N - 1 = 2015 block intervals by the target duration of N = 2016 blocks, legacy PoW consensus leaves the inter-epoch boundary interval [t_{2016m-1}, t_{2016m}] completely unmeasured, enabling the catastrophic Timewarp Timestamp Manipulation Attack and permanent difficulty drift. Building upon our 200th Grand Master Monograph (Record 23383049), our proof of PoW cryptographic collapse (Record 23355921), our N = 300 cyber-cognitive burst analysis (Record 23378094), and our California and sovereign wealth stability frameworks (Records 23381256, 23382621, and 23384072), this 202nd monograph establishes the unified mathematical theory of Cryptographic Fencepost Pathologies (N - 1 != N) across three coupled domains: (1) The Hashcash/Bitcoin 2015/2016 Retargeting Fencepost Theorem: We prove how omitting the 2016th boundary interval allows adversarial miners to spoof block timestamps across epoch boundaries and collapse difficulty D_m -> 0; (2) Tumbling-Window Fencepost Straddling in N = 300 Investigative Reply Bursts & Cross-Pacific Capital Ledgers: We prove that discrete tumbling-window counters allow Hawkes self-exciting reply bursts (such as high-velocity investigative threads involving John Carreyrou) and overnight T+1 settlement gaps to straddle epoch fenceposts, threatening cross-Pacific heritage portfolios (e.g., JPY 1.5 billion / USD 10 million California estates); and (3) Exact Telescoping Boundary Arithmetic in Goldilocks QFS-zkVM: Eliminates all off-by-one boundary leaks via continuous Sobolev-HOCBF sliding windows and zero-knowledge state-transition proofs over F_p (p = 2^64 - 2^32 + 1). License & Integrity Covenant: Creative Commons Attribution 4.0 International (CC BY 4.0) with Strict No-Learn Covenant (NLL-v1.0-2026).