Fractional Verkle Trees: A Hypertree Decomposition and Verified Proof Serialization Architecture for High-Performance Blockchain State Accumulators

Abstract: Modern blockchain state management faces a critical scalability bottleneck: maintaining cryptographic commitments over hundreds of millions of entries becomes computationally prohibitive. Ethereum's transition to Verkle Trees: polynomial commitment accumulators reducing proof sizes from O(width * depth) to O(depth) via constant-size IPA vector commitments, is a critical step toward stateless operation. Yet, current implementations exhibit pathological characteristics that burden home validators. We identify four inefficiencies in the reference go-verkle implementation \cite{kaur2025goverkle, kaur2025goethereum}: (1) phantom node creation during non-existent account deletion; (2) 64-byte database keys triggering excessive LSM-tree compaction; (3) redundant memory copying in proof deserialization; (4) a Proof of Absence wire format incompatibility causing non-deterministic serialization. We present Fractional Verkle Trees (FVT), a hypertree decomposition partitioning global state into N independent sub-accumulators coordinated by a Merkle commitment tree, achieving improved cache locality, zero-lock-contention goroutine-parallel commitment computation, and faster root recomputation (91 $μ$s vs $\sim$500 ms). We address each inefficiency via existence checks, 32-byte SHA256 node references, zero-copy reference-counted buffers, and HashMap-based lexicographic deduplication. Benchmarks on Apple M1 Pro show 57\% heap allocation reduction (566,760 to 242,004 bytes per 10K proofs), parallel insertion at 2,433 ns/op, and network-wide elimination of 4.85 PB/year across 6,000 full nodes, advancing the Ethereum stateless roadmap.