Linear Horizontal Scaling in Pipelined Blockchain Transaction Processing: Architecture, Proof, and Fleet-scale Arithmetic

Abstract

This Online Appendix provides forty supplementary sections supporting the main manuscript. The principal contributions are: (i) a complete multi-input atomicity proof for the UTXO Consistency Result under crash-fault semantics, with six-case exhaustive analysis and sourcecode correspondence; (ii) a formal liveness theorem establishing bounded recovery from Validator crashes during the compensating-unspend protocol; (iii) three alternative scalingefficiency models (η(M): logarithmic, power-law, Amdahl) with cross-validation, bootstrap prediction intervals, and architectural justification for model selection; and (iv) an SPV verification analysis demonstrating that Simplified Payment Verification remains feasible at 10 11-TPS fleet scale without requiring archival nodes. Additional sections provide the full G/G/c throughput-ceiling derivation, 60-point derating calibration methodology, NVMe-spill and mixed-workload production estimates with uncertainty propagation, Aerospike strongconsistency formal model, and responses to all reviewer concerns including a mathematical foundation audit.