Critical Throughput Limits and Consensus Collapse Mechanisms in Large-Scale PBFT Under Falcon-1024 Post-Quantum Signatures: TCP Incast, View Change Storms, and Deterministic Cryptographic Interlocks

This monograph presents a comprehensive mathematical, network-physical, and distributed systems analysis of applying NIST Level-5 post-quantum Falcon-1024 signatures (1,280 bytes) to large-scale Practical Byzantine Fault Tolerance (PBFT) consensus networks operating across wide-area networks (N = 1,000 nodes, f = 333, 1 Gbps full-duplex bandwidth, 100-200 ms RTT). While Falcon-1024 provides compact post-quantum security and sub-100 microsecond verification, its 20x payload amplification relative to classical ECDSA (64 bytes) shifts the primary system bottleneck from computational verification to ingress network bandwidth. Due to PBFT's O(N^2) all-to-all communication complexity during Prepare and Commit phases, each block consensus round injects a mandatory 2.66 MB control-plane overhead per node regardless of transaction batch size, consuming 72% of link capacity for 1 MB blocks and establishing an idealized fluid-model ceiling of ~30-32.3 blocks/sec (61,400-64,600 TPS).Critically, accounting for packet-switching network physics reveals that synchronized 999-node microbursts (~1.4 MB per phase) trigger severe TCP Incast and switch egress buffer overflows well below theoretical link saturation. Within the critical danger zone of 20-25 blocks/sec (40,000-50,000 TPS, 58.6%-73.3% link utilization), tail-drop packet losses invoke minimum TCP Retransmission Timeouts (RTO = 200 ms), breaching consensus liveness timers and initiating a self-reinforcing "View Change Storm." Because PBFT VIEW-CHANGE certificates aggregate 2f+1 Falcon-1024 signatures (~427 KB per message, 300x larger than standard voting packets), simultaneous broadcast by timing-out replicas induces instantaneous bandwidth exhaustion and irreversible system gridlock (0 TPS). To eliminate this collapse boundary, we formulate a multi-layered engineering and deterministic governance architecture integrating: (1) reinforcement-learning-based adaptive throughput throttling and backpressure control, (2) topological refactoring from O(N^2) broadcast to O(log N) gossip and committee-based sub-sampling, (3) recursive STARK-based zero-knowledge signature aggregation (QFS-zkVM over the 64-bit Goldilocks prime field F_p, p = 2^64 - 2^32 + 1), and (4) hardware-enforced deterministic interlocks under Human-in-Command (HIC) oversight.