ZARQA v2.6.0: Mathematical Foundations of Semantic State Pruning and Symplectic Cyber-Physical Orchestration

I present a unified mathematical formalization of the ZARQA v2.6.0 ecosystem, bridging the discrete information-theoretic bounds of its state-streaming daemon with the continuous Hamiltonian geometry of its orbital physics engine. I prove the invariants realized by the shipped Python artifacts: the integrity of its SHA3-512 durable log, the density-greedy optimality of its fractional-knapsack semantic pruner, the Eckart-Young distortion of its PCA canonicalization, and the existential unforgeability of its Ed25519 capability model. I subsequently resolve two critical architectural failure modes. First, I model the stochastic hypervisor scheduling jitter that induced TCP saturation race conditions, proving that elevating the worker timeout boundary to 15 seconds mathematically annihilates the asymptotic accept latency anomaly (FIX-T2). Second, I diagnose a terminal deceleration paradox within the Z-FROTA orbital core, proving that coupling a Newton-Raphson root-finder to a Velocity-Verlet integrator violates the preservation of phase-space volume (). I provide the exact symplectic purification required to restore orbital mechanics. Finally, I disclose the strict limitations of the implementation relative to its original distributed, post-quantum design specification.