The Invariant Boundary Theorem

This paper formalizes the Invariant Boundary Theorem, demonstrating a fundamental mathematical trade-off in the design of permissionless distributed systems. We prove that it is impossible for a protocol to simultaneously achieve Perfect Indistinguishability (where transit data is computationally indistinguishable from uniform random noise to evade censorship) and Resource Exhaustion Resistance (the ability to discard invalid data in $\mathcal{O}(1)$ time). The theorem establishes that any structural invariant introduced to mitigate asymmetric computational denial-of-service attacks inherently creates a vector for deterministic censorship, whereas the complete removal of invariants exposes the receiving entity to catastrophic computational exhaustion.