Can sustained, per-identity participation be engineered into a security resource? Most anti-Sybil defenses price identity creation rather than identity survival. Once admitted, an adversary may sustain many identities without paying a recurring cost. We introduce the Bounded Participation Channel (BPC), a formal primitive for repeatedly verifying participation window by window. BPC issues fresh, identity-bound challenges under a strict deadline and enforces four structural properties: identity binding, freshness, real-time response, and bounded per-channel throughput. Together, these yield a provable cost theorem: sustaining $s$ identities over $T$ windows requires $C(s,T) \geq sT/τ_h$ participation channel-windows. The guarantee is solver-agnostic: a channel may be operated by a human, an AI system, or a hybrid. We give a hash-based construction with publicly verifiable participation proofs, characterize four admissible challenge families, and evaluate two against GPT-4o, Gemini 2.5 Flash, and Claude Sonnet 4.5 across 600 trials. Despite near-perfect accuracy (97--100%) on the perceptual tasks, the evaluated automated channels remain throughput-bounded under the tested deployment conditions. The results illustrate a key distinction: solvability does not imply unlimited throughput. By requiring participation to be re-earned by every identity in every time window, BPC turns sustained participation into a measurable security resource with a linear structural cost floor, independent of whether the participation is supplied by humans, AI systems, or hybrids.

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