aggregateThroughput_zero
plain-language theorem explainer
The theorem establishes that aggregate throughput of a Z-matched transceiver mesh vanishes at zero nodes. Engineers deriving linear scaling for recognition-based mesh networks cite this as the base case supporting induction on node count. The proof is a one-line wrapper that unfolds the throughput definition and simplifies the resulting expression to zero.
Claim. Let $T(N)$ denote aggregate throughput of an $N$-node Z-matched transceiver mesh, given by $T(N) = N · T_{node}$. Then $T(0) = 0$.
background
The module treats a mesh of Z-matched phantom-cavity transceivers whose pairwise channels are independent and distance-decoupled. Aggregate throughput is introduced as the product of node count and the fixed per-node throughput $T_{node}$. This zero-node case anchors the linearity claim that total throughput equals $N · T_{node}$ for any $N$.
proof idea
The proof is a one-line wrapper that unfolds the definition of aggregateThroughput and applies the simp tactic.
why it matters
This supplies the zero case required by zMatchedTransceiverMeshCert, the top-level certification that aggregate throughput scales linearly with node count. It completes the base of the engineering derivation for Z-matched meshes, where each added node contributes exactly $T_{node}$ and pairwise latency remains constant.
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