aggregateThroughput_double
plain-language theorem explainer
Aggregate throughput of a Z-matched transceiver mesh doubles exactly when node count doubles. RS engineers modeling scalable networks cite this to confirm additive scaling. The term-mode proof unfolds the definition as N times T_node, casts to reals, and reduces via ring normalization.
Claim. For every natural number $N$, $T(2N) = 2 T(N)$, where $T(N) := N · T_{node}$ denotes aggregate throughput of the $N$-node mesh.
background
The Z-Matched Recognition-Transceiver Mesh module treats a network of $N$ Z-matched phantom-cavity transceivers whose $(Z, Θ)$-channels are independent. Aggregate throughput is defined as the product of node count and per-node throughput $T_{node}$. Per-pair latency equals the constant 0.07, independent of separation. Upstream results include the J-cost structure from PhiForcingDerived, the ledger factorization from DAlembert.LedgerFactorization, and the gauge content from SpectralEmergence.
proof idea
Unfold aggregateThroughput. Push the natural-number cast to reals. Apply the ring tactic to obtain the identity.
why it matters
The result is invoked inside mesh_one_statement to bundle doubling with successor additivity and constant latency, and inside zMatchedTransceiverMeshCert to certify the mesh. It supplies the doubling clause of the module's linearity claim for track J9, consistent with the self-similar fixed point phi.
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