T_node_pos
plain-language theorem explainer
The per-node throughput reference equals 1 and is therefore positive. Mesh network designers cite this when establishing that aggregate throughput scales linearly with the number of Z-matched transceivers. The proof is a term-mode one-liner that unfolds the constant definition and applies numeric normalization to verify the inequality.
Claim. $0 < T_0$ where $T_0 := 1$ is the dimensionless per-node throughput reference.
background
The Z-Matched Recognition-Transceiver Mesh models a network of N phantom-cavity transceivers in which each (Z, Θ)-channel is independent and distance-decoupled. Per-node throughput is introduced as the dimensionless reference constant T_node := 1. Upstream results supply the independence of spatial semantics (voxels evolve with no neighbor interaction) and RS-coupled axis independence (axes carried by distinct primitives), which together guarantee that pairwise latency remains constant regardless of separation.
proof idea
The proof is a term-mode one-liner. It unfolds the definition T_node := 1 and invokes norm_num to discharge the inequality 0 < 1.
why it matters
This supplies the positivity hypothesis required by aggregateThroughput_pos and aggregateThroughput_strict_mono, which populate the ZMatchedTransceiverMeshCert structure. It closes the engineering derivation for linear scaling T(N) = N · T_node in the Recognition Science mesh model, consistent with distance-independent latency. No open questions remain for this specific claim.
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