pairwiseLatency
plain-language theorem explainer
The definition sets pairwise latency to a fixed value independent of separation distance in a Z-matched transceiver mesh. Network engineers would reference it when proving constant delay across node pairs in linear-throughput meshes. It is realized as a direct alias to the upstream latency_per_pair constant.
Claim. The pairwise latency function satisfies $L(d) = 0.07$ for every real separation $d$, where the constant equals the per-pair $(Z, Θ)$-channel latency.
background
The Z-Matched Recognition-Transceiver Mesh models networks of phantom-cavity transceivers whose $(Z, Θ)$-channels are distance-decoupled. Aggregate throughput is required to equal $N · T_node$ and to double when node count doubles. The upstream definition latency_per_pair records the dimensionless coefficient 0.07, obtained as ℏ_C / (2 · ΔE).
proof idea
The definition is a one-line alias that returns the constant latency_per_pair for any input distance.
why it matters
This definition supplies the constant used by mesh_one_statement to assert linear throughput, doubling at 2N, and distance-independent latency. It completes the engineering derivation for Track J9 and the module falsifier of sublinear throughput in a deployed mesh of four or more nodes.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.