latency_per_pair_pos
plain-language theorem explainer
The theorem establishes positivity of per-pair latency in Z-matched transceiver meshes. Engineers modeling RS_PAT_042 phantom-cavity networks cite it to confirm non-zero (Z, Θ)-channel delay. Proof is a one-line wrapper that unfolds the constant definition and applies norm_num.
Claim. $0 < 0.07$, where $0.07$ is the dimensionless coefficient for per-pair (Z, Θ)-channel latency given by $ℏ_C / (2 · ΔE)$ and independent of distance.
background
The Z-Matched Recognition-Transceiver Mesh module models a network of N Z-matched phantom-cavity transceivers whose aggregate throughput equals N times the single-node throughput T_node. Each (Z, Θ)-channel is independent and distance-decoupled, so pairwise latency remains constant per the upstream Foundation.ZThetaSpatialDecoupling result. The sibling definition records latency_per_pair : ℝ := 0.07 as the coefficient for ℏ_C / (2 · ΔE) ≈ 0.07 µs.
proof idea
The proof is a one-line wrapper. It unfolds the definition of latency_per_pair to expose the constant 0.07, then applies norm_num to discharge the strict inequality.
why it matters
This theorem supplies the latency_pos field required by the master certificate zMatchedTransceiverMeshCert and is invoked directly by pairwiseLatency_pos. It completes the engineering derivation that aggregate throughput scales linearly with node count while per-pair latency stays constant, matching the module's stated goals of linear T(N) and distance-independent channels. No open scaffolding remains in the supplied material.
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