module module high

`IndisputableMonolith.Engineering.ZMatchedTransceiverMesh`

This module defines per-node throughput T_node and related quantities such as aggregateThroughput and pairwiseLatency for a Z-matched transceiver mesh in RS-native units. Engineers constructing communication models within the Recognition framework would cite these definitions when analyzing network performance. The module consists of a collection of basic definitions and monotonicity lemmas with no complex proofs.

claimLet $T$ denote per-node throughput in dimensionless reference units. Aggregate throughput satisfies the recurrence $A(0)=0$, $A(n+1)=A(n)+T$ with $A(n)$ strictly increasing for $n>0$. Pairwise latency $L$ is constant across all node pairs.

background

The module imports Constants, which sets the fundamental RS time quantum as τ₀ = 1 tick, and Cost for cost functions. It introduces engineering primitives for transceiver meshes under Z-matching, with sibling definitions covering T_node, latency_per_pair, aggregateThroughput and its variants (zero, succ, pos, strict_mono, double). These build directly on the imported modules without additional hypotheses.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies foundational engineering objects for transceiver meshes that support higher-level Recognition Science applications in network throughput and latency analysis. No downstream theorems are recorded in the dependency graph.

scope and limits

Does not model physical propagation or geometry of the mesh.
Does not incorporate noise, attenuation, or quantum corrections beyond RS units.
Does not derive quantities from the Recognition Composition Law or phi-ladder.
Does not connect to mass formulas or Berry creation thresholds.

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Cost module_import

declarations in this module (16)

def T_node L39
theorem T_node_pos L41
def latency_per_pair L45
theorem latency_per_pair_pos L47
def aggregateThroughput L53
theorem aggregateThroughput_zero L55
theorem aggregateThroughput_succ L58
theorem aggregateThroughput_pos L62
theorem aggregateThroughput_strict_mono L67
theorem aggregateThroughput_double L74
def pairwiseLatency L82
theorem pairwiseLatency_constant L84
theorem pairwiseLatency_pos L87
structure ZMatchedTransceiverMeshCert L92
def zMatchedTransceiverMeshCert L101
theorem mesh_one_statement L113