IndisputableMonolith.NetworkScience.InternetSpectralGap
The module defines the spectral gap of the Internet graph under k-core decomposition at depth k. Network scientists working in Recognition Science units would cite these objects when extracting core spectral properties from scale-free graphs. The module supplies the gap function together with its positivity and monotonicity statements.
claimLet $G$ be the Internet graph. For each integer $k$, let $G_k$ be its $k$-core and let $s(k)$ be the spectral gap of the normalized Laplacian of $G_k$ expressed in RS-native units with time quantum $τ_0=1$.
background
The module imports only Mathlib and IndisputableMonolith.Constants. The upstream Constants module supplies the fundamental RS time quantum $τ_0=1$ tick. The local setting is k-core decomposition applied to the Internet graph, a standard extraction of the densest subgraph at successive depths $k$.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the spectral-gap objects that later network-analysis results in the Recognition Science framework are expected to consume. It anchors all subsequent gap calculations to the RS time quantum supplied by Constants.
scope and limits
- Does not compute explicit numerical values of the gap for any concrete graph.
- Does not prove that the k-core exists or is nonempty for arbitrary networks.
- Does not relate the gap to the phi-ladder or to the forcing chain T0-T8.
- Does not address weighted edges or directed versions of the Internet graph.