IndisputableMonolith.NetworkScience.InternetSpectralGap
The module supplies definitions for the spectral gap of networks at successive k-core decomposition depths, grounded in Recognition Science units. Network theorists cite it when dissecting topology of internet-scale graphs or similar structures. Content consists of basic objects and properties derived from the imported time quantum, without elaborate proof steps.
claimThe spectral gap at k-core decomposition depth $k$ in a network graph, with associated positivity and monotonicity statements.
background
Recognition Science places network analysis inside its unified framework by importing the fundamental time quantum τ₀ = 1 tick from Constants. The module introduces the spectral gap at each stage of k-core decomposition, the iterative process that removes nodes of degree less than k to expose denser cores. This construction maintains dimensional consistency with the broader RS-native units.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies base objects for spectral analysis of networks inside Recognition Science. It draws unit consistency from the Constants import and prepares definitions for later gap ratios and certificates. No parent theorems are recorded in the current dependency graph.
scope and limits
- Does not compute explicit numerical gaps for concrete graphs.
- Does not extend to weighted or directed networks.
- Does not incorporate time evolution or dynamics.
- Does not link directly to mass or forcing-chain formulas.