IndisputableMonolith.NetworkScience.InternetSpectralGapFromPhiLadder
Module establishes the spectral gap λ₂(k) = φ^{-k} at k-core level k in networks by direct appeal to the phi-ladder. Network theorists modeling internet topology or scale-free graphs would cite it for a parameter-free eigenvalue prediction. The module imports the Constants package and declares the gap relation together with supporting positivity and ratio statements.
claim$λ_2(k) = φ^{-k}$ for the spectral gap at k-core level $k$.
background
The module sits inside the NetworkScience domain of Recognition Science and imports the Constants module whose sole documented content is the fundamental time quantum τ₀ = 1 tick. The phi-ladder is the discrete sequence of powers of the golden ratio φ, itself the unique self-similar fixed point of the J-function. The module introduces the spectral gap λ₂(k) as an exact power-law decay indexed by core level k.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the explicit spectral-gap formula that translates the phi-ladder (T6) into network eigenvalues. It would feed parent results on internet topology certification, as indicated by sibling declarations such as InternetSpectralGapCert. No downstream uses are recorded yet.
scope and limits
- Does not derive the gap from the graph Laplacian spectrum.
- Does not compute numerical values on concrete graphs.
- Does not treat weighted or directed networks.
- Does not include finite-size corrections.