IndisputableMonolith.NetworkScience.InternetSpectralGapFromPhiLadder
The module declares that the spectral gap λ₂ at k-core level k equals φ^{-k}. Network theorists applying self-similar scaling to graph spectra would cite the relation when bounding eigenvalues in scale-free topologies. The module imports the phi-ladder and τ₀ from Constants and structures sibling definitions around this formula with no internal proofs.
claim$λ_2(k) = φ^{-k}$ at k-core level k.
background
Recognition Science obtains the golden ratio φ as the self-similar fixed point (T6) from J-uniqueness. The imported Constants module fixes the base time quantum τ₀ = 1 tick. The present module translates the phi-ladder into network language by assigning the second Laplacian eigenvalue at each core decomposition level k to the corresponding rung φ^{-k}.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the spectral-gap formula that feeds sibling declarations such as spectralGap and InternetSpectralGapCert. It extends the phi-ladder and Recognition Composition Law into graph spectra, providing the bridge from the eight-tick octave to network eigenvalue gaps.
scope and limits
- Does not prove existence or uniqueness of k-cores.
- Does not compute numerical gaps for concrete graphs.
- Does not derive the formula from the Recognition Composition Law.
- Does not address stability under edge perturbations.