IndisputableMonolith.Geology.EruptionRecurrenceLadder
The Geology.EruptionRecurrenceLadder module defines the scaling ratios for volcanic eruption recurrence across VEI classes in the Recognition Science framework. It sets the ratio between adjacent classes to φ², where φ arises as the self-similar fixed point. Researchers applying RS time ladders to geological processes would cite these definitions to construct recurrence intervals. The module consists of a chain of ratio definitions and a certificate structure built directly on the imported time quantum.
claimThe recurrence ratio between adjacent VEI classes is $r = φ^2$, where $φ$ is the golden-ratio fixed point satisfying the Recognition Composition Law. Cumulative ratios across multiple steps are formed by products of this base ratio, and an EruptionRecurrenceCert packages the resulting interval scaling.
background
The module sits in the geology domain and imports the fundamental RS time quantum τ₀ = 1 tick from Constants. It introduces vei_step_ratio as the base multiplier φ² between successive VEI levels, then defines cumulative_ratio as the product over steps and EruptionRecurrenceCert as the packaged certificate for a given rung on the phi-ladder. The local setting applies the self-similar structure of the forcing chain (T6 phi fixed point, T7 eight-tick octave) to recurrence times rather than to mass or energy.
proof idea
This is a definition module, no proofs. It opens with the constant ratio definition vei_step_ratio := φ^2, proves the elementary positivity and band lemmas, then assembles cumulative_ratio and the EruptionRecurrenceCert constructor from those building blocks.
why it matters in Recognition Science
The module supplies the phi-ladder scaling law required for any RS-native treatment of geological recurrence, directly extending the T6–T7 forcing steps to the geology domain. It feeds downstream geological models that need consistent interval ratios derived from the same φ that governs the mass formula and alpha band. No parent theorem is listed in the used-by graph, indicating it functions as a domain-specific leaf that closes the recurrence-ladder scaffolding.
scope and limits
- Does not derive the VEI classification scheme itself.
- Does not calibrate ratios against specific eruption catalogs.
- Does not incorporate spatial or tectonic boundary conditions.
- Does not address recurrence for non-volcanic geological processes.