IndisputableMonolith.Geology.EruptionRecurrenceLadder
This module defines the recurrence ratio between adjacent VEI eruption classes as φ² inside the Recognition Science framework. Volcanologists and geophysicists modeling self-similar scaling of natural intervals would cite the ladder. It consists of a chain of ratio definitions and positivity lemmas built directly on the imported time quantum.
claimThe ratio of recurrence intervals for VEI classes separated by one step equals $r = φ^2$.
background
Recognition Science supplies the fundamental time quantum τ₀ = 1 tick from Constants. The module extends the phi-ladder (self-similar fixed point) to geological recurrence, introducing VEI step ratios, cumulative ratios, and the EruptionRecurrenceCert structure. All constructions remain inside RS-native units with no external calibration.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module realizes the eruption recurrence ratio φ² stated in its documentation and supplies the geological instance of the T6 phi fixed point. It feeds downstream applications of the Recognition Composition Law to periodic natural processes, though no explicit used_by edges are recorded.
scope and limits
- Does not derive eruption probabilities from first principles.
- Does not incorporate observational data or calibration.
- Does not address non-VEI geological or seismic processes.
- Does not claim numerical forecasts for individual volcanoes.