IndisputableMonolith.Geology.VolcanismFromPhiLadder
The module VolcanismFromPhiLadder supplies definitions that scale volcanic explosivity categories and ejection parameters to the phi-ladder in Recognition Science. Geologists working within the RS framework would cite it to express VEI-like quantities in native phi-rung units. It is a pure definition module that imports only the core Constants and introduces no theorems.
claimDefines VEICategory as an enumeration of volcanic classes, veiCategoryCount as the cardinality function, ejectionAtRung(r) = phi^r * base_ejection for energy or mass at rung r, ejectionRatio as the successive ratio, and VolcanismCert as the predicate certifying phi-ladder compliance for a volcanic event.
background
Recognition Science quantizes energies and masses on the phi-ladder via the self-similar fixed point phi forced by T6, with the explicit form yardstick * phi^(rung - 8 + gap(Z)). The upstream Constants module supplies the single RS-native time quantum tau_0 = 1 tick that anchors all rung calculations. This geology module applies the same ladder structure to volcanic ejections, translating the Volcanic Explosivity Index into rung-indexed categories without introducing new physical postulates.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
Supplies the concrete phi-ladder interface for volcanism that extends the mass formula and T8 spatial scaling into the geology domain. It prepares the ground for any future parent theorems that would derive eruption statistics or energy budgets from the J-uniqueness relation and the eight-tick octave. No downstream uses are recorded yet, leaving the module as an open extension point.
scope and limits
- Does not derive the phi-ladder or J-functional equation.
- Does not incorporate observational volcanic data or validation.
- Does not model temporal evolution or dynamics of eruptions.
- Does not address non-volcanic geological processes.
- Does not compute numerical predictions for specific volcanoes.