veiRatio
plain-language theorem explainer
veiRatio normalizes volcanic explosivity index to the saturation threshold of 7, producing a dimensionless fraction in (0,1] for sub-saturation events with equality at the Tambora reference. Climate researchers modeling J-cost impulses on the eight-tick cascade cite this normalization to anchor forcing calculations at the empirical maximum. The definition is a direct division by the constant saturation value.
Claim. For volcanic explosivity index $vei$, the ratio is defined by $vei / 7$, where 7 is the saturation value corresponding to the 1815 Tambora event.
background
The module frames volcanic eruptions as instantaneous sigma-sources on the eight-tick climate attractor, with impulse magnitude after one octave of relaxation given by J-cost of the ratio times the octave period. The period equals 8 from T7 at D=3 via Patterns.eight_tick_min, and J-cost is taken from Cost.Jcost to enforce reciprocal symmetry and non-negativity. Saturation is fixed at the Holocene maximum: 'Saturation eruption magnitude on the climate cascade. The empirical Holocene maximum is the 1815 Tambora event (VEI 7).'
proof idea
One-line definition that divides the input VEI by the saturation constant vei_saturation.
why it matters
This normalization is the input to impulse_per_octave, which computes the per-octave J-cost impulse as J(veiRatio vei) times octavePeriod. Downstream theorems then establish non-negativity for positive VEI, strict positivity away from saturation, and the ordering between VEI 6 and VEI 7 events. It replaces the v4 placeholder exponent with a derivation tied to T7 and the J-cost framework, ensuring the impulse vanishes exactly at the Tambora reference.
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