pinatubo_below_saturation
plain-language theorem explainer
Pinatubo VEI 6 lies strictly below the saturation eruption magnitude of 7 on the climate cascade. Researchers modeling volcanic J-cost impulses in the eight-tick octave would reference this bound when ordering cooling effects. The proof reduces directly to unfolding the saturation constant and verifying the numerical inequality.
Claim. The Pinatubo eruption magnitude satisfies $6 < v$ where $v = 7$ is the saturation eruption magnitude on the climate cascade.
background
The module frames volcanic eruptions as instantaneous sigma-sources on the eight-tick climate attractor. Each impulse magnitude after one octave equals J(VEI ratio) times the period 8, where the period follows from T7 at D=3 and the J-cost contribution is taken from Cost.Jcost. Saturation is the empirical Holocene maximum given by the Tambora event.
proof idea
The proof is a one-line term-mode wrapper that unfolds the definition of vei_saturation and applies norm_num to confirm the inequality 6 < 7.
why it matters
This result supports the ordering of volcanic impulses in the Recognition framework, ensuring Pinatubo (VEI 6) produces a strictly smaller J-cost impulse than the saturation Tambora event (VEI 7). It connects to T7 (eight-tick octave) and the per-octave impulse formula. The declaration closes the sub-saturation claim for empirical Holocene events.
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