impulse_tambora_eq_zero
plain-language theorem explainer
The declaration shows that the per-octave J-cost impulse vanishes exactly when the VEI ratio reaches the saturation reference calibrated to a Tambora-class event. Climate modelers working inside the Recognition Science eight-tick cascade would cite it to anchor the zero of the volcanic forcing scale. The proof is a direct one-line application of the saturation lemma.
Claim. The per-octave J-cost impulse at the saturation VEI ratio equals zero: $I(1)=0$, where $I$ is the impulse function and the argument is the eruption magnitude normalized to the saturation reference.
background
The module frames volcanic eruptions as instantaneous sources applied to the climate's eight-tick attractor. The per-octave impulse is obtained by multiplying the J-cost of the normalized VEI ratio by the octave period of 8, the minimal complete-cover length forced by three spatial dimensions. Saturation is defined at VEI ratio 1, corresponding to a Tambora-scale event (VEI 7), where the J-cost term is required to vanish.
proof idea
This is a one-line wrapper that applies the impulse_at_saturation lemma.
why it matters
The result fixes the zero point of the volcanic impulse scale inside the Recognition framework, consistent with the eight-tick octave (T7) at D=3. It opens the multi-octave decay section that follows the saturation definition. The accompanying note records that any empirical calibration would shift the reference upward rather than treat Tambora as literally zero cooling.
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