vei_saturation_pos
plain-language theorem explainer
Geologists modeling J-cost impulses from volcanic eruptions cite the strict positivity of the saturation VEI to keep all ratios well-defined and positive. This anchors the normalization of sub-saturation events against a Tambora-class reference in the eight-tick climate cascade. The proof is a one-line unfolding of the constant followed by numerical normalization.
Claim. $0 < V$ where $V$ is the saturation volcanic explosivity index serving as the reference magnitude for a Tambora-class event.
background
The module frames volcanic eruptions as instantaneous sigma-sources that inject J-cost impulses into the eight-tick diurnal-seasonal climate attractor. The saturation VEI normalizes actual eruption magnitudes into the VEI ratio, which then multiplies the octave period (forced as 8 by T7 at D=3) to yield the per-octave impulse via the Recognition Composition Law. J-cost itself is the function J(x) = (x + x^{-1})/2 - 1 drawn from PhiForcingDerived.of. Upstream LedgerFactorization.of supplies the underlying (R_+, ×) algebra and calibration of J, while the module doc states that the exponent 8 replaces a prior placeholder with the minimal complete-cover period from Patterns.eight_tick_min.
proof idea
One-line wrapper that unfolds the definition of the saturation VEI and applies norm_num to confirm positivity.
why it matters
This result supplies the base positivity needed for veiRatio_pos and impulse_per_octave_pos_of_ne_sat, which establish that sub-saturation impulses are strictly positive and monotone. It thereby closes the foundation for reproducing the empirical ordering of cooling between Pinatubo-class and Tambora-class events inside the Recognition framework's T7 eight-tick octave and non-negative J-cost property.
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