vei_saturation
plain-language theorem explainer
Saturation eruption magnitude is fixed at 7 to mark the J-cost minimum for impulses on the eight-tick climate cascade. Volcanic forcing researchers in the Recognition Science framework cite this constant when normalizing VEI ratios and evaluating per-octave contributions. The declaration enters as a direct definition anchored to the Tambora reference event.
Claim. The saturation eruption magnitude is defined as $7$.
background
The module treats volcanic eruptions as instantaneous J-cost impulses on the climate attractor whose period of eight follows from the minimal complete-cover result at three spatial dimensions. J-cost is the function satisfying the Recognition Composition Law that vanishes at the self-similar fixed point and remains nonnegative elsewhere. Saturation supplies the reference scale so that the VEI ratio maps any eruption magnitude into the interval (0,1], with equality to one identifying the zero-impulse point. This replaces earlier placeholder exponents with a construction drawn from the Cost and Patterns modules and tied to forcing-chain step T7.
proof idea
The declaration is introduced by direct definition that assigns the constant value seven. No lemmas or tactics are required.
why it matters
This constant supplies the zero point for every impulse theorem in the module, including the result that the saturation-eruption impulse vanishes and that sub-saturation events remain strictly positive. It supplies the empirical calibration to the Tambora event inside the eight-tick octave forced by T7 at D=3, allowing the model to recover the observed ordering between Pinatubo-class and Tambora-class cooling. The placement completes the basic calibration step before multi-octave decay is addressed, leaving open whether the reference value should be adjusted for pre-Holocene events.
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