octavePeriod
plain-language theorem explainer
octavePeriod supplies the integer 8 as the minimal climate-cascade period at D = 3. Volcanic forcing modelers cite it when scaling the J-cost of a VEI ratio over one full relaxation cycle. The definition is the direct assignment 2^3 that matches the eight-tick structure forced by T7.
Claim. The octave period is the natural number $2^3$, the minimal complete-cover length of the three-dimensional pattern space.
background
The module treats a volcanic eruption as an instantaneous source on the climate eight-tick attractor. The resulting impulse after one relaxation cycle is the J-cost of the VEI ratio multiplied by the octave period. This period is fixed at eight by the eight-tick minimum at D = 3, as required by the Recognition forcing chain at T7.
proof idea
The definition is a direct assignment of the natural number eight via the expression 2 raised to the power three. It aligns with the upstream octavePeriod definition in the RS native units module, which records the same quantity as eight base ticks.
why it matters
The value supplies the period factor inside impulse_per_octave, which replaces the v4 placeholder exponent with the T7-forced length at D = 3. It supports the downstream nonnegativity and positivity theorems for the impulse under sub-saturation VEI conditions. The construction rests on the eight-tick octave landmark and the Recognition Composition Law for J-cost.
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