volcanic_forcing_one_statement
plain-language theorem explainer
The declaration establishes that the climate cascade octave period equals 8, the per-octave J-cost impulse vanishes exactly at saturation VEI, and remains strictly positive at VEI 6. Climate modelers applying Recognition Science to volcanic cooling would cite it to fix the forcing term on the eight-tick attractor. The proof is a one-line term constructor that packages three prior lemmas.
Claim. The climate cascade octave period equals 8, the per-octave J-cost impulse vanishes at the saturation VEI, and the per-octave J-cost impulse at VEI 6 is strictly positive.
background
The module frames volcanic eruptions as instantaneous sigma-sources on the eight-tick climate attractor. The octave period is defined as 2^3 and equals 8 by the minimal complete-cover property at D=3. The per-octave impulse is defined as Jcost(veiRatio(vei)) multiplied by the octave period, where veiRatio normalizes to the saturation reference (VEI 7). Upstream results establish the period equality, the zero impulse at saturation via Jcost at unit argument, and the strict positivity at VEI 6 by direct comparison to saturation.
proof idea
The proof is a term-mode constructor that directly assembles the conjunction from octavePeriod_eq_eight, impulse_at_saturation, and impulse_pinatubo_pos.
why it matters
This theorem consolidates the structural facts for volcanic forcing on the eight-tick cascade (T7 at D=3) and replaces the v4 placeholder exponent with a derivation from Patterns.eight_tick_min and Cost.Jcost. It supports Track A8/E8 of Plan v5. No downstream theorems are recorded yet.
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