impulse_after_octaves
plain-language theorem explainer
This definition scales the single-octave J-cost impulse by the geometric factor 1/phi^n to obtain the remaining impulse after n octaves of relaxation in the volcanic forcing model. Climate researchers simulating post-eruption aerosol decay through the eight-tick cascade would cite it when chaining relaxation steps. It is realized as a direct algebraic reduction that divides the upstream per-octave value by Constants.phi raised to n.
Claim. The impulse after n octaves is given by I(vei, n) = J(veiRatio(vei)) * 8 / phi^n, where J is the J-cost function, veiRatio normalizes VEI to the saturation value, 8 is the octave period, and phi is the golden ratio.
background
The module models volcanic eruptions as instantaneous J-cost sources on the climate eight-tick attractor. Upstream, impulse_per_octave is defined as Cost.Jcost(veiRatio vei) multiplied by the octave period, which equals 8 from Patterns.eight_tick_min at spatial dimension D=3. The Constants structure supplies phi as the self-similar fixed point from the forcing chain.
proof idea
This is a one-line wrapper that applies geometric decay: it divides the per-octave impulse by Constants.phi raised to the power n.
why it matters
It supplies the decay law used by impulse_after_octaves_zero, impulse_after_octaves_succ, and impulse_after_octaves_mono_decay, and populates the VolcanicForcingAsJCostImpulseCert. This implements the multi-octave relaxation step required for realistic cooling timelines, directly tying the J-cost impulse to the eight-tick octave from T7 and the phi decay from the Recognition forcing chain.
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