coronalLyapunovCert
plain-language theorem explainer
Coronal Lyapunov timescale certificate asserts that the coronal time sequence satisfies positivity for all steps, exact multiplication by phi at each increment, strict increase, and adjacent ratios equal to phi. Solar physicists modeling magnetic reconnection would cite this to anchor observed coronal events to the Recognition Science phi-ladder. The definition is a direct record construction that supplies the four required fields from prior theorems.
Claim. The coronal Lyapunov certificate is the structure asserting that the coronal time function satisfies $0 < t(k)$ for all natural $k$, $t(k+1) = t(k) · ϕ$, $t(k) < t(k+1)$, and $t(k+1)/t(k) = ϕ$.
background
The module places solar-coronal magnetic evolution on the phi-ladder of timescales. Reference time is the Alfvén crossing time; each subsequent rung multiplies by phi, yielding convective turnover at rung 1, chromospheric evaporation at rung 2, and coronal loop lifetimes at rung 3. The structure CoronalLyapunovCert packages four properties of the coronal time function: positivity, the one-step multiplicative relation, strict monotonicity, and the exact adjacent ratio phi.
proof idea
The definition is a direct record construction that supplies the four fields of CoronalLyapunovCert from the theorems coronalTime_pos, coronalTime_succ_ratio, coronalTime_strictly_increasing, and coronal_adjacent_ratio.
why it matters
This definition bundles the phi-ladder properties for coronal Lyapunov times into a single certificate, completing the local axiomatization described in the module. It sits inside the Recognition Science framework where phi is the self-similar fixed point forced at T6 and adjacent ratios are fixed by the composition law. The module states the falsifier as any systematic deviation of measured adjacent ratios outside (1.5, 1.8) across three or more active regions. No downstream theorems are recorded.
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