The CoronalLyapunovCert structure bundles the formal proofs that the predicted sequence of solar coronal timescales forms a mathematically rigorous $\varphi$-ladder.
1. What the declaration says in plain English The certificate asserts four properties about a sequence of timescales: every timescale in the sequence is strictly positive, the next timescale in the sequence is obtained by multiplying the current one by the golden ratio ($\varphi$), the sequence is strictly increasing, and the exact ratio between any two adjacent steps is $\varphi$.
2. Why it matters in Recognition Science In Recognition Science, characteristic scales of physical systems are derived from a discrete scaling symmetry. This module applies that MODEL to astrophysics. Solar coronal magnetic fields evolve chaotically before reconnecting. The framework makes a specific HYPOTHESIS: the Lyapunov timescales (e.g., Alfvén crossing, granulation, coronal loop lifetimes) sit on adjacent rungs of a $\varphi$-ladder. This provides a hard empirical falsifier for RS: if adjacent coronal timescales ratio by a value systematically outside the predicted range, the model is falsified.
3. How to read the formal statement
The Lean structure takes a natural number $k$ representing the "rung" of the ladder. It requires four proof fields:
time_pos: For any rung $k$, the timescale is greater than 0.one_step_ratio: The timescale at $k+1$ equals the timescale at $k$ multiplied by $\varphi$.strictly_increasing: The timescale at $k$ is strictly less than the timescale at $k+1$.adjacent_ratio_eq_phi: The quotient of the timescale at $k+1$ divided by the timescale at $k$ is exactly $\varphi$.
4. Visible dependencies and certificates
The structure depends on the MODEL definition of coronalTime ($1 \cdot \varphi^k$) and the constant $\varphi$. The certificate is formally inhabited by the declaration coronalLyapunovCert. This definition supplies the four underlying THEOREMS as evidence:
5. What this declaration does not prove This formalization does not prove that the physical sun actually behaves this way. The Lean code establishes the exact mathematical properties of the sequence to formally anchor the RS prediction. Comparing this predicted ladder to empirical astronomical measurements (like chromospheric evaporation times) is an observational task outside the scope of the Lean proof system.