Explanation of the coronalTime declaration
(1) In plain English: coronalTime is a function that, given a natural number rung k, computes the coronal timescale as 1 * phi^k. It models characteristic timescales in the solar corona as successive rungs on a ladder where each step multiplies the previous by the golden ratio phi (approximately 1.618).
(2) Why it matters in Recognition Science: RS derives all structure from a single cost functional whose self-similarity forces timescales to form a phi-ladder. This definition supplies an explicit, parameter-free model for chaotic magnetic evolution in the solar corona, with the property that adjacent rungs differ by exactly phi. The module docstring lists example rungs (Alfvén crossing at rung 0, convective turnover at rung 1, etc.) and states a falsifier: measured adjacent coronal Lyapunov times must lie in (1.5, 1.8) on a corpus of active regions.
(3) How to read the formal statement: The declaration
def coronalTime (k : ℕ) : ℝ := referenceTime * phi ^ k
(with referenceTime := 1) is a non-computable definition returning a real number. It is accompanied by proved properties: coronalTime_pos asserts strict positivity for every k; coronalTime_succ_ratio states coronalTime (k+1) = coronalTime k * phi; coronalTime_strictly_increasing proves the sequence is strictly increasing; and coronal_adjacent_ratio proves the ratio equals phi exactly.
(4) Visible dependencies or certificates in the supplied source: The definition depends only on the local constant referenceTime (also in this module) and the imported phi. All algebraic properties are proved inside the module with no sorry or axiom. The structure CoronalLyapunovCert bundles the four key lemmas, and the concrete instance coronalLyapunovCert supplies the certificate.
(5) What this declaration does not prove: It does not prove any empirical mapping to observed solar data, does not establish the stated falsifier as a theorem, and does not derive the phi-ladder from the upstream forcing chain (those steps live in other modules). The astrophysical interpretation remains a documented hypothesis rather than a proved theorem.