Explain the Lean structure `CoronalLyapunovCert` in module `IndisputableMonolith.Astrophysics.CoronalLyapunovTime`. Write for an educated reader who knows science and programming but may not know Lean. Cover: (1) what the declaration says in plain English, (2) why it matters in Recognition Science, (3) how to read the formal statement, (4) visible dependencies or certificates in the supplied source, and (5) what this declaration does not prove. Cite only declarations present in the supplied Recognition source.

(1) Plain English

CoronalLyapunovCert is a Lean record (structure) that bundles four proved properties of the function coronalTime k (the coronal timescale at rung k on the φ-ladder). In ordinary language it asserts: every timescale is positive; each rung multiplies the previous by exactly the golden ratio φ; the sequence is strictly increasing; and the ratio of any two adjacent rungs equals φ.

(2) Role in Recognition Science

The certificate records that coronal Lyapunov times obey the same self-similar φ-scaling that Recognition Science derives from the J-cost functional equation. It therefore supplies a parameter-free mathematical backbone for the predicted coronal timescale ladder (Alfvén crossing, granulation, loop lifetime, etc.) described in the module.

(3) Reading the formal statement

structure CoronalLyapunovCert where
  time_pos : ∀ k, 0 < coronalTime k
  one_step_ratio : ∀ k, coronalTime (k + 1) = coronalTime k * phi
  strictly_increasing : ∀ k, coronalTime k < coronalTime (k + 1)
  adjacent_ratio_eq_phi : ∀ k, coronalTime (k + 1) / coronalTime k = phi

Each field is a universal statement over k : ℕ. The structure is instantiated by the definition coronalLyapunovCert that supplies the four theorems as its fields.

(4) Visible dependencies and certificates

• Depends on coronalTime and referenceTime (both defined in the same module) and on phi from Constants.
• Instantiated by coronalLyapunovCert using the supporting theorems coronalTime_pos, coronalTime_succ_ratio, coronalTime_strictly_increasing and coronal_adjacent_ratio.
• No external axioms or sorry appear in the supplied source for this structure.

(5) What the declaration does not prove

It proves only the listed algebraic properties of the abstract function coronalTime. It does not prove any physical measurement, the existence of the predicted timescales in the solar corona, or the falsifiability criterion stated in the module documentation.