Explanation of coronalTime_strictly_increasing

(1) Plain English

The theorem states that the coronal timescale at any rung k is strictly less than the timescale at rung k+1. The sequence of timescales on the phi-ladder is strictly increasing.

(2) Importance in Recognition Science

Recognition Science models solar-coronal magnetic evolution on a phi-ladder of characteristic times. Strict increase ensures each higher rung corresponds to a longer physical process, supporting the predicted hierarchy from Alfvén crossings (rung 0) to active-region emergence (higher rungs). This is part of the broader phi-ladder structure across astrophysical timescales.

(3) Reading the Formal Statement

 theorem coronalTime_strictly_increasing (k : ℕ) :
     coronalTime k < coronalTime (k + 1) := by
   rw [coronalTime_succ_ratio]
   have hk : 0 < coronalTime k := coronalTime_pos k
   have hphi_gt_one : (1 : ℝ) < phi := by
     have := Constants.phi_gt_onePointFive; linarith
   have : coronalTime k * 1 < coronalTime k * phi :=
     mul_lt_mul_of_pos_left hphi_gt_one hk
   simpa using this

It takes a natural number k, rewrites the successor case, invokes positivity of the current term, uses phi > 1.5 to obtain phi > 1, applies the left-multiplication inequality, and simplifies.

(4) Visible Dependencies and Certificates

The proof depends on coronalTime_succ_ratio and coronalTime_pos. The module exports the bundled certificate coronalLyapunovCert whose strictly_increasing field is exactly this theorem. The module states zero sorry and zero axioms.

(5) What It Does Not Prove

It does not prove the physical identification of specific rungs with observed solar events, the falsifier (adjacent ratios outside (1.5, 1.8) on ≥3 active regions), or any empirical calibration to SI units. Those appear only in the module docstring.