Horns are hard things that sit at the top. Nine at the Top, with firmness, occupies the utmost point of the Gua; hence the horn is taken as its image. As a yang line dwelling at the top, it is the peak of rigidity; at the top of Progress, it is the peak of advancement.
When firmness reaches its extreme, there is the fault of fierce violent force; when advancement reaches its extreme, there is the error of rash haste. To reach the extreme of advancement through firmness is to stray exceedingly from the mean.
It cannot be employed for anything, but only for chastising one's own city; then, though it brings peril, there is good fortune and no fault. Chastising the four quarters means governing the exterior; chastising one's own dwelling city means governing the interior.
Speaking of chastising one's city refers to internal self-regulation. In man's self-regulation, the more extreme the firmness, the more steadfastly the Way is guarded; the more extreme the advance, the swifter the turning toward goodness.
For one like Nine at the Top, using this for self-regulation, though marred by severity, brings good fortune and no fault. Stern severity is not the path of peaceful harmony, yet in self-discipline it yields merit.
It further states "perseverance brings regret" to exhaust its meaning: culminating in rigid advance, though successful in self-governance, it lacks the virtue of central harmony; hence regarding the path of upright perseverance, it is cause for regret.
Not losing central correctness constitutes true perseverance.