The sun and moon are seen to rise up from the earth at the horizon and if the celestial bodies can rise from the earth at the horizon then the spiritual body may also have been thought to have ascended at the horizon, or simply ascended.
In my opinion the pyramid may be regarded as the place for the ascension of the soul which was not literally at the horizon, but as a metaphor of the horizon.
As such Akhet Khufu might then be translated as ''Portal of Khufu'' rather than the ''Horizon of Khufu'' meaning Khufu's grand gateway to the celestial realm.
If Akhet of Khufu was understood as the pyramid of Khufu then perhaps the term Akhet provides us with an insight into the essence or function of the nature of a pyramid from Khufu's special point of view.
In my opinion Akhet Khufu was a model of the sun, with ascension of the king's soul seen as as after the manner of the ascension of the sun from a primordial mound of earth at the first dawn of creation, as re-enacted at the dawn of each new day on the horizon.
Khufu's ascension was envisaged as from the pyramid, so in a sense the pyramid was the horizon. Akhet may not have been the original name, but may have been the most appropriate name reflecting Khufu's view of his own pyramid.
If so then this name may be regarded as valid if the legend in the Westcar Papyrus was a parable of what the pyramid meant to Khufu. ie Khufu would have approved the name even if it was not actually the name he had given it.
I think Khufu's sarcophagus was a model of sphere with a diameter equal to the height of the pyramid because 112 x diameter of a sphere equal to the internal volume of the open sarcophagus is equal to he height of the pyramid, and the internal diagonal of the sarcophagus is 112 digits. The virtual sphere may be envisaged as two circles in the planes of the north-south and east-west axes of the pyramid with the circles equal to the triangular cross-section of the pyramid.
The sealed sarcophagus is a scale model of the same sphere assuming a lid fitted the rebate flush with the top. ie two models of the same sphere which is unlikely to be a coincidence.
The secret of the moon was keeping time with 309 lunar months in 25 calendar years of 365 days.
Mark