The claim that the three Giza pyramids were laid out as a mirror of Orion's belt, around 10,450 BC.
Documented
The geometry is measurable and disputed
In The Orion Mystery (1994), Bauval and Gilbert showed that the Giza layout matches Orion's belt with an offset third star, and that the Great Pyramid's southern shafts pointed, in the Old Kingdom, toward Orion and Sirius, stars tied to Osiris and Isis in the Pyramid Texts. The precession argument backdates the ground plan to 10,450 BC, when the match was exact.
Assessment: The shaft alignments are accepted as intentional by many Egyptologists. The belt correlation and the 10,450 BC date are not: critics note the match is approximate, that pyramid sizes are driven by construction sequence, and that the builders left inscriptions dating themselves to Khufu and Khafre. A rare fringe claim with measurable content, which is why it is still argued rather than dismissed.
Interesting claims
Giza is a clock set to the First Time
The full thesis: the pyramids memorialize Zep Tepi, the First Time, when the gods walked Egypt, and the entire necropolis is a terrestrial map of the sky as it looked in 10,450 BC, the age of Leo, the sphinx's true face. Bauval and Hancock's Keeper of Genesis made this the cornerstone of the lost-civilization case.
Assessment: The sphinx water-erosion argument, its geological partner, has serious dissenters and serious rebuttals in equal measure. What keeps this on the Interesting shelf rather than the folklore shelf: the claims are checkable with a protractor and a planetarium, and a few of the checks have come back uncomfortably close.
Stories
Osiris in the sky
The Egyptians' own story: Orion was Sah, the soul of Osiris, and Sirius was Isis, and the king's spirit rose to join them among the imperishable stars. The Pyramid Texts say it plainly. The sky-map theory begins where the actual mythology already put its dead.
Assessment: Documented theology, and the honest foundation under all the speculation. The Egyptians really did believe the pharaoh's soul traveled to Orion. Whether they also surveyed the pyramids to match is the fight.
Sources and further reading
Robert Bauval & Adrian Gilbert, The Orion Mystery, 1994
Rudolf Gantenbrink's Upuaut shaft survey, Deutsches Archäologisches Institut, 1993
Ed Krupp's critique, Griffith Observer, 1997
Worth asking
Egyptologists date Giza to 2500 BC by quarry marks naming the pharaohs. Bauval dates the design to 10,450 BC by precession. Which clock do you trust, the one in the stone or the one in the sky?