what is the secret door theory?
Excellent question! In short, we don't exactly know.
It's mentioned just once in chapter 27 of GtN:
“I don’t know how the hell they did it.” “I do,” said Harrow, “and if my calculations are right I can replicate it. But all this is more than unsustainable, Sextus. The things they’ve shown us would be powerful - would bespeak impossible depth of necromantic ability - if they were replicable. These experiments all demand a continuous flow of thanergy. They’ve hidden that source somewhere in the facility, and that’s the true prize.” “Ah. Your secret door theory. Very Ninth.” She bristled. “It’s a simple understanding of area and space. Including the facility, we’ve got access to maybe thirty percent of this tower. That’s what’s called hard evidence, Warden. Your megatheorem is based on supposition and your so-called ‘instinct.’” “Thanks! Anyway, I don’t like how many of these spells are about sheer control,” said Palamedes. “Don’t be feeble. Necromancy is control.”
Basically, given that context, it seems that Harrow believes there's a massive continuous source of thanergy hidden somewhere, accessible via "secret door". I would imagine that this theory may have sprouted from whatever she deduced from the information she's collected through her time "counting doors" and mapping out the premises.
Any further than that? Entirely speculation at this point.