The title refers to Labyrinths of the Mind, a book written by Dr Marina Derex, a Betazoid and one of the group that hid the Progenitor technology 800 years prior. A labyrinth is also a term for a maze, the original designed by the inventor Daedelus of Greek myth to house the Minotaur.
As mentioned in DIS: “Erigah”, L’ak was the Scion, a direct descendant of the Breen emperor, and held the genetic code of the Yod-Thot, “they who rule”, without whom his uncle, Primarch Ruhn, could not claim the throne. In DIS: “Jinaal”, Stamets discovered the the Progenitor techonlogy could potentially bring someone back to life.
Discovery jumps to just outside the Badlands, first appearing in DS9: “The Maquis” as an area of violent plasma storms in proximity to Bajor and Cardassia.
The shape of Hy’Rell’s head bumps resemble those of Xindi-Primates, first appearing in ENT: “The Xindi”, one of six intelligent Xindi species that were native to Xindus. The other possibility, taking into account her long white hair and blue eyes, is that she’s an Efrosian (ST VI).
Cerenkov radiation is created when particles exceed the speed of light in a given medium, creating a shockwave with a characteristic blue glow. In real life, it is most often seen around nuclear reactors submerged in water (the speed of light in water is 75% of that in vacuum, allowing emissions from the reactor to exceed that).
Discovery was given the ability to cloak when it was refitted (DIS: “That Hope is You, Part 2”). During the 24th Century, the Treaty of Algeron forbade the Federation from using or developing cloaking devices (TNG: "The Pegasus"), with a notable exception being the Defiant during the Dominion War (DS9: “The Search”). Apparently that prohibition no longer applies in the 32nd Century. Cerenkovn, Book’s world, was destroyed in DIS: “Kobayashi Maru”, making him one of the last of his species.
The scenes in the Eternal Archive were filmed at the Thomas Fisher Rare Book Library in Toronto, Canada.
An oubliette is a specific type of dungeon, of which the only access is a trap door installed in the ceiling of the dungeon, and usually extremely narrow, such that the prisoner was unable to sit down.
The Tuli tree was native to Kwejian and had a distinctive smell to its sap. The decor of Book’s ship was made to simulate Tuli wood (DIS: “Stormy Weather”). Inside the box are cuttings from the World Root, a tree root system that reached all the way around the planet (DIS: “Kobayashi Maru”) and was sacred to the Kwejian.
Culber identifies the device affecting Burnham as a nucleonic emitter. Nucleonic particles appear in a number of places in Star Trek lore, but most appropriately in TNG: “The Inner Light”, where a nucleonic beam from a Kataan probe was responsible for sending Picard into a mindscape where he lived out a simulated lifetime in a similar manner to what Burnham is experiencing. In that episode, an attempt to disrupt the beam nearly killed Picard, which is the risk Culber is alluding to.
The old school card index drawers Burnham looks at makes me nostalgic for the days when I was a student librarian (yes, I’m old). The mindscape Archives’ category number for history is 002818/5 - in our Dewey Decimal System, history (and geography) is 900.
Book says “Those who learn history aren’t doomed to repeat it.” The usual phrasing of that adage is “Those who do not learn from history are doomed to repeat it.” The philosopher George Satayana is credited with the original “Those who cannot remember the past are condemned to repeat it.”
Burnham refers to the itronok, a predatory species they encounted on Trill while searching for the clue there (DIS: “Jinaal”).
Trémaux’s algorithm is a maze-solving method devised by Charles Pierre Trémaux, which involves drawing lines on the floor marking a path. A version of it - called a depth first search - is used to search tree or graph data structures.
Derex’s reading list references Talaxians, Neelix’s species from VOY and Hupyrians, the species of the Ferengi Grand Nagus’ servants (DS9: “The Nagus”, et al.). Euclid was a Greek mathematician who devised an axiomatic system for geometry.
Rhys intends to use the plasma storms for cover, which is exactly what made the Badlands effective as a hiding place for the Bajoran Resistance and the Maquis back in their day.
Matching weapons to shield frequencies to get past them is a tried and true method, demonstrated most dramatically when the Enterprise-D was destroyed in ST: Generations. Duodeca is a base-20 system.
Hysperia is a planet where the inhabitants have a culture based on a medieval fantasy motif (LD: “Where Pleasant Fountains Lie”). In the 24th Century, Chief Engineer Billups of the USS Cerritos was a native of Hysperia and the ostensible Crown Prince, although he abdicated that position.
Commander Jemison shares a last name with former astronaut Mae Jemison, the first African-American woman in space, who appeared in TNG: “Second Chances” as LT jg Palmer.
A tergun is a sacred Breen oath. Ruhn’s remark that the Federation to save the few would risk the many is reminiscent of Kirk’s inversion in ST III of Spock’s adage about the needs of the many and the few from ST II: “The needs of the one outweighed the needs of the many.”
“Never turn your back on a Breen” is a Romulan saying (DS9: “By Inferno’s Light”), cited by Rayner in DIS: “Erigah”.