Harrow and Gideon visit the Sixth House quarters, where Palamedes tries to negotiate a wider exchange of Lyctoral keys, notes, and access. Harrow refuses a simple key-for-key swap and argues that the trials point toward a hidden thanergy source somewhere in the inaccessible parts of Canaan House, while Palamedes insists the trials are pieces of a larger theorem about Lyctorhood. Palamedes warns that if Lyctorhood is the synthesis of the individual trials, then the underlying logic contains a serious flaw.

Palamedes offers Harrow all his theorem notes if Harrow helps pick a Lyctoral lock matching the grey Sixth key, which Silas currently holds. On the way, Gideon and Camilla briefly talk as cavaliers; Gideon deduces that Camilla truly fights with two short blades rather than a rapier, and Camilla explains she trained that way because the Sixth chose the most practical weapons for Palamedes long ago.

Behind an old picture, Palamedes reveals a Lyctoral door whose keyhole has been deliberately filled with regenerating ash, the same kind of perpetual bone matter used in an earlier transferral construct. Harrow concludes that whoever blocked the lock had extraordinary necromantic skill. Determined to prove herself capable, Harrow tries to remove it, but the material repeatedly snaps back into place.

Seeing Harrow struggling and bleeding with effort, Gideon offers herself as a power source. Harrow reluctantly siphons Gideon, causing Gideon intense pain but giving Harrow enough strength to compress and remove the obstruction completely. Palamedes disapproves of Harrow using Gideon that way, then reveals the current key distribution: the Sixth has three, the Ninth has had two but gave one to Dulcinea, the Eighth has three including Dulcinea's stolen keys, and one key remains unaccounted for.

After Palamedes tells Gideon to keep an eye on her, Harrow realizes he likely means Dulcinea. Harrow formally bans Gideon from visiting Dulcinea, arguing that Dulcinea is dangerous and doomed without a cavalier. Gideon refuses, and the argument becomes a vicious reckoning over duty, trust, Jeannemary's death, and the false closeness between Gideon and Harrow. Harrow insists Gideon is unnecessary to Lyctorhood and insults Dulcinea, and Gideon asks to be released to the Seventh House; when Harrow refuses, Gideon decides on betrayal.