The Initial Conditions (The Abstract)
We have reached t = 10 weeks, 2 days. In most biological systems, ten weeks is enough time for a new habit to become a permanent neural pathway. For Alexandra Fainter, the "William Variable" is no longer an external disturbance; it has become the primary component of her daily function.
I observe her in the faculty lounge - the red pen moves, but the "Glowing" state suggests an internal thermal energy that exceeds her usual resting state.
The Analytical Body
Axiom 1: On Following Blindly (With Mathematical Precautions)
As they navigate the corridor, they debate the efficiency of the hypotenuse versus the right angle. Alex's willingness to follow him - even when the path is obstructed by the "Vending Machine Variable" - indicates that her Trust Coefficient has reached an all-time high.
Axiom 2: On Predictable Constants
The faculty lounge, with its "Bickering English Teacher" background noise, has become their Steady State. It is a predictable constant in a life once defined by solitary variables. When William whispers for her to close her eyes, he is asking her to shut down her primary data input and rely entirely on the Tactile Connection.
Axiom 3: On Trust and Empty Hallways
As they move through the dark, I record a series of "Small Surrenders":
Theorem: On Statistical Impossibilities
They stop in an empty hallway. To a casual observer, it is a null set (empty). But for the Architect, it is the perfect canvas.
The High-Fidelity Visual Artifact
The Evidence (The Climax)
The "I Love You" exchange is the final Q.E.D. of the fall Fall. Two weeks later, the system exhibits Phase-Locking. In the high-entropy environment of the lounge, they remain "In Phase." A secret gaze passed through the noise of clattering trays and bells. The red pen in Alex's hand is lighter now; her "Overactive Brain" is finally quieted by a Steady Constant.
When they walk to their cars, the intertwining of fingers is a public confirmation - a physical proof that requires no further variables. William's explanation for the hallway is the ultimate architectural truth: Love does not need grand coefficients or elaborate blueprints. It just needs two points in an ordinary space, being extraordinary together.