The researchers on the receiving end quickly grasp the message.
Cryptography Lead: "The first circle"? That's what the incantation says?
He suddenly remembers a detail that has eluded him all along.
Cryptography Lead: That's it! The investigator in Vienna reported a similar thing! "An ancient miracle, a circle of salvation."
Cryptography Lead: Arcana even drew a circle in the air while saying it. She did it so nonchalantly, as if it were a meaningless gesture.
Cryptography Lead: We didn't think much of it at the time. Once we confirmed that it did not affect the casting of the incantation, we forgot about it and moved on.
Cryptography Lead: I can't believe I overlooked it!
The hot-tempered cryptography lead slams the table and buries his face into his hands, clearly exasperated.
Lucy: This is not your fault, Ulrich.
Lucy: The gesture was overlooked because it did not really help the research. Our focus was on practical application rather than understanding the incantation itself.
Lucy: If the incantation means "the first circle" ...
The pragmatist's voice is still serene.
Lucy: How will this be helpful to the research?
37: I see! I understand now!
A moment of epiphany.
She snatches a handful of papers, sprawls out on the floor, and scribbles frantically.
Regulus: Well, Vertin, I don't know why you can read it, but I do know that gal is thrilled by your interpretation.
Regulus: Because you mentioned her favorite shape, the circle.
The irrational number is spot on. 37 has drifted into a world of her own.
37: Yes, yes! The essence of the incantation is a circle!
37: But what kind of circle is it? In topology, any closed curve on a plane can be classified as a circle.
Regulus: Aha. Told you!
Regulus spreads her hands, speechless. She takes a step back, giving 37 more room to calculate.
Everyone is talking quietly so as not to disturb her, even Ms. Radio has lowered her volume.
Just as her sheets are about to engulf the entire floor, she finally stands up.
37: Look, Vertin, let's go back to the Rosetta Stone hypothesis.
37: Based on the hypothesis, if the incantation and the numerical code share a common essence, which is the key to the "Storm" immunity,
37: and we now know the incantation refers to a circle ...
Vertin: Then, the essence of this numerical code should also be a "circle," right?
37 nods.
37: Yes. Before this conversation, I had no idea which direction to take. The numerical code could be a snippet of an incantation, or it could be a geometrical ritual array.
37: I had a lot of theories to go on, but testing them could take weeks or even months. Worse yet, if my line of thinking was completely wrong, we could waste decades of time and effort.
37: But the Rosetta Stone hypothesis is easy to verify!
37: Let us suppose that the incantation and numerical code share a similar essence.
37: We know that the incantation does work, as proven by the Awakened.
37: If the incantation is a circle, then the numerical code should also be circular in nature, and has the same effect as the incantation,
37: which is, a circle that saves people from the "Emanation," and can also be experimented with by the Awakened.
Vertin: If the experiment works, then the hypothesis is true. And vice versa.
Vertin: I see what you mean here. It really is an easily provable hypothesis.
Regulus: To my ears, you're just trying to prove that the code means a circle, because you're really into circles!
37: Umm, not specifically. I simply like it because it's a great shape.
Sonetto: But, I don't understand.
She picks up the numerical code and studies it carefully.
Sonetto: +1, -1, +2, -3, 3, -3, +2, -1, +1 …
Sonetto: How do these numbers relate to the "circle"?
Enigma: "The first circle"?
Enigma narrows his brows, spinning a pen between his fingers.
His drafts are scattered across his desk, each of them a dead end.
Cryptographer V: Yes, it was the Timekeeper who translated the incantation.
Cryptographer V: And according to the investigator in Vienna, Arcana also drew a circle when she cast the ritual.
Cryptographer V: But experiments have shown that the gesture has no effect on the ritual. We thought, maybe it was a symbolic gesture.
Enigma: No no no! It is no way just symbolic!
He jumps to his feet. The cryptographer sneezes at the cloud of dust he just stirred up.
Enigma: Arcanists excel at condensing their experiences into symbolic representations.
Enigma: Signs, totems, elements, these are primitive symbols, and some are sources of power for arcanum. At least that's what the Foundation's textbooks tell me!
Enigma: That's why arcane skills can only be enhanced by mediums that align with their symbolic nature. Precise materials are required when creating soft disks for each incantation.
He stops spinning his pen.
Enigma: If the incantation symbolizes "the first circle,"
Enigma: and if we were to create a physical form that could be mass-produced for everyone,
Enigma: will that form have to be a circle, too?
In the cave, discussions and theories about the circle are also in full swing.
Every inch of the floor is now covered with paper.
On each sheet is a differently drawn circle. Some are spheres, some have crossings, some are in distorted forms ...
Just as the sea of papers is about to drown everyone in the room, she finally stands up.
37: Oh! I should have thought of this!
37: The simplest things often hold the deepest meaning, as always. So, "the first circle" ...
37: What could it be? A wheel? A piece of rope? A pendulum?
37 shakes her head and kicks away some paper balls at her feet.
37: I spent too long on the wheel and the bearing, not realizing there was something more promising: a circle can also be seen as a knot with no crossings—an unknot.
37: This could be a variation of a closed curve, a knot. Knots were how the ancients of the Incas and Chinese collected data and kept records.
37: But which knot is it exactly?
37 extends her hand, intricate geometric shapes take form in the radiance of her arcane light.
37: The Jones polynomial of the trefoil knot is t+t3-t4.
37: The figure-eight knot is t-2-t-1+1-t+t2 …
37: While the Cinquefoil knot, t2+t4-t5+t6-t7 …
37: I could go on all day. There are 165 different knots with 10 crossings, 9988 knots with 13 crossings ...
37: But which knot is the code referring to?
37: +1-1+2-3+3-3+2-1+1 …
She stops.
37: Of course. Of course, I would hear these digits instead of anything else.
37: The scroll transcribes the Truth into a format I can understand, so it must be based on a mathematical system I already know.
37: I have all the knowledge needed to break the code, just need to follow my instincts and pick a system.
37: And the Jones polynomial is the first thing I could think of!
Struck by an idea, she drops to her knees and starts calculating again on the floor.
37: Right. The second 3 I heard sounded different from the other 3s. That 3 must be the constant term of the polynomial!
37: Then, if we use this 3 as the origin, like a number axis, the left side is the coefficients for the negative exponents, and the right side is the coefficients for the positive exponents.
37: Eureka! This string of coefficients is the shorthand of a Jones polynomial! If we assign the 8 coefficients to the 8 corresponding exponents in a Jones polynomial, we get its true form: t-4-t-3+2t-2-3t-1+3-3t+2t2-t3+t4 … A knot with 8 crossings!
She looks up, her bright aquamarine eyes shine with delight.
A golden knot projects from her fingertips.
37: See, Vertin, Apeiron did give us the answer.
37: The key we've been looking for, the most profound secret, the language of the divine.
37: No sound or text is needed, just pure structure. The very form of the essence itself.
37: It is a beautiful shape, a simple knot!
Vertin: A knot ...
Vertin: Great. Now there is only one step left: the verification.
She nods and looks at the communicator.
Vertin: Did you hear that, Madam Lucy? Can you help us verify the authenticity of this knot?
After an unsettling silence, Ms. Radio finally remembers that she has turned down the volume.
When she turns it back on, Lucy's voice comes through clearly over the channel.
Lucy: Of course. I have paid close attention to the discussion.
Lucy: This polynomial produces a single, unique knot. We can now tie a knot to test it.
The call goes silent again.
The cave is silent too, as if any noise would alter the outcome. Even Regulus has turned off her personal speakers.
In the quiet hush, Ms. Radio cranks up her volume once more, but all they hear is a sharp hiss of static.
And a soft, strange rustling.
Twenty minutes have passed.
Vertin: Madam Lucy?
The only sound is a constant static, accompanied by a faint, scratchy reverberation.
Vertin: Is the signal dropping?
Vertin: Madam Lucy, can you hear us?
Lucy: ...
Lucy: I ... can ...
The robot utters with effort.
The knot slips from her grip and falls. It has completed its great mission.
Then the robot starts to fall apart and melt.
Before the curse could get to her core, the fire thief flashes a smile.
She needs to ensure the next message is clear on the radio.
Lucy: It ... worked.
