(a) All algorithms are universal and valid, regardless of whether they are executed.
(b) Cognition is a sub algorithm whose behavior is to perceive properties of the parent algorithm describing it.
(c) Any algorithm giving rise to cognitive entities will be perceived as reality by the entities described.
About this Note Edit
This is a purple note, written in English by Athetos or an Athetos Variant. This is the only Note that triggers a cutscene when you pick it up. This Note may have some relation to the Rusalka Veruska's ability to manipulate the mind and create dream world algorithms.
Although Trace's paper proposed what was allegedly a new theory, the first line A can essentially be seen as just a sort of watered down Platonistic stance towards "algorithms" (which appears to refer to base natural laws and all they entail, etc) in the sense that algorithms retain the validity of their structure in all potential circumstances, even if algorithms are merely abstract rather than actually present. However, one can notice that in computer science, the term universal can also be used to refer to "Turing completeness", a property of computing systems/algorithms that is considered the ceiling of what is computationally possible within our universe. An algorithm that is universal can be used to compute any other function that is computable. So with line B it could be argued that more than Platonistic idealism, this could also be a positivistic stance by Trace, suggesting that all universes work the same, on some computational fabric, and are basically algorithms built-up of sub-algorithms, and each can be considered its own subuniverse, whether that universe be real (executed) or virtual (conceivable but not executed).
No mention of the existential "properties" of the "algorithms" is given, however, line B could suggest that they are taken to simply precede such concepts and aren't measured out to be real or nonreal. Line B could alternatively suggest a point of view akin to the Yoneda perspective in category theory, where mathematical objects are not defined by their properties, but by their relationship to one another - same with interactions between components in the universe, these components being described by the catch-all term "algorithm". In this context, line B is probably a reference to Douglas Hofstadter's Gödel, Escher, Bach, the main thesis of which is that self-reference in computational/formal systems is the cause of some of the most meaningful and intractable behavior in said system. Hofstadter makes this same parallel between self-reference in logic allowing to alter the semantics of a formal system (as seen in his interpretation of the proof of Gödel's Incompleteness Theorems), and self-reference in cognition being a way to alter the semantics of our own formal system, the mind (we are technically matter in this universe becoming aware that is it matter in this universe to better influence the flow of this parcel of the universe...).
Line C is a statement about how one can come up with a common definition of "reality" in a world where every consciousness is an isolated solipsist silo: what one calls their "reality" is necessarily the computational structure/mathematical space upon which their own "consciousness algorithm" can run. Note that the word "perceived" should be read more like "detected/understood" rather than the word "believed," and that the sentence as a whole is more or less providing a relativistic sort of definition for reality rather than asserting anything in particular as real or nonreal.
This is Note 18.
The Note can be found in the middle of Edin, in the tall room to the left of the large Rusalki room where you get the Address Bomb. The player can use the Address Disruptor on a Giant Greenworm in the room to get them to break open a wall so that the Note can be collected, or just use the Laser Drill to destroy the blocks.