"To my beloved son
As you are probably aware, one with an ingenious
mind such as my own would doubtlessly be able to
untie even the most intricately knit strings of history.
And this would signify the new fall and rise of humanity...
Have you ever pondered the very definition of history, Takuya?
I once thought history to be an account of changes from
the past to the future... Which, in other words, would be a record
of both the transitions and the progressive development human society
has undergone. Yes... my old self would probably respond in this
fashion. History is all about written records... and we, the historians,
who believed this, devoted our days to studying it. Those days were
squandered with research. Let us entertain another idea. What if
there were multiple paths in which the past could form the present.
What could be called history in that case... would it be the records of
mankind's transitional phases. No. As that would it naight but a record
of the events that ocurred at some point in time. That's not history.

You must realize that the passage of time exists not as an irreversible,
but reversible concept. But wouldn't that imply that it's possible to recreate
history...? That's not quite right. History is an irreversible concept. Know
the thin line. After having come to understand that difference, I have decided
on heading to a certain place. One cannot repeat history, yet the passage
of time itself is reversible. By the time you read this letter, it is likely that
I have already concealed myself from you. But this serves not as an indication
of my death. There should be two objects before you. The first is a mirror,
and the second is a device to be used to a certain end. The mirror is a memento
of your mother. Consequently, this strong connection to your real mother will
become the trigger to tightly bind you to that place. And then there's the device...
The instructions are contained within the documents in the second drawer down
from the top. That stand-alone has but enough energy to reverse time within an interval
of a few dozen hours at best... The real system is elsewhere. Make sure that the eight Jewels
are inserted within...And head out to Sword Cape tonight at ten o'clock sharp. A certain
person should be awaiting your arrival. You may hand over the device to that person.
Everything will be revealed to you there.

Don't say a single word about this to Ayumi.
You must come alone. She must not know of this... I'm not at liberty to speak on it at
the moment. But one way or the other, I'll end up explaining things to her eventually.
Think of it as my way of showing integrity. Take heed of this fact:
there is no meaning if all eight Jewels aren't fitted into it. If they are not assembled..."

?◆◆ Reflector User's Manual ◆◆

?［How to use the Jewels?］

A "Jewel" is a device that retains the present time and space. It reacts upon the touch of the hand, and is then temporarily annihilated from the Reflector. A Jewel, once used, will remain in the same world and at the same place, until the player returns there once again. A save state made by using a Jewel will henceforth be called a "Jewel-save." After making a Jewel-save, it is possible to load that state from the map."

Locations where Jewel-saves have been made are denoted by feather marks on the map. By clicking these icons from the map, it is possible to transport to those places instantaneously. Furthermore, the items and number of Jewels you hold will be retained when transporting to places where you made Jewel-saves.

?［How to use the map?］

By touching the gem in the lower center of the Reflector, the parallel world map will be displayed. Time is denoted by the horizontal axis on the map. The map displays roughly 50 hours' worth of worlds. Worlds you have visited before will be detailed on this map. When a new divergence is found, a sound effect will be played, and the path you have walked will be drawn on the interface. The white, blinking circle denotes your current position. The sparkling, star-shaped marks denote places where undiscovered Jewels reside. If you can reach a star-shaped mark, it means there will be a Jewel located in some place within that time. Investigate carefully, and you will surely be able to find them.

［Reflector applications?］

The gem at the bottom center of the Reflector will start blinking on occasion. This means that a divergence of worlds is imminent. It is the only way to figure out the timing of divergences, which are hard to see on the map." By paying attention to this, it is possible to predict divergences, and search out the various parallel worlds efficiently

Excerpts from Imagawa Yurika's "An Inquiry into the Fundamental Composition of the Universe"

First of all, I would like to refer to the intrinsic energy entities that exist as carriers for causal flows that are both parallel and infinite as [events], each respective history of these events as [worlds], and string these together under the umbrella term [parallel worlds]."

It is to be assumed that we are living in one of such parallel worlds.

［Reflector operating principles?］

In order to explain the operation of the Reflector, I must hypothesize the existence of certain particles, which I shall henceforth name [event elements]. So, what exactly are these [event elements]? I define these as particles that course through imaginary space, specifically anti-photons that correspond to the photons that exist in the real space we live in. These event elements are constantly emitted from the Reflector, and radiate according to the intrinsic event spectrum of target events. Due to resonance in the event spectrum, excited event element reflect waves are sent back to the Reflector."

Interference between the transmission wave from the Reflector and reflect waves from target events subsequently causes nodes and antinodes to form along the event element waves, or [event density waves]."

Nodes → Points where event density is lowest"
     i.e., "unlikely worlds."

Antinodes → Points where event density is highest"
     i.e., "highly likely worlds."

By manipulating event density wave interference to set nodes to present event (present world) conditions, and antinodes to target event (the neighboring parallel world) conditions, a "causal flow" that facilitates present event ?¨ target event migration will take shape in event space.

Following the formation of this event density-rooted unstable system, causal energy is steered toward the target event. By arousing an artificial Event Collision through these means, a present event ?¨ target event [event snap-through buckling] which takes advantage of the instability of the system is spawned, and instant migration along this path, i.e. a transfer to a different parallel world, is made possible. I shall proceed to increase the credibility of this theory by providing a more rigorous definition of "event density."

［Definition of event density［

Sensors inside the Reflector device radiate particles, called "event elements," at velocity V, and measure the rebound velocity v following collision with the target object.

1/2m(V-v)^2 (m = event equivalent mass)

With the above formula, the sensors measure the causal energy absorption of the target, and determine a [causal energy absorption function]. This function is expressed in terms of target event density and physicality of event elements.

In addition, the [causal energy absorption function] is variable with regards to time t. It is resolved according to event spectrum transformations. I theorize the spectrum value corresponding to the event chosen as target event (i.e. the wave frequency of something happening) to be the desired [event density].

However, since actual parallel worlds hold vast amounts of "possibility," the measured event spectrum values are compared one by one to the present event (reality), and each time, the event density is corrected and updated. The Reflector proceeds to select event densities of target events in accordance to Darwin's natural selection principle. There are, however, limitations to the operation of the Reflector. It is not possible to freely move to any world. In case the event density ?I of a world is exceedingly high, it becomes unavoidable after having moved into its limit radius (1/?I).

I shall denote this limit radius as the [event Schwarzschild radius], and this condition of inevitability, [fate].

［Theory of the constitution of the universe［

Theorizing about the constitution of parallel worlds is no simple feat.

Up until now, I have devised six theories: The [Simple Parallel Model], the [Series-parallel Model], the [Pyramid Model], the [Klein Bottle Model], the [Distributed Network Model], and the [ES Model]. In this document, I shall refer to the most credible theory, the pyramid model, in order to reinforce the veracity of the Reflector hypothesis.

The pyramid system enables us to define three worlds that immediately neighbor the present world.

The first is the "original world that conceived the present world."
The second is the "parallel world with an equivalent existence potential to the present world.""
And lastly, the "subordinate world formed due to division of existence potential (division of fate) in the present world (this present world then becomes its original world).
These three.

The worlds derived and formed as a consequence of actions conducted in the present world are all classified as subordinate worlds, and worlds generally known as "parallel worlds" denote those subordinate worlds identified as running parallel to the present world.A transfer between subordinate worlds follows in accordance to the [Infinitely Fixed Room Number] concept of the [Simple Parallel] model described in "Legacy," but a transfer from within a subordinate world that extends to affect the present (that is, a transfer from the subordinate world to the present world by ascending through layers) requires one order more energy than a descent through the layers. [Infinitely Fixed Room Number]: preservation of energy of sorts. For every world that disappears, a new one is created.

Retracing events requires an immense amount of energy.

(1) Transfer to a higher stratum:
A transfer from a subordinate world (layer i+1) to the present world (layer i) means one will "disappear from the subordinate worlds," i.e. "the subordinate worlds of which one was a part of will vanish." Hence, such a transfer would require the creation energy of all subordinate worlds in layer i+1."

(2) Transfer to a lower stratum:
This is equivalent to "creating a new subordinate world from the present world." A transfer requires the creation energy of one subordinate world." It is possible to apply the expanded Einstein formula (E = mc^2) to the creation/annihilation energy E, leading to the following form:

E = ΣM(ρ,φ,H,t){C(ρ,φ)}^2"

M: total dimensional equivalent mass"
ρ: event density (probability density of an event happening in the present world)"
φ: total event potential"
H: total conserved space within a dimension"
t: total conserved time within a dimension"
C: total event element velocity"

Furthermore, it is possible to apply the creation/annihilation energy E to a system comprised solely of a present world. In this case, under the assumption that event density and event potential are constant throughout, then:

? ＿　＿
C(ρ，φ) = c (speed of light)
＿　＿
M(ρ，φ，H，t) = m (object mass)

From this, E = mc^2 holds. The fact that the speed of light cannot be surpassed is the most fundamental causal law of the present world.

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To read the rest of Imagawa's synthesis, you can download the 25 page paper in PDF form, translated by Phar of the YU-NO team. It was originally published with the guide book.

An Inquiry into the Fundamental Composition of the Universe PDF