#### Symbols used in this section

As a general rule the symbol "$\blacktriangleleft$ " will replace the expression $\xleftarrow{Compaction} \dot= \xrightarrow{Elaboration}$ for the purpose of brevity and simplicity in most equations.

#### Transorimultiplicity equations

Transorimultiplicity equations represent the concepts of Transorimultiplicity in symbolic and mathematical formulations.

$1_u1_wBO_a^b \blacktriangleleft Ori_u(O_a,U,E,D,T,S,F) =\!\!B\!\!= Ori_w(O_b,U,E,D,T,S,F)$

This equation states that if two different originals Ou, and Ow,are made or templated from two different originals Oa, and Ob, and every other factor like structure and functioning are the same then they will have identical behavior.

Since $Ori_u(E,D,T) == Ori_w(E,D,T)$ They are made of the same matter in the same place and time they are actually the same body but with two different names. It can be considered as a tautology that an original will have the same behavior as itself. This can be corrected by having them being compared at different times or made of different matter in a different place.

$1_u1_vCO_a^b \blacktriangleleft Ori_u(O_a,U,E,D,T,S,F) =\!\!C\!\!= Ori_w(O_b,U,E,D,T,S,F)$

This equation states that if two different originals are made from two different originals Oa, and Ob, as itotemplates, and every other factor like structure and functioning are the same then they will have identical consciousness.

$1_w1_vXO_a^b \blacktriangleleft Ori_u(O_a,U,E,D,T,S,F) =\!\!X\!\!= Ori_v(O_b,U,E,D,T,S,F)$

This equation states that if two different originals are made from two different originals Oa, and Ob, as itotemplates, and every other factor like structure and functioning are the same then they will have identical ixperiencitness.

$1_u1_wMO_a^b \blacktriangleleft Ori_u(O_a,U,E,D,T,S,F) =\!\!M\!\!= Ori_w(O_b,U,E,D,T,S,F)$

This equation states that if two different originals are made from two different originals Oa, and Ob, as itotemplates, and every other factor like structure and functioning are the same then they will have identical mentality. Mentalilty means both the same consciousness and ixperiencitness.

#### Transoridimatmultiplicity

$1_11_v_B^=O_a^b,E_n^m,D_x^y \xleftarrow{Compaction} \dot= \xrightarrow{Elaboration} Ori_1(O_a,U,E_n,D_x,T,S,F) =\!\!B\!\!= Ori_v(O_b,U,E_m,D_y,T,S,F)$

This equation represents the concept that a specific original that we call number 1 but could be called by any name, will have the identical behavior to that of any other original made of different matter, in a different place, and made from the template of other different originals, at the same time with the same structure and functioning.

$1_11_v_C^=O_a^b,E_n^m,D_x^y \blacktriangleleft Ori_1(O_a,U,E_n,D_x,T,S,F) =\!\!C\!\!= Ori_v(O_b,U,E_m,D_y,T,S,F)$

This equation represents the concept that a specific original that we call number 1 but could be called by any name, will have the identical consciousness to that of any other original made of different matter, in a different place, and made from the template of other different originals, at the same time, with the same structure and functioning.

$1_11_v_X^=O_a^b,E_n^m,D_x^y \blacktriangleleft Ori_1(O_a,U,E_n,D_x,T,S,F) =\!\!X\!\!= Ori_v(O_b,U,E_m,D_y,T,S,F)$

This equation represents the concept that a specific original that we call number 1 but could be called by any name, will have the identical ixperiencitness to that of any other original made of different matter, in a different place, and made from the template of other different originals, at the same time, with the same structure and functioning.

$1_11_v_M^=O_a^b,E_n^m,D_x^y \blacktriangleleft Ori_1(O_a,U,E_n,D_x,T,S,F) =\!\!M\!\!= Ori_v(O_b,U,E_m,D_y,T,S,F)$

This equation states that you the original will be mentally equal to a different original Ori(v) when you are created from or linked to a different original Oa, than the original Ori(v) is.

General case: $1_w1_v_M^=O_a^b,E_n^m,D_x^y \blacktriangleleft Ori_w(O_a,U,E_n,D_x,T,S,F) =\!\!M\!\!= Ori_v(O_b,U,E_m,D_y,T,S,F)$

#### Transoricitodimatmultiplicity Equations

Transoricitodimatmultiplicity Equations are more than the above equations in that they are more than a tautology. They are either true or false based on specific empirical evidence. and or the coherence of scientific evidence as a whole.

Specific case:

$1_14_wMO_a^bE_n^mD_x^y \blacktriangleleft Ori_1(O_a,U,E_n,D_x,T,S,F) =\!\!M\!\!= Cito_w(O_b,U,E_m,D_y,T,S,F)$

This equation states that you Ori(1) will be mentally equal to any other cidentireplica Cito(w), that are templated from different original itobodies, made of different matter, in a different place, and where the other conditions (U,T,S,F) are identical. O(a) and O(b) do not have to be identical to each other. What matters is the resulting structure and functioning in Ori(u) and Cito(w) being identical. The reason this can happen is that there can be errors in the transcription process or modification to it to make the desired changes.

General case:

$1_u4_wMO_a^bE_n^mD_x^y \blacktriangleleft Ori_u(O_a,U,E_n,D_x,T,S,F) =\!\!M\!\!= Ori_w(O_b,U,E_m,D_y,T,S,F)$

This equation states that any original will be mentally equal to any other cidentireplica, that are templated from different original itobodies, made of different matter, in a different place, and where the other conditions (U,T,S,F) are identical. O(a) and O(b) do not have to be identical to each other. What matters is the resulting structure and functioning in Ori(u) and Cito(w) being identical.

#### Citotransoridimatmultiplicity

$4_w4_v_M^=O_a^bE_n^mD_x^y \blacktriangleleft Cito_w(O_a,U,E_n,D_x,T,S,F) =\!\!M\!\!= Cito_v(O_b,U,E_m,D_y,T,S,F)$

In this case Oa does not equal Ob. This means that the originals, that the two different cidentireplicas were made from, are different. They can be different in place or time or materially. Because the functioning and structure is the same the mentality will be the same.

$1_w4_v_M^=O_a^bE_n^m,D_x^y \blacktriangleleft Ori_w(O_a,U,E_n,D_x,T,S,F) =\!\!M\!\!= Cito_v(O_b,U,E_m,D_y,T,S,F)$

In this case Oa does not equal Ob. This means that the original that $Ori_w$ and $Cito_v$ were made from are different. They can be different in place or time or materially. Because the functioning and structure is the same the mentality will be the same. For this to be the case we have to have the situation where:

$1^{=^4}_{wvab}USC \blacktriangleleft Ori_w(U,S,F) == Ori_v(U,S,F) == Ori_a(U,S,F) == Ori_b(U,S,F)$.

#### Synchronization concepts

If something is synchronized it is in the same time frame or happening at the same time. When we talk about bodies, when they are synchronized they will be functioning exactly the same at the same time. Their behavior will be identical at the same time.

If we talk about the mentality of two different bodies then they will have the same mentality at the exact same time. Synchronization occurs when the theocept for time $T$ is identical in each term for each body. Orisynchronization is when there is synchronization between the originals. Oricitosynchronization is the synchronization between the originals and the cidentireplicas.

The symbol $\models$ represents the relational operator of synchronization. It means identically synchronized.

The symbol $\models = \$ represents the relational operator of synchronization and identity together.

Synchronous itobodies will produce identical functioning, structure, behavior, consciousness and ixperiencitness at the same rate and time.

#### Orisynchronization

The symbols $\vDash =$ means total synchronization of all the factors (B,X,C,X,M,T,S,F)

The symbols $\vDash\!\!B\!\!=$ means the total behavior is equal and in starting through ending time synchronization.

The symbols $\vDash\!\!C\!\!=$ means the consciousness is equal and in starting through ending time is in time synchronization.

The symbols $\vDash\!\!X\!\!=$ means the ixperiencitness is equal and in starting through ending time is in time synchronization.

The symbols $\vDash\!\!M\!\!=$ means the consciousness and ixperiencitness or mentality is equal and in starting through ending time is in time synchronization.

The symbols $\nvDash =$ means none of these factors (B,X,C,X,M,T,S,F) are in starting through ending time synchronization

The symbols $\nvDash\!\!B\!\!=$ means the total behavior is equal but not in starting through ending time synchronization.

The symbols $\nvDash\!\!C\!\!=$ means the consciousness is equal but not in starting through ending time synchronization.

The symbols $\nvDash\!\!X\!\!=$ means the ixperiencitness is equal but not in starting through ending time synchronization.

The symbols $\nvDash\!\!M\!\!=$ means the consciousness and ixperiencitness or mentality is equal but not in starting through ending time synchronization.

The equations for Orisynchronization are:

$1_u1_w\overset{\models}{\underset{S}{=}}O_a^bE_n^mD_x^y \blacktriangleleft Ori_u(O_a,U,E_n,D_x,T,S,F) \ \vDash\!\! S\!\!= \ Ori_w(O_b,U,E_m,D_y,T,S,F)$

$1_u1_w\overset{\models}{\underset{F}{=}}O_a^bE_n^mD_x^y \blacktriangleleft Ori_u(O_a,U,E_n,D_x,T,S,F) \ \vDash\!\! F\!\!= \ Ori_w(O_b,U,E_m,D_y,T,S,F)$

$1_u1_w\overset{\models}{\underset{B}{=}}O_a^bE_n^mD_x^y \blacktriangleleft Ori_u(O_a,U,E_n,D_x,T,S,F) \ \vDash\!\! B\!\!= \ Ori_w(O_b,U,E_m,D_y,T,S,F)$

$1_u1_w\overset{\models}{\underset{C}{=}}O_a^bE_n^mD_x^y \blacktriangleleft Ori_u(O_a,U,E_n,D_x,T,S,F) \ \vDash\!\! C\!\!= \ Ori_w(O_b,U,E_m,D_y,T,S,F)$

$1_u1_w\overset{\models}{\underset{X}{=}}O_a^bE_n^mD_x^y \blacktriangleleft Ori_u(O_a,U,E_n,D_x,T,S,F) \ \vDash\!\! X\!\!= \ Ori_w(O_b,U,E_m,D_y,T,S,F)$

ixperiencitly synchronous and ixperiencitly identical

$1_u1_w\overset{\models}{\underset{M}{=}}O_a^bE_n^mD_x^y \blacktriangleleft Ori_u(O_a,U,E_n,D_x,T,S,F) \ \vDash\!\! M\!\!= \ Ori_w(O_b,U,E_m,D_y,T,S,F)$

$1_w1_v\overset{\nvDash}{\underset{S}{=}}O_a^bE_n^mD_x^y \blacktriangleleft Ori_u(O_a,U,E_n,D_x,T_i,S,F) \; \nvDash\!\!S\!\!= \; Ori_w(O_b,U,E_m,D_y,T_j,S,F)$ where $i \neq j$

$1_u1_w\overset{\nvDash}{\underset{F}{=}}O_a^bE_n^mD_x^y \blacktriangleleft Ori_u(O_a,U,E_n,D_x,T_i,S,F) \; \nvDash\!\!F\!\!= \; Ori_w(O_b,U,E_m,D_y,T_j,S,F)$ where $i \neq j$

$1_u1_w\overset{\nvDash}{\underset{B}{=}}O_a^bE_n^mD_x^y \blacktriangleleft Ori_u(O_a,U,E_n,D_x,T_i,S,F) \; \nvDash\!\!B\!\!= \; Ori_w(O_b,U,E_m,D_y,T_j,S,F)$ where $i \neq j$

$1_u1_w\overset{\nvDash}{\underset{C}{=}}O_a^bE_n^mD_x^y \blacktriangleleft Ori_u(O_a,U,E_n,D_x,T_i,S,F) \; \nvDash\!C\!\!= \; Ori_w(O_b,U,E_m,D_y,T_j,S,F)$ where $i \neq j$

$1_u1_w\overset{\nvDash}{\underset{X}{=}}O_a^bE_n^mD_x^y \blacktriangleleft Ori_u(O_a,U,E_n,D_x,T_i,S,F) \; \nvDash\!\!X\!\!= \; Ori_w(O_b,U,E_m,D_y,T_j,S,F)$ where $i \neq j$

$1_u1_w\overset{\nvDash}{\underset{M}{=}}O_a^bE_n^mD_x^y \blacktriangleleft Ori_u(O_a,U,E_n,D_x,T_i,S,F) \; \nvDash\!\!M\!\!= \; Ori_w(O_b,U,E_m,D_y,T_j,S,F)$ where $i \neq j$

$1_w1_v_{\models}^=_F^{\ 2}O_a^bE_n^mD_x^y \blacktriangleleft F(Ori_w(O_a,U,E_n,D_x,T,S,F)) \ \stackrel{\models}{==} \ F(Ori_v(O_b,U,E_m,D_y,T,S,F))$

$1_w1_v_{\models}^=_B^{\ 2}O_a^bE_n^mD_x^y \blacktriangleleft B(Ori_w(O_a,U,E_n,D_x,T,S,F)) \ \stackrel{\models}{==} \ B(Ori_v(O_b,U,E_m,D_y,T,S,F))$

$1_w1_v_{\models}^=_C^{\ 2}O_a^bE_n^mD_x^y \blacktriangleleft C(Ori_w(O_a,U,E_n,D_x,T,S,F)) \ \stackrel{\models}{==} \ C(Ori_v(O_b,U,E_m,D_y,T,S,F))$

$1_w1_v_{\models}^=_X^{\ 2}O_a^bE_n^mD_x^y \blacktriangleleft X(Ori_w(O_a,U,E_n,D_x,T,S,F)) \ \stackrel{\models}{==} \ X(Ori_v(O_b,U,E_m,D_y,T,S,F))$

$1_w1_v_{\models}^=_M^{\ 2}O_a^bE_n^m}D_x^y \blacktriangleleft M(Ori_w(O_a,U,E_n,D_x,T,S,F)) \ \stackrel{\models}{==} \ M(Ori_v(O_b,U,E_m,D_y,T,S,F))$

#### Citosynchronization

$4_w4_v\overset{\models}{\underset{F}{=}}O_a^bE_n^mD_x^y \blacktriangleleft Cito_w(O_a,U,E_n,D_x,T,S,F) \models\!\!F\!\!= Cito_v(O_b,U,E_m,D_y,T,S,F)$

$4_w4_v\overset{\models}{\underset{B}{=}}O_a^bE_n^mD_x^y \blacktriangleleft Cito_w(O_a,U,E_n,D_x,T,S,F) \models\!\!B\!\!= Cito_v(O_b,U,E_m,D_y,T,S,F)$

$4_w4_v\overset{\models}{\underset{C}{=}}O_a^bE_n^mD_x^y \blacktriangleleft Cito_w(O_a,U,E_n,D_x,T,S,F) \models\!\!C\!\!= Cito_v(O_b,U,E_m,D_y,T,S,F)$

$4_w4_v\overset{\models}{\underset{X}{=}}O_a^bE_n^D_x^y \blacktriangleleft Cito_w(O_a,U,E_n,D_x,T,S,F) \models\!\!X\!\!= Cito_v(O_b,U,E_m,D_y,T,S,F)$

$4_w4_v\overset{\models}{\underset{M}{=}}O_a^E_n^D_x^y \blacktriangleleft Cito_w(O_a,U,E_n,D_x,T,S,F) \models\!\!M\!\!= Cito_v(O_b,U,E_m,D_y,T,S,F)$

When two different cidentireplicas are synchronized their functioning, behavior, mentality are identical, and is happening all at the same time.

$4_w.4_v_{\models}^=^2_MO_{a^b}E_{n^m}D_{x^y} \blacktriangleleft M(Cito_w(O_a,U,E_n,D_x,T,S,F)) \ \models}= \ M(Cito_v(O_b,U,E_m,D_y,T,S,F))$

States that the mentality of the cidentireplica(w) is synchronized with the mentality of the cidentireplica(v). This is true because $T_w = T_v, S_w = S_v, F_w = F_v)$. This is stating that the structure and functioning over time is staying the same.

$4_w4_v_{\models}^=^2_FO_a^bE_n^mD_x^y \blacktriangleleft F(Cito_w(O_a,U,E_n,D_x,T,S,F)) \ \stackrel{\models}{==} \ F(Cito_v(O_b,U,E_m,D_y,T,S,F))$

This states that the functioning of the cidentireplica(w) will be in synchronization with the functioning of the cidentireplica(v).

$4_w4_v_{\models}^=^2_BO_a^bE_n^mD_x^y \blacktriangleleft B(Cito_w(O_a,U,E_n,D_x,T,S,F)) \ \stackrel{\models}{==} \ B(Cito_v(O_b,U,E_m,D_y,T,S,F))$

This states that the behavior of the cidentireplica(w) will be in synchronization with the behavior of the cidentireplica (v). All behavior will happen at the same time.

$4_w4_v_{\models}^=O_a^bE_n^mD_x^y \blacktriangleleft Cito_w(O_a,U,E_n,D_x,T,S,F) \ \stackrel{\models}{==} \ Cito_v(O_b,U,E_m,D_y,T,S,F)$

This states that the cidentireplica(w) will be in synchronization with the cidentireplica(v). When T= T All behavior mentality functioning will happen at exactly the same time.

#### Oricitosynchronization

$1.4_v\overset{\models}{\underset{F}{=}}E_n^mD_x^y \blacktriangleleft Ori(O,U,E_n,D_x,T,S,F) \;\;{\models}F\!\!= \;\; Cito_v(O,U,E_m,D_y,T,S,F)$

$1_w4_v\overset{\models}{\underset{B}{=}}O_w^bE_n^mD_x^y \blacktriangleleft Ori_w(O_w,U,E_n,D_x,T,S,F)\;\; {\models}B\!\!= \; Cito_v(O_b,U,E_m,D_y,T,S,F)$

$1_w4_v\overset{\models}{\underset{C}{=}}O_a^aE_n^mD_x^y \blacktriangleleft Ori_w(O_a,U,E_n,D_x,T,S,F)\; {\models}C\!\!= \; Cito_v(O_a,U,E_m,D_y,T,S,F)$

$1_w4_v\overset{\models}{\underset{X}{=}}O_a^bE_n^mD_x^y \blacktriangleleft Ori_w(O_a,U,E_n,D_x,T,S,F)\; {\models}X\!\!=\; Cito_v(O_b,U,E_m,D_y,T,S,F)$

$1_w4_v\overset{\models}{\underset{F}{=}}O_a^bE_n^mD_x^y \blacktriangleleft Ori_w(O_a,U,E_n,D_x,T,S,F) \ =\!\!F^{\models}\!\!\!\!= \ Cito_v(O_b,U,E_m,D_y,T,S,F)$

This equation represent the theocept that an original(w) templated original(a) will be functionally identical and in time synchronization with a cidentireplica(v) templated from a different original(b), if they exist in the same time and have the same structure and functioning.

$1_w4_v\overset{\models}{\underset{B}{=}}O_a^bE_n^mD_x^y \blacktriangleleft Ori_w(O_a,U,E_n,D_x,T,S,F) \ =\!\!B^{\models}\!\!\!\!= \ Cito_v(O_b,U,E_m,D_y,T,S,F)$

$1_w4_v\overset{\models}{\underset{C}{=}}O_a^bE_n^mD_x^y \blacktriangleleft Ori_w(O_a,U,E_n,D_x,T,S,F) \ =\!\!C^{\models}\!\!\!\!= \ Cito_v(O_b,U,E_m,D_y,T,S,F)$

$1_w4_v\overset{\models}{\underset{X}{=}}O_a^bE_n^mD_x^y \blacktriangleleft Ori_w(O_a,U,E_n,D_x,T,S,F) \ =\!\!X^{\models}\!\!\!\!= \ Cito_v(O_b,U,E_m,D_y,T,S,F)$

$1_w4_v\overset{\models}{\underset{M}{=}}O_a^bE_n^mD_x^y \blacktriangleleft Ori_w(O_a,U,E_n,D_x,T,S,F) \ =\!\!M^{\models}\!\!\!\!= \ Cito_v(O_b,U,E_m,D_y,T,S,F)$

$1_w4_v_{\models}^=_M^{\ 2} O_a^bE_n^mD_x^y \blacktriangleleft M(Ori_w(O_a,U,E_n,D_x,T,S,F)) \ \stackrel{\models}{==} \ M(Cito_v(O_b,U,E_m,D_y,T,S,F))$

States that the mentality of the original is synchronized with the mentality of the cidentireplica. This is true because $T= T$. From $Ori_w(T,S,F) == Cito_v(T,S,F)$

Equation $1_w4_v_{\models}^=_F^{\ 2}O_a^bE_n^mD_x^y \blacktriangleleft F(Ori_w(O_a,U,E_n,D_x,T,S,F))\ \stackrel{\models}{==} \ F(Cito_v(O_b,U,E_m,D_y,T,S,F))$

This states that the functioning of any original w will be in synchronization with the functioning of any cidentireplica v. This is true when they are made identically to different originals, different materially, dimensionally, but are identical temporally structurally and functionally.

$1_w4_v_{\models}^=_B^{\ 2}O_a^bE_n^mD_x^y \blacktriangleleft B(Ori_w(O_a,U,E_n,D_x,T,S,F)) \ \stackrel{\models}{==} \ B(Cito_v(O_b,U,E_m,D_y,T,S,F))$

This states that the behavior of the original will be in synchronization with the behavior of the cidentireplica. All behavior will happen at the same time.

$1_w4_v_{\models}^=O_a^bE_n^mD_x^y \blacktriangleleft Ori_w(O_a,U,E_n,D_x,T,S,F) \ \stackrel{\models}{==} \ Cito_v(O_b,U,E_m,D_y,T,S,F)$

This states that he original will be in synchronization with the cidentireplica. When T = T , all behavior, mentality, functioning, will happen at exactly the same time.