# Pactum De Singularis Caelum

# Covenant of One Heaven

## Principles

## Article 12 - Existence

Existence is: (1) an observer and (2) a thing observed. The observer observes the object and so validates the existence of the object. The observed object exists so therefore validates the existence of the observer.

If either the observer stops observing, or the observed object ceases to exist, then the very definition of existence also ceases. If the observer chooses not to observe, then even if an observable object exists, its existence is denied by non-observation.

Existence therefore depends upon the existence of both concepts (observer and observed) together in an active relationship.

Dimension is defined as the position observed by the observer, relative to other objects. An object does not exist in dimension unless they have position relative to other things and are observed.

Dimension cannot exist independently without objects.

Therefore to exist in three (3) dimensions, we must have seven (7) objects. The observed object and six (6) objects that give us the observed objects relative position.

In space, all objects have three (3) dimensional relative position. That means that; say for a star, there will be stars above, below, front and back and to the sides of its relative position.

Matter cannot exist without rules. Without rules, there is chaos. With complete chaos there is nothing, no existence.

By the same logic, rules themselves cannot exist in reality without matter to apply them. They have no physical weight nor measure as an independent thing. They are without mass and without matter.

In reality, neither can exist independently of one another, which means existence depends upon something existing outside of reality in order for reality to function.

This is generically called awareness. All awareness is non-locational.

The only example of something being able to exist in theory and in reality at the same time is a dream.

A dream provides a mechanism whereby all objects within the dream are real and all rules apply. At the same time, rules can exist in theory. A dream is also the only example of dimension being created.

The existence and survival of a dream for an extended age depends upon well structured principles of existence. Unless such principles are perfect and perfectly simple, the dream would cease and existence would cease to be.

The most important and simple principles of existence are the twelve (12) laws of creation. Each expresses a unique aspect and requirement in order to fulfill the basis of existence as something (an object):

**1st laws of creation - Goal - "I wish to exist"**

The first expression of Universal creation is free will, also defined as the goal law - “I wish to exist.” The importance of the goal law being the first expression of creation is that it reflects a willful thought as opposed to some mechanistic rule, or chance event.

**2nd law of creation - Logos - "to exist I use common sense"**

The second expression of Universal creation is the use of common sense - or infinite resources of awareness.

These rules of awareness and common sense are known as the EIKOS and LOGOS rules.

**3rd law of creation - Creation "to exist I exist as"**

- To exist, UCA began by conceiving itself in a dream as the smallest theoretical point possible. In this action UCA created the dream, a theoretical object and the potential to exist.
- "I am unique in dimension" is the first point of the Universe.

**4th law of creation - Co-dependence - "For I to exist, you exist"**

- A single point of UCA does not guarantee existence in dimension, therefore existence. To have dimension, an object must have a relative position with at least six points around it in three (3) dimensional space.

**5th law of creation - Specialization - "for I to exist, you exist as"**

In the process of ensuring dimension and existence, points of UCA specialize into different types - core points, anchor points and outer anchor points.

**6th law of creation - Geometry -"to exist, I use geometric principles"**

- To exist, something must have shape and occupy space. Both concepts have strong ties to common sense principles of geometric shape.

**7th law of creation - Awareness of position - "I am aware of my position"**

- While the existence of infinite points of UCA provides a framework to exist in dimension, it also requires active observation or awareness.
- It is not enough for UCA to observe the dream, UCA needs to be able to validate existence by observation within the dream as well.
- This is achieved by the inherent awareness of position in dimension of pure points of UCA being pure awareness.
- By each infinitely small point of UCA being aware of its position in dimension, the requirement for existence to be observed for each and every theoretical object is validated.

**8th law of creation - Immediate near neighbours**

- Points of awareness being pure awareness can interact with points well beyond its immediate position. However, if one (1) point of awareness ceased to exist, dimension would collapse. To reduce this risk, only immediate near neighbours interact in the creation of greater form.

**9th law of creation - Exclusiveness of position**

No two (2) points of UCA, no two (2) objects may occupy the same space.

**10th law of creation - Change of position**

- While each of the previous rules provide an important component towards guaranteeing sustainable existence, there is still the need for points of UCA to actual move. This is the tenth law - everything is in motion.

**11th law of creation - Conservation of effort**

- To achieve the goals of existence with the minimum of complexity.

**12th law of creation - maximum change constant**

The fastest potential rate for a point of UCA is infinity. Yet if a point did travel at such a rate it would cease to have unique location (it would be all at once) and dimension / existence would collapse. My fastest rate is always less than infinity. A point of UCA need only travel at one half (1/2) x infinity to achieve form, leaving less than one half (1/2) x infinity for motion in form.

The laws of LOGOS and existence state:

**Nothing**

- Nothing exists as pure concept.

**Existence**

- Existence is a matter of degree (relative)
- Existence is to exist as a unique object in dimension
- Existence (universe) is a concept of objects (awareness in motion) in motion
- Existence is dependent on rules in motion

**Paradox**

- Nothing is absolute, everything is a matter of degree (relative)
- 0 = 1 = 0
- The sum of the whole is greater than its parts
- Within, the universe reality exists, without, the universe is a dream

**Uniqueness**

- Everything is unique. Everything is Unique Collective Awareness (UCA) in motion.

The laws of NUMERICS and existence state:

**Numbers**

- All numbers are both unique concepts and objects in themselves.
- All numbers are real by virtue of their existence.
- The degree of reality of a number is dependent upon the degree to which the number represents real world objects and / or measurements and relationships of real world objects.
- The set of all numbers may be defined as the UNISET.

**Uniset**

- All numbers may be defined as belonging to a certain set within UNISET.
- All numbers of the UNISET may be defined as existing between the prime numbers of 0 and 1 by some multiplying degree (ratio).
- All numbers may be defined as either perfect (can be expressed as a ratio of itself) or imperfect (cannot be expressed as a ratio of itself).

**Perfect numbers**

- A perfect number is any number that can be expressed as a ratio of itself or other numbers.
- Infinity is a perfect prime number related to itself, 1 and 0.
- All perfect numbers may be defined as either unique, similar or idea (theoretical): Unique – can represent uniquely real objects (e.g. 1, 3,5, 7, 9, 11 etc) Similar - can only represent collective real objects (e.g. 2, 4, 6) Idea - cannot represent real objects (e.g. 2.5)

**Imperfect numbers**

- An imperfect number is any number that cannot be expressed as a ratio of itself.
- ∏ - Pi is an imperfect unique number expressing the level of perfection of geometric configuration of perfect numbers in a circle.
- All imperfect numbers may be defined as either unique, similar or idea (theoretical): Unique – can represent uniquely real ratios (e.g. pi, e) Similar - can only represent collective real ratios (e.g. 180º) Idea - cannot represent real ratios .

**Perfect Unique Number**

- A perfect unique number is a number that can be expressed as a ratio of itself uniquely.
- A perfect unique number is divisible only by itself and 1.
- The simplest perfect unique numbers are 0 and 1.
- The largest perfect unique number is infinity.
- All perfect numbers are a sum of similar numbers ultimately derived from perfect unique numbers.
- Existence tends towards a perfect unique number.
- Perfect unique numbers exist within the UNISET as a perfect pattern of randomness called the Prime (itself an imperfect unique number).
- The Prime may be defined as unique pattern of existence of perfect unique numbers within the UNISET related to a multiple ratio of the simplest synergetic number 6.

**Perfect Similar Number**

- A perfect similar number is a number that can only be expressed as a ratio of itself as a collective of perfect unique numbers.
- All perfect similar number are divisible by itself, perfect unique numbers, perfect similar numbers and 1.
- The simplest perfect similar number is 2
- The largest perfect similar number is infinity.
- All perfect similar numbers may be further defined as either sympathetic or synergetic.
- Synergetic perfect similar numbers are those that are equal to the sum of all their possible divisors except itself. The smallest synergetic numbers are 6, 28, 496 and 8128.
- Sympathetic perfect similar numbers are two (2) numbers where each is the sum of all the possible divisors of the other.
- The smallest sympathetic pairs are (220 - 284), (1184 - 1210), (17,296 - 18,416) and (9,363,584 - 9,437,056)

The laws of UNISET and existence state:

**Paradox of set membership**

- 0 is a member of 1 and itself, 1 is a set and a member of itself

**Sets**

- All numbers are a set of 1
- Infinity is a unique set
- All numbers may be described by the number infinity
- All numbers may be described in sets of degrees of infinity

**Dependency of set existence to set members**

- If one (1) number ceased to exist in the total set of infinity of numbers then the total set would cease to exist

**Set patterns**

- All sets are specialized and unique to some degree
- All sets are co-dependent to some degree
- All sets are similar to some degree and relationships of real world objects.

The laws of GEOLEX and existence state:

**Points**

- A number may be described as point in two (2) or three (3) dimensional space.
- No two (2) points may ever occupy the same position.
- A point is uniquely aware of its position in dimension.
- Points can only interact with immediate neighbour points.

**Construct**

- All relationships between two (2) or more points create geometric patterns in two (2) and three (3) dimensional space called constructs possessing common and unique properties.

**Path**

- A shape made from the analysis of the past, present or future position of points are called paths.
- All paths may be defined by type of motion and themselves have common and unique properties.

**Morphology**

- All geometric constructs change shape to some degree when in motion along a particular path. This change from one (1) shape to another is called a morph track.

**Frame**

- The rate of time measure of change from one (1) place on a path or morph to another is called a frame. A collection of measured time changes is called frameset.

**Model**

- The combination of a construct and a path or morph track to a frameset is called a model. The existence of a construct in relation to a model is called an instance.

**System**

- The combination of more than one (1) model interacting together is called a system having common and unique properties / behaviour.

The laws of SYMERICS and existence state:

**Variable**

- All known types of logos, numerics and Geolex may be represented as unique sets of theoretical symbols representing possible values called variables.
- All variables are specialized and unique to some degree (unique variables).
- All variables are co-dependent to some degree (co-dependent variables).
- All variables are common and interchangeable to some degree (universal variables).

**Formula**

- All geometric models, systems and number patterns may be expressed as formulas of variables.
- All variables contained within a formula must be defined by their type (unique, co-dependent or universal) and type.
- For a formula to function properly, the correct substitution of variables by type and purpose must take place.

**Formula type**

- The function of a formula (in terms of structure and flow of variables) may be expressed as linear, matrix or multi-dimensional types.
- The utility and scope of a formula to describe theoretical and real is limited by its type (linear, matrix, multi-dimensional).

The laws of AXIOMATICS and existence state:

**Axiom**

- All ideas may be stated as axioms based on functional symeric formulas themselves based on assumptions.
- All axioms may themselves be described as a process of inputs inserted into a function to produce an output.

**Axiom utility**

- The utility of an axiom is relative to the purpose and function it is used.
- An axiom that balances inputs to output according to purpose is in harmony (harmonic axiom).
- An axiom that produces less output to input according to purpose is in decay (dissonant axiom).
- An axiom that produces more output to input according to purpose is in growth (dynamic axiom).

**Axiomatic proof**

- The proof of an axiom is relative to the purpose and function it is used.
- An axiom that adheres to the rules of EIKOS in its construction and use is true and proof itself. An axiom that does not adhere to the rules of EIKOS is false and unprovable.
- Mathematical rules of proof may not be applied as test of axiomatic proof.
- Only true axioms may be used as proof relative to EIKOS and the UCADIAN model of knowledge.

**Complexity and axioms**

- Complex axiom resolve themselves to describe only simple systems.
- Simple axiom resolve themselves to describe both simple and complex systems.

The laws of KINESIS (motion) and existence state:

**Kinesis**

- All objects in motion may be expressed in Kinesis - higher axiomatics
- Simple axiom resolve themselves to describe both simple and complex systems.

**Simple kinetic axioms**

- All objects in motion may be expressed in Kinesis - higher axiomatics
- Simple axiom resolve themselves to describe both simple and complex systems.

**Motion**

- Existence is awareness (UCA) in motion
- Existence is awareness in motion (as form) in motion.
- Existence is specialized motion (structural as form), (harmonic as vibration in form) and velocity (movement in form).
- All motion is relative. The total motion of an object is relative to its type and structural relationships.
- All motion of an object is conserved. An object may not travel faster than its fastest rate.
- All motion is relative.
- All motion is unique.
- All motion is similar in terms of common types of objects and patterns of motion.

**Paradox of motion**

- The sum of the whole motion of a form is greater than the parts that make it.

**Property of motion**

- All objects share the property of motion and share common characteristics inherited from the smallest particles that create the form.

**Kinesis**

- Kinesis is the description and understanding of motion.
- There are only three (3) types of kinesis (motion) kinetic, structural and harmonic. - Kinetic is motion in form expressed as the free velocity of an object; - Structural.kinesis is motion in form expressed as the structural association with other like and larger objects; - Harmonic.kinesis is motion within form expressed as vibration and spin.

**Energis**

- Energis is the measure of aggregated motion of all particles in motion to create mass (accumulative kinesis).
- There are only three (3) types of energis (motion) kinetic, structural and harmonic. - Kinetic is motion in form expressed as the free velocity of an object; - Structural.energis is motion in form expressed as the structural association with other like and larger objects; - Harmonic.energis is motion within form expressed as vibration and spin.

**Mass**

- Mass is equal to the number of benchmark objects by their like accumulative Kinesis (kinetic, structural and harmonic).
- The greater the geometric structural integrity (harmony) of benchmark objects, the greater structural kinesis, the greater the mass, the greater its energis.
- Mass is a measure of the tendency of a body (of objects) to resist changes (dissonance) in its state of kinetic and harmonic motion.
- All individual objects smaller than or equal to up-quarks that are not up-quarks have no measurable mass.
- This boundary exists and is the kinetic-mass boundary.

**Force**

- No independent non-object exists within the universe capable of physically influencing matter. Only matter can influence matter. No forces exist.
- All phenomena observed as the apparent interaction of forces is the exclusive interaction of only matter, its attributes and motion.
- A fortis is an aggregate feature of all structures of matter that has the capacity to produce a change in another structure behaviour, in terms of make-up and rate of motion. A unit of measured fortis is called an ergo.
- All objects of matter possess three (3) fortis in varying degrees of strength derived from each and every Unita possessing self-awareness of form: Creation - all matter wishes to create greater (and therefore more complex) form; Attraction - all matter has relative attractiveness to other forms of matter by virtue of the spin configuration of its smallest pieces of matter, built up to an aggregate spin;
- Repulsion - all matter has relative repulsiveness to other forms of matter by virtue of the spin configuration of its smallest pieces of matter, built up to an aggregate spin;
- Fortis of harmonic attraction
- Matter vibrating in unison, or harmonic ratio, is mutually attracted to forming closer bonds.

**Fortis of dissonant repulsion**

- Matter vibrating in discord is mutually repelled

**Volume**

- Volume is the measure of the perceived amount of space a particular structure takes up.
- Volume is relative as an object may be said to have perceived volume without actually constituting stationary matter in each compartment of its space.
- The measure of volume is always changing as the real and perceived volume of matter and space changes.
- Size is equal to the volume of space taken up by a certain number of benchmark objects, according to their configuration.

**Aggregate motion**

- Matter of like spin create greater forms of matter.
- Groups of like particles in closer form modify their motion to be in relative harmony with other particles. This may be defined as aggregate motion.
- The harmonic pitch of vibration of the form is a multiple of the pitch of vibration of smaller objects within its form.
- So long as the bonds retaining form are greater than the fortis of separation, aggregate motion will adjust and retain unison within the form

**Multi-model motion system**

- No perfect vacuum exists whereby less than three (3) objects are interacting.
- All particles at all levels of matter are influenced in their motion by the unique proximity of similar and different matter.
- All complex models of the effects of particle motion can be defined by three (3) or more object models.

**Density**

- Density is the number of particles (Mass) in a given volume.
- Densis is the number of particles (Mass), their structure and state in a given volume.
- Densis is a superior concept to density as densis enables a greater scope of description of the core attributes of matter than density.
- Particles with the same Mass, but with superior structure tend towards a smaller given volume and therefore densis.
- Particles with the same Mass, but with inferior structure tend towards a greater given volume and therefore lower densis.
- Densis is a measure of kinesis in that the greater the density, the lower the kinetic.energis and the higher the harmonic.energis and structural.energis.

**Kinetic transfer**

- All kinesis (motion) is transferable from one (1) type to another.
- All kinetic transfer is relative to the states of kinesis (harmonic, structural and velocity) of the objects at the time and position.
- All kinetic transfer is resistive to change is dissonant, balanced to change is harmonic and dynamic to change is dynamic.
- The conversion of motion from kinetic.energis to harmonic.energis (frequency/spin) in an isolated system never increases unless external intervention occurs.
- The rate of transfer of kinetic.energis from one (1) object to another is directly proportional to the size of the applying mass and inversely proportional to the reacting mass of the other object.
- In a simple two (2) object model, the relative kinetic result is always balanced as equal and opposite action and reaction.

**Kinetic-Mass Paradox**

- The smaller an object is to a benchmark object (e.g. proton), the greater its overall accumulative kinesis. The smallest of objects (unita) have a accumulative kinesis approaching infinity.
- The larger an object is to a benchmark object (e.g. proton), the greater its overall accumulative kinesis. The largest of objects (sub universes) have an accumulative kinesis approaching infinity.
- This is called the kinetic-mass paradox.

**Kinetic-Energis Mass Limit**

- The maximum potential rate of kinetic.energis of an object (e.g. proton) is limited to the maximum rate of kinetic.energis (velocity) of its relative benchmark object (e.g. photon).

**Kinetic result**

- A relative kinetic.result will always be a relative balance of all energis (motion).
- The degree to which one (1) or more objects affect the kinetic energis of other objects is always relative and is determined by the degree of common characteristics, the structure of each object set and their initial harmonic state.
- Relativity of kinetic.result is such that an input of less kinetic.energis of a particular type of particle will produce a different result to a different type or mix of particles.
- A resistant relative kinetic.result is where the total output of kinetic.energis is less than total input.
- A balanced relative kinetic.result is where the total output of kinetic.energis balances the total input of kinetic.energis
- A dynamic relative kinetic.result is where the total output of kinetic.energis is greater than the total input of kinetic.energis

**Kinetic harmonic ratio**

- The closer objects come in terms of distance, the greater their harmonic kinesis and the slower their velocity.
- The more distant objects separate, the lower their harmonic kinesis and the greater their individual velocity.
- All objects in the universe behave in this same way when interacting with other objects. This is called the Kinetic - Harmonic Ratio.

**Unique harmonic ratio**

- The harmonic motion of an object may be defined as its unique harmonic ratio constructed from the harmonic motion of all its components. This may be expressed as a wave model.
- The harmonic motion (spin / vibration) of all objects of similar structure are the same.
- The harmonic ratio between different types of matter sharing similar characteristics may be defined in ratios, or harmonics.

**Harmonic-volume boundary**

- The smaller the volume of an object to its benchmark object (eg proton), the greater its harmonic kinesis. The smallest of objects (unita) have a harmonic kinesis approaching infinity and infinitely small volume.
- The larger the volume of an object to its benchmark object (eg proton), the greater its overall harmonic kinesis. The largest of objects (sub universes) have a harmonic kinesis approaching infinity and infinitely large volume.
- This is called the harmonic-volume paradox.