The CS (Common-Schema) for any functional entity.

Main conclusions and implications of the Common-Schema

The rigorous application of the Common-Schema leads to a series of conclusions that challenge current paradigms. Each point stated below is demonstrated logically and visually throughout the 15 steps of this document and the entire site.

• A universal blueprint for the functional: The CS is revealed to be the structural blueprint of any functional entity. The more optimized a system is, the more perfectly it adheres to this schema. The CS has two co-existing modes of expression: a sequential mode (process, vertical) and a centered mode (structure, horizontal), and it demonstrates an ability to generate complex and ordered information structures.
• An enantiomorphic cosmology: The Universe is not unitary but enantiomorphic, composed of two entangled chiralities (concrete and abstract). This document maps these two "faces" of the universe, the gear mechanism that links them, and the entanglement path that leads to an "outside" whose existence is logically demonstrated.
• The resolution of the paradox of imperfection: The concept of enantiomorphism resolves the paradox of the "imperfection of nature." Biological structures, like the human body or a tree leaf, are not imperfectly symmetrical; they are perfectly enantiomorphic, a necessary condition for their dynamic functionality.

Each section of this document traces a major advance in the formalization of the CS.

Foundations of the Common-Schema (CS)

The starting postulate is the existence of a "common-schema," a structural and logical pattern underlying any functional system. Without such a universal "binder," the coherence and compatibility observed between distinct entities would be improbable, giving way to generalized chaos. This document presents this schema not as a simple idea, but as an observable and demonstrable model.

The interest of this model may seem abstract, but it is fundamental. For a programmer, knowing the source code of a software allows for complete understanding and mastery. In the same way, the CS acts as the "source code" of functional systems. Once its rules are understood, it unfolds like a language that allows for the decryption of the structure of reality.

Fundamental properties of the Common-Schema

The CS is characterized by several interdependent properties that explain its universal nature:

• A fractal nature: The CS is an infinite fractal structure. What differentiates one entity from another is not a difference in nature, but in context and position within this fractal. It is this geometry that explains the following paradox: the CS can elucidate existential questions with great simplicity, while describing the simplest phenomena with infinite complexity.
• A contextual language: The schema is not made up of fixed "words," but of "families of concepts." These concepts become precise and turn into specific elements ("words") only when a context is defined. The detailed examples in the following sections will illustrate this mechanism.

The consequence of this model is that the fundamental sciences (Mathematics, Biology, Chemistry...) are not called into question, but reorganized. They fit in as master branches within the global fractal structure described by the CS, which thus places itself as a meta-model at the top of the hierarchy.

Step 1: The Emergence of the Pattern via Digital Painting

Decomposition of the creation process

The digital painting process was first broken down into three major successive steps, each itself subdivided into three logical sub-steps.

1. The Drawing (The initial structure)
   1. Composition of subjects (people, objects).
   2. Management of depth (placement in space).
   3. Definition of interactions (links between subjects).
2. The Matter (The treatment of values)
   1. Basic fills (flat gray areas per plane).
   2. Detailing of values (shadows, lights, nuances).
   3. Application of texture effects (unification of the matter).
3. The Color (The final harmonization)
   1. Base colors (one dominant color per subject).
   2. Variance of colors (adding nuances and subtleties).
   3. Application of global effects (light layers, final adjustments).

Analysis: Identification of a recurring pattern

The analysis of this 3x3 structure revealed an unexpected recurrence. The concepts at each level (the first, second, and third of each triad) share a common nature, as shown in the following table:

A tetrahedron from the initial theory.

Conceptual Modeling: The Tetrahedron Metaphor

The initial goal of this decomposition was pragmatic: to find the best possible painting method. To conceptualize this quest, each triad (Drawing, Matter, Color) was modeled as the base of a tetrahedron. The apex of this pyramid, a symbolic point 'o', represented the ideal of perfection for that step. The artist's work then consisted of advancing each component (for example, the "Subjects") along the edge connecting its starting point on the base to the apex 'o', thus approaching mastery.

Illustration of the theory of 4 tetrahedra.

Conclusion: The "Theory of 4 Tetrahedra"

It was this modeling, combined with the observation of the triple analogy (Base, Variance, Coherence) on four occasions, that constituted the first formalization of the Common-Schema. The name "The theory of 4 tetrahedra" therefore stems directly from this conceptual vision.

Step 2: Generalization of the Pattern through Fundamental Archetypes (2012)

The Primordial Cosmological Triad

The analysis revealed a direct resonance between the functional triad of the CS and the way reality is structured from the point of view of a terrestrial observer:

The Double Analogy: Functional and Cosmological

The analysis reveals a double resonance between the functional triad of the CS and the most fundamental archetypes of perception, both in the world of pure concepts (geometry) and in that of lived experience (primordial cosmology).

Synthesis: Towards a Fundamental Terminology

This double correspondence allows the initial triad to be distilled into a more rigorous and universal philosophical terminology, derived directly from these functions.

• The function of Base and Stability is the very essence of the Concrete.
• The function of Variance and Movement is the very essence of the Abstract.
• The function of Coherence and Unification is the very essence of the Transcendent.

Step 3: Overcoming an Apparent Contradiction — The Hypothesis of the Quinary Model

The "Concrete - Abstract - Transcendent" model, to be valid, had to apply to everything. It was therefore immediately confronted with a simple but problematic case: the five fingers of the hand. A quinary system (with 5 terms) seemed to invalidate a ternary model (with 3 terms).

However, an analysis of the properties of each finger revealed an underlying structure that, far from invalidating the model, suggested a possible complexification of it.

Functional analysis of the five fingers

• The Pinky (the "first" finger): The smallest, it represents a base, a starting point. It corresponds to the Concrete pole.
• The Thumb (the "last" finger): Morphologically distinct, its opposability gives it a unifying and functional role (the "pincer grip"). It is essential for the coherence of the hand. It corresponds to the Transcendent pole.
• The Middle, Ring, and Index fingers: These three central fingers must therefore correspond to the Abstract pole. Their analysis revealed an internal sub-structure:
  • The Middle finger: The largest, central. It is associated with the concept of "quantity" and dominance.
  • The Index and Ring fingers: Often of similar size, they act as satellites on either side of the middle finger.

Hypothesis: an internal structure within the Abstract pole

The observation of the fingers led to the hypothesis that the "Abstract" pole was not monolithic, but itself a triad `Air - Fire - Air`, where the central "Fire" would be the dominant element (the middle finger) and "Air" the surrounding element (index and ring fingers).

This idea was reinforced by an analogy with the Taiji Tu (Yin/Yang). This symbol, often associated with the serpent (fire), represents a rotational energy stemming from two polarities (Fire+ and Fire-). This "Fire squared" (Fire²) would be a central energy that would draw the Air into its rotation, thus justifying its double presence.

Step 4: Application of the Quinary Hypothesis to the Five Senses

To test the validity of this new five-term structure, it was applied to another fundamentally human system: the five senses and their associated organs. The following table presents the system of correspondences that results from this.

Morphological analysis of the correspondences

• Touch (Earth): The sense most directly linked to physical and concrete Contact. The hand, thanks to its sensitivity and precision, is its most specialized organ.
• Hearing and Smell (Air): These two senses operate through an aerial medium. Their respective organs present spiral shapes, one external and visible (ear), the other internal (nasal turbinates).
• Sight (Fire²): Vision depends on light (fire). The morphology of the eye presents several analogies:
  • The overall shape of the eye and its immediate surroundings is reminiscent of flames depending on the lighting. (fig.01)
  • The pupil (black circle) within the iris (colored circle) recalls the duality of the Taiji Tu (Fire+ / Fire-). (fig.02)
  • By inverting the colors (white pupil, black iris), the image strongly evokes a sun and its core, reinforcing the analogy with fire². (fig.03)
  • Binocular vision, which allows for the appreciation of distances, could be a manifestation of the dual nature of "Fire²".
  

  fig.01: the overall shape of the eye and its immediate surroundings (palpebral-jugal groove, superior palpebral arch, brow ridge), is reminiscent of flames depending on the lighting.

  

  fig.02: duality or polarity in the Taiji Tu.

  

  fig.03: inversion of eye color resembling a sun against a space background.

• Taste (Water): The organ, the mouth, is intrinsically linked to the element Water (saliva). Its morphology presents several notable analogies:
  • Its basic structure seems to be composed of two horizontal and symmetrical "drop" shapes that intersect.
  • At the intersection of these two shapes, a central triangle emerges, reminiscent of the "Triangle of divine presence".
  • The philtrum (the area between the nose and the upper lip) itself takes the shape of a drop in three dimensions, reinforcing the symbolism of water.
  • Unlike the other sensory organs which are paired (hands, ears, eyes, nostrils), the mouth is unique, which emphasizes its unifying and transcendent character.
  

Step 4b: Analysis of a Polarized Inversion — The Mouth and the Eye

Observation of a chromatic anomaly

The analysis of the sensory organs reveals a functional polarity between the mouth and the eye. According to the Common-Schema, the former is associated with the element Water (the Transcendent pole) and the latter with the element Fire² (the dominant Abstract pole). However, a study of their usual coloration highlights an apparent contradiction with respect to the color spectrum defined previously.

Hypothesis of a functional inversion

This observation leads to the hypothesis of a chromatic inversion for the two senses associated with the "temperate" elements (Fire and Water), as opposed to the "neutral" senses (Earth and Air). This inversion echoes other biological processes, notably the inversion of the image performed by the retina of the eye.

The relevance of this inverted polarity seems to be confirmed during the transition from life to death. An inverse trend would be observed:

• The mouth tends to take on a cyanotic (blue) hue, due to a lack of oxygenation.
• The eyes may show redness (conjunctival hemorrhages).

Thus, the colors that signal "non-life" in these places correspond to the colors expected by the Common-Schema for a functional state, which suggests that the inversion is an intrinsic characteristic of the "living" state.

Step 5: The Revelation of the Cyclical Principle through the Chromatic Spectrum

The quinary model (`Earth → Air → Fire² → Air → Water`), although relevant for the five senses, remained a linear and open sequence. To test its validity and completeness, it was confronted with another fundamental and universally recognized system: the color spectrum. The objective was to see if a logical correspondence could be established with the primary (Yellow, Red, Blue) and secondary (Orange, Violet, Green) colors.

Initial Hypothesis: Placement of Primary Colors

The three primary colors were positioned on the most obvious poles of the model, defining a basic skeleton:

• Red is instinctively associated with the central Fire² pole.
• Blue is universally associated with the final Water pole.
• Therefore, Yellow was logically assigned to the initial pole, Earth.

This first assignment created a sequence `Yellow (Earth) → ? (Air) → Red (Fire²) → ? (Air) → Blue (Water)`.

Partial Validation by Secondary Colors

The introduction of secondary colors allowed the validity of this skeleton to be tested. These should logically fit between their parent primaries:

• Orange (Yellow + Red) placed itself perfectly between Earth (Yellow) and Fire (Red).
• Violet (Red + Blue) placed itself just as logically between Fire (Red) and Water (Blue).

The sequence then became: Yellow → Orange → Red → Violet → Blue. The model was filling up coherently, but there remained one unplaced secondary color and a fundamental contradiction.

The Contradiction of Green and the Discovery of the Cycle

The place of the last secondary color, Green (resulting from the mix of Blue and Yellow), became a crucial test. Unable to fit into the linear sequence, its only logical position was between the last term (Blue) and the first (Yellow).

This logical necessity constituted the first observational and independent proof that the Common-Schema is not a linear structure, but a cyclical and closed structure. The model had to be amended: the arrow of progression does not stop at Blue, but continues via Green to return to Yellow.

Step 6: The Resolution of the Chromatic Anomaly and the Splitting of the Transcendent Pole

The discovery of the loop principle resolved a major contradiction, but immediately created another, more subtle one. In the cycle `Yellow → Orange → Red → Violet → Blue → Green → Yellow...`, the "Water" pole (the Transcendent) is now associated with two distinct colors: Blue (which leads to Green) and Green (which returns to Yellow).

This anomaly suggested that the Transcendent pole was not monolithic, but possessed a dual nature. The model had to be refined again to account for this observation.

Hypothesis: The Concrete Transcendent and the Abstract Transcendent

The most logical solution to this anomaly was to postulate that the Transcendent pole splits into two functional aspects, corresponding to the two colors:

• Green, the color of nature, of the plant world, and of the beginning of a visible cycle, embodies the aspect that initiates the sequence. It was named the Concrete Transcendent (CT).
• Blue, the color of the sky, of the depths, and of the abstract horizon, embodies the aspect that closes the sequence. It was named the Abstract Transcendent (AT).

The Finalized Senary Model

This new understanding allowed the cyclical model to be finalized. The cycle is no longer a simple 5-term loop, but an ordered sequence of 6 functional poles. The position of Green is no longer a "patch" to close the cycle, but the logical manifestation of the initiator pole.

Step 7: The polarized coding of the chromatic spectrum

The investigation continues by seeking to discover a deeper and more structural layer of information beneath the color spectrum. The goal is to translate the colors into a language of polarities, inspired by the dual nature of the Fire pole (Fire+ / Fire-), and then to analyze the resulting sequence.

Basic Postulate: The ternary coding of colors

After dismissing the RGB model (computer science) as being out of context, the system of primary colors (Yellow, Red, Blue) served as the foundation. The starting postulate is to assign a unique ternary code to each primary color, by distributing a single positive polarity (+) within a structure of three signs.

The derivation rule for secondary colors is a logical addition: their code is obtained by combining the positive polarities (+) of their two parent primary colors.

Analysis of the global polarized sequence

By ordering these codes according to the sequence established in Step 7 (Green → Yellow → Orange → Red² → Violet → Blue), we obtain the complete polarity chain:

This chain is then visually reorganized by grouping identical polarity pairs (`++` and `--`) to facilitate its structural analysis:

Identification of a cyclical and asymmetrical structure

This new representation reveals a complex structure organized around a central axis (`Fire-`). On either side of this axis, we observe a balance of asymmetrical correspondences between the "strong" poles (pairs `++`, `--`) and the "weak" poles (single signs `+`, `-`).

A directional and **cyclical** flow emerges from these asymmetries. The final diagram is constructed according to a dual logic that forms a complete loop:

• The initiator flow (bottom arrows): The movement starts from the "strong" poles and moves towards the corresponding "weak" poles. The rule is: ++ → + and -- → -. This is the impulse phase of the system.
• The return flow (top arrows): To complete the cycle, the movement is reversed. It starts from the "weak" poles and returns to the "strong" poles. The rule is: + → ++ and - → --. This is the response phase that closes the loop.

The reason why the movement initiates in one way (strong → weak) and completes in another (weak → strong) will be demonstrated later. The diagram below is the mechanical representation of this polarized cycle, which corresponds to the underlying structure of the Common-Schema.

Step 9: The mechanics of cosmic gears

At this stage, the analysis shifts from a static mapping of polarities to a dynamic description of the movements and interactions that result from them. The Common-Schema reveals itself to be not just a structure, but a true mechanism.

Identification of internal movements

The system's energy comes mainly from the Abstract pole, which is in constant motion. Two of these movements are direct consequences of the `Air - Fire² - Air` structure:

• The movement of Fire on itself (Fire- ↔ Fire+): The Fire pole, by its dual nature, is a source of rotational energy that initiates the overall movement of the system.

• The movement of Air on itself: Driven by the central rotation of Fire, the surrounding Air is set in motion, which justifies its double presence and its function as a dynamic medium.

Projection in spherical geometry

The next step is to use the property of the "Concrete Transcendent" (Green) to shift the model from a line to a spatial structure. By placing it vertically as a pole, the linear sequence wraps around to form a perfect circle, creating a geometry that evokes a planetary structure (a core of Fire, a surface of Earth and Water, etc.).

This projection reveals a remarkable confirmation: in this configuration, the flow arrows associated with the two Transcendent poles (Water1/Green and Water2/Blue) are **inverted** relative to all the others. The principle of transcendence is therefore manifested here by an inversion of the system's fundamental mechanics, once again validating its exceptional nature.

Explanation: the mechanical transmission sequence

To understand how this inversion occurs, one must break down the chain of motion transmission, which originates in the Abstract pole. The image below illustrates this sequence:

1. Impulse: The movement is initiated in the Abstract, between the strong pole of Air (associated with Orange) and the weak pole of Fire-.
2. Chain reaction: This impulse triggers a reaction between the weak pole of Fire+ and the strong pole of Air (associated with Violet).
3. Internal rotation initiated: Consequently, Fire² rotates on itself, and Air rotates around Fire².
4. Transmission and Inversion: Finally, the two Air poles, acting like drive wheels, engage the adjacent poles (Earth and Waters) via a gearing effect, causing them to move in the opposite direction.

It is this indirect mechanical interaction, initiated by the Abstract and transmitted to the rest of the system, that explains the inversion of flows observed in the spherical geometry.

Step 9: The duality of viewpoints — Vertical axis and horizontal axis

Until now, the Common-Schema has been applied sequentially, as a progression in time or space. However, this approach reveals its limits and leads to the discovery of a second mode of expression of the CS, which is just as fundamental.

Reminder: The sequential model (Vertical Axis)

The `Concrete → Abstract → Transcendent` model works perfectly to describe linear processes or structures with vertical development.

• Concrete: The two legs, at the base, ensuring Contact with the ground.
• Abstract: The torso and the two arms, a larger and more extended version of the legs, containing the majority of the organs.
• Transcendent: The head, unique, which unifies the whole. On one hand, it contains most of the senses that allow the individual to interact with the world as a coherent whole. On the other hand, it houses the brain, which centralizes the command of the body and generates the unified consciousness of the being.

The contradiction: The horizontal axis of symmetry

The "hiccup" appears when one tries to apply this same `C → A → T` sequence to structures organized around a central axis of symmetry, such as a horizontal reading of the human body or the shape of a tree leaf.

In these cases, the linear sequence no longer makes sense. Instead, we observe a bilateral structure where the center plays a unifying role distinct from the two sides.

Resolution: The centered model (Horizontal Axis)

The solution is that the CS changes its mode of expression. For symmetrical structures, it no longer organizes itself in a sequence but in a spatial manner:

In this model, the Transcendent pole is no longer at the end, but in the **center**. It acts as an axis (the spine for humans, the central vein for the leaf) that connects the two lateral poles. Its transcendent nature is manifested by the fact that it **completely changes the form**: it does not simply duplicate or invert the structure of the Concrete and Abstract poles, but unifies them through a new and unique structure.

Unification: The Common-Schema of the Functional

The discovery of these two modes raises a question: when does one or the other apply? The answer is that they are not exclusive, but **coexist permanently within any entity**. This is explained by the very nature of the CS, which must now be specified:

This is the very definition of the "right solution." The first example of digital painting aimed to obtain the best possible functional result. Therefore, the more functional and optimized an entity is, the more perfectly it applies the CS, and it does so at all scales of its fractal structure. The two modes, sequential and centered, are thus always present, because any functional entity has both a development in time (a process, a vertical axis) and a structure in space (a form, a horizontal axis).

Step 10: The Resolution of the Paradox of the Two Modes — The Enantiomorphic Universe Hypothesis

Step 9 revealed a fundamental contradiction at the heart of the Common-Schema: the existence of two apparently incompatible modes of expression. The sequential mode (`C → A → T`) describes an asymmetrical and directional process, like an arrow of time. The centered mode (`C ↔ T ↔ A`) describes a perfectly symmetrical and spatial structure. How can a single universe be fundamentally both at the same time?

The resolution of this paradox can only come from a complexification of the cosmological model. The most logical hypothesis is that these two modes are not competing descriptions of a single reality, but the precise descriptions of two distinct, complementary, and entangled realities.

Hypothesis: From the Duality of Modes to the Duality of the Universe

This conclusion forces us to postulate that the Universe is not unitary, but enantiomorphic. It is composed of two "chiralities" (non-superimposable mirror images), each corresponding to one of the modes of expression of the CS:

• The Abstract Chirality (ours): It is governed by the sequential and asymmetrical mode. This is the universe of process, time, and movement. Its polarity structure, which we have already derived, is intrinsically asymmetrical, making it the "engine" of the cosmos.
• The Concrete Chirality (its complement): It is governed by the centered and symmetrical mode. This is the universe of structure, space, and stability.

This hypothesis resolves the paradox of the "imperfection of nature." A tree leaf is not a failed attempt at symmetry; it is a perfect manifestation of abstract chirality. Its structure is therefore perfectly enantiomorphic, a necessary condition for its dynamic functionality.

Deduction of the Structure of the Concrete Chirality

Having postulated the existence of this concrete chirality, we can deduce its structure through a rigorous analysis of polarities. By analyzing the symmetrical structure of a leaf (centered model), two color sequences are possible. Their conversion into polarity chains reveals that they both exhibit perfect symmetry.

This perfect symmetry is the key to validation. A perfectly symmetrical structure cannot possess autonomous movement, as it has no central "Fire²" to initiate it. This brilliantly confirms the axiom from Step 9: "the concrete is originally immobile." The concrete chirality is immobile because its structure is symmetrical.

To choose between the two hypotheses, the principle of complementarity is applied: since the abstract chirality (ours) is a sequence of 13 polarities, its counterpart must be as well. Case 2 is therefore the correct solution.

T+: Water as a spatial transcendent

■ ● ▲

green yellow orange red red violet blue

+-+ +-- ++- -+- -+- -++ --+

+ - ++ -- ++ -- + -- + -- ++ -- + (13 polarities, odd)

+ - ++ -- ++ -- + -- + -- ++ -- + (enantiomorphic, spherical)

Enantiomorphic.

E+: - Case 2: Inverted sequence

● ▲ ■

red violet blue green yellow orange red

-+- -++ --+ +-+ +-- ++- -+-

- + -- ++ -- ++ - ++ -- ++ -- + - (13 polarities, odd)

- + -- ++ -- ++ - ++ -- ++ -- + - (perfect symmetry)

Axial symmetry: no autonomous movement.

This final correspondence allows us to unambiguously define the structure of the Concrete Common-Schema and the gear mechanism that links the two chiralities.

Step 11: The six fundamental viewpoints

After defining the two chiralities (concrete and abstract), it became clear that they were composed of the same terms (`Concrete`, `Abstract`, `Transcendent`), but ordered differently. This order is what defines a "viewpoint" and generates the infinite diversity of the universe. To discover all the fundamental viewpoints at the basis of reality, the tetrahedron, symbol of the CS, was rotated to reveal all its possible orientations.

The result of this rotation is a set of **six fundamental viewpoints**:

New terminology: the Tridimensions

For greater clarity, the terminology is transposed to the lexicon of dimensions. The six viewpoints are classified into three categories, each with its own type of symmetry:

• The Concrete Chiralities (Space+, Time+): Characterized by perfect symmetry.
• The Abstract Chiralities (Space-, Time-): Characterized by enantiomorphy (a balance of asymmetries).
• The Entanglements (Mass+, Mass-): Characterized by pure asymmetry.

Deduction of the polarity of the Masses

Unlike the chiralities, the polarized structure of the Masses (the entanglements) was not known. An exhaustive analysis revealed a unique solution, defined by a remarkable property of double inversion:

• For Mass+, Water (Blue) is at the beginning of the sequence and Air (Violet) is at the end.
• For Mass-, the opposite is true: Air (Violet) is at the beginning and Water (Blue) is at the end.

Although lacking direct observations at this stage, this solution was later confirmed. The detailed analysis of their polarities confirms their nature as entanglements.

m-: case study #3: water and sky as spatial transcendents.

▲ ■ ●

violet red red orange yellow green blue

-++ -+- -+- ++- +-- +-+ --+

- ++ - + -- + - ++ - + -- + - + -- + (16 polarities, even)

- ++ - + -- + - ++ - + -- + - + -- +
(axially incompatible polarities)

m+: case study #3: water and sky as spatial transcendents.

■ ● ▲

blue green yellow orange red red violet

--+ +-+ +-- ++- -+- -+- -++

-- ++ - ++ -- ++ -- + -- + -- ++ (12 polarities, even)

-- ++ - ++ -- ++ -- + -- + -- ++
(axially incompatible polarities)

Analysis: Chiralities vs. Entanglements

The analysis of this new polarized structure reveals two fundamental differences that allow us to distinguish an entanglement from a chirality:

1. The parity of the number of polarities: Chiralities (Space, Time) have an odd number of polarities (13). Entanglements (Mass+, Mass-) have an **even** number.
2. The nature of symmetry: Entanglements manifest a **fundamental incommensurability with axial geometry**, unlike chiralities which exhibit a balance of asymmetries or perfect symmetry.

This distinction once again confirms the transcendent nature of Mass relative to Space and Time.

Return to the gear model

This new understanding helps to clarify the role of each component in the cosmic gear schema. The distinction between concrete/abstract entanglement and concrete/abstract transcendent is a fractal complexity that will be explored later. To simplify here:

• Mass+ (Blue) is the entanglement of the Concrete (Yellow) and the Abstract (Red).
• Mass- (Green) is driven by the interaction of the two states of Mass+ (symbolized by the Orange and Violet circles).

Step 12: Deduction of Entanglement Dynamics through Polarity Analysis

After defining the six viewpoints and the polarized structure of the two chiralities of our universe (`T+` and `E+`), the next step is to model their dynamic interaction. The Common-Schema, as an architectural model, must contain within itself the rules that govern this interaction. The key is found in analyzing the "boundary conditions" of each chirality, that is, their peripheral polarities.

Working Hypothesis: The Peripheral Element Rule

A fundamental logical principle is that the interaction of a system with another occurs through its "surface" or periphery. We therefore postulate that the most important dynamic properties of a chirality (such as the opposition of the "arrows" of time or mass) are governed by the elements found at the ends of its polarity sequence.

Analysis of Polarized Sequences and Deduction

By examining the sequences of `T+` and `E+` established previously, we identify their peripheral elements:

• For the Abstract chirality (T+): The sequence begins and ends with polarities from the colors Green and Blue. These two colors correspond to the element Water, which, in the CS, is the analogue of Mass. The dynamics of our chirality must therefore manifest as a duality of Mass.
• For the Concrete chirality (E+): The sequence begins and ends with polarities from the color Red. This color corresponds to the element Fire, which is the analogue of Time. The dynamics of the concrete chirality must therefore manifest as a duality of Time.

T+ (Our Chirality)

green yellow orange red red violet blue

+-+ +-- ++- -+- -+- -++ --+

Peripheral elements: Water/Mass. Prediction: `Mass+ / Mass-` duality.

E+ (Concrete Chirality)

red violet blue green yellow orange red

-+- -++ --+ +-+ +-- ++- -+-

Peripheral element: Fire/Time. Prediction: Temporal duality ("opposing arrows of time").

This purely internal analysis of the model leads us to predict the existence of the two dynamic phenomena necessary to construct a complete model of entanglement.

Construction of the Entanglement Model

Armed with these deductions, we can now model the interaction. Our chirality (`T+`) manifests a `Mass+ / Mass-` duality. The concrete chirality (`E+`) manifests a temporal duality `→t / ←t`. Space, not being a peripheral element, does not exhibit this opposition of arrows.

Step 13: The dimensional hexagons and the path of entanglement

The next step is to visualize the geometry of the relationships between the six fundamental viewpoints. By extracting the colors from the bases of the six tetrahedra, it is possible to construct a new representation that recontextualizes the tridimensions into chiralities and entanglements.

Construction of the dimensional hexagons

These color bases organize into **dimensional hexagons**, each representing a fundamental pole of the CS: Concrete, Abstract, and Transcendent.

Geometry of recontextualization of the tridimensions into hexagons.

The three dimensional hexagons: Concrete, Abstract, Transcendent.

This geometry reveals a cross-shaped logic that governs how the dimensions entangle. The principle `Space)m+(Time → m+)m-(m+` (the entanglement of Space and Time produces Mass+, which in turn leads to Mass-) is the key to this structure.

The cross-shaped geometric logic that governs entanglement.

The universal entanglement path

By relating the hexagons of the two chiralities (Concrete and Abstract) with their entanglement (the Transcendent hexagon), we obtain a basic geometric module.

Basic module of entanglement between chiralities.

By duplicating and connecting this module, it is possible to map the **complete entanglement path between the inside and the outside of the universe**. The following animation represents this "dimensional helix."

The dimensional helix of the CS is a model suggesting that many other entanglements besides S)(T are possible if the context allows.

Analysis of the path and confirmations of the inversion principle

This path is not a simple passage; it is a transformation process where an entity successively loses and gains dimensions. The movement along this helix, popularized in the animation below, shows that the effective parts of the hexagons on the outside are inverted relative to those on the inside.

This principle of inversion between the inside and the outside is a powerful confirmation, as it resonates with several previous observations:

• The biological phenomenon of the inversion of the image by the human retina.
• The inversion of the directions of rotation between the inside and the outside in the cosmic gear model.

Step 14: The Entanglement Table of Chiralities — The Theoretical Matrix of the CS

This final step is the culmination of the theoretical genesis of the Common-Schema. Having deduced the rules of polarity, the viewpoints, and the dynamics of interaction, we can now use these principles to construct the most complete model of the CS: a matrix describing the structure of the fundamental interaction between the two chiralities of the universe.

Construction of the Matrix from the Polarities

The Matrix is generated by superimposing the polarized signatures of the four local tridimensions (`T+`, `E+`, `m+`, `m-`) and applying to them the contextual transformation rules that arise from the logic of the CS. The process is entirely deterministic.

Organization of the CS polarities serving as the basis for the construction of the Matrix.

Generation from the Abstract Viewpoint (`C-A-T`)

By applying the rules of our chirality (`C-A-T`), where the Transcendent is final and the Abstract is central and dual (`Fire²`):

• The transcendent column **"y" disappears**.
• The abstract column **"x" splits in two**.

This transformation is the visual signature of the `C-A-T` logic. It generates the first part of the matrix:

Part of the matrix generated according to the `C-A-T` logic.

Generation from the Concrete Viewpoint (`A-T-C`)

By applying the rules of the complementary chirality (`A-T-C`), where the Transcendent is central:

• The transcendent column **"x" disappears**.
• The variation column **"y" undergoes an inversion**. Except for its relative T (its center).

This distinct set of rules is the visual signature of the `A-T-C` logic. It generates the second part of the matrix:

Part of the matrix generated according to the `A-T-C` logic.

After applying the rules.

Resolution of the non-entangled parts of S)m+(T:

Resolution of the non-entangled parts of m+)m-(m+:

The Complete Matrix and its Exploitable Logic

By extending these rules to all the polarities (including the non-entangled zones), the CS generates a complete and highly structured binary matrix.

Complete table, quaternary version.

16b. Hypothesis on the origin of life

Paradoxically, the CS seems to answer the biggest questions most easily and the details with the most difficulty. We can proceed with readings of anomalies around us. This is an example of interpretation before proceeding to scientific applications.

An analysis of the behavior of newborns, interpreted through the prism of the four elements of the Common-Schema, leads to a series of observations on the nature of their consciousness before incarnation.

Behavioral Observations

• Knowledge of Water: The sucking reflex is innate, indicating a primordial knowledge of the element Water and the concepts of its category.
• Knowledge of Air: Breathing is an automatism from birth, demonstrating a familiarity with the element Air.
• Unfamiliarity with Earth: Motor skills are initially clumsy. The sense of balance and physical space must be entirely acquired, which suggests an absence of experiential knowledge of the element Earth.
• Unfamiliarity with Fire: A fascination for light (fire) is observable, but it is coupled with a total lack of understanding of its danger. Interaction with this element is not mastered.

Deduction on the pre-incarnate state

These observations lead to the following hypothesis: consciousness, before incarnation, would exist in a state where the elements Water and Air are known, but where the concepts related to the elements Earth and Fire are absent. The process of birth would involve a loss of memory of this previous state.

• The element Earth is associated, among other things, with the existence of physical bodies and with materiality.
• The element Fire² is linked, among other things, to the ability to move matter (create) and to procreation.

This model shows a strong correlation with the concept of immaterial spiritual beings, who would exist in a state of non-physical consciousness before integrating a material body.