Test-1

1 Introduction: Toward a Unified Multilevel Formalization of Physical Reality
2 Elementary Field, Event-Points, and Elementary Events
3 From Micro Dynamism to Emergent Structure
4 The Hierarchy of Reality
- 4.1 Summary of the Hierarchy of Reality
5 Diagram of the Hierarchy of Reality
6 Epistemic Representation and Scientific Frameworks
7 Hierarchical Structure of the Formalization
8 Synthetic Pathway from the Source to Forms
9 10-Line Ultra-Synthetic Schema
10 Synthetic Proto Mathematical Map of the Formalization Pathway Across Levels
11 Links to the tables of contents of TFNR Paper

Introduction: Toward a Unified Multilevel Formalization of Physical Reality

This formalization scheme is presented as a coherent and structured proposal — an organized set of hypotheses aimed at exploring a possible pathway from Elementary Field Dynamics to the emergence of Physical Structures. It does not claim to provide a definitive solution to the open problems of modern physics, but rather offers a conceptual framework that may help illuminate their underlying architecture. The intention is to suggest, with due humility, a possible direction for theoretical research: a pathway that may achieve a meaningful level of analytical detail while preserving a unified, large scale perspective on the structure of Physical Reality.

Although the formalization is articulated through a sequence of levels and sub levels, it should not be interpreted as a fragmented collection of models or analytical devices. Its structure mirrors the intrinsic order of the Process of Formation of Physical Reality itself. The hierarchy of the formalization is therefore not an external framework imposed upon the theory, but the natural reflection of the ontological, phenomenological, and dynamical sequence through which Reality emerges. In this sense, the mathematical and conceptual architecture proposed here follows — rather than constructs — the order of the Real.

The conceptual pathway proceeds through a hierarchy of levels — from Elementary Events and their decomposition, to the Modes of Elementary Action, the emergence of informational and energetic content, the formation of InfoStructures, their equilibrium equations, and finally the quantum and field-theoretic equations that map onto Quantum Field Theory and the Standard Model of Particles. The accompanying conceptual figure summarizes this hierarchical architecture.

Elementary Field, Event-Points, and Elementary Events

At the foundational level, the Elementary Field is understood as a continuous, pre-geometric field-like medium whose intrinsic variational nature responds to the causal impulse of the Fundamental Force. The Force is conceived as a pure scalar causal source, devoid of intrinsic directionality. Direction, orientation, chirality, and structure do not belong to the Force itself (source of Causality); they emerge from the Field's response, through the organization of its fluctuations (source of Variationality).

Within this framework, the Event-Point (EP) represents an infinitesimal, arbitrarily centered sampling region of the Field — not a physical unit, but an analytical focus where the Field's pre-spatial dynamism becomes locally expressible. The EP is the locus where the Field's continuous activity is decomposed into analyzable components.

For each EP, the Elementary Event (EE) captures the instantaneous pre-spatial fluctuation generated by the internal interaction between the two aspects of the Primary Source of Reality: the Fundamental Force and the Elementary Field. EE have no identity, no persistence, no trajectory; they are the elementary manifestations of the Field's incessant variational activity.

By tracking the evolution of EE along the pre-temporal parameter τ, one obtains the τ evolution and the associated τ distribution (τ DIST), which encode the statistical structure of the local micro dynamism of the Field under the continuous pressure of the Force. These distributions constitute the proto informational/energetic substrate from which significant quantities emerge — such as local Time Curvature, Field Temperature, and the vibrational spectrum of EE.

From Micro Dynamism to Emergent Structure

The conceptual and mathematical pathway proceeds through a layered sequence:

the continuous Elementary Field
the Event-point as a local sampling operator on the pre-physical dynamism of the Field
the Elementary Event as a pre-spatial σ-fluctuation
the pre-temporal τ based statistical formalization of Elementary Events
the emergence of dynamical and geometric quantities
the macroscopic physical behavior arising from spatial correlations

This layered structure provides a consistent path toward the mathematical formalization of the Dynamics of Elementary Action, grounding macroscopic Phenomena in the dynamical and informational behavior of the Field at its most elementary level.

Conventional physics, although less explicitly, also organizes its theories across different layers of Reality — each addressing a specific domain of phenomena, from the macroscopic to the quantum, from geometry to fields. This stratification has produced extraordinary analytical power, but it has also encouraged fragmentation and hindered the emergence of a unified conceptual framework.

A central principle of this work is that analysis without synthesis can lead to conceptual dead ends, where progress becomes increasingly difficult. For this reason, the formalization proposed here aims to integrate both perspectives: the precision of detailed analysis and the coherence of a global, multilevel architecture. Within this broader framework, the major theories of modern physics (SR, GR, QM, QFT, SMP, etc.) can be situated as effective epistemic layers that describe specific domains of emergent structure, while remaining embedded within a deeper ontological continuum.

The Hierarchy of Reality

The formation of physical Reality can be understood through a hierarchical sequence of ontological levels, each introducing a new mode of organization of the Field's dynamism. This hierarchy is not an arbitrary construction: it reflects the intrinsic structure of the Process of Formation of Reality.

The hierarchy consists of five fundamental ontological levels (0–5), which describe what exists and how it is organized. By examining the levels and their corresponding sub-levels in a concise sequence, I will highlight—where appropriate—the associated epistemic aspects, which describe how human observers represent, model, and interpret these levels, with occasional references to the models and theories of conventional physics.”

The levels:

Level 0 — Source (Force and Field)
Level 1 — Elementary Events (τ distributions of σ fluctuations)
Level 2 — Elementary Action (discrepancies of τ distributions)
Relational Bridge — Correlation (between discrepancies)
Level 3 — Information/Energy (Unstructured -or weakly structured - Physical Quantities: Physical Potentials)
Level 4 — InfoStructures (Structured Physical Quantities)
Level 5 — Forms (Physical Universe)

Summary of the Hierarchy of Reality

LEVEL 0 — Origin (Primary Source, Fundamental Force, Elementary Field)

Ontological foundation of Reality. The Primary Source is the primordial entity from which the Fundamental Force and the continuous Elementary Field arise as two complementary aspects of its Agency. The Source is not physical, not geometric, not energetic: it is the ontological root of Action.

LEVEL 1 — Elementary Events (τ distributions of σ fluctuations)

Elementary Events (EE) are the τ level statistical distributions of instantaneous σ fluctuations of the Field. Elementary variations of the Field, represented as τ level statistical distributions of σ fluctuations. A pre-physical, unmanifest, unstructured level.
Each σ fluctuation is characterized by four aspects:

Amplitude A(σ)

Orientation n(σ)

Chirality χ(σ)

Axis Orientation u(σ)

EE represent the pre-physical, pre-spatial, pre-temporal micro variations of the continuous Elementary Field.

LEVEL 2 — Elementary Action (discrepancies or inhomogeneities of τ distributions)

Elementary Action (EA) arises from the discrepancies / inhomogeneities in the τ distributions of EE, that manifest as linear deformation content (proto-stress intensity and orientation) and angular deformation content (proto-vorticity chirality and axis orientation). These discrepancies correspond to four deformation Modes/Sub Modes:

Perturbation (intensity discrepancies)

Translation (orientation discrepancies)

Rotation:Chirality (chirality discrepancies)

Rotation:AxisOrientation (axis orientation discrepancies)

EA is pure dynamics — tendencies, not yet physical content. Still a pre-physical, unmanifest, unstructured level.
These discrepancies are the objects of the correlation process that will occur as described at the next point about the “Relational Bridge”.

RELATIONAL BRIDGE — Correlation between discrepancies (From Action to Information / Energy)

Conceptual bridge between Level 2 and Level 3.
Here the key transformation occurs: Spatial correlations between discrepancies (ΔP) in the τ distributions transform Action (EA) into Information/Energy.
The correlation is not generated by the discrepancies themselves, but by the causal Agency of the Primary Source, expressed secondarily through the dynamism of the Elementary Field.
Discrepances (ΔP) are the objects of the correlation, not its sources.
Action takes form, configuring the physical potentials. From Action (a pre-physical, unmanifest, unstructured level of Realty) to In Form Action (Information / Energy: physical, manifest but still unstructured).
This bridge is not a level, but a Process:

Elementary Action = pure dynamical tendencies

Correlation = configurational process (organization)

Information/Energy = emergent physical content

LEVEL 3 — Information/Energy (Physical Potentials: Metric, Potential Motion: Acceleration Electric and Magnetic Potentials)

The four physical potentials emerge from correlated discrepancies in the τ distributions: Metric (unstructured potential Mass or unstructured Time-Curvature) ← correlations of Perturbation Potential Motion (Acceleration) ← correlations of Translation Electric potential ← correlations of Rotation:Chirality Magnetic potential ← correlations of Rotation:Axis Orientation
These are unstructured physical quantities: energetic informational contents, potentials present in fields, not yet organized as (physical properties of) objects like Particles, Waves, Dark Halos, etc.

LEVEL 4 — InfoStructures (Structured Physical Quantities: Mass, Inertial Motion, Charge, Spin)

Organization of Level 3 potentials into coherent dynamical patterns (InfoStructures) within the Elementary Field:

Waves (Dark Waves, GW-like, and Ordinary Waves, EMW-like)

Vortices (Dark Vortices and Elementary Particles)

Interactions (manifesting as Composite InfoStructures)

Elementary physical content:

Structured effective Mass (Mass of Dark and Ordinary Vortex and Composite InfoStructures)

Effective Motion (Inertia)

Charge (electric)

Spin (magnetic)

Here appear:

equilibrium equations that describe the existence and the essence / form of InfoStructures with their Properties and Behaviors

proto physical equations that describe their phenomena and dynamics

projections into QM, QFT, and the Standard Model

LEVEL 5 — Forms: Atoms, Molecules, Stars, Galaxies, Cosmic Structures

The level of composite Physical Forms (physical, manifest, composite structured level):

atoms

molecules

stars

galaxies

cosmic structures

up to the entire physical Universe.

This is the domain of observable physics.

Diagram of the Hierarchy of Reality

This hierarchy serves as the conceptual map of the entire section and guides the reader through the subsequent levels.

Diagram of the Hierarchy of Reality - Formalization Levels

Epistemic Representation and Scientific Frameworks

Although the hierarchy of Levels 0–5 describes the ontological structure of Reality, any scientific theory must also address the epistemic dimension: the way human observers represent, model, and interpret these levels. This epistemic layer is not an additional ontological level of Reality, but a meta-level that organizes our knowledge of the underlying physical structure.

Scientific theories, mathematical formalisms, and conceptual frameworks belong to this epistemic domain. They provide the languages, tools, and symbolic structures through which the ontological hierarchy becomes intelligible and analytically tractable.

Scientific Theories as Epistemic Layers

Modern physics is composed of multiple theoretical frameworks — SR, GR, QM, QFT, SMP, thermodynamics, statistical mechanics — each describing a specific domain of emergent structure. These theories are extraordinarily powerful, yet each capture only a portion of the deeper ontological continuum.

Within the present framework, these theories are understood as effective epistemic layers:

they approximate the behavior of Forms and InfoStructures,
they operate within specific domains of validity,
they provide partial but indispensable representations of the emergent manifestations of the underlying Field dynamics.

Mathematical and Conceptual Models

Mathematical models — differential equations, geometric structures, algebraic formalisms, probabilistic frameworks — are representational instruments. They do not constitute Reality; rather, they express specific aspects of its organization. As such, they are cognitive constructions belonging to the domain of Cognitive Reality (or Meta-Reality).

Conceptual frameworks — ontologies, taxonomies, diagrams, symbolic systems — provide interpretative structures that articulate relations among the different levels of the hierarchy. They operate at the epistemic level and do not form part of the ontological structure of Reality itself.

Role of the Epistemic Layer

The epistemic layer:

organizes scientific knowledge,
mediates between observation and ontology,
clarifies the domain of validity of each theory,
supports the construction of a unified multilevel formalization.

It is therefore a necessary complement to the ontological hierarchy, even though it does not constitute an ontological level in itself.

Hierarchical Structure of the Formalization

Let us begin with the list of the levels and sub-levels, which naturally reproduce the hierarchical scheme of the Process of Formation of Physical Reality. For each point, I will propose an operational guideline that succinctly indicates what seems to be the most promising pathway toward a precise, effective, and integrated formalization.

LEVEL 0 — Primary Source of Reality (Ontological Root)

Conceptual Definition

The Primary Source of Reality is the origin of Existence (sub-Process of Creation) and of the dynamical potential that unfolds toward Essence and Form (sub-Process of Evolution). It is not a physical entity and does not belong to the domain of measurable phenomena. Rather, it is the ontological ground from which the Fundamental Force and the Elementary Field arise as inseparable aspects of a single underlying Reality.

The Primary Source, in these two active and passive aspect, is therefore the pre-physical root of all dynamical, structural, and informational Processes that will later manifest as Physical Quantities, Structures, and Forms.

The Source expresses its Agency in two complementary modes:

direct (creative) Agency, which, through its active aspect — the Fundamental Force — incessantly generates the Elementary Events and, through their discrepancies, the Elementary Action;
indirect (evolutionary) Agency, which, through the re-Action by its passive aspect — the Elementary Field — gives rise to the correlations that organize into Information / Energy (physical potentials) and InfoStructures (the constituents of the Dark and Ordinary Matter / Energy: Waves, Particles, Dark Halos, etc.).

In these two modes, the Source is the pre-physical root of all dynamical, structural, and informational Processes that manifest as Physical Quantities, Potentials, Structures, and Forms.

Role in the Hierarchy

The Primary Source stands at the causal beginning of the Process of Formation of Physical Reality.

It provides:

the incessant causal impulse that will express itself as the Fundamental Force,
the continuous receptive variational substrate that will manifest as the Elementary Field,
the internal interAction between these two aspects, which generates the first dynamical expressions of Reality: the Elementary Events, and subsequently the Elementary Action. Events and Action, as the products of the creative direct Agency of the Source.

It does not introduce parameters, structures, or degrees of freedom. Its role is purely generative: it establishes the conditions for the emergence of the physical domain.

Operational Guidelines

The Primary Source is not modelled directly.
No parameters, variables, or equations are associated with it.
It provides the existence condition for the expression of the Fundamental Force and the manifestation of the Elementary Field.
All formalization begins at the level of the Force–Field complementary duality; the Source remains a conceptual boundary condition for the entire framework.

SUB-LEVEL 0.1 — Fundamental Force (Causal Input Parameter)

Conceptual Definition

The Fundamental Force is the first physical expression of the Primary Source. It is a pure scalar causal intensity, devoid of direction, polarity, or internal structure. Its role is not to shape variation, but to enable it: it provides the causal impulse that drives the Elementary Field out of equilibrium, generating local fluctuations. Its defining Property is Causality, the active side of the direct Agency of the Source.

Role in the Hierarchy

The Fundamental Force is the active aspect of the Source. It initiates all dynamical phenomena by exerting a causal pressure on the Elementary Field. Every form of motion, variation, inhomogeneity, asymmetry, and structure ultimately traces back to this scalar causal input.

Operational Guidelines

Introduce a single scalar parameter F₀, representing the intensity of the causal impulse.
F₀ is the the only causal input of the entire model.
All dynamical phenomena must be derivable from F₀ and the intrinsic resistances of the Field to variation / deformation.
No additional forces, potentials, or interaction terms are introduced at this level.

SUB-LEVEL 0.2 — Elementary Field (Intrinsic Resistances of the Variational Response)

Conceptual Definition

The Elementary Field is the continuous receptive substrate through which the Fundamental Force expresses itself. In its primordial state (absolute condition, absolute vacuum), it possesses no geometry, no metric, no orientation, and no internal structure.

Its defining Property is Variationality: the intrinsic capacity to respond to the causal impulse by generating local fluctuations. Through the organization of these pre-spatial fluctuations in the pre-temporal dimension arise the various levels and types of Potentials and Structures that constitute the relative conditions of the Field ("emergent" conditions: relative vacuum or Void, structured Elementary Field → Derived Physical Fields, dark and ordinary Radiation, dark and ordinary Matter/Energy).

The Elementary Field is also the "medium" through which the indirect (evolutionary) Agency of the Source operates, producing correlations that, at higher levels of causal and variational Complexity, organize into physical potentials and InfoStructures.

Role in the Hierarchy

The Elementary Field is the receptive aspect of the Source. It provides the pre-physical, unmanifest, unstructured medium in which pre-spatial and pre-temporal dynamism can arise. Its intrinsic resistances to variation and deformation determine how the Field reacts to the causal impulse, shaping the four aspects of the Elementary Event.

Operational Guidelines

Define the equation of the Elementary Field, 𝓕 = F₀ (A, n, χ, u; k_A, k_n, k_χ, k_u)

which describes the Field's re-Action to the Action of the Force through the intrinsic "resistances" that encode the Field's dynamical constraints.

Introduce four intrinsic resistances:
- k_A — intensity resistance, k_n — linear‑orientation resistance (proto-stress sector)
  - k_A — intensity resistance → resistance to amplitude deformation (A)
  - k_n — linear‑orientation resistance → resistance to orientation deformation (n)
- k_χ — chirality‑reorientation resistance, k_u — intrinsic‑angular‑orientation resistance (proto-vorticity sector)
  - k_χ — chirality‑reorientation resistance → resistance to chirality induction (χ)
  - k_u — intrinsic‑angular‑orientation resistance → resistance to axis orientation induction (u)
Explore the hypothesis:
- k_χ — chirality‑reorientation resistance ≈ ε₀ (vacuum permittivity)
- k_u — intrinsic‑angular‑orientation resistance ≈ μ₀ (vacuum permeability)
No additional free parameters are allowed.
All physical constants or so called constants (c, ħ, G, coupling constants, masses…) must be derived, not assumed.
Define the Field Equation explicitly in the terms of the four intrinsic resistances above.
Fix the physical dimensions of the four 𝑘 parameters starting from a prototypical form of the Field Equation, and determine which conventional constants can naturally emerge from them.

Sector	Parameters	Basic physical intuition
Proto stress sector	k_A, k_n	Elastic–tensive response of the Field
Proto vorticity sector	k_χ, k_u	Vortical / inductive response of the Field

Hypothesis on the Structure of the Field's Total Resistances

As an operational hypothesis, each intrinsic resistance of the Elementary Field can be treated as a composite quantity consisting of two contributions: an intrinsic component, independent of the ongoing dynamical configuration, and a dynamic component, which depends on the actual state of the Field. The intrinsic component represents the baseline variational rigidity of the Field and is expected to behave in a predominantly linear manner with respect to the intensity of the causal impulse. Within this framework, the conventional physical constants (ε₀, μ₀, c, ħ, G, coupling constants, mass scales) may correspond to the limiting values or reference scales associated with these intrinsic components, in accordance with the requirement that no additional free parameters be introduced.

The dynamic component, by contrast, captures how the Field's resistances change as dynamism develops, as fluctuations organize, and as local densities of Action evolve. This contribution is inherently non linear, reflecting the Field's capacity for self modulation and self organization. It is therefore the natural locus for state dependent behaviors, effective parameters, and the emergence of regime specific scales. In this view, the total resistance in each sector (proto stress and proto torsion or vorticity) becomes a state sensitive quantity, encoding both the fundamental constraints of the Field and the transformations induced by its own internal activity.

Proto Vorticity and the Statistical Emergence of Electromagnetic Physical Quantities

Each Elementary Event normally exhibits non-zero proto-vorticity components (χ and u). In the absence of structures, these components fluctuate randomly along τ (the pre-temporal dimension) and do not generate physical quantities. When the inhomogeneities of their τ-distributions become correlated, physical quantities emerge:

correlations of χ aspect → Charge and Electric Potential,
correlations of u aspect → Spin and Magnetic Potential,
mixed correlations → full electromagnetic phenomena.

SUB-LEVEL 0.3 — Internal Interaction (Force–Field Coupling)

Conceptual Definition

The internal interaction between the Fundamental Force and the Elementary Field is the true dynamical origin of all subsequent Levels. The scalar causal impulse F₀ acts on the Field 𝓕, and the Field responds according to its total resistances {k_A, k_n, k_χ, k_u} (intrinsic + dynamic components), producing the first dynamical expressions of Reality: the Elementary Events.

This interaction does not merely generate dynamism: it also modulates the Field’s total resistances, altering the balance between their intrinsic (state-independent) and dynamic (state-dependent) components. This modulation is the earliest manifestation of the Field’s capacity for self-adjustment and self-organization.

The Elementary Action (EA) arises from the discrepancies in the τ-distributions of the Elementary Events.

Role in the Hierarchy

This interaction is the first causal act of dynamical Creation. It generates the pre-spatial and pre-temporal fluctuations that become the building blocks of Physical Quantities, Potentials, Structures, and Forms.

By modulating the Field's resistances, the causal impulse determines the local regime in which each Elementary Event is produced, shaping the earliest differentiation between linear and non-linear responses of the Field.

Operational Guidelines

Model the interaction as a local variational response of the Elementary Field to the scalar causal impulse:

EE(𝑥,τ)= δ𝓕(𝑥,τ) = Resp_𝓕 (𝑥,τ; F₀, k_A, k_n, k_χ, k_u)

The response depends only on:
- the causal input F₀,
- the total resistances {k_A, k_n, k_χ, k_u}, each understood as the sum of an intrinsic component and a dynamic component modulated by the ongoing Field configuration.
No background metric, no external potentials, no additional structures.
The Elementary Event is the minimal dynamical unit generated by this interaction, encoding both:
- the immediate effect of the causal impulse,
- the instantaneous modulation of the Field's resistances.

SUB-LEVEL 0.4 — Event-Point (Analytical Sampling Locus)

Conceptual Definition

The Event-Point is an infinitesimal analytical locus — a pre-spatial and pre-temporal sampling locus — through which the local micro-dynamism of the Field becomes expressible. It is not a physical entity, nor a component of the Field, nor a primitive of Reality: it is a conceptual operator used to extract the instantaneous configuration of the Field's variational activity.

The Event-Point is an infinitesimal analytical locus — a pre-spatial and pre-temporal sampling operator — through which the local micro-dynamism of the Field becomes expressible. It is not a physical entity, nor a component of the Field, nor a primitive of Reality: it is a conceptual device used to extract the instantaneous configuration of the Field's variational activity.

Role in the Hierarchy

The Event-Point does not belong to the ontological hierarchy of Reality. It introduces no structure, no geometry, no parameters, no dynamics, and no ontological content. Its sole role is to provide the analytical interface that allows us to define the Elementary Event as the local fluctuation of the Field generated by the Force–Field interaction.

Through the Event-Point, the Field's micro-dynamism — shaped by the causal impulse and by the instantaneous configuration of the Field's total resistances — becomes analytically accessible.

Operational Guidelines

Treat the Event-Point as an analytical operator, never as a physical object.
It introduces no parameters, no dynamics, and no ontological content.
Use it solely to define EE(𝑥,τ)= δF(𝑥,τ) as the local fluctuation of the Field at the infinitesimal sampling locus.

𝑥— Pre-spatial analytical label

𝑥 is not a spatial coordinate and does not refer to a point in physical space. It is an analytical label used to identify a local sampling locus of the Field's micro dynamism before the emergence of geometry. It carries no metric, no distance, no orientation, and no geometric structure. Its sole purpose is to allow the analytical extraction of a local fluctuation of the Field. In short: 𝑥="pre-spatial analytical index of the sampling locus\"".

τ— Pre-temporal evolution parameter

τ is the pre temporal evolution parameter along which the micro dynamism of the Field unfolds. It is not physical time. It is the internal ordering parameter of the Field's variational activity, providing the sequence along which Elementary Events are generated and organized. It becomes the proto temporal axis from which physical time will later emerge. In short: τ="pre-temporal ordering parameter of the Field's dynamism".

Interpretation of EE(𝑥,τ)=δF(𝑥,τ)

EE(x,τ)=δF(x,τ) means that:

at the analytical locus x (pre-spatial),
at the pre-temporal stage τ,
the Elementary Event is the local fluctuation of the Field
produced by the causal impulse and modulated by the Field's total resistances.

Thus:

𝑥 specifies "where" (pre-spatially) the fluctuation is sampled,
τ specifies "when" (pre-temporally) the fluctuation occurs.

Sampling, not generating

The Event-point does not generate dynamism. It only samples the dynamism produced by the Force–Field interaction and by the instantaneous modulation of the Field's resistances.

LEVEL 1 — Elementary Events (Pre-Spatial and Pre-Temporal Dynamism)

Conceptual Definition

Elementary Events (EE) are the first dynamical expressions generated by the interaction between the Fundamental Force (active aspect of the Source) and the Elementary Field (variational, receptive aspect of the Source). They represent the minimal units of pre-spatial and pre-temporal variation.

An EE is not a particle, not a wave, and not a physical event in spacetime. It is a local fluctuation of the Elementary Field, defined at an Event-point, and decomposed into four intrinsic aspects:

A — amplitude
n — orientation
χ — chirality
u — axis orientation

Each aspect configures a distinct mode of variational response of the Field.

An EE configures simultaneously: the instantaneous pre-spatial configuration (σ fluctuation), the statistical pre-temporal evolution (τ distribution).

Role in the Hierarchy

Elementary Events constitute the first true dynamical level of the Process of Formation of Physical Reality. They provide:

the pre-spatial structure of variation (σ),
the pre-temporal statistical evolution (τ),
the four foundational aspects from which all physical quantities emerge,
the raw dynamical content from which Elementary Action arises.

EE are therefore the bridge between the ontological ground (Level 0) and the emergence of dynamical tendencies (Level 2).

Operational Guidelines

Define EE(x, τ) as the local fluctuation of the Field at an Event-Point.
Decompose each EE into the four aspects {A, n, χ, u}.
Treat σ-fluctuations as instantaneous pre-spatial variations.
Treat τ-distributions as statistical pre-temporal evolutions.
No geometry, metric, or spacetime structure is introduced at this level.
Analyze the possible influences/interactions among the manifestations of the four variational aspects of the Field's dynamism.

SUB-LEVEL 1.1 — σ-Fluctuations (Pre-Spatial Aspects)

Conceptual Definition

σ-Fluctuations represent the instantaneous pre-spatial configuration of an Elementary Event. They encode the local state of the Field in terms of four variational aspects:

A — amplitude of the fluctuation,
n — orientation tendency,
χ — chiral asymmetry,
u — axis-orientation tendency.

These aspects do not occur in space; they are the pre-spatial precursors of spatial structure.

Role in the Hierarchy

σ-Fluctuations provide the structural snapshot”' of the Field's local dynamism. They define the intrinsic configuration from which τ-evolution will extract statistical tendencies.

Operational Guidelines

Represent σ-fluctuations as instantaneous values of {A, n, χ, u}.
No temporal evolution is associated with σ.
σ defines the local “shape” of the EE before any statistical accumulation.

SUB-LEVEL 1.2 — τ-Distributions (Pre-Temporal Aspects)

Conceptual Definition

τ-Distributions describe the statistical evolution of each σ-aspect along the pre-temporal parameter τ. They encode how the instantaneous fluctuations manifest as a process and accumulate giving rise to emergent tendencies that will later (in a causal sense) become physical quantities.

Role in the Hierarchy

τ-Distributions transform instantaneous variation into structured dynamical content. They provide:

variability profiles for A,
alignment tendencies for n,
chiral asymmetry accumulation for χ,
axis-orientation coherence for u.

These statistical tendencies are the foundation of Elementary Action (Level 2).

Operational Guidelines

Model τ as a pre-temporal parameter with no metric or duration.
Represent τ-distributions as statistical functions of τ for each σ-aspect.
Use τ-distributions to derive the four components of Elementary Action.
No physical time or spacetime structure is introduced at this level.

LEVEL 2 — Elementary Action (EA)

Conceptual Definition

Elementary Action (EA) consists of the inhomogeneities in the dynamics of the Elementary Field, the local asymmetries (ΔP) that arise in the τ distributions of the four σ aspects (A, n, χ, u) of an Elementary Event (EE), when compared to their corresponding σ–τ stochastically symmetric distributions. A σ–τ stochastically symmetric distribution is defined by:

no pre-spatial prevalence in the σ fluctuations (isotropy), and
no pre-temporal prevalence in the single aspects of σ fluctuations, or equivalently, full pre-temporal homogeneity of the σ fluctuations in each aspect.

When this σ–τ symmetry holds for an aspect, the corresponding discrepancy is zero: ΔP_x=0.

When the symmetry is broken — in σ, in τ, or in both — an inhomogeneity appears: ΔP_x≠0.

Discrepancies are intended as measures of inhomogeneity, of asymmetry.

These inhomogeneities constitute the four Modes of Elementary Action, one for each σ aspect:

ΔP_A → Perturbation (fluctuation intensity asymmetry / discrepancy)
ΔP_n → Translation (fluctuation orientation asymmetry / discrepancy)
ΔP_χ → Rotation:Chirality (vortical chirality asymmetry / discrepancy)
ΔP_u → Rotation:AxisOrientation (vortical intrinsic axis asymmetry / discrepancy)

EA is therefore the first differentiation of the Field's dynamism: a set of pure, local, pre-physical tendencies, asymmetries, not yet correlated, not yet structured, and not yet manifest as physical content.

EA is not a force, not a potential, not a structure, and not a relation. It is simply the pattern of σ–τ asymmetries that emerge from the spontaneous dynamics of the Field and become the objects of correlation.

EA is the first appearance of dynamical asymmetry in the Field. It is pure differentiation — not yet relational, not yet structured, not yet physical. EA provides the dynamical material that the Relational Bridge will later configure into Information/Energy.

Role in the Hierarchy

Elementary Action plays a pivotal role in the Process of Formation of Physical Reality. It provides:

the first differentiated dynamical content extracted from τ distributions,
the four proto tendencies, which, in causally more advanced phases, will be correlated
the objects of the Relational Bridge (Level 2 → Level 3),
the pre-physical dynamical material from which Information/Energy (potentials) will emerge.

EA is the level where dynamical asymmetry appears, but no correlation yet exists.

Operational Guidelines

Derive EA from the discrepancies of the τ-distributions: ΔP_A, ΔP_n, ΔP_χ, ΔP_u.
For each σ aspect, compute the discrepancy (each discrepancy ΔP_x corresponds to one Mode/sub-Mode of EA):

ΔP_x=τ_x^"actual" -τ_x^"σ-τ symmetric" .

- If the τ distribution is σ–τ symmetric → ΔP_x = 0.
- If the τ distribution is σ–τ asymmetric → ΔP_x ≠ 0.
EA is the four component vector:

EA=(ΔP_A,ΔP_n,ΔP_χ,ΔP_u).

- Proto-stress intensity (ΔP_A → Perturbation)
- Proto-stress orientation (ΔP_n → Translation)
- Proto-vorticity chirality (ΔP_χ → Rotation:Chirality)
- Proto-vorticity intrinsic axis orientation (ΔP_u → Rotation:AxisOrientation)
No geometry, metric, spatial relation, or correlation is introduced at this level.
EA is not (yet) Energy, Metric/Mass, Accelerated or Inertial Motion, Electric potential or Charge, Magnetic potential or Spin — only the pre-physical tendencies' from which these will emerge.

SUB-LEVEL 2.1 — Intensity Asymmetry (ΔP_A → Perturbation)

Conceptual Definition

ΔP_A, proto-stress intensity discrepancy, measures the deviation of the amplitude τ distribution from σ–τ stochastic symmetry. It configures the Field's tendency toward local intensity (of σ-fluctuations) variation -> Perturbation.

Role in the Hierarchy

Proto-stress intensity provides:

the intensity component of the Field's linear deformation tendency,
the foundation (the causal precursor) for Metric and Mass at Level 3 and 4 respectively,
the seed of gravitational and inertial behavior.

Operational Guidelines

Compute proto-stress intensity as ΔP_A -> Perturbation EA Mode.
Treat ΔP_A as a pre-physical intensity tendency, not (yet) as Metric / Mass.

SUB-LEVEL 2.2 — Orientation Asymmetry (ΔP_n → Translation)

Conceptual Definition

ΔP_n , proto stress orientation discrepancy, measures the deviation of the orientation τ distribution from σ–τ isotropy and homogeneity. It configures the Field's tendency toward directional asymmetry (Translation). It is the causal precursor of Motion, inertia, acceleration, and kinetic behavior.

Role in the Hierarchy

Proto-stress orientation provides:

the orientation component of the Field's linear deformation tendency,
the foundation (the causal precursor) for Motion: acceleration and inertia and at Level 3 and 4 respectively,
the seed of kinetic and dynamical behavior.

Operational Guidelines

Compute proto-stress orientation as ΔP_n -> Translation EA Mode.
Treat it as a pre-physical motion tendency, not (yet) as acceleration or inertia, velocity or momentum.

SUB-LEVEL 2.3 — Chirality Asymmetry (ΔP_χ → Rotation:Chirality)

Conceptual Definition

ΔP_χ, proto vorticity chirality discrepancy, measures the deviation of the chirality τ distribution from σ–τ symmetric behavior. It configures the Field's intrinsic tendency toward chiral asymmetry. It is the causal precursor of Electric potential and electric Charge.

Role in the Hierarchy

Proto-vorticity chirality provides:

the chiral component of the Field's intrinsic angular deformation tendency,
the foundation (the causal precursor) for Electric potential and Charge at Level 3 and 4 respectively,
the seed of chiral and electric asymmetry.

Operational Guidelines

Compute proto-vorticity chirality as ΔP_χ -> Rotation:Chirality EA Mode.
Treat it as a pre-physical polarity tendency, not (yet) as electric Charge.

SUB-LEVEL 2.4 — Axis Orientation Asymmetry (ΔP_u → Rotation:AxisOrientation)

Conceptual Definition

ΔP_u, proto vorticity intrinsic axis orientation discrepancy, measures the deviation of the intrinsic axis orientation τ distribution from σ–τ symmetry. It configures the Field's tendency toward intrinsic axial asymmetry (Rotation:AxisOrientation). It is the precursor of Magnetic potential and Spin.

Role in the Hierarchy

Proto-vorticity intrinsic axis orientation provides:

the axial component of the Field's intrinsic angular deformation tendency,
the foundation (the causal precursor) for Magnetic potential and Spin at Level 3 and 4 respectively,
the seed of intrinsic vortical /angular polarization.

Operational Guidelines

Compute proto-vorticity intrinsic axis orientation as ΔP_u -> Rotation:AxisOrientation EA Mode.
Treat it as a pre-physical intrinsic vortical tendency, not (yet) as Spin or magnetic moment.

LEVEL 3 — Information/Energy (Emergent Physical Content)

Conceptual Definition

Information/Energy is the level at which the four components of Elementary Action, once correlated through the Relational Bridge, manifest as unstructured physical quantities — the physical potentials within the Field and acquire a recognizable physical meaning.

At this level:

the pre-physical tendencies of EA become physical content, acquire a recognizable physical meaning,
the Field expresses Fundamental Physical Quantities in their non structured, diffuse form,
the four Modes of EA give rise to four Fundamental Physical Potentials:
- Mass potential: “Metric”'
- Motion potential: “Acceleration”
- “Electric potential”
- “Magnetic potential”

They represent the unstructured energetic forms through which the turbulent dynamics of the Field can be described. InfoStructures do not emerge from these potentials, but from the underlying turbulence of the Field; as we will see in Level 4, once formed, they acquire their own physical identity and become sources of the corresponding potentials (Metric deformation, potential Motion or “Acceleration” through gravitational, electric and magnetic attraction/repulsion, Electric and Magnetic potentials in their surroundings).

In other words:

Level 3 is the emergence of physical quantities in their potential (unstructured) form.
Level 4 is the emergence of physical quantities in their effective (structured) form.

At this level, the Field's variational tendencies become physical potentials, although not yet physical structures:

Perturbation configures Metric as a physical potential;
Translation configures Motion as a physical potential (acceleration);
Rotation:Chirality configures Electric potential;
Rotation:AxisOrientation configures Magnetic potential.

Mapping between EA Modes / Components, Physical Potentials, and InfoStructures

Mode/Sub Mode of EA Information/Energy (Unstructured Physical Quantity — Potential) InfoStructure (Structured Physical Quantity — Effective) Perturbation Metric deformation/curvature (Mass potential) Mass Translation Motion potential: Acceleration Effective Motion: Inertial or accelerated Motion Rotation:Chirality Electric potential Electric Charge Rotation:AxisOrientation Magnetic potential Magnetic Spin

This level of Information / Energy is the first level at which a preliminary form of “structure” manifests itself, represented by the Relations that organize Events, by the correlation patterns of Elementary Action in its Modes / Components. I recall that “structure” is what we observe—the apparently more stable aspect of a Physical Reality in incessant transformation. It is the outward aspect of the underlying dynamic Processes that enable the continuous formation of the Existence and the Essence Form of what we observe, of the “structure” of Potentials and of InfoStructures (Waves, Particles, Dark Halos, Interactions that produce Composite Structures).

At this level, structure manifests in a “potential” mode, in what we indeed call Potentials (Metric deformation or curvature, i.e., Mass Potential; Motion Potential, i.e., acceleration; Electric Potential; and Magnetic Potential). At the next level, that of InfoStructures, structure will manifest in an “effective” mode, as the Fundamental Physical Quantities of the InfoStructures themselves (Mass, Effective Motion, electric Charge, magnetic Spin).

The dynamic Processes underlying the “structure” of the objects of Physical Reality (Processes = Events produced by Entities/Sources/Force–Field pairs, organized by Relations) can—and must—be formally modeled through mixed processes, stochastic and deterministic. These correspond, respectively, to the omnipresent indeterminate component, the manifestation of the fundamental uncertainty and randomness of the dynamism of the Elementary Field—of Elementary Action, therefore—upon which the deterministic component is partially superimposed, representing the organization of Relations (correlations of Elementary Action in its various Modes), the Information / Energy that expresses the form we observe, the Structures, the Forms that populate the Physical Universe.

The “indeterminate” component, which we model through stochastic processes, enables the Existence of Reality and of everything we observe, and provides the substrate for the “determinate” component, which we describe through deterministic processes—this component representing precisely the Essence / Form of everything that exists. No Form can exist without the underlying dynamic Processes (organizable chaos, pure potentiality) that sustain it. Everything that exists has a Form. Existence and Essence / Form are the two fundamental Properties of Reality—or, more precisely, of the “Formation of Reality.”

At the level of Information / Energy—the level of Potentials—the deterministic component (the portion of organization within the dynamism of the Field) manifests in simple forms (e.g., gradients with quadratic behavior, such as the gravitational potential, the electric potential, and the magnetic potential). At the next level, that of InfoStructures, this component appears organized into more complex forms (Waves, Vortices, Interactions). The two levels thus express two degrees of structural organization.

The random, indeterminate component is ineliminable, because it constitutes the foundation of the Existence of Reality—the direct manifestation of the Primary Source of Reality. We can describe it only through statistics and probability, through stochastic processes. This component is omnipresent, even though in increasingly complex Forms (classical objects, rocks, planets, galaxies, etc.) its manifestation becomes progressively less evident, overshadowed by the deterministic component, by the more defined, more stable, more certain Form. And in the middle world—the world of quantum objects, Waves, Particles, Interactions—uncertainty and indeterminacy emerge forcefully in the “weirdness” of what we observe and measure.

Reality is neither determined nor undetermined, neither certain nor uncertain, neither deterministic nor probabilistic. Reality is a composite dynamical process in which these two tendencies interact and co-evolve in a state of perpetual (dis)equilibrium.

A chaotic dynamism continuously reshapes the Form of Reality through incessant mutation. A structured dynamism tends to preserve the Form by stabilizing its patterns.

The actual evolution of Reality emerges from the interplay between these two regimes — one generative, one conservative — whose interaction produces the ongoing transformation and partial persistence of Form.

Role in the Hierarchy

Information/Energy is the first level of Physical Reality. The bridge between dynamical tendencies of Elementary Action (EA) and the organized physical structures of Level 4 (InfoStructures). At this level, the Field exhibits:

the first emergence of physical content from EA,
the unstructured physical quantities corresponding to the structured physical quantities that will characterize InfoStructures,
the energetic substrate in the form of turbulence within the Field, through which the dynamics of EA can be described and from which, under specific conditions and through specific dynamical processes, InfoStructures emerge, stabilize, and organize,
the energetic substrate in the form of physical potentials within the Field, produced by InfoStructures in their surroundings (Metric deformation due to Infostructure's Mass, Potential Motion, or Acceleration, through gravitational, electric and magnetic attraction/repulsion, Electric and Magnetic potentials generated by Charge and Spin respectively).

Without this level, the transition from EA (pre-physical asymmetries) to InfoStructures (structured physical entities) would be discontinuous and conceptually opaque.

Operational Guidelines

Derive Information/Energy exclusively from the correlations of the four components of EA.
Interpret the correlations of each EA component as a physical potential within the Field, not yet as a physical property of an InfoStructure. Both potentials and InfoStructures are pattern of less or more (respectively) organized correlations of the inhomogeneities in the τ–σ dynamism of the Field — inhomogeneities that constitute the embryonic forms of the Modes/Components of Elementary Action.

SUB-LEVEL 3.1 — Mass Potential (Metric) (from Perturbation)

Conceptual Definition

Mass potential (or Metric) is the physical content emerging from the Perturbation component of EA. It configures the Field's intrinsic tendency to accumulate intensity and curvature — a systematic alteration in the dynamism of the Field's amplitude aspect.

It is Mass as a physical potential — not the Mass of a Particle or of a Dark Halo, but the potential/energetic form – a deformation of the Metric - that corresponds to, and is produced by, the Mass of a massive InfoStructure (Vortex or Composite type).

Metric and Mass potential are two complementary descriptions of the same phenomenon: a pattern of organized discrepancy in the amplitude related dynamism of the Field.

This form of Information/Energy appears as a more or less structured pattern of local discrepancy in the rhythm of the flow of physical Time (curvature of the Metric or Mass) — two complementary perspectives on the same underlying alteration in the amplitude aspect of the pre-physical dynamism of the Elemental Field.

Role in the Hierarchy

Mass potential provides:

the metric-like physical content of the Field,
the precursor of gravitational behavior,
both the origin (the Field's turbulence that contributes to the formation of massive InfoStructures) and the product (the Metric deformation, or Mass potential, produced by the effective Mass of an InfoStructure) of Mass of InfoStructures.

Operational Guidelines

Compute Mass potential from the “statistical accumulation” of Perturbation.
Treat it as Metric-content (Metric deformation), not as particle Mass.

“Statistical configuration” refers to the emergence of a physical potential from systematic deviations in the τ distribution of EA — not a temporal accumulation, but a configurational one.

SUB-LEVEL 3.2 — Motion Potential (Acceleration) (from Translation)

Conceptual Definition

Motion potential (or Acceleration) is the physical content emerging from the Translation component of EA. It configures the Field's tendency toward directional asymmetry, acceleration.

It is Motion as a physical potential — not yet the inertial or the accelerated Motion of a structured InfoStructure, a wave or particle.

Role in the Hierarchy

Motion potential provides:

the precursor of inertial and accelerated Motion and kinetic behavior of InfoStructures and Forms (objects, etc.),
the foundation for effective motion in InfoStructures,
the energetic basis for dynamical quantities.

Operational Guidelines

Compute Motion potential from the directional asymmetry of Translation.
Treat it as motion-content (source of variation of motion), not as velocity or momentum.

SUB-LEVEL 3.3 — Electric Potential (from Rotation:Chirality)

Conceptual Definition

Electric potential is the physical content emerging from the Rotation:Chirality component of EA. It configures the Field's intrinsic tendency toward chiral asymmetry.

It is Charge as a physical potential — not yet the electric Charge of a structured InfoStructure, not yet the Charge of a particle.

Role in the Hierarchy

Electric potential provides: the precursor of electric behavior, the foundation for electric Charge in InfoStructures, the energetic basis for electromagnetic asymmetry.

Operational Guidelines

Compute Electric potential from the statistical chiral asymmetry. Treat it as electric content (polarization of the Field), not as electric Charge.

SUB-LEVEL 3.4 — Magnetic Potential (from Rotation:AxisOrientation)

Conceptual Definition

Magnetic potential is the physical content emerging from the Rotation:AxisOrientation component of EA. It configures the Field's intrinsic tendency toward intrinsic axial asymmetry.

It is 'Spin as a physical potential — not yet the magnetic Spin of a structured InfoStructure, not yet the Spin of a particle.

Role in the Hierarchy

Magnetic potential provides:

the precursor of magnetic behavior,
the foundation for Spin in InfoStructures,
the energetic basis for intrinsic vortical asymmetry.

Operational Guidelines

Compute Magnetic potential from the statistical directional axial asymmetry.
Treat it as magnetic content (magnetization of the Field), not as magnetic Spin.

LEVEL 4 — InfoStructures (Waves, Vortices, Interactions)

Conceptual Definition InfoStructures are the first true structured physical organizations of the pre-physical dynamism of the Elementary Field. They arise when the informational and energetic manifestations of Level 3 self organize into coherent (Wave-like, Vortex-like, Interaction-mediating) configurations of the Field.

An InfoStructure is:

a structured pattern of/within the Field's dynamism,
a localized or extended organization of Information/Energy,
the first physical form in the Process of Formation of Reality.

InfoStructures do not emerge from the potentials; they emerge from the turbulent dynamics of the Field, which the potentials describe. Once formed, InfoStructures acquire their own physical identity and configure the Field around them, becoming sources of the corresponding potentials.

Two complementary families naturally arise:

dark InfoStructures → structured but diffuse, low density, extended, non concentrated,
ordinary InfoStructures → structured and concentrated, the precursors of particle like entities.

Both families share the same ontological root: they are structured organizations of the Field's informational and energetic content.

Role in the Hierarchy

Vortex-type and Interactions (Composite) InfoStructures provide the first coherent manifestation of the four structured physical quantities:

Mass,
Effective Motion (inertial or accelerated Motion),
Electric Charge,
Magnetic Spin.

Wave-type InfoStructures provide the first coherent manifestation of only the two structured physical quantities:

Effective Motion (in the form of inertial Motion),
Magnetic Spin, in the form of wave polarization.

InfoStructures constitute:

the bridge between unstructured physical content (Level 3) and effective physical Forms (Levels 5–7),
the structural basis for the internal equilibrium conditions (Level 4.4),
the organizational templates from which Waves, Vortices, and Interaction patterns will emerge, both in the dark/invisible and ordinary/visible sides,
the first structures capable of configuring the Field and generating potentials in their surroundings.

Without InfoStructures, the transition from Information/Energy to physical Forms would be impossible.

Operational Guidelines

Construct InfoStructures exclusively from the four informational-energetic non-structured physical quantities that correspond to the Level 3 potentials.
Treat InfoStructures as 'dynamical organizations of the Field , not as classical fields, and not as geometric objects.
Maintain the distinction between:
- dark InfoStructures (diffuse, extended, low density),
- ordinary InfoStructures (concentrated, high density).
Identify three primary families of organization:
- 'Wave-like InfoStructures
- Vortex-like InfoStructures
- Interaction-mediating InfoStructures
Avoid introducing spacetime geometry, curvature, or metric structure: these appear only as potentials configured by InfoStructures, not as geometric entities.

SUB-LEVEL 4.1 — Wave-Like InfoStructures

Conceptual Definition

Wave like InfoStructures are structured organizations of the pre-physical dynamism of the Elementary Field that configure coherent oscillatory patterns. Ontologically, they are not waves in spacetime, nor geometric oscillations, nor classical field modes. They are organized dynamical patterns of Information/Energy within the Field itself.

These configurations arise when the dynamical content described at Level 3 becomes structured into forms that assume single cycle or multi cycle wave like organizations. They are patterns of correlation among the Modes of EA:

Translation, giving rise to the Property and Behavior we call Effective Motion (Inertia) -> linear momentum
Rotation:AxisOrientation, the wave version of Spin, expressed as magnetization -> angular momentum

These oscillatory forms may be:

diffuse and extended (dark wave like InfoStructures),
localized and concentrated (ordinary wave like InfoStructures).

In both cases, the oscillation is a pattern of the dynamism “of” the Field — something that propagates “within” the Field — not a propagation through a pre given geometric medium.

Role in the Hierarchy

Wave-like InfoStructures provide:

the first organized (physical, manifest, structured) form of propagation within the Field,
the pre-geometric precursor of wavefunctions and field oscillations,
the oscillatory templates from which quantum-like behavior will later be represented.

They are the first way in which the Field manifests its own dynamism in oscillatory form.

Operational Guidelines

Construct wave like InfoStructures from the EA Modes Translation and Rotation:AxisOrientation
Derive the fundamental quantities Effective Motion and polarization (the counterpart of Spin in Waves)
Treat them as oscillatory organizations of the Field, not as waves in spacetime.
Maintain the distinction between:
- dark wave like InfoStructures → diffuse, extended, low density oscillatory patterns,
- ordinary wave like InfoStructures → concentrated oscillatory patterns.
Do not introduce geometry, metric, or spacetime propagation (even though, from a phenomenological and dynamical perspective, they can be described in such terms; ontologically, however, they must be described in terms of the forms and dynamics of Elementary Action).
Identify oscillatory coherence as the defining feature. In the case of single cycle waves, the originating phenomenon is not periodic. These are single events that may repeat in phase while still remaining single events (e.g., the motion of an electron within the electronic cloud, across different energy levels).

SUB-LEVEL 4.2 — Vortex-Like InfoStructures

Conceptual Definition

Wave like InfoStructures are structured organizations of the pre-physical dynamism of the Elementary Field that configure vortical patterns. Ontologically, they are not vortices in spacetime, nor geometric structures, nor classical field organizations. As Waves, even if their shape and dynamics is profoundly different, they are organized dynamical patterns of Information/Energy within the Field itself.

These configurations arise when the dynamical content described at Level 3 becomes structured into forms that assume vortex like organizations. They are patterns of correlation among the Modes of EA:

Perturbation, giving rise to the Property and Behavior we call Mass -> deformation of the local Metric (time flow rate)
Translation, giving rise to the Property and Behavior we call Effective Motion (Inertia) -> linear momentum
Rotation:Chirality, the electric Charge
Rotation:AxisOrientation, the magnetic Spin -> angular momentum

Vortex InfoStructures can be:

diffuse and extended (dark vortex like InfoStructures),
localized and concentrated (ordinary vortex like InfoStructures).

In both cases, Rotation is an intrinsic pattern of the Field's own dynamism, not a motion through a geometric background.

Role in the Hierarchy Vortex-like InfoStructures provide:

the first organized (physical, manifest, structured) form of conservation within the Field,
the pre-geometric precursor of halos and particles,
the vortical templates from which quantum-like behavior will later be represented in particles.

They are the Field's first way of configuring its dynamism into vortical form.

Operational Guidelines

Treat them as vortical organizations of the dynamism of the Field, not as classical vortices.
Construct wave like InfoStructures from all the EA four Modes Perturbation, Translation, Rotation:Chirality and Rotation:AxisOrientation
Derive the fundamental quantities Mass, Effective Motion, Charge and Spin
Treat them as vortical organizations of the Field, not as particles in spacetime.
Maintain the distinction between:
- dark vortex like InfoStructures → diffuse, extended, low density vortical patterns (dark halos),
- ordinary vortex like InfoStructures → concentrated vortical patterns (ordinary Matter Particles).
Do not introduce geometry, metric, or spacetime conservation (even though, from a phenomenological and dynamical perspective, they can be described in such terms; ontologically, however, they must be described in terms of the forms and dynamics of Elementary Action).
Identify vortical coherence as the defining feature: the Field manifests intrinsic rotation through the structured interplay of Spin and Charge, with Mass, the fulcrum that stabilizes, and Motion, which confers its dynamical behaviors.

SUB-LEVEL 4.3 — Interaction-Mediating InfoStructures

Conceptual Definition

Interaction mediating InfoStructures are structured physical organizations of the pre-physical dynamism of the Elementary Field in which wave like and vortex like patterns configure relational coherence. They do not “transmit” forces, nor act as carriers, nor propagate interactions through a geometric medium. They are relational organizations of structured Information/Energy through which different InfoStructures interact and influence one another.

These structures do not “transmit” forces; they are the dynamical patterns through which different InfoStructures influence each other.

These configurations arise when Perturbation, Translation and Rotation patterns (Mass, Effective Motion, Charge and Spin) become mutually correlated, giving rise to:

diffuse relational patterns (dark interaction mediating InfoStructures, like dark-web components),
localized relational patterns (ordinary interaction mediating InfoStructures, like composite particles: hadrons).

In both cases, Interaction is not a force acting between entities, but a coherent relational pattern within the Field.

Role in the Hierarchy

Vortex-like InfoStructures provide:

a more complex form of organized (physical, manifest, structured) form within the Field,
the pre-geometric precursor of dark-cosmic-web components and composite particles, the pre-geometric precursor of couplings, interaction channels, and gauge like behavior,
the multi-vortical templates from which complex quantum-like behavior will later be represented in composite particles.

They are a more complex way of configuring the Field's dynamism into vortical form.

Operational Guidelines

Treat them as multi-vortical organizations of the dynamism of the Field, not as classical vortices.
Construct interaction-mediating InfoStructures from couplings between vortex-like patterns, with or without the interaction with wave-like structures (mediators).
Derive the fundamental quantities Mass, Effective Motion, Charge and Spin (a very difficult task, as QFT / SMP theorists can attest)
Treat them as multi-relational organizations, not as force carriers or mediators in spacetime.
Maintain the distinction between:
- dark interaction mediating InfoStructures → diffuse, extended relational composite patterns,
- ordinary interaction mediating InfoStructures → concentrated relational composite patterns.

SUB-LEVEL 4.4 — Equilibrium Equations (Internal Conditions of Coherence)

Conceptual Definition

Equilibrium Equations are the internal conditions of coherence that govern the Existence and the Essence/Form of InfoStructures. These equations do not introduce new content or new levels of Reality. They are the mathematical expression of the Field's intrinsic requirement for coherent organization. An InfoStructure exists only insofar as it satisfies its corresponding equilibrium condition that defines shape, properties, behaviors, dynamics of the Structure.

While InfoStructures represent organized configurations of Information/Energy, the Equilibrium Equations express the dynamical constraints that such configurations must satisfy in order to persist, to conserve, to propagate in Time. An InfoStructure is not something that exists and then satisfies an equation. An InfoStructure is the Field in a configuration that satisfies its corresponding equilibrium condition.

These equations therefore express:

the internal balance among the structured quantities (Mass, Effective Motion, Charge, Spin),
the coherence of oscillatory, vortical, or relational patterns,
the compatibility of the Field's dynamism with the form that the InfoStructure manifests,
the way in which Structures produce the manifestation of Potentials in the Field, and the way in which they react to the Potentials present within the Field.

They are pre-geometric, pre-spatiotemporal, and they do not describe evolutions in time: they describe conditions of form. In the sense that they are expressed in terms of the dynamics of Elementary Action (pre-physical, pre-geometric, etc.) and define how Structures manifest within the physical environment that we describe through derived Structures and Processes we call spacetime, electric field, magnetic field, and so on.

Role in the Hierarchy

Equilibrium Equations play a foundational role within Level 4. They provide:

the internal law that governs the formation and persistence, and dissolution of InfoStructures,
the dynamical constraints that determine the possible forms of waves, vortices, and interaction patterns (which oscillatory, vortical, and relational organizations are possible),
the structural basis from which quantum-like and field-theoretic equations (Levels 5–6) will later emerge,
the mathematical bridge between pre-geometric organization and effective physical equations.

They do not come “after” InfoStructures; they are the condition for their existence, the very condition by which an organization of the Field can manifest as an InfoStructure.

Operational Guidelines

Derive Equilibrium Equations exclusively from the internal dynamics of the InfoStructure.
Do not introduce external forces, potentials, or spacetime geometry.
Treat the equations as conditions of internal coherence, not as dynamical laws imposed from the outside.
Distinguish three families of conditions:
- Wave-like InfoStructures → oscillatory equilibrium conditions,
- Vortex-like InfoStructures → vortical equilibrium conditions,
- Interaction-mediating InfoStructures → coupling/relational equilibrium conditions.
Use these equations to determine:
- domains of coherence,
- allowed configurations,
- internal symmetries,
- emergent conservation tendencies.
Maintain the distinction between:
- dark equilibrium patterns → diffuse, extended coherence conditions,
- ordinary equilibrium patterns → conditions of concentrated coherence.

Equilibrium Equations are therefore the mathematical core of Level 4 — the internal law that shapes the form and essence of InfoStructures.

SUB-LEVEL 4.5 — Proto-Physical Equations (Emergent Effective Equations)

Conceptual Definition

Proto Physical Equations are the effective mathematical expressions that emerge when the Equilibrium Equations are reorganized into a more compact, operational, and structurally recognizable form. They do not introduce new content, new forces, or new levels of Reality. They are the effective reformulation of the internal coherence conditions that define wave like, vortex like, and interaction mediating InfoStructures.

While the Equilibrium Equations express the internal balance that an InfoStructure must satisfy to manifest as a coherent configuration of the Field, the Proto Physical Equations express the same coherence in a form that anticipates the structure of familiar physical relations — oscillatory, vortical, and relational — without yet invoking geometry, spacetime, or quantization.

They are pre-geometric, pre-quantum, and pre-spacetime: they describe relations of form, not evolution in time or propagation in space.

Role in the Hierarchy

Proto Physical Equations provide:

the first effective mathematical description of the internal dynamics of InfoStructures,
the structural seeds of wave like, vortex like, and interaction like behavior,
the bridge between internal coherence (previous sub-level) and effective physical representations (next levels),
the pre-geometric precursors of wave equations, vortex like relations, and interaction like couplings.

They are not physical laws: they are the effective form of the Field's coherence conditions when it organizes itself into InfoStructures.

Operational Guidelines

Derive Proto Physical Equations exclusively from the Equilibrium Equations of Level 4.4
Do not introduce geometry, metric, spacetime, or quantization.
Identify three families of effective relations:
- proto-wave equations → arising from the oscillatory coherence of wave like InfoStructures,
- proto-vortex equations → arising from the vortical coherence of vortex like InfoStructures,
- proto-interaction equations → arising from the relational coherence of interaction mediating InfoStructures.
Maintain the distinction between:
- dark proto equations → diffuse, extended effective relations,
- ordinary proto equations → concentrated effective relations.
Treat these equations as relations of form, not as temporal dynamics or propagation laws.

Proto Physical Equations are therefore the first effective mathematical form of Level 4: the operational translation of the Field's internal conditions of coherence at the base of the different shapes of the InfoStructures (Wave, Vortex, Interaction).

SUB-LEVEL 4.5.1 — Proto-Wave Equations

Conceptual Definition

Proto Wave Equations are the effective mathematical relations that arise when the oscillatory Equilibrium Conditions of wave like InfoStructures are expressed in compact form. They describe the coherent oscillatory organization of the Field's structured quantities:

Effective Motion (correlation of Translation EA Mode, inertia, linear momentum, wave impulse)
Magnetic Spin (wave version) (correlation of Rotation:AxisOrientation, angular momentum, wave polarization),

without invoking geometry, spacetime, or temporal evolution.

These equations do not represent waves propagating in space or oscillations in time. They represent oscillatory form, the intrinsic coherence of the Field when it manifests a Wave-type InfoStructure.

Operational Guidelines

Derive Proto Wave Equations exclusively from the oscillatory equilibrium conditions of wave like InfoStructures.
Treat them as pre-geometric oscillatory relations, not as wave equations in spacetime.
Maintain the distinction between:
- dark proto wave relations → oscillatory coherence in diffuse, extended patterns,
- ordinary proto wave relations → oscillatory coherence in concentrated patterns.
Do not introduce frequency, wavelength, or propagation speed: these appear only after geometric projection (4.6).

Proto Wave Equations are the effective form of the Field's oscillatory coherence.

SUB-LEVEL 4.5.2 — Proto-Vortex Equations

Conceptual Definition

Proto Vortex Equations are the effective mathematical relations that arise when the vortical Equilibrium Conditions of vortex like InfoStructures are expressed in compact form. They describe the coherent vortical organization of the Field's structured quantities:

Mass (Effective Metrics) (correlation of Perturbation EA Mode, Mass density, inhomogeneity in the local rate of the flow of Time, inhomogeneity in the local velocity of Causality, Action, Information, inhomogeneity in the temperature of the Elementary Field, deformation of the local Metric of the Field),
Effective Motion (correlation of Translation EA Mode, inertia, linear momentum, vortex kinetic Energy),
Electric Charge (correlation of Rotation:Chirality, chirality of the Vortex),
Magnetic Spin (vortex version) (correlation of Rotation:AxisOrientation, angular momentum, spatial orientation of the axis of vorticity),

without invoking geometry, spacetime, or temporal evolution.

These equations do not represent physical vortices, nor spatial rotations, nor geometric angular momenta. They represent the vortical form, the internal coherence of the Field when it manifests a vortical InfoStructure.

Operational Guidelines

Derive Proto Vortex Equations exclusively from the vortical equilibrium conditions of vortex like InfoStructures.
Treat them as pre-geometric vortical relations, not as classical vortex equations.
Maintain the distinction between:
- dark proto vortex relations → vortical coherence in diffuse, extended patterns,
- ordinary proto vortex relations → vortical coherence in concentrated patterns.
Do not introduce angular momentum, chirality, circulation, or geometric/dynamic spin: these emerge only after the geometric projection (4.6).

Proto Vortex Equations are the effective form of the Field's vortical coherence.

SUB-LEVEL 4.5.3 — Proto-Interaction Equations

Conceptual Definition

Proto Interaction Equations are the effective mathematical relations that arise when the relational Equilibrium Conditions of interaction mediating InfoStructures are expressed in compact form. They describe the coherent relational organization of the Field when oscillatory and vortical patterns become mutually correlated.

They do not represent forces, do not describe exchanges, and do not introduce mediating fields. They represent the relational form, the internal coherence of the Field when different InfoStructures mutually influence the organization of one another.

Operational Guidelines

Derive Proto Interaction Equations exclusively from the relational equilibrium conditions of interaction mediating InfoStructures (composite InfoStructures).
Treat them as pre-geometric relational constraints, not as force laws or coupling terms.
Maintain the distinction between:
- dark proto interaction relations → relational coherence in diffuse, extended patterns,
- ordinary proto interaction relations → relational coherence in concentrated patterns.
Do not introduce coupling constants, gauge fields, or interaction strengths: these emerge only after the geometric projection (4.6).

Proto Interaction Equations are the effective form of the Field's relational coherence.

SUB-LEVEL 4.6 — Emergence of QM/QFT Equations (Geometric / Quantum Projection of Field Structures)

Conceptual Definition

The equations of Quantum Mechanics and Quantum Field Theory emerge when the internal coherence of InfoStructures — expressed through the Proto Physical Equations (4.5) — is projected into geometric and algebraic representation spaces — including Hilbert space for quantum representation. This projection does not introduce new entities, new forces, or new levels of Reality. It provides a geometric and algebraic representation of the Field's internal organization.

The Field manifests structured dynamisms (Level 4).
Mathematics represents these dynamisms through geometric, algebraic, and symmetry based formalisms (QM/QFT).

QM/QFT equations are therefore representational shadows of the Field's intrinsic coherence, not fundamental ontological laws. They describe how the internal forms of oscillation, vortical form, and relational coherence appear when expressed in:

geometric spaces (spacetime),
algebraic spaces (Hilbert space),
symmetry spaces (gauge groups).

Role in the Hierarchy

This sub level provides:

the geometric representation of wave like, vortex like, and interaction mediating InfoStructures,
the emergence of effective equations such as Schrödinger, Dirac, Klein Gordon, Maxwell, and Yang Mills,
the mathematical bridge between the Field's internal coherence and the observable behavior of physical systems,
the formal language through which InfoStructures become experimentally accessible.

QM/QFT equations do not describe the Field itself. They describe how the Field's internal forms appear when expressed in geometric and algebraic terms.

Operational Guidelines

Derive QM/QFT equations by projecting Proto Physical Equations (4.5) into:
- geometric spaces (spacetime),
- algebraic spaces (Hilbert space),
- symmetry spaces (gauge groups).
Treat these equations as effective representations, not as ontological primitives.
Maintain the distinction between:
- internal dynamics (Level 4),
- geometric representation (Sub Level 4.6).
Identify the three main families of emergent equations:
- wave equations ← geometric projection of wave like InfoStructures,
- spinor equations ← geometric projection of vortex like InfoStructures,
- gauge equations ← geometric projection of interaction mediating InfoStructures.
Do not introduce geometry or quantization at Level 4: these appear only at the representational stage.

QM/QFT equations are thus the final representational expression of Level 4 — the geometric and algebraic appearance of the Field's internal coherence.

Notes on Gravity, Quantum Theory, and the Search for a Third Way

We should not call photons particles. And perhaps not even the other bosons, including those with Mass (where the situation becomes even more confusing). Photons are Single Cycle Waves, therefore “Waves”, constituting Ordinary (visible) Radiation — not Matter Particles like Vortices and the Composite InfoStructures resulting from Vortex interactions.

Bringing gravity and quantum theory together is one of the most demanding and difficult tasks physics has ever faced. Some believe gravity must be quantized; others think quantum physics must be “gravitized.” I prefer to think that a different path is needed: that both theoretical worlds (GR and QM/QFT/SMP) are incomplete, mistaken in some aspects, and certainly in their interpretations. In my view, we must go deeper, to uncover the Fundamental Nature of Reality; to identify the dynamical and structural basis underlying Metric of Space time, Mass, and the other Fundamental Physical Quantities (Motion, Charge and Spin) that characterize InfoStructures (Waves, Vortices, Interactions) in both the ordinary/visible sector (EM waves and particles of Ordinary Matter) and the dark/invisible sector (GW waves and halos of Dark Matter). A third way, therefore.

In my view, it is not true that one can determine with infinite precision the distance between two classical objects. This is an illusion, arising from several factors:

dimensional: classical objects, even the smallest ones, are immensely larger than quantum objects and especially than their uncertainty margins;
perspectival: classical objects, by their nature and size, are observed and measured from considerable distances, whereas the quantum effects that make the quantum world so “weird” occur at much smaller scales;
mediative and compensatory: in classical systems — always composed of a large number of quantum objects — the individual quantum contributions average out and compensate each other, reducing their relevance and observability.

LEVEL 5 — Forms (Composite Physical Structures)

Conceptual Definition

Forms are composite physical organizations arising from the coupling of multiple InfoStructures.

While Level 4 describes the elementary structured dynamisms of the Field (wave like, vortex like, relational interactions), Level 5 describes how these dynamisms combine into composite structures — atoms, molecules, materials, cells, organisms, planets, stars, galaxies — the familiar architectures of the physical world.

Forms are not new ontological entities. They are multi scale organizations of InfoStructures, dynamically stabilized around characteristic attractors.

Dynamism Expressing Structure

I recall that, as with InfoStructures, what we perceive as structure in Forms — whether more or less persistent — is in fact dynamism (the dynamism of the Elementary Field, Events organized by Relations) that organizes itself stochastically around a form attractor, a sufficiently stable dynamic process, though in ceaseless variation around a characteristic variational trajectory of the type of InfoStructure or Form we are observing.

We see the Structure (e.g., the particle, the atom, etc.), but what truly exists and evolves is a dynamic Process which, in its incessant unfolding, expresses structure — the Essence / Form of what we observe.

We observe an electron and assume it is an electron like all the others, all identical. From the standpoint of the Properties and Behavior of the Structure, this is correct; yet the dynamic Process that enables its Existence and the Essence / Form we perceive is unique and in continuous formation, like all of Reality.

Nothing is stable, certain, eternal, or immutable. Even the Forms that appear most stable (e.g., an Egyptian pyramid), when observed across sufficiently large temporal extensions and sufficiently small spatial scales, reveal themselves to be in incessant mutation.

Descending through dimensional scales, toward the most elementary levels of Reality, we would see a teeming of ceaseless activity, down to Elementary Action — the Events we can characterize as pre-spatial fluctuations that shake the Elementary Field under the incessant Action of the Fundamental Force.

Dynamism and structure are two faces of the same coin, two fundamental perspectives. The first, which we cannot directly observe, focuses on Action; the second, which we do observe, focuses on Information / Energy, structure, InfoStructures, Forms.

Role in the Hierarchy

Forms provide:

the first composite organizations of structured physical quantities,
the multi scale architectures underlying Matter, Life, and cosmic structure,
the bridge between Elementary Field organization (Level 4) and the domains studied by the natural sciences,
the context in which conventional physical laws (thermodynamics, chemistry, biology, astrophysics) apply.

Level 5 is therefore the point where the Process of Formation of Physical Reality becomes scientifically familiar.

Operational Guidelines

Construct Forms exclusively from coupled InfoStructures.
Do not introduce new fundamental forces or entities.
Treat Forms as 'emergent composite multi-scale organizations.
Recognize three broad families, corresponding to established scientific domains:
- atomic and molecular Forms (chemistry, materials science),
- mesoscopic and biological Forms (biology, physiology, ecology),
- astrophysical and cosmological Forms (astronomy, astrophysics, cosmology).

SUB-LEVEL 5.1 — Atomic and Molecular Forms

Atomic and molecular Forms arise from the organization of (essentially) vortex/particle like InfoStructures into (more or less) persistent composite units. They constitute the domain of chemistry and materials science, which already provides the detailed models of bonding, structure, and interaction.

SUB-LEVEL 5.2 — Mesoscopic and Biological Forms

Mesoscopic and biological Forms arise from the organization of molecular Forms into composite structures and, at higher thresholds, into living systems.

Mesoscopic Forms include inorganic and organic assemblies that exhibit stability and organized complexity without yet being alive.

Biological Forms emerge when mesoscopic organization attains living functionality, giving rise to metabolism, replication, and adaptive behavior.

This corresponds to the domains of mesoscopic physics, pre-biotic organization, and the biological sciences, which already provide detailed models of structure, function, and interaction.

SUB-LEVEL 5.3 — Astrophysical and Cosmological Forms

Astrophysical and cosmological Forms arise from the large scale organization of InfoStructures into gravitationally and dynamically coherent systems.

These Forms include stars, planetary systems, galaxies, clusters, and cosmic filaments, which constitute the macroscopic architecture of the universe.

This corresponds to astronomy, astrophysics, and cosmology, which already provide detailed models of structure, evolution, and interaction at cosmic scales.

Transversal Perspectives on Forms

(non ontological; apply across all sub levels)

These sections do not introduce new entities. They are analytical perspectives that describe how Forms behave, cooperate, recur, or situate themselves within broader contexts.

Processes (Dynamics of Forms)

Processes are the dynamical behaviors through which Forms evolve, interact, transform, and reorganize across time and scale. They are not new entities: they are the time dependent expressions of Forms interacting with other Forms and with their environment.

They correspond to the dynamical transformations studied in physics, chemistry, geoscience, biology, ecology, planetary science, astrophysics, and cosmology.

This perspective applies across all three families of Forms and includes the established scientific classifications:

Physical and Chemical Processes, arising from atomic and molecular Forms, encompassing phase transitions, reaction pathways, diffusion and transport phenomena, crystallization, and the thermodynamic transformations that structure materials and chemical environments.
Geologic, Pre-biotic, Biological, Ecological Processes, arising from mesoscopic and biological Forms, encompassing mineral and material transformations, morphogenetic and metabolic dynamics, adaptive and evolutionary behaviors, and the multi scale interactions of organisms and environments that structure ecosystems and biospheres.
Astrophysical and Cosmological Processes, arising from large scale astrophysical Forms, encompassing stellar formation and evolution, nucleosynthesis, galactic dynamics, gravitational collapse, and the large scale processes that shape cosmic structure and cosmological evolution.

Systems (Integrated Multi Form Organizations)

Systems are integrated ensembles of Forms interacting through more or less persistent Processes. They are not new entities: they are higher order organizations of Forms whose interactions generate emergent properties such as regulation, coordination, feedback, stability, adaptation, and collective behavior.

They correspond to the integrated organizations studied in engineering, physiology, systems biology, ecology, Earth system science, planetary science, astrophysics, and cosmology.

This perspective applies across all three families of Forms and includes the established scientific classifications:

Physical and Technological Systems, arising from atomic, molecular, and material Forms, encompassing mechanical, electrical, thermodynamic, and engineered assemblies, and the coordinated behaviors that structure instruments, machines, infrastructures, and technological environments.
Biological and Ecological Systems, arising from mesoscopic and biological Forms, encompassing organisms, organs, populations, ecosystems, and biospheres, and the self regulating, adaptive, and cooperative dynamics that sustain living organization across scales.
Planetary, Stellar, and Galactic Systems, arising from large scale astrophysical Forms, encompassing planetary systems, stellar networks, galactic structures, and cosmic webs, and the gravitational and dynamical couplings that generate coherent astrophysical organization.

Patterns (Cross Scale Recurrence)

Patterns are recurring structural and dynamical motifs that emerge from the organization of Forms and Systems. They are not new entities: they are universal modes of organization through which Forms and Systems repeat, resonate, and self organize across scales.

They correspond to the universal structures studied in complexity science, nonlinear dynamics, network theory, morphology, fractal geometry, dynamical systems theory, and cosmic structure formation.

This perspective applies across all three families of Forms and includes the established scientific classifications:

Geometric Patterns, arising from the spatial organization of atomic, molecular, mesoscopic, and astrophysical Forms, encompassing lattices, spirals, polyhedra, fractals, tilings, and symmetry structures that recur across physical and cosmic scales.
Dynamical Patterns, arising from physical, chemical, geologic, pre-biotic, biological, ecological, and astrophysical Processes, encompassing cycles, oscillations, waves, feedback loops, attractors, and rhythmic or recurrent temporal structures.
Organizational Patterns, arising from the integration of Forms into Systems across technological, biological, ecological, planetary, and cosmological scales, encompassing networks, hierarchies, modularity, redundancy, and self similarity in multi scale organization.

Domains (Macro Realms of Organization) Domains are large scale contexts in which Forms, Processes, Systems, and Patterns manifest and interact. They are not new entities: they are macro realms within which structures acquire meaning, function, and evolutionary direction. They can be understood as macro contexts within the broader physical domain of Reality.

They correspond to the large scale contexts studied in physics, chemistry, geoscience, biology, ecology, Earth system science, planetary science, astrophysics, and cosmology.

This perspective applies across all three families of Forms and includes the established scientific classifications:

Physical and Chemical Domains, arising from the large scale organization of atomic and molecular Forms, encompassing phases of matter, chemical environments, reaction networks, and material ecosystems that structure physical and chemical organization.
Biological, Ecological, and Geologic Domains, arising from the large scale organization of mesoscopic and biological Forms, encompassing ecosystems, biomes, biospheres, evolutionary landscapes, and geologic environments that shape the dynamics of life and Earth systems.
Planetary, Astrophysical, and Cosmological Domains, arising from the large scale organization of astrophysical Forms, encompassing planetary environments, stellar regions, galactic structures, and cosmic networks that define the macro contexts of cosmic evolution.

Synthetic Pathway from the Source to Forms

This subsection provides a synthetic overview of the conceptual structures associated with each level of the Process of Formation of Physical Reality. It does not introduce new content; rather, it organizes the ontological architecture developed above into a unified pathway from the Source to Forms, offering the reader a clear conceptual map that supports the detailed treatments presented in the preceding sections and prepares the ground for the proto mathematical map that follows.

0 — SOURCE (Ontological Origin)

A pre-physical, non measurable entity.
It expresses its Agency in two modes:
- Direct (creative) → generates the Fundamental Force.
- Indirect (evolutionary) → operates through the Elementary Field.
The Source is the ontological engine of the entire process.

0.1 — FUNDAMENTAL FORCE (Causal Impulse)

The first physical act of the Source.

A pure scalar impulse, without direction or internal structure.

It is the only causal input of the model.

0.2 — ELEMENTARY FIELD (Variational Response)

A continuous, pre-spatial and pre-temporal substrate.

It possesses four intrinsic resistances to variation:
k_A, k_n → proto stress sector

k_χ, k_u → proto vorticity sector

The Force perturbs the Field → the Field responds → dynamism emerges.

0.3 — FORCE–FIELD INTERACTION

The Force acts.

The Field reacts according to its resistances.

This interaction generates the first local fluctuations.

The Elementary Events (EE) arise.

0.4 — EVENT-POINT (Analytical Operator)

Not a physical entity.

It serves to sample the local fluctuation of the Field.

1 — ELEMENTARY EVENTS (EE)

The first dynamical expressions of the Field.
Each EE has four pre-physical aspects:
- A — intensity
- n — orientation
- χ — chirality
- u — intrinsic axis
Two faces:
- σ → instantaneous configuration (pre‑spatial)
- τ → statistical distribution (pre‑temporal)

σ → instantaneous configuration (pre‑spatial)

2 — ELEMENTARY ACTION (EA)

Asymmetries in the τ distributions of the four aspects.
Four discrepancy modes (ΔP):
- ΔP_A → proto stress (intensity)
- ΔP_n → proto stress (orientation)
- ΔP_χ → proto vorticity (chirality)
- ΔP_u → proto vorticity (axis orientation)
EA = pre-physical tendencies, not yet physical quantities.

3 — INFORMATION / ENERGY (Unstructured Physical Potentials)

The Relational Bridge correlates the four EA components → physical potentials emerge:
- Φ_M → mass / metric potential
- Φ_A → motion / acceleration potential
- Φ_E → electric potential
- Φ_B → magnetic potential
These are diffuse physical contents, not yet (individuable, individuate) structures.

4 — INFOSTRUCTURES (Elementary Physical Structures)

The Field organizes the potentials into coherent dynamical forms:
- Wave like
- Vortex like
- Interaction mediating
Two levels:
- Equilibrium Equations → internal coherence conditions
- Proto Physical Equations → effective forms (proto wave, proto vortex, proto interaction)
Geometric projection →
- QM equations (Schrödinger, Dirac, Klein–Gordon)
- QFT equations (quantum fields)
- Gauge equations (Maxwell, Yang–Mills)
- Geometric equations (GR)

5 — FORMS (Composite Physical Structures)

The level of conventional physics.
Three major families:
- atomic and molecular
- mesoscopic and biological
- astrophysical and cosmological
Forms are multi scale organizations of InfoStructures.

10-Line Ultra-Synthetic Schema

Source → ontological origin
Fundamental Force → causal impulse
Elementary Field → variational response
Interaction → local fluctuations
Event-point → sampling operator
Elementary Events → four aspects (A, n, χ, u)
Elementary Action → four asymmetries (ΔP)
Potentials Φ → diffuse physical content
InfoStructures → elementary forms + projection → physical equations
Forms → composite structures of conventional physics

Synthetic Proto Mathematical Map of the Formalization Pathway Across Levels

This subsection provides a synthetic proto-mathematical overview of the formal structures associated with each level of the Process of Formation of Physical Reality. It does not introduce new conceptual content; rather, it organizes the mathematical expressions that accompany the ontological architecture developed above. Its purpose is to offer a unified map of the formalization pathway, preparing the ground for the more detailed mathematical development that will be presented in subsequent work.

LEVEL 0 — SOURCE, FORCE, FIELD

0.1 — Fundamental Force

Formal role: Single scalar causal impulse generated by the Source.

Symbol:

F₀

primitive scalar causal parameter (no associated dynamical equation).

0.2 — Elementary Field

Formal role: Pre-spatial, pre-temporal continuous substrate that responds to F₀.

General Field expression:

𝓕 = F₀ (A, n, χ, u; 𝑘_𝐴, 𝑘_𝑛, 𝑘_χ, 𝑘_u)

Resistance parameters:

𝑘_𝐴, 𝑘_𝑛 — proto stress resistances
𝑘_χ, 𝑘_u — proto vorticity resistances

Structure of resistances:

k_x = k_x^(intr) + k_x^(dyn) with x ∈ {A,n,χ,u}

Operational hypotheses (to be refined):

k_χ ≈ ε₀
k_u ≈ μ₀

0.3 — Force–Field Interaction

Formal role: Local variation of the Field induced by the Fundamental Force.

Elementary Event definition:

EE(𝑥,τ)= δF(𝑥,τ)

0.4 — Event-Point

Analytical operator used to sample local Field fluctuations.

No additional equation.

LEVEL 1 — ELEMENTARY EVENTS (EE)

Formal role: First dynamical expressions of the Field's response.

Decomposition into four aspects:

EE = {A,n,χ,u}

σ fluctuations (instantaneous configuration):

σ = (A,n,χ,u)_inst

τ distributions (statistical configuration):

(A(τ),n(τ),χ(τ),u(τ))

No dynamical equation is associated with this level: EE are local variations of the Field, not autonomous dynamical entities in the Field.

LEVEL 2 — ELEMENTARY ACTION (EA)

Formal role: Asymmetries in the τ distributions of the four aspects of EE.

General definition:

EA = (ΔP_A,ΔP_n,ΔP_χ,ΔP_u)

Discrepancy definition:

ΔP_x = τ_x^actual - τ_x^{σ - τ symmetric} with x∈{A,n,χ,u}

Modes:

ΔP_A → Perturbation
ΔP_n → Translation
ΔP_χ → Rotation:Chirality
ΔP_u → Rotation:AxisOrientation

EA is pre-physical: it encodes sub-elementary dynamical tendencies, not yet physical quantities.

LEVEL 3 — INFORMATION / ENERGY (POTENTIALS Φ)

(Non structured physical content)

Each potential emerges as the solution of an internal coherence condition of the Field, based on a single EA Mode.

Equilibrium conditions:

𝓒_M ≡ 𝓒(ΔP_A) = 0
𝓒_A ≡ 𝓒(ΔP_n) = 0
𝓒_E ≡ 𝓒(ΔP_χ) = 0
𝓒_B ≡ 𝓒(ΔP_u) = 0

Diffuse solutions (emergent potentials):

Φ_M ∈ Sol(𝓒_M)
Φ_A ∈ Sol(𝓒_A)
Φ_E ∈ Sol(𝓒_E)
Φ_B ∈ Sol(𝓒>_B)

These potentials are weakly structured physical contents, but not yet organized into individuable forms with any degree of stability.

LEVEL 4 — INFOSTRUCTURES

At this level, the Field's structured dynamism becomes organized form. Two types of equations appear:

Equilibrium Equations → internal coherence conditions (constraints on form).
Proto Physical Equations → effective pre-geometric forms (proto wave, proto vortex, proto interaction).

4.1 — Wave like InfoStructures

Derived primarily from: ΔPₙ and ΔPᵤ

Wave like equilibrium condition:

𝓒_wave(ΔP_n,ΔP_u) = 0

This expresses the internal coherence requirement that allows Translation and Rotation: Axis Orientation tendencies to organize into a persistent oscillatory form.

Proto wave equation:

𝓦[Ψ;ΔP_n,ΔP_u] = 0

The Wave like InfoStructure Ψ is the Field configuration that satisfies the oscillatory coherence condition generated by the EA Modes ΔP_n and ΔP_u.

4.2 — Vortex like InfoStructures

Derived from: all four EA Modes

Vortex like equilibrium condition:

𝓒_vortex(ΔP_A,ΔP_n,ΔP_χ,ΔP_u) = 0

This expresses the internal coherence requirement that allows all four tendencies (Perturbation, Translation, Rotation: Chirality, Rotation: Axis Orientation) to organize into a persistent, topologically confined vortical configuration.

Proto vortex equation:

𝓥[Ξ;ΔP_A,ΔP_n,ΔP_χ,ΔP_u] = 0

The Vortex like InfoStructure Ξ is the Field configuration that satisfies the vortical coherence condition, giving rise to a localized structure with intrinsic circulation and dynamic topological persistence.

4.3 — Interaction mediating InfoStructures

Relational equilibrium conditions:

𝓒_int(Ψ,Ξ) = 0

This expresses the internal coherence requirement that allows wave like forms (Ψ) and vortex like forms (Ξ) to correlate their organizations in a stable way, generating a relational structure not reducible to the individual InfoStructures.

Proto interaction equation (effective form):

𝓘[Ψ,Ξ] = 0

The Interaction like InfoStructure I is the Field configuration that satisfies the relational coherence condition between Ψ and Ξ, giving rise to an integrated form in which different InfoStructures (multiple Vortices, Vortices and Waves, etc) mutually influence each other in a persistent and structured manner.

4.6 — Geometric Projection

When the Proto Physical Equations are projected into geometric and algebraic representation spaces:

Wave like → Schrödinger / Klein–Gordon
Vortex like → Dirac / spinor equations
Interaction-mediating → Maxwell / Yang–Mills

Symbolically:

Proj (𝓦) → QM wave equations 
Proj (𝓥) → spinor equations 
Proj (𝓘) → gauge equations

These are representations, not ontological primitives: they express the geometric and algebraic translation of the Field's coherence structures into conventional physical form.

LEVEL 5 — FORMS

No new fundamental equation is introduced at this level.

Symbolic relations:

Forms → organized systems of InfoStructures
Processes → dynamical modes of Forms
Systems → integrated organizations of Forms and Processes; networks exhibiting coherence or individuality
Patterns → cross-scale recurrent emergent structures
Domains → macro-contexts where Forms,Processes,Systems,Patterns act as derived causal sources

Conventional equations of chemistry, biology, astrophysics, and cosmology are understood as effective descriptions of composite organizations of InfoStructures.

SUMMARY TABLE (all equations by level)

Level	Level name	Equations / Symbols
0.1	Fundamental Force	F₀ Single scalar causal impulse generated by the Source.
0.2	Elementary Field	𝓕 = F₀(A, n, χ, u; k_A, k_n, k_χ, k_u) k_𝓲 = k_𝓲^intr + k_𝓲^dyn, 𝓲 ∈ {A, n, χ, u} Proto-resistances: k_A, k_n, k_χ, k_u
0.3	Force–Field Interaction	EE(𝑥,τ) = δ𝓕(𝑥,τ) Elementary Event definition.
0.4	Event-Point	Analytical operator sampling local Field fluctuations. No additional equation.
1	Elementary Events (EE)	Decomposition: EE = {A,n,χ,u} Instantaneous configuration: σ = (A,n,χ,u)_ist Statistical configuration: (A(τ), n(τ), χ(τ), u(τ))
2	Elementary Action (EA)	EA = (ΔP_A, ΔP_n, ΔP_χ, ΔP_u) ΔP_𝓲 = τ_𝓲^actual − τ_𝓲^{σ−τ\ symmetric}, 𝓲 ∈ {A,n,χ,u} Modes: Perturbation, Translation, Rotation: Chirality, Rotation: Axis Orientation.
3	Information / Energy (Potentials Φ)	Equilibrium conditions: 𝓒_M = 𝓒(ΔP_A) = 0 𝓒_A = 𝓒(ΔP_n) = 0 𝓒_E = 𝓒(ΔP_χ) = 0 𝓒_B = 𝓒(ΔP_u) = 0 Diffuse solutions: Φ_M, Φ_A, Φ_E, Φ_B ∈ Sol(𝓒)
4.1	Wave-like InfoStructures	Derived from: ΔP_n, ΔP_u Equilibrium: 𝓒_wave(ΔP_n,ΔP_u) = 0 Proto-wave equation: 𝓦[Ψ;ΔP_n,ΔP_u] = 0
4.2	Vortex-like InfoStructures	Derived from all EA Modes. Equilibrium: 𝓒_vortex(ΔP_A,ΔP_n,ΔP_χ,ΔP_u) = 0 Proto-vortex equation: 𝓥[Ξ;ΔP_A,ΔP_n,ΔP_χ,ΔP_u] = 0
4.3	Interaction-mediating InfoStructures	Relational equilibrium: 𝓒_int(Ψ,Ξ) = 0 Proto-interaction equation: 𝓘[Ψ,Ξ] = 0
4.6	Geometric Projection	Proj(𝓦) → QM wave equations Proj(𝓥) → spinor equations Proj(𝓘) → gauge equations
5	Forms	Composite organizations of InfoStructures. No new fundamental equation.

Links to the tables of contents of TFNR Paper

Go to the contents list of the paper "The Fundamental Nature of Reality"

Go to Chapter 2 "A first look"

Test-1

Contents

Introduction: Toward a Unified Multilevel Formalization of Physical Reality

Elementary Field, Event-Points, and Elementary Events

From Micro Dynamism to Emergent Structure

The Hierarchy of Reality

Summary of the Hierarchy of Reality

LEVEL 0 — Origin (Primary Source, Fundamental Force, Elementary Field)

LEVEL 1 — Elementary Events (τ distributions of σ fluctuations)

LEVEL 2 — Elementary Action (discrepancies or inhomogeneities of τ distributions)

RELATIONAL BRIDGE — Correlation between discrepancies (From Action to Information / Energy)

LEVEL 3 — Information/Energy (Physical Potentials: Metric, Potential Motion: Acceleration Electric and Magnetic Potentials)

LEVEL 4 — InfoStructures (Structured Physical Quantities: Mass, Inertial Motion, Charge, Spin)

LEVEL 5 — Forms: Atoms, Molecules, Stars, Galaxies, Cosmic Structures

Diagram of the Hierarchy of Reality

Epistemic Representation and Scientific Frameworks

Scientific Theories as Epistemic Layers

Mathematical and Conceptual Models

Role of the Epistemic Layer

Hierarchical Structure of the Formalization

LEVEL 0 — Primary Source of Reality (Ontological Root)

SUB-LEVEL 0.1 — Fundamental Force (Causal Input Parameter)

SUB-LEVEL 0.2 — Elementary Field (Intrinsic Resistances of the Variational Response)

SUB-LEVEL 0.3 — Internal Interaction (Force–Field Coupling)

SUB-LEVEL 0.4 — Event-Point (Analytical Sampling Locus)

LEVEL 1 — Elementary Events (Pre-Spatial and Pre-Temporal Dynamism)

SUB-LEVEL 1.1 — σ-Fluctuations (Pre-Spatial Aspects)

SUB-LEVEL 1.2 — τ-Distributions (Pre-Temporal Aspects)

LEVEL 2 — Elementary Action (EA)

SUB-LEVEL 2.1 — Intensity Asymmetry (ΔP_A → Perturbation)

SUB-LEVEL 2.2 — Orientation Asymmetry (ΔP_n → Translation)

SUB-LEVEL 2.3 — Chirality Asymmetry (ΔP_χ → Rotation:Chirality)

SUB-LEVEL 2.4 — Axis Orientation Asymmetry (ΔP_u → Rotation:AxisOrientation)

LEVEL 3 — Information/Energy (Emergent Physical Content)

SUB-LEVEL 3.1 — Mass Potential (Metric) (from Perturbation)

SUB-LEVEL 3.2 — Motion Potential (Acceleration) (from Translation)

SUB-LEVEL 3.3 — Electric Potential (from Rotation:Chirality)

SUB-LEVEL 3.4 — Magnetic Potential (from Rotation:AxisOrientation)

LEVEL 4 — InfoStructures (Waves, Vortices, Interactions)

SUB-LEVEL 4.1 — Wave-Like InfoStructures

SUB-LEVEL 4.2 — Vortex-Like InfoStructures

SUB-LEVEL 4.3 — Interaction-Mediating InfoStructures

SUB-LEVEL 4.4 — Equilibrium Equations (Internal Conditions of Coherence)

SUB-LEVEL 4.5 — Proto-Physical Equations (Emergent Effective Equations)

SUB-LEVEL 4.5.1 — Proto-Wave Equations

SUB-LEVEL 4.5.2 — Proto-Vortex Equations

SUB-LEVEL 4.5.3 — Proto-Interaction Equations

SUB-LEVEL 4.6 — Emergence of QM/QFT Equations (Geometric / Quantum Projection of Field Structures)

LEVEL 5 — Forms (Composite Physical Structures)

SUB-LEVEL 5.1 — Atomic and Molecular Forms

SUB-LEVEL 5.2 — Mesoscopic and Biological Forms

SUB-LEVEL 5.3 — Astrophysical and Cosmological Forms

Transversal Perspectives on Forms

Synthetic Pathway from the Source to Forms

0 — SOURCE (Ontological Origin)

0.1 — FUNDAMENTAL FORCE (Causal Impulse)

0.2 — ELEMENTARY FIELD (Variational Response)

0.3 — FORCE–FIELD INTERACTION

0.4 — EVENT-POINT (Analytical Operator)

1 — ELEMENTARY EVENTS (EE)

2 — ELEMENTARY ACTION (EA)

3 — INFORMATION / ENERGY (Unstructured Physical Potentials)

4 — INFOSTRUCTURES (Elementary Physical Structures)

5 — FORMS (Composite Physical Structures)

10-Line Ultra-Synthetic Schema

Synthetic Proto Mathematical Map of the Formalization Pathway Across Levels

LEVEL 0 — SOURCE, FORCE, FIELD

0.1 — Fundamental Force

0.2 — Elementary Field

0.3 — Force–Field Interaction

0.4 — Event-Point

LEVEL 1 — ELEMENTARY EVENTS (EE)

LEVEL 2 — ELEMENTARY ACTION (EA)

LEVEL 3 — INFORMATION / ENERGY (POTENTIALS Φ)

LEVEL 4 — INFOSTRUCTURES

4.1 — Wave like InfoStructures

4.2 — Vortex like InfoStructures

4.3 — Interaction mediating InfoStructures

4.6 — Geometric Projection

LEVEL 5 — FORMS