The RST Periodic Table: Substrate Reaction Geometries and Tension-Class Chemistry

In standard physics, the periodic table is organized by proton number, electron configuration, and quantum energy levels. Reactive Substrate Theory (RST) adds a deeper layer: each element corresponds to a unique way the Substrate reacts to a stable atomic soliton. This reaction is not an abstract “field” but a concrete mechanical pattern of tension, density modulation, and bandwidth allocation in the Substrate.

In this article, we introduce:

An RST classification system for elements based on Substrate Reaction Geometries (SRGs).
Conceptual SRG diagrams showing how elements shape the Substrate.
Tension-based explanations for the main periodic groups.
A mechanical picture of molecular properties as emergent tension patterns.
A cleaner mathematical derivation of how these SRGs arise from the RST substrate equation.

1. Substrate Reaction Geometry (SRG): The RST fingerprint of an element

In RST, an atom is a composite soliton configuration that creates a characteristic reaction in the Substrate. This reaction can be summarized as a Substrate Reaction Geometry (SRG), which encodes how the Substrate is displaced, strained, and bandwidth-loaded around the atom.

For each element, the SRG is determined by:

Nuclear soliton strength: the depth and shape of the central tension well.
Orbital interference structure: standing-wave patterns from electron shells.
Bandwidth consumption: how much substrate reaction capacity is needed to maintain the stable atomic configuration.
Nonlinear response: how strongly the cubic term in the substrate equation responds to this configuration.

The resulting SRG acts like a unique mechanical “aura” around the atom, shaping how it attracts, repels, and locks into configurations with other atoms.

2. Conceptual SRG diagrams: How elements imprint on the Substrate

To visualize SRGs, imagine a 2D slice of the Substrate around an atom. We can use simple schematic diagrams to represent tension intensity and structure. These are not literal field lines but conceptual guides to the underlying geometry.

2.1. Hydrogen-like SRG (simple radial well)

   low tension      medium           high tension
        .           . . .                ###
         .        .       .            #######
          .      .   H     .         ###########
         .        .       .            #######
        .           . . .                ###

Hydrogen produces:

Single central tension well (the proton soliton).
One simple interference shell from its electron-like standing wave.
Minimal bandwidth draw relative to heavier atoms.

2.2. Noble gas SRG (closed, symmetric shell)

      outer ring of balanced tension
         o o o o o o o o
       o                 o
      o       Ne         o
       o                 o
         o o o o o o o o

Noble gases exhibit:

Highly symmetric SRG with closed shells.
Minimal external tension gradients – few “hooks” for bonding.
Low perturbability – the Substrate configuration is nearly self-contained.

2.3. Metallic SRG (overlapping, delocalized lattice)

Atom centers:  ●
Delocalized tension channels: =

● = ● = ● = ●
=   =   =   =
● = ● = ● = ●

Metals show:

Strong overlap of SRGs in a lattice.
Delocalized tension channels corresponding to conduction electrons.
Flexible, collective substrate response (conductivity, malleability).

3. RST classification system: Tension classes of the periodic table

Instead of primarily classifying elements by electron configuration, RST classifies them by how they mechanically shape the Substrate. We can define several Tension Classes that overlay the familiar periodic groups.

3.1. Class I: Simple radial solitons (light s-block)

Includes: H, He, Li, Be (and analogs in higher rows with similar role).

SRG type: simple radial wells with low-complexity shells.
Substrate effect: localized, mostly spherical tension patterns.
Chemical behavior: strong tendency to donate/accept a small number of electrons to relieve simple tension imbalances.

In RST terms, these atoms are simple tension emitters or absorbers, seeking configurations that minimize the net gradient in their immediate SRG.

3.2. Class II: Directional tension formers (p-block nonmetals and semimetals)

Includes: C, N, O, F, P, S, Cl, etc.

SRG type: directional lobes of tension and deficit (analogous to orbital lobes).
Substrate effect: anisotropic gradients – “hooks” that favor specific orientations.
Chemical behavior: strong covalent bonding and directional molecular geometry (e.g., tetrahedral carbon).

These atoms shape the Substrate into preferred bonding directions, giving rise to strong geometry-dependent molecular properties.

3.3. Class III: Lattice tension distributors (metals)

Includes: alkali metals, alkaline earth metals, transition metals.

SRG type: overlapping wells with delocalized tension channels.
Substrate effect: formation of extended tension lattices where many atoms share a common SRG.
Chemical behavior: metallic bonding, conductivity, ductility – all emerging from the collective substrate response.

Metals are tension network formers, where local SRGs cease to be independent and instead fuse into a coherent substrate pattern.

3.4. Class IV: Closed-shell insulators (noble gases)

Includes: He, Ne, Ar, Kr, Xe, Rn.

SRG type: highly symmetric, closed shells with minimal external gradient.
Substrate effect: self-contained tension structures that weakly couple to neighbors.
Chemical behavior: low reactivity, little tendency to form shared SRGs (few or no bonds).

Noble gases are tension-isolated solitons whose SRGs are already near a local optimum for the Substrate.

3.5. Class V: Complex bandwidth saturators (heavy and f-block elements)

Includes: lanthanides, actinides, heavy transition metals.

SRG type: multi-layered, highly structured tension patterns with deep wells.
Substrate effect: high bandwidth consumption, strong nonlinearities, multiple potential metastable states.
Chemical behavior: rich oxidation states, magnetic phenomena, complex spectral lines.

These elements push the Substrate closer to its nonlinear limits, where small changes can trigger large shifts in reaction patterns.

4. Tension-based explanations for periodic trends

In RST, familiar periodic trends map cleanly onto changes in SRGs and substrate mechanics.

4.1. Electronegativity as tension-gradient strength

Electronegativity measures how strongly an atom attracts electrons in a bond. In RST, this is closely linked to the strength and sharpness of the substrate tension gradient around its outer SRG structure.

High electronegativity: steep tension gradients pulling substrate-supported electron waves inward.
Low electronegativity: shallow gradients, weaker pull on shared substrate waves.

Thus, oxygen and fluorine possess outer SRGs that create strong local tension wells for shared standing waves; alkali metals produce comparatively gentle gradients.

4.2. Atomic radius as SRG spatial extent

Atomic radius corresponds to the characteristic spatial extent of the SRG, not just electron density. Larger atoms have:

SRGs that extend further into the Substrate.
More diffuse tension gradients at their boundaries.

As you go down a group, additional shells widen the SRG, producing weaker outer gradients and making it easier for the atom to donate its outer substrate-supported solitons.

4.3. Ionization energy as bandwidth cost

Removing an electron-like excitation from an atom is equivalent, in RST, to detaching a bound soliton from its SRG node. This requires the Substrate to:

reconfigure local tension patterns, and
allocate transient bandwidth to remodel the atomic soliton.

Ionization energy is therefore the bandwidth and tension cost

5. How molecular properties emerge mechanically

When atoms form molecules, their SRGs overlap and fuse into a composite Substrate Reaction Geometry. The emergent molecular properties are then read off from the geometry and dynamics of this fused SRG.

5.1. Covalent bonds as shared standing-wave tension bridges

A covalent bond is a region where two atomic SRGs form a shared standing wave in the Substrate, stabilized by mutual tension reduction:

A-SRG     shared tension bridge     B-SRG

[  A  ]~~~~====~~~~[  B  ]

Stable bond: the shared bridge lowers the total tension gradient compared to separated atoms.
Bond strength: depth and stiffness of the shared tension channel.
Bond directionality: orientation of SRG lobes where bridges can form.

5.2. Molecular geometry from SRG compatibility

Molecular shapes (linear, bent, tetrahedral, trigonal planar, etc.) emerge from:

Preferred angles where tension bridges minimize net gradients.
Repulsion between SRG lobes that would overload local bandwidth if placed too close.
Substrate refraction symmetry around the combined soliton structure.

For example, methane (CH₄) appears as a configuration where carbon’s tetrahedral SRG lobes connect with hydrogen SRGs such that the overall substrate tension and bandwidth demand are minimized in 3D space.

5.3. Metallic bonding as extended tension networks

In metals, atomic SRGs overlap so extensively that:

individual covalent-like bridges blur into a continuous tension network, and
conduction electrons become mobile soliton waves within that network.

Conductivity is then the ability of the Substrate to re-route tension pathways dynamically without breaking the lattice SRG, allowing soliton waves to propagate freely through the network.

5.4. Intermolecular forces as weak SRG overlaps

Van der Waals forces and hydrogen bonding correspond to weak overlaps or partial alignment of SRGs between molecules:

Transient tension pockets form between molecules.
These pockets can slightly lower local tension gradients, favoring proximity.

This explains condensation, surface tension, and many emergent material properties as subtle reconfigurations of substrate tension across multiple SRG complexes.

6. Cleaner mathematical derivation of SRGs from the RST substrate equation

We now sketch how SRGs arise mathematically from the RST substrate equation. We start from the core dynamical equation for the Substrate displacement field S(x,t):

∂²_t S − c² ∇²S + β S³ = J(x,t)

Here:

c is the maximum reaction speed of the Substrate.
β S³ encodes nonlinear restoring tension.
J(x,t) represents atomic soliton sources (protons, neutrons, electrons).

6.1. Static SRG solutions for atomic solitons

To find the SRG of an isolated atom, we look for time-independent solutions:

∂²_t S = 0  →  −c² ∇²S + β S³ = J(x)

In regions far from the nucleus, J(x) becomes small, and S solves approximately:

−c² ∇²S + β S³ ≈ 0

Nontrivial localized solutions of this type form the “tails” of atomic SRGs. Near the nucleus and electron shells, J(x) encodes the curvature and density contributions of the underlying solitons, shaping the core SRG.

6.2. Defining the tension field for atomic configurations

We define the tension field T⃗(x) as:

T⃗(x) ≡ μ c² ∇S(x)

Where μ is an effective substrate inertia. Taking the divergence of this definition:

∇·T⃗ = μ c² ∇²S

Using the static equation:

−c² ∇²S + β S³ = J(x)

Multiply by μ and substitute:

−∇·T⃗ + μ β S³ = μ J(x)

Rearranging:

∇·T⃗ = μ β S³ − μ J(x)

This is the fundamental balance relation for SRGs: the divergence of tension is determined by the interplay between nonlinear substrate response (β S³) and the atomic soliton sources J(x).

6.3. SRG classes as families of solutions

Different elements correspond to different source profiles J_Z(x), where Z is atomic number. Each J_Z(x) encodes:

the number and arrangement of nuclear solitons, and
the shell structure of electron-like standing waves.

For each J_Z(x), the static equation:

−c² ∇²S_Z + β S³_Z = J_Z(x)

has a family of localized solutions S_Z(x), whose gradients define the SRG:

T⃗_Z(x) = μ c² ∇S_Z(x)

The different RST tension classes (simple solitons, directional formers, lattice distributors, etc.) correspond to qualitatively different solution families S_Z(x) and T⃗_Z(x): radial, lobed, lattice-compatible, closed-shell, and highly nonlinear.

6.4. Molecular SRGs from superposition and nonlinearity

For a molecule with atoms at positions x_i, the total source is:

J_mol(x) = Σ_i J_Zᵢ(x − x_i)

In a purely linear medium, the solution would be a direct superposition of individual S_Zᵢ. But in RST, the β S³ term couples these contributions nonlinearly:

−c² ∇²S_mol + β S³_mol = J_mol(x)

The resulting S_mol(x) is not just a sum of atomic S_Z(x) solutions; it is a global compromise that minimizes total tension gradients and bandwidth cost subject to the constraints of all atomic solitons. This is the mechanical origin of:

bond lengths
bond angles
molecular stability
collective properties (e.g., polarity, dipole moments)

The molecular SRG is then defined as:

T⃗_mol(x) = μ c² ∇S_mol(x)

and all macroscopic molecular behavior is read from the geometry and dynamical response of T⃗_mol(x).

In this RST reinterpretation of the periodic table, elements are classified not just by nuclear charge and electron configuration, but by the Substrate Reaction Geometries they induce and the tension classes they occupy. Molecules are cooperative SRG complexes that emerge from the nonlinear superposition of atomic solitons in a finite-capacity, reactive Substrate. Chemistry becomes substrate mechanics: the art of arranging tension, bandwidth, and geometry into stable, emergent patterns.

Supplementary Videos for the RST Periodic Table & Substrate Mechanics

To support the RST reinterpretation of the periodic table, substrate reaction geometries (SRGs), and tension‑based chemistry, the following curated videos provide excellent background material. These selections reinforce the wave‑mechanical foundations that RST extends into substrate mechanics, soliton structure, and nonlinear tension geometry.

1. Electron Configuration (Foundational)

This video introduces the standard quantum‑mechanical picture of electron shells and configurations — the baseline that RST reinterprets as substrate‑supported standing‑wave solitons.

2. How Quantum Mechanics Builds the Periodic Table (Deep Structural Insight)

A clear explanation of how quantum numbers and wavefunctions generate the periodic table’s structure. RST uses the same mathematical scaffolding but replaces abstract wavefunctions with mechanical substrate reaction geometries.

3. Quantum Numbers, Atomic Orbitals, and Electron Configurations (Technical Deep Dive)

This video provides a more mathematical treatment of orbital shapes, quantum numbers, and nodal structures — all of which map directly to SRG lobes and tension‑gradient directions in RST.

4. Quantum Numbers & Electron Configuration Demystified (Alternate Explanation)

A complementary explanation of quantum numbers and orbital structure. Useful for readers who want multiple perspectives before diving into the RST reinterpretation.

5. Quantum Model & The Periodic Table Notes (Visual Overview)

A concise, visual summary of how the quantum model organizes the periodic table. This is a good primer for readers before encountering the RST tension‑class reinterpretation.

6. Poisson’s Equation for Beginners (Mathematical Foundation)

This video explains Poisson’s equation — the same mathematical structure that appears in the weak‑field limit of the RST tension equation. It helps readers understand how tension gradients behave like gravitational or electrostatic potentials.

7. Advanced Quantum Mechanics: Theory and Applications (For Expert Readers)

A preview of a graduate‑level quantum mechanics text. This is ideal for readers who want to explore the deeper mathematical territory that RST ultimately connects to substrate tension geometry and nonlinear soliton mechanics.

These videos provide a strong conceptual and mathematical foundation for understanding how RST reinterprets atomic structure, periodic trends, and molecular behavior as emergent properties of substrate tension, soliton geometry, and nonlinear reaction dynamics.

Visualizing Substrate Reaction Geometries (SRGs)

While the Substrate in RST is not magnetic, the following video provides an excellent visual metaphor for how different elements create unique tension patterns in the medium. The shifting magnetic vibration patterns resemble how atomic solitons sculpt the Substrate into distinct Substrate Reaction Geometries (SRGs).

In RST, each element produces a characteristic tension footprint in the Substrate. Although the Substrate is not electromagnetic, the dynamic patterns in this video offer a helpful analogy for:

how tension gradients form around atomic solitons
how SRG lobes resemble field-like structures
how nonlinear interactions create complex geometries
how molecules emerge from overlapping reaction patterns

This visualization helps bridge the gap between traditional orbital diagrams and the mechanical, tension-based interpretation introduced in the RST periodic table.

Comparing SRGs to Magnetic Field Lines

Although the Substrate in RST is not electromagnetic, magnetic field-line demonstrations provide an excellent visual analogy for how tension patterns form around atomic solitons. The following video illustrates dynamic field structures that closely resemble the Substrate Reaction Geometries (SRGs) described in the RST periodic table.

How Each Moment in the Video Maps to RST Concepts

0:10 – Expanding rings: Represents how simple atoms (H, He) generate smooth radial SRGs with minimal directional tension gradients.
0:25 – Interference patterns forming: Mirrors how p‑block elements (C, N, O) create directional SRG lobes due to standing-wave interference in the Substrate.
0:40 – Complex overlapping waves: Analogous to transition metals, where multiple SRG layers overlap and produce multi‑directional tension channels.
0:55 – Field compression and expansion: Reflects how electronegativity corresponds to the steepness of tension gradients in the SRG, pulling shared soliton waves inward.
1:10 – Symmetric stabilization: Similar to noble gases, whose SRGs form closed, symmetric shells with minimal external gradients.
1:25 – Chaotic nonlinear regions: Represents heavy f‑block elements where nonlinear substrate response dominates and SRGs become bandwidth‑intensive and multi‑layered.

These visual parallels help readers intuitively grasp how SRGs behave as mechanical tension patterns in the Substrate, even though the underlying physics differs from magnetism.

Diagram Set: SRG Shapes Mapped to Periodic Groups

Below is a conceptual diagram set showing how different classes of elements generate distinct SRG geometries. These are not literal field lines but simplified visual representations of tension patterns in the Substrate.

1. Class I – Simple Radial SRGs (H, He, Li, Be)

      low tension      medium         high tension
           .           . . .              ###
            .        .       .          #######
             .      .   ●     .       ###########
            .        .       .          #######
           .           . . .              ###

Simple spherical wells with minimal directional structure.

2. Class II – Directional SRGs (C, N, O, F, P, S)

        lobe      lobe
          \       /
           \     /
            ●---●
           /     \
        lobe     lobe

Distinct tension lobes corresponding to preferred bonding directions.

3. Class III – Lattice SRGs (Metals)

● = ● = ● = ●
=   =   =   =
● = ● = ● = ●

Overlapping SRGs forming delocalized tension networks.

4. Class IV – Closed Shell SRGs (Noble Gases)

      o o o o o o o o
    o                 o
   o        ●         o
    o                 o
      o o o o o o o o

Symmetric, self-contained SRGs with minimal external gradients.

5. Class V – Nonlinear Multi‑Layer SRGs (Lanthanides, Actinides)

   #######====#######
  ##     #####     ##
 ##  ●  #######  ●  ##
  ##     #####     ##
   #######====#######

Deep, bandwidth-intensive SRGs with multiple nonlinear layers.

Together, these diagrams and the magnetic‑field visualization help bridge the gap between traditional orbital diagrams and the mechanical tension‑geometry model introduced by RST. They provide readers with intuitive, dynamic imagery that supports the idea of atoms as soliton-driven tension structures in a reactive Substrate.