The Space Stress Vector (SSV) field at any grid point

View in map → is the superposition of contributions from all Charged Conscious Points (CPs) within the Planck Sphere Radius:

\[\vec{S}_{\text{GP}} = \sum_i \frac{S_0 \, p_i \, t_i \, f(\text{type}) \, \hat{r}_i}{r_i^2}\]

where \(S_0 = 0.2555\) MeV is the elementary stress magnitude, \(p_i = \pm 1\) is CP polarity, and \(t_i\) is a type factor (1 for eCP, 0.5 for qCP). The force on a test CP is \(\vec{F}_j = -q_j \, \vec{S}(\vec{r}_j)\), giving a \(1/r^2\) dependence analogous to Coulomb's law. Opposite polarities attract; same polarities repel.

Binding energy follows from the scalar potential: \(E_{\text{bind}} = -\tfrac{1}{2} \sum_j q_j \, \Phi(\vec{r}_j)\). Cage stability is governed by eigenvalue analysis of the SSV Hessian at each vertex. Preferred geometries drawn from 600-cell

View in map → subgroups yield characteristic binding energies: tetrahedral (4 vertices, \(E \approx 2\) lattice units), icosahedral (12 vertices, \(E \approx 6\)), dodecahedral (20 vertices, \(E \approx 10\)), and fullerene-like (~60 vertices, \(E \approx 30\)).

The stability threshold is at four cage vertices (tetrahedral symmetry), where gradient cancellation ensures all Hessian eigenvalues are positive. Below this threshold: 1 CP is fully unstable, 2 CPs are metastable, and 3 CPs are highly unstable.

Calibration: the electron (tetrahedral cage, \(\Phi_{\text{total}} = -4\), \(E_{\text{bind}} = 2\) l.u.) fixes \(S_0 = m_e / 2 = 0.2555\) MeV.

SSV Force Law Derivation

Each Charged Conscious Point (CP) sources a radial stress field that propagates along lattice hyperedges. At an arbitrary grid point, the total SSV is the vector sum over all CPs within range:

\[\vec{S}_{\text{GP}} = \sum_i \frac{S_0 \, p_i \, t_i \, f(\text{type}) \, \hat{r}_i}{r_i^2}\]

The force on a test CP with charge \(q_j\) is \(\vec{F}_j = -q_j \, \vec{S}(\vec{r}_j)\). Defining a scalar potential \(\Phi\) such that \(\vec{S} = -\nabla \Phi\), the total potential energy of the cage is:

\[E_{\text{bind}} = -\frac{1}{2} \sum_j q_j \, \Phi(\vec{r}_j)\]

The factor of \(\tfrac{1}{2}\) avoids double-counting pairwise interactions.

Cage Geometry Table

Geometry	Vertices	Binding (l.u.)	Particle Map
Tetrahedral	4	2.0	Electron, muon, strange
Icosahedral	12	6.0	Charm, tau, Z
Dodecahedral	20	10.0	Bottom, Higgs
Fullerene-like	~60	30.0	Top

Stability Conditions

Cage stability depends on vertex count and symmetry of the SSV Hessian:

• 1 CP: Fully unstable — no restoring gradient.
• 2 CPs: Metastable — saddle point in the potential; perturbation along the axis destabilises the pair.
• 3 CPs: Highly unstable — planar arrangement cannot cancel all gradient components.
• 4+ CPs (tetrahedral symmetry): Stable — the three-dimensional symmetry ensures all Hessian eigenvalues are positive, producing a true potential minimum.

Worked Example: Electron Binding Energy

The electron is modelled as a central negative eCP surrounded by 4 positive compensating CPs at tetrahedral vertices. Each positive CP contributes \(\Phi_i = -1\) (unit charge, unit distance in lattice units), so:

\[\Phi_{\text{total}} = 4 \times (-1) = -4\]

\[E_{\text{bind}} = -\frac{1}{2} \times (-1) \times (-4) \;=\; -\frac{1}{2}(4) \;=\; 2 \;\text{lattice units}\]

Calibrating against the physical electron mass: \(S_0 = m_e / E_{\text{bind}} = 0.511\,\text{MeV} / 2 = 0.2555\,\text{MeV}\). This single calibration fixes the elementary stress magnitude used for all heavier cages.