Discrete Lattice Mechanics
Space as a 3D lattice of spherical nodes — gravity, time, and particle structure from a single ternary state vector
A Discrete Mechanical Model of Space
Space is a cubic lattice of spherical nodes. Each node carries a four-component ternary state vector:
The four components — Movement, Position, Rotation, Charge — are bipolar wave modes sampled at the Nyquist minimum. M and P form a sin/cos quadrature pair governing transverse oscillation. R encodes angular velocity (helicity). C is isotropic radial breathing.
A node with C = 0 and T = 3 is a photon. A node with C ≠ 0 and T = 4 is matter. The radial mode traps energy locally, producing rest mass and electric charge.
Time is the update rate of local state transitions, governed by structural lattice tension T. Gravity emerges as accumulated tension: T(r) = 1 + GM/(rc²). The coupling constant k = 1/c² is forced by dimensional analysis and verified by GPS time dilation with a residual of 0.01 μs/day.
Axioms and State Equation
The Lattice
Space is a discrete, quantifiable, 3D geometric lattice of physical Spherical Nodes connected by geometric structural threads (tension). A node has perfect spherical symmetry in its vacuum state: X = −X′, Y = −Y′, Z = Z. The Z axis carries no prime — it is the structural depth axis that holds the sphere's diameter intact. Z does not oscillate; it is geometry, not dynamics.
The MPRC Modes
| Mode | Symbol | +1 | −1 | 0 | Physical Role |
|---|---|---|---|---|---|
| Movement | M | East | West | still | Horizontal translation (cos θ) |
| Position | P | North | South | still | Vertical translation (sin θ) |
| Rotation | R | CW | CCW | still | Angular momentum (helicity) |
| Charge | C | Expand | Contract | neutral | Radial breathing |
Tension and Particle Types
Gravity as Tension
Key Results and Epistemic Status
| Claim | Status | Source |
|---|---|---|
| GPS +38.6 μs/day | VERIFIED (residual 0.01 μs/day) | exp1–2 |
| Photon = minimum complete transverse wave | DERIVED (T=1,2 cannot self-propagate) | exp7 |
| B₄ symmetry, order 384 | DERIVED | exp8 |
| Pati–Salam 3+3+1+1 per C-sector | DERIVED | exp8 |
| Solar system clock chain (Mars +489, Moon +56 μs/day) | DERIVED | exp3 |
| No event horizon (f > 0 everywhere) | PREDICTION | exp4 |
| Gravity-induced entanglement decoherence | PREDICTION | exp6 |
| Torus winding number constant across galaxies | FALSIFIED (CV = 152%) | exp2 |
| f ≥ 2/3 minimum | WRONG (corrected: f → 0 as r → 0) | exp4 |
B₄ Symmetry and Gauge Structure
Symmetry analysis (exp8) reveals that the tension Hamiltonian ĤL is invariant under the hyperoctahedral group B₄ = S₄ ⋉ ℤ₂⁴ (order 384). The Weyl groups of SU(4), SU(3), and SU(2) embed naturally as subgroups via the breaking chain:
The 81-state space organizes into tension levels, and the symmetry breaking chain maps directly to the observed gauge group structure of the Standard Model — not as an input assumption but as a derived consequence of the B₄ lattice symmetry.
Strong-Field Divergence from GR
In the weak-field regime, the discrete lattice and General Relativity agree. GPS time dilation is verified to 0.01 μs/day. The solar system clock chain (Sun → Mercury → Venus → Earth → Mars → Moon) is derived from the same tension equation.
In the strong-field regime, the lattice and GR diverge fundamentally. GR gives f = 0 at the Schwarzschild radius rs — the event horizon, a boundary from which nothing escapes. The lattice gives f > 0 everywhere.
The stability analysis (exp7) resolved a further question: sub-photon excitations at T = 1 and T = 2 cannot self-propagate. T = 1 states migrate under coupling but lack coherent direction. T = 2 non-propagating states split apart. The photon at T = 3 is the minimum complete transverse wave — its maximum clock rate is now derived, not assumed.