Gravitational Sign Reversal from Lattice Stretching in the Canvas Model

The canvas model derives gravity as lattice compression: gravitational acceleration is the negative gradient of the local spacetime lattice spacing, \vec{a} = -\nabla L(x). While ordinary matter compresses the lattice (producing attraction), this paper examines the converse: lattice stretching produces repulsion.

What this paper provides:

· A derivation of gravitational sign reversal from first principles within the canvas model. The sign of acceleration depends on the sign of \nabla L. Compression (\nabla L pointing away from source) gives attraction. Stretching (\nabla L pointing toward source) gives repulsion. This is not a new force—it is ordinary gravity with the sign reversed by geometry rather than by exotic matter.
· Three candidate mechanisms for lattice stretching consistent with the canvas model:
  1. Negative energy density (Casimir effect). The Casimir effect produces a region of negative energy density between conducting plates. This decreases wave field intensity, increasing lattice spacing. Theorem 1 proves that a test mass near such a region experiences repulsive acceleration away from it.
  2. Phase-controlled acceleration waves. The Unified Wave Equation includes an acceleration term c\,\partial_v^2\Phi that oscillates in sign. Theorem 2 shows that controlling the phase of oscillating fields across a spatial array could produce net lattice stretching on one side of a test mass.
  3. Asymmetric source configurations. Theorem 4 proves that symmetric compression cancels (no net force), while asymmetric compression produces net acceleration away from the stronger source. This is ordinary Newtonian gravity for asymmetric mass distributions, reproduced here through the canvas model's lattice formalism.
· A proof of symmetric cancellation (Theorem 3). If identical lattice-compressing sources are arranged symmetrically around a test mass, the gradients cancel and net acceleration vanishes.
· A proof of asymmetric net acceleration (Theorem 4). If two sources have different compression strengths, a test mass between them accelerates away from the stronger source.
· A comparison table of gravitational repulsion mechanisms (inflation/dark energy, negative mass, Casimir, and lattice asymmetry), showing that lattice asymmetry is the only mechanism that does not require exotic sources (negative pressure, negative mass, or negative energy density). The repulsion comes from geometry—the arrangement of ordinary positive-energy sources—not from what the sources are.

How this differs from known mechanisms:

In general relativity, gravitational repulsion already exists, but every known mechanism requires something exotic. Inflation and dark energy require negative pressure. Negative mass (Bondi) requires M < 0. The Casimir effect requires negative energy density. The lattice asymmetry mechanism proposed here requires none of these. The sources are ordinary matter—positive energy, positive mass. The repulsion comes from how they are arranged, not from what they are.

Limitations (honestly acknowledged):

· No numerical predictions. The canvas model does not yet provide a closed-form expression for L(x) in terms of underlying field configurations.
· The lattice-energy coupling—the relationship between electromagnetic field configurations and lattice spacing—remains an open problem.
· The Casimir effect produces gravitational effects far below current detection thresholds (a \sim 10^{-40} m/s² for laboratory-scale plates).
· No experimental verification has been performed. This paper is a theoretical prediction awaiting test.

Why this matters:

If the canvas model is correct, gravitational sign reversal is not just theoretically possible—it is a necessary consequence of the lattice formalism. Unlike existing mechanisms that require exotic physics, lattice asymmetry operates with ordinary matter. This paper establishes the theoretical framework. Numerical predictions and experimental protocols await future work.

Keywords: gravitational repulsion, lattice stretching, canvas model, Casimir effect, acceleration waves, asymmetric compression, symmetric cancellation, sign reversal, anti-gravity, negative energy density