The Feynman path integral formulation of quantum mechanics expresses the transition amplitude as a sum over all possible paths between two points, weighted by e^{iS/\hbar}. This formulation is remarkably powerful, but its physical origin is obscure: why should a particle explore all paths simultaneously, and why is the weight given by the classical action? This paper shows that the path integral emerges naturally from the threshold dynamics of the canvas model. What this paper provides: · A physical ontology for the path integral. A particle propagating through the discrete voxel lattice does not follow a single trajectory. It traverses the lattice through a sequence of threshold crossing events—the nucleation of new voxels along its path. Each possible sequence of nucleations defines a discrete path. The sum over all such sequences, in the continuum limit, reproduces the Feynman path integral with the action identified as the count of threshold events.· The discrete propagator as a sum over threshold histories. Each elementary step has probability p_0. The probability of a specific path \gamma of N steps is P[\gamma] = \exp(-S_{\text{th}}[\gamma]), where S_{\text{th}}[\gamma] is the threshold action. The discrete propagator sums over all paths of length N.· The phase factor from polarity. Each threshold crossing can occur with positive or negative polarity. A nucleation with negative polarity contributes a factor of e^{i\pi} = -1 relative to positive polarity. The total phase of a path is \Phi[\gamma] = (-1)^{n_-}, where n_- is the number of steps with negative polarity.· The continuum limit to the Feynman path integral. As the lattice spacing a \to 0 with N a fixed, the sum over discrete threshold histories converges to \int \mathcal{D}x(t) \, e^{iS/\hbar}. The classical action emerges as the continuum limit of the threshold count.· A resolution of the double-slit experiment. Interference arises because histories passing through different slits differ by an odd number of polarity reversals, producing relative minus signs. Which-path information destroys the interference by introducing additional uncorrelated threshold crossings.· An extension to quantum field theory. Each vertex in a Feynman diagram corresponds to a threshold crossing event where multiple wave amplitudes intersect. The sum over all Feynman diagrams is the sum over all threshold histories with fixed incoming and outgoing particles. Why this matters: The canvas model provides a physical ontology for the path integral. The "sum over histories" is not a mathematical trick—it is a sum over actual sequences of voxel nucleations on the discrete spacetime lattice. The classical action is the large-N limit of the threshold crossing count. Quantum interference arises from the superposition of threshold histories that differ by an odd number of polarity reversals. This interpretation differs from standard interpretations: Copenhagen treats the path integral as a calculational tool; Many-Worlds treats all paths as realized in different branches; Bohmian mechanics posits one actual path guided by a wavefunction. The canvas model offers a distinct alternative: there is one actual history of threshold crossings. The path integral sums over possible histories, weighted by probability. The actual history is determined dynamically as the thresholds are crossed. Keywords: Feynman path integral, canvas model, threshold dynamics, voxel nucleation, threshold action, polarity phase, discrete propagator, continuum limit, double-slit experiment, quantum interference, quantum field theory, Feynman diagrams