Abstract: We present a computational demonstration of the Zeno Threshold (Zα) on the paradigmatic double-slit experiment. A Gaussian wave packet is propagated on a 256×128 tight-binding lattice using only two ingredients: graph topology (nearest-neighbor hopping) and unitarity (U = e-iHΔt, with the imaginary unit i forced by information conservation). No wave equation is assumed; interference fringes emerge as a strict consequence of lattice unitarity. We then introduce a which-path detector modeled as a tensor-product qubit that entangles with the particle at the slits. The entanglement entropy of the reduced detector state grows from zero toward Smax = ln 2 ≈ 0.693 nats. At the moment this entropy exceeds the observer's finite Zeno Threshold Zα, the observer's rendering engine is forced to perform Born Rule truncation—algorithmic garbage collection—erasing the off-diagonal coherence terms. The interference pattern is destroyed, leaving two classical bumps. Computational Verification Highlights: Emergent Interference: Fringes emerge strictly from discrete graph topology and unitarity, without assuming continuous wave equations. Forced Complex Phases: The complex unit i is mathematically forced by probability conservation (unitarity). The Z-Scale Breach: Which-path detection creates real entanglement entropy that breaches the observer's finite processing limit. Born Rule Garbage Collection: Truncation at the Z-Scale breach produces a detection pattern identical to the classical, incoherent sum |ψ1|2 + |ψ2|2. The full Python verification script and simulation code are available at github.com/srdrymn/atr-double-slit-simulation.
Serdar Hanzala Yaman (Thu,) studied this question.