Spectral Invariance in 300 keV Electron Superposition: Time as Recursive Eigenmode Spacing

In superposition-based electron microscopy at 300 keV, we observe interference structures that accumulate deterministically over time without requiring timestamped particle histories. Using scanning transmission electron microscope holography data, we produce phase reconstruction images and detect iso-magnetic contours that span screen boundaries and internal features. Strikingly, these patterns are visible not only in processed spectral data but also in raw brightfield images—indicating that magnetic field structure is encoded directly in spatial amplitude, prior to phase unwrapping. We introduce a spectral time model in which time emerges not as a continuous parameter but as a recursive projection index, Δt=∣λ_n+1−λ_n∣, where eigenmode spacing governs temporal progression. Topological constraints on eigenmode transitions—including bifurcations and field curvature—determine pattern stability and coherence. Our results imply a non-ontological conception of time: spectral recursion, rather than clocked iteration, organizes physical coherence. This framework opens a pathway for deterministic, non-probabilistic interpretations of quantum measurement and phase evolution, with experimental signatures in spectral invariants, iso-line morphology, and finite diffraction cutoffs.