Topological Plasma Signatures in Black Aurora

This project is an observational test of a new theoretical framework—**topological spectral plasma dynamics**—applied to one of the most puzzling auroral phenomena: **black aurora**.[1] Black aurora are narrow, long‑lived dark gaps embedded within otherwise bright auroral curtains; they exhibit extremely sharp boundaries, complex dynamics (including so‑called “anti‑black” behavior where bright patches switch sides), and persistence that are not fully captured by existing models based on ionospheric cavities, wave–particle interactions, or simple magnetosphere–ionosphere coupling.[1] The central scientific question is whether these structures can be understood, at least in part, as **boundaries between regions of different topological charge** in magnetospheric plasma, characterized by an effective second Chern number C₂ and associated spectral asymmetry (η‑invariant) of the underlying field configuration.[1] The theoretical foundation builds on three prior works (Papers A, B, C). Paper A provides high‑precision numerical evidence for the quantization relation η = 4C₂ in SU(2) Yang–Mills theory on a 4‑torus, confirming a specific case of the Atiyah–Patodi–Singer index theorem to machine precision.[1] Paper B argues that non‑zero η implies a fundamental obstruction to exact time‑reversal symmetry at the spectral level in Lorentzian spacetimes, while Paper C introduces an “Einstein–Chronos” framework in which η (or an associated field) plays a dynamical role in cosmology.[1] The present work extends these mathematical ideas into a **novel but conjectural plasma context**, positing that magnetospheric regions hosting black aurora can carry an effective C₂, which in turn modifies particle trajectories and wave propagation in specific, testable ways.[1] From this framework arise **three quantitative, falsifiable predictions**, each tied to a different observational signature in the black aurora environment.[1] (1) *Chiral wave splitting*: left‑ and right‑hand circularly polarized electromagnetic waves should exhibit a small but finite frequency splitting $$\Delta f = 0.020 \pm 0.005\,\text{Hz}$$, with a characteristic growth rate, if a chiral coupling induced by C₂ is present.[1] (2) *Alfvén wave spectral modulation*: the magnetic field power spectrum in the Alfvénic range should show a weak, periodic modulation of amplitude $$A = (1.2 \pm 0.4)\times 10^{-3}$$ superimposed on a Kolmogorov‑like background, reflecting interference of topologically nontrivial wave modes at domain boundaries.[1] (3) *Berry‑phase azimuthal asymmetry*: electron pitch‑angle distributions in black aurora should display an m=1 azimuthal Fourier component with amplitude $$A_\varphi = 0.06 \pm 0.02$$, arising from geometric (Berry) phase accumulated by guiding centers in the mirror geometry; this third prediction is grounded in established guiding‑center theory and also serves as a sensitivity baseline.[1] The **empirical testbed** consists of NASA’s GNEISS and BaDASS sounding rocket missions launched from Poker Flat, Alaska, in February 2026, supported by all‑sky auroral cameras that identify and map black aurora structures.[1] The rockets carry high‑time‑resolution electron spectrometers and field instruments that measure particle distributions and electromagnetic fluctuations as the payloads traverse black aurora regions.[1] “Events” in this study are defined as individual black aurora crossings during which the mapped rocket footprint lies entirely within an optically identified dark structure and all instruments operate nominally.[1] For each event, the analysis pipeline extracts event‑level summary statistics corresponding to the three predictions (Δf, A, A_φ), and formal hypothesis tests are performed across events with pre‑specified 5σ (discovery), 3σ (evidence), and