We propose the 2C-Anomaly Index Conjecture, which suggests a natural correspondence at the level of index theory between axial anomaly-induced spectral flow in bulk Dirac systems and boundary spectral rearrangements in two-dimensional topological lattice models. Motivated by the boundary version of the Atiyah-Patodi-Singer (APS) index theorem and the Callan-Harvey anomaly inflow mechanism, we argue that a non-zero variation of the bulk Dirac index must manifest on the boundary as a compensating spectral flow. Under strong magnetic fields, this boundary spectral flow leads the system into a regime where the lowest Landau level (LLL) contribution to the vacuum energy becomes dominant. The LLL correction produces a strongly enhanced negative Casimir energy density, offering a concrete route toward local violation of the strong energy condition without singularities. Furthermore, extreme spectral compression causes the effective quantum channel capacity to approach zero. We interpret this as an operational suppression of information-theoretic temporality. The name '2C-Anomaly' reflects the direct connection to the 2C Theory framework, in which the critical transition at C=2/3 governs the onset of this spectral compression regime.
(Demian) et al. (Thu,) studied this question.
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