Modular Strip Analyticity as the Order Parameter for Semiclassical Spacetime
Abstract
I isolate a basis-free identity equating the mismatch between the modular Berry curvature two-form and the Bogoliubov–Kubo–Mori (BKM) symplectic form to a kernel-weighted KMS boundary term. Working on the quotient bundle by the modular centralizer, with the BKM-orthogonal gauge-fixing throughout, I show that this mismatch tensor ∆µν vanishes precisely on KMS-compatible state families and equals the failure of a contour deformation to close in the KMS strip otherwise. The result is basis-free and survives passage from finite dimensions through Type III von Neumann algebras to the crossed-product Type II setting relevant to holographic gravity. Four corollaries identify ∆µν as the order parameter for semiclassicality (Region IV), the obstruction to state-independent bulk reconstruction, the phase-leaving rate bounded by the MSS chaos bound (under an explicit assumption), and a trace-volume criterion for singularity resolution. A fully specified numerical protocol in n≤6 qubits allows direct falsification.
Fields of Study & Subjects
Black Holes and Theoretical Physics
Advanced Operator Algebra Research
Noncommutative and Quantum Gravity Theories
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 7 March 2026
- Language
- EN