Where the Lovelock Bridge Breaks: Negative Results and New Directions for Connecting Discrete and Continuous Spacetime Emergence

Key Points

• This research examines the failure of discrete-to-continuous spacetime emergence in specific models.
• Analyzed Fisher information geometry in relation to spacetime emergence.
• Evaluated Ising-type lattice models for continuum limits.
• Assessed Type II contributions like critical beta formula, Tree Fisher Identity, and Lorentzian dominance.
• Demonstrated that continuum limits of the models do not converge to Lovelock gravity.
• Identified critical beta formula and Tree Fisher Identity as significant constructive contributions.