A map of problems, methods and public results

First identify the area term, defect matter entropy and endpoint variation. Follow the bulk decomposition into the lower-dimensional island prescription to establish the dictionary needed for later comparisons.

Apply the static dictionary to the time-dependent AdS₃/BCFT₂ construction and its matching Page curves. Then examine the higher-dimensional comparison, where the bulk DES entropy is generally lower than the boundary low-energy island result.

After the entropy calculation, examine causal structure. This preprint makes its argument for effective micro-causality conditional on no extra propagation channels, a local bulk-supported operator dictionary, and matching effective spacelike separation to bulk causal accessibility.

Finally turn to grouped storage for fixed finitely many separated intervals. Public Zenodo v1 connects entropy partitions to free-perimeter-plus-area optimization using leading RT entropies and a controlled ultraviolet error. Actual-state entropies need separate error bounds; the compact-BTZ annulus has a mismatch at the same tariff.

Begin with quantum entropy on the defect and its role in surface variation. This locates the boundary degrees of freedom in the calculation and prepares a dictionary for gravitational and matter terms after partial reduction.

Next retain both the EOW brane and a finite radial cutoff. Follow partial reduction to brane-world gravity coupled to a TT̄-deformed bath, comparing entanglement entropies and Page curves on the two sides.

Then ask whether the deformation acts on the boundary. Follow the paper's two constructions through boundary entropy and the finite-interval spectrum, and through field-theory/gravity comparisons of entanglement and Rényi entropies.

Finish with the journal version: no independent boundary stress tensor, a reflective boundary, a semiclassical factorized state, and separately treated contact terms. It assigns distinct roles to the local algebraic constraint and internal RT/BCFT entropy consistency checks with matched prescriptions.

Start by tracing the variables: in the three-dimensional partial-reduction construction, a small transverse brane fluctuation becomes the dilaton and yields the JT action. Record the small-fluctuation assumption, variable map and prescriptions used in the entropy match.

Next compare the inputs to two calculations. This preprint reformulates the shock-wave and entanglement-wedge methods as initial data inserted into gravitational constraint equations, interpreting the matching butterfly velocities through that shared structure.

Finish by aligning the objects being compared: list the induced geometry, Weyl frame, endpoints and contact terms explicitly. Use the paper to distinguish a local Ward constraint from an internal entropy consistency check, and label what each check actually supports.