Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Replica saddles and islands retain their model assumptions
A source-based limitation on island and quantum-extremal-surface calculations in selected semiclassical gravity models. It records their regulator, state-factorization, replica-continuation, and gravitational-saddle assumptions; it asserts no empirical observation or theorem of microscopic unitarity for an unspecified four-dimensional black hole.
Statement
For selected semiclassical gravity-plus-bath models, an island or quantum-extremal-surface calculation uses a specified boundary state and region factorization, a regulator and renormalization prescription, and gravitational path-integral assumptions. The replica prescription for a density matrix computes by analytic continuation from replica number ; the gravitational calculation must also specify which saddle configurations contribute and which dominates. A Page-like curve here means a model entropy profile that rises and later falls under its stipulated parameter evolution. Such a curve is a conditional prediction of that selected calculation; it does not establish microscopic unitarity of an unspecified four-dimensional evaporating black hole or prove that a candidate saddle contributes in another theory.