Alphabeta Math
RemarkRemark: Literature-sourcedProof: Not applicable
How 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.

Authors' qualified novelty claims

PDF p. 3: end of introductory literature paragraph; PDF p. 5: §1.4, opening paragraph

Statement

To the best of their knowledge, the authors describe Theorems 1.1–1.5 and Corollary 1.6 as the first exact controllability results for the nonlinear Schrödinger equation in an exterior domain. They also describe Theorem 1.1 as the first exact controllability result for a nonlinear Schrödinger equation with controls acting only on the outer part of the boundary of a domain surrounding an obstacle. These are the authors' qualified priority claims, not a certification of priority by this item.

An exterior domain here is the connected complement in Euclidean space of a compact obstacle with smooth boundary. Exact controllability means that each pair of admissible initial and terminal states can be connected by an admissible control in the specified time and solution class; a local result restricts the endpoints to a specified neighborhood. The individual theorems determine the equation, control region, solution classes and endpoint restrictions.

Facts & Assumptions

[F1]

The geometry and the meaning of the obstacle's exterior are fixed by Exterior and truncated obstacle domains.

[F2]

The endpoint reachability and local controllability terminology is specified by Reachability and observation vocabulary for controlled evolutions; it does not assert controllability for an unspecified evolution.

Source notes

The frozen article makes the qualified priority statements in the cited passages. The reference is used to attribute those statements, not as a proof of the underlying controllability results or as an independent verification of literature priority.

Depends on

Dependency tree · 2 levels

Each result is drawn at its shortest distance from this item. Arrows run from prerequisites to the items that use them; this item has a heavier outline. External source nodes link directly to the cited text. The view shows up to two dependency steps; open a prerequisite to continue.

Sources