Open question · OPEN-D-EXCHANGE-CONSISTENCY

Do exchange-stable solutions converge?

Openpublication: open

Meaning

Study population limits for local exchange-stable D solutions, rather than only global optima.

Statement

Determine whether empirical one-point-exchange-stable D solutions converge to the population stationary set and what stability margins prevent persistent spurious branches.

Relationships

Related settled results

Finite D exchange stability implies strict self-consistent VoronoiD-EXCHANGE-IMPLIES-VORONOI
Exact finite inductive closure / compilerD-FINITE-INDUCTIVE-CLOSURE

The full chain beneath it

Exact finite D log-determinant gainD-LOGDET-GAINdepth 2
D leverage inequalityD-LEVERAGEdepth 2
Exact weighted rank-two relocationD-RANK2-MOVEdepth 3
Quantized Fisher-information identityFI-QUANT-IDENTITYdepth 3

Where it comes from

Raised by

Finite D exchange stability implies strict self-consistent VoronoiD-EXCHANGE-IMPLIES-VORONOI
Exact finite inductive closure / compilerD-FINITE-INDUCTIVE-CLOSURE

Local graph

Prerequisites to the left, what it enables or raises to the right, boundary cases below. Open in the map.

The question in full

Consistency of exchange-stable D solutions

Do one-point-exchange-stable empirical D quantizers converge to the population stationary set? What prevents spurious local branches from persisting? Tools: set-valued M-estimation, stability margins, uniform convergence of move gains.

From OPEN_PROBLEMS.md