Open question · OPEN-E-COMMON-SUPERGRADIENT

Can one supergradient describe population E geometry?

Openpublication: open

Meaning

Seek a common geometric description under the smallest-eigenvalue criterion.

Statement

Determine whether every suitable population E optimum admits one common supergradient supporting all cell-assignment inequalities almost everywhere.

Relationships

Related settled results

E-optimality supergradient structureE-SUPERGRADIENT
Repeated minimum eigenvalues make one-transfer first-order E geometry non-identifyingE-REPEATED-EIGEN-DEGENERACY

The full chain beneath it

Infinitesimal cell-transfer identityGENERAL-FIRST-VARIATIONdepth 2
Quantized Fisher-information identityFI-QUANT-IDENTITYdepth 3

Where it comes from

Raised by

Repeated minimum eigenvalues make one-transfer first-order E geometry non-identifyingE-REPEATED-EIGEN-DEGENERACY
E-optimality supergradient structureE-SUPERGRADIENT

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

E6. Common-supergradient population geometry

It remains open whether every suitable population E optimum admits one common supergradient that supports all cell-assignment inequalities almost everywhere.

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