Observer / CONCEPT
Informationally complete pairs and forests
Two finite real random variables determine every probability weight exactly when their joint value map is injective and their bipartite fiber graph is a forest.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES0
PROOF DEPTH5
DOCUMENT LINKS0
The forest characterization
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
None recorded in this release.
RELATED KNOWLEDGE
Structural connections
- A steady-state symmetry block without Markov formstructural-affinity · Closed
- An equilibrium complete graph defeats the activity boundstructural-affinity · Closed
- Bhattacharyya Affinity and the Bretagnolle--Huber Boundstructural-affinity · Closed
- Diagonal correlance exceeds its proposed normalizationstructural-affinity · Closed
- Glauber relaxation times do not order energy relaxation ratesstructural-affinity · Closed
- Jensen-Shannon balls need not have majorization-minimizersstructural-affinity · Closed
- Le Cam's Two-Point Lemma for Every Finite Teststructural-affinity · Closed
- Model-level equivalence does not imply measure-level equivalencestructural-affinity · Closed
- Sharp coupling budgets on a permutation cyclestructural-affinity · Closed
- The maximal index for arithmetic and geometric mean matricesstructural-affinity · Closed
Documents & exposition
None recorded in this release.
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
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