Triple

T19782743
Position Surface form Disambiguated ID Type / Status
Subject Hahn decomposition theorem E475178 entity
Predicate hasConsequence P812 FINISHED
Object Jordan decomposition theorem — NE NERFINISHED

How this triple was built (2 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Jordan decomposition theorem | Statement: [Hahn decomposition theorem, hasConsequence, Jordan decomposition theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Jordan decomposition theorem
Context triple: [Hahn decomposition theorem, hasConsequence, Jordan decomposition theorem]
  • A. Jordan–Chevalley decomposition
    The Jordan–Chevalley decomposition is a fundamental result in linear algebra and representation theory that expresses a linear operator (or matrix) as the sum or product of commuting semisimple and nilpotent parts.
  • B. Lebesgue decomposition theorem chosen
    The Lebesgue decomposition theorem is a fundamental result in measure theory that states any σ-finite measure can be uniquely decomposed into a part that is absolutely continuous with respect to another measure and a part that is singular to it.
  • C. Jordan normal form theorem
    The Jordan normal form theorem is a fundamental result in linear algebra that states every square matrix over an algebraically closed field is similar to a block diagonal matrix composed of Jordan blocks, providing a canonical form for linear operators.
  • D. Hahn decomposition theorem
    The Hahn decomposition theorem is a fundamental result in measure theory that states any signed measure space can be partitioned into a positive set and a negative set on which the measure is respectively nonnegative and nonpositive.
  • E. Schur decomposition
    Schur decomposition is a matrix factorization in linear algebra that expresses a square matrix as a unitary (or orthogonal) matrix times an upper triangular matrix times the inverse of the unitary matrix, revealing its eigenvalues and simplifying many numerical computations.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69d8e51b014081908b263e167370529a completed April 10, 2026, 11:55 a.m.
NER Named-entity recognition batch_69e653852e848190b8971981a164e8f9 completed April 20, 2026, 4:25 p.m.
Created at: April 10, 2026, 1:49 p.m.