Triple

T7685069
Position Surface form Disambiguated ID Type / Status
Subject Lev Pontryagin E174094 entity
Predicate notableIdea P4 FINISHED
Object Pontryagin duality for locally compact abelian groups E681628 NE FINISHED

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: Pontryagin duality for locally compact abelian groups | Statement: [Lev Pontryagin, notableIdea, Pontryagin duality for locally compact abelian groups]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Pontryagin duality for locally compact abelian groups
Context triple: [Lev Pontryagin, notableIdea, Pontryagin duality for locally compact abelian groups]
  • A. Pontryagin duality chosen
    Pontryagin duality is a fundamental theorem in harmonic analysis and topological group theory that establishes a duality between locally compact abelian groups and their groups of continuous characters.
  • B. Introduction to Abstract Harmonic Analysis
    Introduction to Abstract Harmonic Analysis is a foundational graduate-level textbook that systematically develops the theory of harmonic analysis on topological groups and related abstract structures.
  • C. L’intégration dans les groupes topologiques et ses applications
    L’intégration dans les groupes topologiques et ses applications is a foundational mathematical monograph by André Weil that develops the theory of integration on topological groups and explores its far-reaching applications in analysis and number theory.
  • D. Plancherel theorem for real reductive groups
    The Plancherel theorem for real reductive groups is a fundamental result in representation theory that describes how square-integrable functions on a real reductive Lie group decompose into irreducible unitary representations, generalizing Fourier analysis to this non-abelian setting.
  • E. Abelian groups
    Abelian groups are algebraic structures in which the group operation is commutative, meaning the order of combining elements does not affect the result.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69c6995840408190a19de6c51090f46f completed March 27, 2026, 2:51 p.m.
NER Named-entity recognition batch_69c7022118908190a3a93cfda79be0a4 completed March 27, 2026, 10:18 p.m.
NED1 Entity disambiguation (via context triple) batch_69c8aca0b5b08190b178f0908612164c completed March 29, 2026, 4:37 a.m.
Created at: March 27, 2026, 4:02 p.m.