Triple

T16249773
Position Surface form Disambiguated ID Type / Status
Subject Steinhaus theorem E394469 entity
Predicate hasGeneralization P2372 FINISHED
Object Steinhaus theorem for locally compact abelian groups E394469 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: Steinhaus theorem for locally compact abelian groups | Statement: [Steinhaus theorem, hasGeneralization, Steinhaus theorem for locally compact abelian groups]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Steinhaus theorem for locally compact abelian groups
Context triple: [Steinhaus theorem, hasGeneralization, Steinhaus theorem for locally compact abelian groups]
  • A. Steinhaus theorem chosen
    The Steinhaus theorem is a fundamental result in measure theory stating that the difference set of any subset of the real numbers with positive Lebesgue measure contains an open interval around zero.
  • B. Plancherel theorem for locally compact abelian groups
    The Plancherel theorem for locally compact abelian groups is a fundamental result in harmonic analysis that identifies the Fourier transform as a unitary isomorphism between an L²-space on the group and an L²-space on its dual group, preserving inner products and norms.
  • C. 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.
  • D. Harmonic Analysis on Homogeneous Spaces
    Harmonic Analysis on Homogeneous Spaces is a mathematical monograph by Nolan Wallach that develops the theory of harmonic analysis and representation theory on Lie groups and their homogeneous spaces.
  • E. Kesten’s theorem on random walks on groups
    Kesten’s theorem on random walks on groups is a fundamental result in probability theory that characterizes amenability of groups via the spectral radius of associated random walks.
  • 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_69d87f2171208190951025e526947816 completed April 10, 2026, 4:40 a.m.
NER Named-entity recognition batch_69e2459606f88190a53905186f7f73be completed April 17, 2026, 2:37 p.m.
NED1 Entity disambiguation (via context triple) batch_6a000ee568a48190835ce76f84461044 completed May 10, 2026, 4:51 a.m.
Created at: April 10, 2026, 5:04 a.m.