Triple

T11411575
Position Surface form Disambiguated ID Type / Status
Subject Gelfand–Naimark theorem E270382 entity
Predicate isRelatedTo P37 FINISHED
Object Pontryagin duality 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 | Statement: [Gelfand–Naimark theorem, isRelatedTo, Pontryagin duality]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Pontryagin duality
Context triple: [Gelfand–Naimark theorem, isRelatedTo, Pontryagin duality]
  • 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. 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. Poincaré duality
    Poincaré duality is a fundamental theorem in algebraic topology that relates the homology and cohomology groups of an oriented closed manifold in complementary dimensions.
  • D. Gelfand transform
    The Gelfand transform is a fundamental construction in functional analysis that represents elements of a commutative Banach algebra as continuous functions on its space of maximal ideals, linking algebraic structure with topological and spectral properties.
  • E. Poitou–Tate duality
    Poitou–Tate duality is a fundamental result in Galois cohomology that establishes deep duality relationships between global and local cohomology groups of number fields.
  • 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_69d6aaddeaa8819088b30ef7b50598c9 completed April 8, 2026, 7:22 p.m.
NER Named-entity recognition batch_69d8015017d08190b4020c76545556d6 completed April 9, 2026, 7:43 p.m.
NED1 Entity disambiguation (via context triple) batch_69e5d352283c8190b3ae7cefbd3bd5da completed April 20, 2026, 7:18 a.m.
Created at: April 8, 2026, 9:34 p.m.