Triple

T29565588
Position Surface form Disambiguated ID Type / Status
Subject Brauer group E753153 entity
Predicate hasIsomorphism P29599 FINISHED
Object H^2(Gal(K^sep/K), (K^sep)^×) for a field K with separable closure K^sep LITERAL 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: H^2(Gal(K^sep/K), (K^sep)^×) for a field K with separable closure K^sep | Statement: [Brauer group, hasIsomorphism, H^2(Gal(K^sep/K), (K^sep)^×) for a field K with separable closure K^sep]
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: hasIsomorphism
Context triple: [Brauer group, hasIsomorphism, H^2(Gal(K^sep/K), (K^sep)^×) for a field K with separable closure K^sep]
  • A. isIsomorphicTo chosen
    Indicates that two structures have a one-to-one, structure-preserving correspondence between their elements, making them equivalent in form even if not identical in content.
  • B. hasHomomorphism
    Indicates that there exists a structure-preserving map (homomorphism) from one mathematical structure to another.
  • C. hasAutomorphism
    Indicates that there exists a structure-preserving bijection from an entity to itself that maintains all relevant relations and operations.
  • D. isLocallyIsomorphicTo
    Indicates that two structures are isomorphic within some local neighborhood or restricted region, even if they may differ globally.
  • E. isIsogenousTo
    Indicates that two mathematical structures, typically elliptic curves or abelian varieties, are related by an isogeny, i.e., a non-constant morphism with finite kernel that preserves their group structure.
  • F. None of above.

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_69f0ef7fcb4881908a933110adb9bda1 completed April 28, 2026, 5:33 p.m.
NER Named-entity recognition batch_69f68f670b608190a0b6ab60d722b4e0 completed May 2, 2026, 11:57 p.m.
PD Predicate disambiguation batch_69f68b7b03488190b1db5fde4c7dd6e5 completed May 2, 2026, 11:40 p.m.
Created at: April 28, 2026, 5:52 p.m.