Triple

T26255024
Position Surface form Disambiguated ID Type / Status
Subject SL(2,ℤ) E656692 entity
Predicate abelianizationIs P77186 FINISHED
Object cyclic group of order 12 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: cyclic group of order 12 | Statement: [SL(2,ℤ), abelianizationIs, cyclic group of order 12]
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: abelianizationIs
Context triple: [SL(2,ℤ), abelianizationIs, cyclic group of order 12]
  • A. hasAbelianization chosen
    Indicates that one algebraic structure is related to the abelian group obtained by quotienting it by its commutator subgroup (its abelianization).
  • B. isAbelianFor
    Indicates that the operation or structure associated with the given entity is commutative (i.e., forms an Abelian group) with respect to the specified context or parameters.
  • C. hasTrivialAbelianization
    Indicates that the group’s abelianization is trivial, meaning its commutator subgroup is the whole group and it has no nontrivial abelian quotient.
  • D. isNonAbelian
    Indicates that the operation or structure in question does not satisfy commutativity, so the order of applying the operation matters.
  • E. associatedGradedIs
    Indicates that one mathematical object is the associated graded object (e.g., graded structure derived from a filtration) of another.
  • 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_69ee5b4d25ac819086acb51184602576 completed April 26, 2026, 6:37 p.m.
NER Named-entity recognition batch_69f60dcd2e688190b54e36b0ff0d9187 completed May 2, 2026, 2:44 p.m.
PD Predicate disambiguation batch_69f5f7ff548c8190a23e98c5e66e0bc7 completed May 2, 2026, 1:11 p.m.
Created at: April 26, 2026, 9:08 p.m.