Triple

T26255018
Position Surface form Disambiguated ID Type / Status
Subject SL(2,ℤ) E656692 entity
Predicate PSL2ZIsomorphicTo P160549 FINISHED
Object free product C₂ * C₃ 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: free product C₂ * C₃ | Statement: [SL(2,ℤ), PSL2ZIsomorphicTo, free product C₂ * C₃]
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: PSL2ZIsomorphicTo
Context triple: [SL(2,ℤ), PSL2ZIsomorphicTo, free product C₂ * C₃]
  • A. automorphismGroupIsomorphicTo
    Indicates that the automorphism group of one structure is isomorphic, as a group, to the automorphism group of another structure.
  • B. isAutomorphismGroupOf
    Indicates that a group is the full automorphism group consisting of all structure-preserving bijections (automorphisms) of a given mathematical object.
  • C. hasNonAbelianSylow2Subgroups
    Indicates that the Sylow 2-subgroups of a given group are non-abelian, i.e., their group operation is not commutative.
  • D. congruenceSubgroups
    Indicates that there is a relationship between groups where one is a congruence subgroup of the other, typically defined by congruence conditions modulo some integer or ideal.
  • E. hasAutomorphismGroupContaining
    Indicates that the automorphism group of one mathematical structure includes the other group as a subgroup or component.
  • F. None of above. chosen

Provenance (4 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_69f602d2ec748190ae95154f34c7878f completed May 2, 2026, 1:57 p.m.
PDg Predicate description generation batch_69f6037bf7a081908862a8359be80cf8 completed May 2, 2026, 2 p.m.
Created at: April 26, 2026, 9:08 p.m.