Triple

T6833946
Position Surface form Disambiguated ID Type / Status
Subject Jordan–Hölder theorem E157402 entity
Predicate hasVersion P455 FINISHED
Object Jordan–Hölder theorem for modules E157402 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: Jordan–Hölder theorem for modules | Statement: [Jordan–Hölder theorem, hasVersion, Jordan–Hölder theorem for modules]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Jordan–Hölder theorem for modules
Context triple: [Jordan–Hölder theorem, hasVersion, Jordan–Hölder theorem for modules]
  • A. Jordan–Hölder theorem chosen
    The Jordan–Hölder theorem is a fundamental result in group theory stating that any two composition series of a finite group have the same length and the same (up to order and isomorphism) simple factor groups.
  • B. Noether's isomorphism theorems
    Noether's isomorphism theorems are fundamental results in abstract algebra that relate quotient structures and substructures of groups, rings, and modules, providing a unifying framework for understanding homomorphic images and factor structures.
  • C. Hilbert’s syzygy theorem
    Hilbert’s syzygy theorem is a fundamental result in commutative algebra that describes the finite length and structure of free resolutions of modules over polynomial rings.
  • D. Auslander–Buchsbaum formula
    The Auslander–Buchsbaum formula is a fundamental result in commutative algebra that relates the projective dimension of a finitely generated module over a Noetherian local ring to the depth of the module and the depth of the ring.
  • E. The Poincaré-Birkhoff-Witt theorem in ring theory
    "The Poincaré-Birkhoff-Witt theorem in ring theory" is a mathematical work, attributed here to N. G. de Bruijn, that studies and applies the Poincaré–Birkhoff–Witt theorem in the context of associative and Lie-theoretic ring structures.
  • 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_69c6882c53608190b99aebef079b23bd completed March 27, 2026, 1:37 p.m.
NER Named-entity recognition batch_69c6d67936288190829fedc3729aadd8 completed March 27, 2026, 7:11 p.m.
NED1 Entity disambiguation (via context triple) batch_69c723fd50c88190af005fd58ca0aee6 completed March 28, 2026, 12:42 a.m.
Created at: March 27, 2026, 2:18 p.m.