Triple

T1382919
Position Surface form Disambiguated ID Type / Status
Subject Noether's isomorphism theorems E29378 entity
Predicate alsoKnownAs P39 FINISHED
Object isomorphism theorems E29378 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: isomorphism theorems | Statement: [Noether's isomorphism theorems, alsoKnownAs, isomorphism theorems]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: isomorphism theorems
Context triple: [Noether's isomorphism theorems, alsoKnownAs, isomorphism theorems]
  • A. Noether's isomorphism theorems chosen
    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.
  • B. Abelian groups
    Abelian groups are algebraic structures in which the group operation is commutative, meaning the order of combining elements does not affect the result.
  • C. Lagrange's theorem in group theory
    Lagrange's theorem in group theory is a fundamental result stating that the order of any subgroup of a finite group divides the order of the group.
  • D. 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.
  • E. Erlangen Program
    The Erlangen Program is Felix Klein’s influential 1872 framework that classifies and studies geometries based on their underlying symmetry groups and transformation properties.
  • 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_69a498d883a48190bfdca525296ef7ee completed March 1, 2026, 7:51 p.m.
NER Named-entity recognition batch_69a4c3361bf08190b3f6bbf82e17685b completed March 1, 2026, 10:52 p.m.
NED1 Entity disambiguation (via context triple) batch_69acd48c41f4819092f7e1302d803662 completed March 8, 2026, 1:44 a.m.
Created at: March 1, 2026, 7:59 p.m.