Triple

T2636370
Position Surface form Disambiguated ID Type / Status
Subject Hans Fitting E59755 entity
Predicate notableConcept P201 FINISHED
Object Fitting lemma
The Fitting lemma is a result in group theory and module theory that characterizes how certain algebraic structures decompose into direct sums of invariant subcomponents, often involving nilpotent and invertible parts.
E283604 NE FINISHED

How this triple was built (4 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: Fitting lemma | Statement: [Hans Fitting, notableConcept, Fitting lemma]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Fitting lemma
Context triple: [Hans Fitting, notableConcept, Fitting lemma]
  • A. Tucker’s lemma
    Tucker’s lemma is a combinatorial analog of the Borsuk–Ulam theorem that provides conditions guaranteeing the existence of certain complementary edge labels in triangulated spheres.
  • B. Kronecker’s lemma
    Kronecker’s lemma is a result in real analysis and summability theory that links the convergence of series with weighted averages of their partial sums, often used in the study of Fourier series and ergodic theorems.
  • C. Sperner's lemma
    Sperner's lemma is a fundamental result in combinatorial topology that guarantees the existence of a fully labeled simplex in certain labeled triangulations, and is widely used to prove fixed-point and equilibrium theorems.
  • D. Glicksberg fixed-point theorem
    The Glicksberg fixed-point theorem is a result in functional analysis that extends Kakutani’s fixed-point theorem to certain infinite-dimensional or compact convex subsets of locally convex topological vector spaces.
  • E. Schwarz lemma
    Schwarz lemma is a fundamental result in complex analysis that constrains holomorphic self-maps of the unit disk, particularly bounding their magnitude and derivative at the origin.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Fitting lemma
Triple: [Hans Fitting, notableConcept, Fitting lemma]
Generated description
The Fitting lemma is a result in group theory and module theory that characterizes how certain algebraic structures decompose into direct sums of invariant subcomponents, often involving nilpotent and invertible parts.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Fitting lemma
Target entity description: The Fitting lemma is a result in group theory and module theory that characterizes how certain algebraic structures decompose into direct sums of invariant subcomponents, often involving nilpotent and invertible parts.
  • A. Tucker’s lemma
    Tucker’s lemma is a combinatorial analog of the Borsuk–Ulam theorem that provides conditions guaranteeing the existence of certain complementary edge labels in triangulated spheres.
  • B. Kronecker’s lemma
    Kronecker’s lemma is a result in real analysis and summability theory that links the convergence of series with weighted averages of their partial sums, often used in the study of Fourier series and ergodic theorems.
  • C. Sperner's lemma
    Sperner's lemma is a fundamental result in combinatorial topology that guarantees the existence of a fully labeled simplex in certain labeled triangulations, and is widely used to prove fixed-point and equilibrium theorems.
  • D. Glicksberg fixed-point theorem
    The Glicksberg fixed-point theorem is a result in functional analysis that extends Kakutani’s fixed-point theorem to certain infinite-dimensional or compact convex subsets of locally convex topological vector spaces.
  • E. Schwarz lemma
    Schwarz lemma is a fundamental result in complex analysis that constrains holomorphic self-maps of the unit disk, particularly bounding their magnitude and derivative at the origin.
  • F. None of above. chosen

Provenance (5 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_69ab4ac8596c8190b34997e73d9e991c completed March 6, 2026, 9:44 p.m.
NER Named-entity recognition batch_69abd8e1fffc81908e4921690098c8db completed March 7, 2026, 7:50 a.m.
NED1 Entity disambiguation (via context triple) batch_69af90b3e9b48190857ae21022a4fb15 completed March 10, 2026, 3:32 a.m.
NEDg Description generation batch_69af922043508190a9a9ceced2425109 completed March 10, 2026, 3:38 a.m.
NED2 Entity disambiguation (via description) batch_69af927bb1d0819081ab11eb4470e28d completed March 10, 2026, 3:39 a.m.
Created at: March 6, 2026, 9:50 p.m.