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.