Triple

T16574848
Position Surface form Disambiguated ID Type / Status
Subject Mikhail Gromov E402682 entity
Predicate notableFor P22 FINISHED
Object Gromov’s theorem on groups of polynomial growth
Gromov’s theorem on groups of polynomial growth is a fundamental result in geometric group theory stating that any finitely generated group with polynomial growth is virtually nilpotent.
E1221217 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: Gromov’s theorem on groups of polynomial growth | Statement: [Mikhail Gromov, notableFor, Gromov’s theorem on groups of polynomial growth]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Gromov’s theorem on groups of polynomial growth
Context triple: [Mikhail Gromov, notableFor, Gromov’s theorem on groups of polynomial growth]
  • A. Tarski’s theorem on amenable groups
    Tarski’s theorem on amenable groups is a fundamental result in group theory and measure theory that characterizes amenable groups as precisely those that do not admit Banach–Tarski-type paradoxical decompositions.
  • B. Kesten’s theorem on random walks on groups
    Kesten’s theorem on random walks on groups is a fundamental result in probability theory that characterizes amenability of groups via the spectral radius of associated random walks.
  • C. Burger–Iozzi–Wienhard inequalities for higher rank groups
    The Burger–Iozzi–Wienhard inequalities for higher rank groups are a family of sharp bounds in bounded cohomology and representation theory that extend the classical Milnor–Wood inequality to representations of surface groups into higher rank Lie groups.
  • D. Gowers inverse theorem in additive combinatorics
    The Gowers inverse theorem in additive combinatorics is a fundamental result that characterizes functions with large Gowers uniformity norms by showing they must correlate with structured objects such as polynomial phase functions, underpinning much of modern higher-order Fourier analysis.
  • E. Cheeger–Gromov compactness theorem
    The Cheeger–Gromov compactness theorem is a fundamental result in Riemannian geometry that gives conditions under which a sequence of Riemannian manifolds has a subsequence converging (in the Gromov–Hausdorff or smooth sense) to a limit space.
  • 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: Gromov’s theorem on groups of polynomial growth
Triple: [Mikhail Gromov, notableFor, Gromov’s theorem on groups of polynomial growth]
Generated description
Gromov’s theorem on groups of polynomial growth is a fundamental result in geometric group theory stating that any finitely generated group with polynomial growth is virtually nilpotent.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Gromov’s theorem on groups of polynomial growth
Target entity description: Gromov’s theorem on groups of polynomial growth is a fundamental result in geometric group theory stating that any finitely generated group with polynomial growth is virtually nilpotent.
  • A. Tarski’s theorem on amenable groups
    Tarski’s theorem on amenable groups is a fundamental result in group theory and measure theory that characterizes amenable groups as precisely those that do not admit Banach–Tarski-type paradoxical decompositions.
  • B. Kesten’s theorem on random walks on groups
    Kesten’s theorem on random walks on groups is a fundamental result in probability theory that characterizes amenability of groups via the spectral radius of associated random walks.
  • C. Burger–Iozzi–Wienhard inequalities for higher rank groups
    The Burger–Iozzi–Wienhard inequalities for higher rank groups are a family of sharp bounds in bounded cohomology and representation theory that extend the classical Milnor–Wood inequality to representations of surface groups into higher rank Lie groups.
  • D. Gowers inverse theorem in additive combinatorics
    The Gowers inverse theorem in additive combinatorics is a fundamental result that characterizes functions with large Gowers uniformity norms by showing they must correlate with structured objects such as polynomial phase functions, underpinning much of modern higher-order Fourier analysis.
  • E. Cheeger–Gromov compactness theorem
    The Cheeger–Gromov compactness theorem is a fundamental result in Riemannian geometry that gives conditions under which a sequence of Riemannian manifolds has a subsequence converging (in the Gromov–Hausdorff or smooth sense) to a limit space.
  • 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_69d88387363c8190a97a0c942130de97 completed April 10, 2026, 4:58 a.m.
NER Named-entity recognition batch_69e3595bbbbc8190b023f4872908c031 completed April 18, 2026, 10:13 a.m.
NED1 Entity disambiguation (via context triple) batch_6a006eea409c8190808170a0b3f4bd17 completed May 10, 2026, 11:41 a.m.
NEDg Description generation batch_6a006f7ca0dc8190a75d84d9ffbf83e0 completed May 10, 2026, 11:43 a.m.
NED2 Entity disambiguation (via description) batch_6a00705453c081909e8401024e92b5aa completed May 10, 2026, 11:47 a.m.
Created at: April 10, 2026, 5:16 a.m.