Triple

T12177372
Position Surface form Disambiguated ID Type / Status
Subject virial theorem E290121 entity
Predicate relatedTo P37 FINISHED
Object Jeans theorem
Jeans theorem is a fundamental result in stellar dynamics stating that any steady-state solution of the collisionless Boltzmann equation depends on phase-space coordinates only through integrals of motion.
E965549 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: Jeans theorem | Statement: [virial theorem, relatedTo, Jeans theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Jeans theorem
Context triple: [virial theorem, relatedTo, Jeans theorem]
  • A. Cauchy's theorem in group theory
    Cauchy's theorem in group theory is a fundamental result stating that if a finite group’s order is divisible by a prime p, then the group contains an element (and hence a subgroup) of order p.
  • B. Peter–Weyl theorem
    The Peter–Weyl theorem is a fundamental result in representation theory and harmonic analysis that decomposes square-integrable functions on a compact topological group into a direct sum of finite-dimensional irreducible unitary representations.
  • C. Schur’s lemma
    Schur’s lemma is a fundamental result in representation theory stating that any homomorphism between irreducible representations is either zero or an isomorphism, and that endomorphisms of an irreducible representation over an algebraically closed field are scalar multiples of the identity.
  • D. Janet–Cartan theorem
    The Janet–Cartan theorem is a fundamental result in differential geometry stating that any real-analytic Riemannian manifold can be locally isometrically embedded into a Euclidean space of sufficiently high dimension.
  • E. 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.
  • 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: Jeans theorem
Triple: [virial theorem, relatedTo, Jeans theorem]
Generated description
Jeans theorem is a fundamental result in stellar dynamics stating that any steady-state solution of the collisionless Boltzmann equation depends on phase-space coordinates only through integrals of motion.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Jeans theorem
Target entity description: Jeans theorem is a fundamental result in stellar dynamics stating that any steady-state solution of the collisionless Boltzmann equation depends on phase-space coordinates only through integrals of motion.
  • A. Cauchy's theorem in group theory
    Cauchy's theorem in group theory is a fundamental result stating that if a finite group’s order is divisible by a prime p, then the group contains an element (and hence a subgroup) of order p.
  • B. Peter–Weyl theorem
    The Peter–Weyl theorem is a fundamental result in representation theory and harmonic analysis that decomposes square-integrable functions on a compact topological group into a direct sum of finite-dimensional irreducible unitary representations.
  • C. Schur’s lemma
    Schur’s lemma is a fundamental result in representation theory stating that any homomorphism between irreducible representations is either zero or an isomorphism, and that endomorphisms of an irreducible representation over an algebraically closed field are scalar multiples of the identity.
  • D. Janet–Cartan theorem
    The Janet–Cartan theorem is a fundamental result in differential geometry stating that any real-analytic Riemannian manifold can be locally isometrically embedded into a Euclidean space of sufficiently high dimension.
  • E. 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.
  • 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_69d6ab4d6c00819095a9a7c35de83cfb completed April 8, 2026, 7:23 p.m.
NER Named-entity recognition batch_69d915fa6ff08190a1ddb3606c229cad completed April 10, 2026, 3:23 p.m.
NED1 Entity disambiguation (via context triple) batch_69f5f6ab19288190a882c842d74a2e30 completed May 2, 2026, 1:05 p.m.
NEDg Description generation batch_69f600b7385881909ddb86a1d39ff5d4 completed May 2, 2026, 1:48 p.m.
NED2 Entity disambiguation (via description) batch_69f601ebaa448190ba59485d9d7d68d1 completed May 2, 2026, 1:53 p.m.
Created at: April 8, 2026, 9:50 p.m.