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.