Triple

T15030951
Position Surface form Disambiguated ID Type / Status
Subject Einstein–Yang–Mills equations E378340 entity
Predicate generalizes P2372 FINISHED
Object flat-space Yang–Mills equations
The flat-space Yang–Mills equations are the fundamental nonlinear field equations describing gauge fields in a fixed Minkowski spacetime, forming the core of non-abelian gauge theory in particle physics.
E244516 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: flat-space Yang–Mills equations | Statement: [Einstein–Yang–Mills equations, generalizes, flat-space Yang–Mills equations]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: flat-space Yang–Mills equations
Context triple: [Einstein–Yang–Mills equations, generalizes, flat-space Yang–Mills equations]
  • A. Einstein–Yang–Mills equations
    The Einstein–Yang–Mills equations are the coupled field equations that describe how non-abelian gauge fields (such as those in Yang–Mills theory) interact with and curve spacetime within the framework of general relativity.
  • B. Yang–Mills theory
    Yang–Mills theory is a gauge field theory describing the behavior of non-abelian gauge fields, forming the mathematical foundation for modern particle physics, including the strong and electroweak interactions.
  • C. Einstein–Maxwell equations
    The Einstein–Maxwell equations are the coupled set of field equations in general relativity that describe how spacetime curvature and electromagnetic fields interact and influence each other.
  • D. Schwinger–Dyson equations
    The Schwinger–Dyson equations are a set of integral equations in quantum field theory that relate correlation functions and encode the full dynamics of a quantum field.
  • E. Weyl’s gauge theory
    Weyl’s gauge theory is an early 20th-century theoretical framework that introduced the concept of local gauge invariance, laying foundational ideas for modern gauge theories in particle physics.
  • 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: flat-space Yang–Mills equations
Triple: [Einstein–Yang–Mills equations, generalizes, flat-space Yang–Mills equations]
Generated description
The flat-space Yang–Mills equations are the fundamental nonlinear field equations describing gauge fields in a fixed Minkowski spacetime, forming the core of non-abelian gauge theory in particle physics.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: flat-space Yang–Mills equations
Target entity description: The flat-space Yang–Mills equations are the fundamental nonlinear field equations describing gauge fields in a fixed Minkowski spacetime, forming the core of non-abelian gauge theory in particle physics.
  • A. Einstein–Yang–Mills equations
    The Einstein–Yang–Mills equations are the coupled field equations that describe how non-abelian gauge fields (such as those in Yang–Mills theory) interact with and curve spacetime within the framework of general relativity.
  • B. Yang–Mills theory chosen
    Yang–Mills theory is a gauge field theory describing the behavior of non-abelian gauge fields, forming the mathematical foundation for modern particle physics, including the strong and electroweak interactions.
  • C. Einstein–Maxwell equations
    The Einstein–Maxwell equations are the coupled set of field equations in general relativity that describe how spacetime curvature and electromagnetic fields interact and influence each other.
  • D. Schwinger–Dyson equations
    The Schwinger–Dyson equations are a set of integral equations in quantum field theory that relate correlation functions and encode the full dynamics of a quantum field.
  • E. Weyl’s gauge theory
    Weyl’s gauge theory is an early 20th-century theoretical framework that introduced the concept of local gauge invariance, laying foundational ideas for modern gauge theories in particle physics.
  • F. None of above.

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_69d85cd46b2c819090d054c27787f677 completed April 10, 2026, 2:13 a.m.
NER Named-entity recognition batch_69ded7e2416081908dfba48d7f7b4a84 completed April 15, 2026, 12:12 a.m.
NED1 Entity disambiguation (via context triple) batch_69fe9ddb46888190b1d2fe2992fc120b completed May 9, 2026, 2:37 a.m.
NEDg Description generation batch_69fe9efce5dc8190909b891c476d5291 completed May 9, 2026, 2:42 a.m.
NED2 Entity disambiguation (via description) batch_69fea2bd5d2c8190b26d2393cd8abb3e completed May 9, 2026, 2:58 a.m.
Created at: April 10, 2026, 2:59 a.m.