Triple

T15030950
Position Surface form Disambiguated ID Type / Status
Subject Einstein–Yang–Mills equations E378340 entity
Predicate generalizes P2372 FINISHED
Object vacuum Einstein equations E1603 NE FINISHED

How this triple was built (2 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: vacuum Einstein equations | Statement: [Einstein–Yang–Mills equations, generalizes, vacuum Einstein equations]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: vacuum Einstein equations
Context triple: [Einstein–Yang–Mills equations, generalizes, vacuum Einstein equations]
  • A. Einstein field equations chosen
    The Einstein field equations are the core mathematical framework of general relativity, relating the curvature of spacetime to the distribution of matter and energy.
  • B. 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.
  • C. 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.
  • D. Raychaudhuri equation
    The Raychaudhuri equation is a fundamental relation in general relativity that describes how the expansion of a congruence of nearby geodesics evolves, playing a key role in the formulation of gravitational focusing and singularity theorems.
  • E. Schwarzschild–Milne equations
    The Schwarzschild–Milne equations are fundamental integro-differential equations in radiative transfer theory that describe the propagation and scattering of radiation through a plane-parallel, absorbing and emitting medium.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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.
Created at: April 10, 2026, 2:59 a.m.