Triple

T3096209
Position Surface form Disambiguated ID Type / Status
Subject Lorentzian geometry E64599 entity
Predicate hasKeyConcept P533 FINISHED
Object 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.
E327454 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: Raychaudhuri equation | Statement: [Lorentzian geometry, hasKeyConcept, Raychaudhuri equation]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Raychaudhuri equation
Context triple: [Lorentzian geometry, hasKeyConcept, Raychaudhuri equation]
  • A. Tolman–Oppenheimer–Volkoff equation
    The Tolman–Oppenheimer–Volkoff equation is the general relativistic equation of hydrostatic equilibrium that describes the internal structure and pressure balance of spherically symmetric, non-rotating stars such as neutron stars.
  • B. Kerr metric
    The Kerr metric is the exact general relativity solution describing the spacetime geometry around a rotating, uncharged black hole.
  • C. Einstein field equations
    The Einstein field equations are the core mathematical framework of general relativity, relating the curvature of spacetime to the distribution of matter and energy.
  • D. 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.
  • E. Reissner–Nordström metric
    The Reissner–Nordström metric is an exact solution in general relativity describing the spacetime geometry outside a static, spherically symmetric, electrically charged black hole.
  • 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: Raychaudhuri equation
Triple: [Lorentzian geometry, hasKeyConcept, Raychaudhuri equation]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Raychaudhuri equation
Target entity description: 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.
  • A. Tolman–Oppenheimer–Volkoff equation
    The Tolman–Oppenheimer–Volkoff equation is the general relativistic equation of hydrostatic equilibrium that describes the internal structure and pressure balance of spherically symmetric, non-rotating stars such as neutron stars.
  • B. Kerr metric
    The Kerr metric is the exact general relativity solution describing the spacetime geometry around a rotating, uncharged black hole.
  • C. Einstein field equations
    The Einstein field equations are the core mathematical framework of general relativity, relating the curvature of spacetime to the distribution of matter and energy.
  • D. 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.
  • E. Reissner–Nordström metric
    The Reissner–Nordström metric is an exact solution in general relativity describing the spacetime geometry outside a static, spherically symmetric, electrically charged black hole.
  • 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_69ad857dc98481909e585dc3372e3ed5 completed March 8, 2026, 2:19 p.m.
NER Named-entity recognition batch_69ada23b04188190919a69987d2c180f completed March 8, 2026, 4:22 p.m.
NED1 Entity disambiguation (via context triple) batch_69b2037483fc8190b8343faa58fb9893 completed March 12, 2026, 12:06 a.m.
NEDg Description generation batch_69b204a8c5348190a2cb102b08fd6fa5 completed March 12, 2026, 12:11 a.m.
NED2 Entity disambiguation (via description) batch_69b205bdf5c881908bc6ef7c3c30df65 completed March 12, 2026, 12:15 a.m.
Created at: March 8, 2026, 3:03 p.m.