Triple

T130826
Position Surface form Disambiguated ID Type / Status
Subject Hermann Minkowski E2649 entity
Predicate knownFor P22 FINISHED
Object Minkowski sum
The Minkowski sum is a fundamental operation in geometry and convex analysis that combines two sets by adding every vector in one set to every vector in the other, widely used in areas such as optimization, robotics, and computational geometry.
E14947 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: Minkowski sum | Statement: [Hermann Minkowski, knownFor, Minkowski sum]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Minkowski sum
Context triple: [Hermann Minkowski, knownFor, Minkowski sum]
  • A. Minkowski space-time
    Minkowski space-time is a four-dimensional geometric framework that unifies three-dimensional space and time into a single continuum used to describe events and motion in special relativity.
  • B. Mathematical Bridge
    The Mathematical Bridge is a famous wooden footbridge at Queens' College, Cambridge, known for its elegant arch that is constructed entirely from straight timbers.
  • C. Namba
    Namba is a major commercial and entertainment district in Osaka, Japan, known for its bustling nightlife, shopping, and iconic neon-lit streets.
  • D. Nash embedding theorem
    The Nash embedding theorem is a fundamental result in differential geometry that shows any Riemannian manifold can be isometrically embedded into some Euclidean space, thereby realizing abstract curved spaces as concrete subsets of standard Euclidean space.
  • E. Huygens–Fresnel principle
    The Huygens–Fresnel principle is a fundamental concept in wave optics that explains how every point on a wavefront acts as a source of secondary wavelets whose interference determines the wave’s subsequent propagation and diffraction.
  • 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: Minkowski sum
Triple: [Hermann Minkowski, knownFor, Minkowski sum]
Generated description
The Minkowski sum is a fundamental operation in geometry and convex analysis that combines two sets by adding every vector in one set to every vector in the other, widely used in areas such as optimization, robotics, and computational geometry.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Minkowski sum
Target entity description: The Minkowski sum is a fundamental operation in geometry and convex analysis that combines two sets by adding every vector in one set to every vector in the other, widely used in areas such as optimization, robotics, and computational geometry.
  • A. Minkowski space-time
    Minkowski space-time is a four-dimensional geometric framework that unifies three-dimensional space and time into a single continuum used to describe events and motion in special relativity.
  • B. Mathematical Bridge
    The Mathematical Bridge is a famous wooden footbridge at Queens' College, Cambridge, known for its elegant arch that is constructed entirely from straight timbers.
  • C. Namba
    Namba is a major commercial and entertainment district in Osaka, Japan, known for its bustling nightlife, shopping, and iconic neon-lit streets.
  • D. Nash embedding theorem
    The Nash embedding theorem is a fundamental result in differential geometry that shows any Riemannian manifold can be isometrically embedded into some Euclidean space, thereby realizing abstract curved spaces as concrete subsets of standard Euclidean space.
  • E. Huygens–Fresnel principle
    The Huygens–Fresnel principle is a fundamental concept in wave optics that explains how every point on a wavefront acts as a source of secondary wavelets whose interference determines the wave’s subsequent propagation and diffraction.
  • 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_69a2520c0f3481908b0ed054a2fca8d0 completed Feb. 28, 2026, 2:25 a.m.
NER Named-entity recognition batch_69a25785ad5c819097c00f31719fea7e completed Feb. 28, 2026, 2:48 a.m.
NED1 Entity disambiguation (via context triple) batch_69a2a3d73bf08190b0c3dd227206cab0 completed Feb. 28, 2026, 8:14 a.m.
NEDg Description generation batch_69a2a50e4bec8190ab7e27d852460f67 completed Feb. 28, 2026, 8:19 a.m.
NED2 Entity disambiguation (via description) batch_69a2a624eaf48190a7c31047832cbf34 completed Feb. 28, 2026, 8:24 a.m.
Created at: Feb. 28, 2026, 2:30 a.m.