Triple

T1382029
Position Surface form Disambiguated ID Type / Status
Subject Theorema Egregium E29359 entity
Predicate publishedIn P309 FINISHED
Object Disquisitiones Generales Circa Superficies Curvas
Disquisitiones Generales Circa Superficies Curvas is Carl Friedrich Gauss’s foundational 1827 work on differential geometry, in which he developed the intrinsic theory of curved surfaces and introduced concepts such as Gaussian curvature.
E157377 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: Disquisitiones Generales Circa Superficies Curvas | Statement: [Theorema Egregium, publishedIn, Disquisitiones Generales Circa Superficies Curvas]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Disquisitiones Generales Circa Superficies Curvas
Context triple: [Theorema Egregium, publishedIn, Disquisitiones Generales Circa Superficies Curvas]
  • A. Theorema Egregium
    Theorema Egregium is Gauss’s celebrated theorem in differential geometry showing that the Gaussian curvature of a surface is an intrinsic property independent of how the surface is embedded in space.
  • B. Disquisitiones Arithmeticae
    Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
  • C. Elementa curvarum linearum
    Elementa curvarum linearum is a 17th-century mathematical treatise by Johan de Witt that systematically studies the geometry and properties of linear curves.
  • D. Treatise on Demonstration of Problems of Algebra
    Treatise on Demonstration of Problems of Algebra is a seminal mathematical work by Omar Khayyam in which he systematically analyzes and geometrically solves cubic equations.
  • E. Commentary on the Difficulties of Certain Postulates of Euclid
    Commentary on the Difficulties of Certain Postulates of Euclid is a mathematical treatise by Omar Khayyam in which he critically examines and attempts to resolve issues in Euclid’s postulates, especially the parallel postulate, laying early groundwork for later developments in geometry.
  • 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: Disquisitiones Generales Circa Superficies Curvas
Triple: [Theorema Egregium, publishedIn, Disquisitiones Generales Circa Superficies Curvas]
Generated description
Disquisitiones Generales Circa Superficies Curvas is Carl Friedrich Gauss’s foundational 1827 work on differential geometry, in which he developed the intrinsic theory of curved surfaces and introduced concepts such as Gaussian curvature.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Disquisitiones Generales Circa Superficies Curvas
Target entity description: Disquisitiones Generales Circa Superficies Curvas is Carl Friedrich Gauss’s foundational 1827 work on differential geometry, in which he developed the intrinsic theory of curved surfaces and introduced concepts such as Gaussian curvature.
  • A. Theorema Egregium
    Theorema Egregium is Gauss’s celebrated theorem in differential geometry showing that the Gaussian curvature of a surface is an intrinsic property independent of how the surface is embedded in space.
  • B. Disquisitiones Arithmeticae
    Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
  • C. Elementa curvarum linearum
    Elementa curvarum linearum is a 17th-century mathematical treatise by Johan de Witt that systematically studies the geometry and properties of linear curves.
  • D. Treatise on Demonstration of Problems of Algebra
    Treatise on Demonstration of Problems of Algebra is a seminal mathematical work by Omar Khayyam in which he systematically analyzes and geometrically solves cubic equations.
  • E. Commentary on the Difficulties of Certain Postulates of Euclid
    Commentary on the Difficulties of Certain Postulates of Euclid is a mathematical treatise by Omar Khayyam in which he critically examines and attempts to resolve issues in Euclid’s postulates, especially the parallel postulate, laying early groundwork for later developments in geometry.
  • 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_69a498d883a48190bfdca525296ef7ee completed March 1, 2026, 7:51 p.m.
NER Named-entity recognition batch_69a4c3361bf08190b3f6bbf82e17685b completed March 1, 2026, 10:52 p.m.
NED1 Entity disambiguation (via context triple) batch_69acd48c41f4819092f7e1302d803662 completed March 8, 2026, 1:44 a.m.
NEDg Description generation batch_69acd543a0ac8190b9fd5e921b5ad9ea completed March 8, 2026, 1:47 a.m.
NED2 Entity disambiguation (via description) batch_69acd5b8fa2481908fd52d94e55b6377 completed March 8, 2026, 1:49 a.m.
Created at: March 1, 2026, 7:59 p.m.