Triple

T2667156
Position Surface form Disambiguated ID Type / Status
Subject Elias Loomis E55662 entity
Predicate notableWork P4 FINISHED
Object Elements of Analytical Geometry and of the Differential and Integral Calculus
Elements of Analytical Geometry and of the Differential and Integral Calculus is a 19th-century mathematics textbook that systematically introduces analytic geometry alongside the fundamentals of differential and integral calculus.
E288299 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: Elements of Analytical Geometry and of the Differential and Integral Calculus | Statement: [Elias Loomis, notableWork, Elements of Analytical Geometry and of the Differential and Integral Calculus]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Elements of Analytical Geometry and of the Differential and Integral Calculus
Context triple: [Elias Loomis, notableWork, Elements of Analytical Geometry and of the Differential and Integral Calculus]
  • A. 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.
  • B. 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.
  • C. Vorlesungen über Geometrie
    Vorlesungen über Geometrie is a foundational 19th-century textbook on geometry authored by German mathematician Alfred Clebsch.
  • D. Cours d’Analyse
    Cours d’Analyse is a foundational 19th-century mathematics textbook by Augustin-Louis Cauchy that rigorously developed the theory of functions, limits, and continuity, helping to formalize modern analysis.
  • E. 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.
  • 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: Elements of Analytical Geometry and of the Differential and Integral Calculus
Triple: [Elias Loomis, notableWork, Elements of Analytical Geometry and of the Differential and Integral Calculus]
Generated description
Elements of Analytical Geometry and of the Differential and Integral Calculus is a 19th-century mathematics textbook that systematically introduces analytic geometry alongside the fundamentals of differential and integral calculus.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Elements of Analytical Geometry and of the Differential and Integral Calculus
Target entity description: Elements of Analytical Geometry and of the Differential and Integral Calculus is a 19th-century mathematics textbook that systematically introduces analytic geometry alongside the fundamentals of differential and integral calculus.
  • A. 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.
  • B. 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.
  • C. Vorlesungen über Geometrie
    Vorlesungen über Geometrie is a foundational 19th-century textbook on geometry authored by German mathematician Alfred Clebsch.
  • D. Cours d’Analyse
    Cours d’Analyse is a foundational 19th-century mathematics textbook by Augustin-Louis Cauchy that rigorously developed the theory of functions, limits, and continuity, helping to formalize modern analysis.
  • E. 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.
  • 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_69ab49e54de48190be708cd1cf8be073 completed March 6, 2026, 9:40 p.m.
NER Named-entity recognition batch_69abd97040e48190b0a87489f108810e completed March 7, 2026, 7:53 a.m.
NED1 Entity disambiguation (via context triple) batch_69afa05b008881908049751b73e800d0 completed March 10, 2026, 4:38 a.m.
NEDg Description generation batch_69afa21322248190bd472fc7578840fe completed March 10, 2026, 4:46 a.m.
NED2 Entity disambiguation (via description) batch_69afa286c218819084a525556cb7b3e3 completed March 10, 2026, 4:48 a.m.
Created at: March 6, 2026, 9:54 p.m.