Triple

T5915433
Position Surface form Disambiguated ID Type / Status
Subject Commentary on the Difficulties of Certain Postulates of Euclid E131567 entity
Predicate relatedWork P37 FINISHED
Object Treatise on the Division of Quadrants (Omar Khayyam)
Treatise on the Division of Quadrants is a mathematical work by Omar Khayyam in which he investigates geometric constructions and the division of arcs and quadrants, contributing to the development of geometry beyond Euclid.
E555120 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: Treatise on the Division of Quadrants (Omar Khayyam) | Statement: [Commentary on the Difficulties of Certain Postulates of Euclid, relatedWork, Treatise on the Division of Quadrants (Omar Khayyam)]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Treatise on the Division of Quadrants (Omar Khayyam)
Context triple: [Commentary on the Difficulties of Certain Postulates of Euclid, relatedWork, Treatise on the Division of Quadrants (Omar Khayyam)]
  • A. Al-Farghani's Elements of Astronomy
    Al-Farghani's Elements of Astronomy is a foundational 9th-century Arabic treatise that systematically summarizes and explains Ptolemaic astronomy and became highly influential in both the Islamic world and medieval Europe.
  • B. Al-Khwarizmi's Al-jabr wa-l-muqabala
    Al-Khwarizmi's *Al-jabr wa-l-muqabala* is a foundational 9th-century mathematical treatise that systematically introduced and developed algebra as an independent discipline.
  • C. Ulugh Beg's Zij-i Sultani
    Ulugh Beg's Zij-i Sultani is a 15th-century astronomical star catalogue and set of planetary tables compiled at the Samarkand observatory, renowned for its remarkably accurate measurements and lasting influence on later astronomy.
  • D. Treatise on Astronomy
    Treatise on Astronomy is a 19th-century textbook by American mathematician and astronomer Elias Loomis that systematically presents the fundamental principles and observations of astronomy for students and general readers.
  • E. Al-Zarqali's Toledan Tables
    Al-Zarqali's Toledan Tables are a highly influential set of medieval astronomical tables, compiled in Toledo, that provided precise planetary positions and were widely used across the Islamic world and later in Europe.
  • 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: Treatise on the Division of Quadrants (Omar Khayyam)
Triple: [Commentary on the Difficulties of Certain Postulates of Euclid, relatedWork, Treatise on the Division of Quadrants (Omar Khayyam)]
Generated description
Treatise on the Division of Quadrants is a mathematical work by Omar Khayyam in which he investigates geometric constructions and the division of arcs and quadrants, contributing to the development of geometry beyond Euclid.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Treatise on the Division of Quadrants (Omar Khayyam)
Target entity description: Treatise on the Division of Quadrants is a mathematical work by Omar Khayyam in which he investigates geometric constructions and the division of arcs and quadrants, contributing to the development of geometry beyond Euclid.
  • A. Al-Farghani's Elements of Astronomy
    Al-Farghani's Elements of Astronomy is a foundational 9th-century Arabic treatise that systematically summarizes and explains Ptolemaic astronomy and became highly influential in both the Islamic world and medieval Europe.
  • B. Al-Khwarizmi's Al-jabr wa-l-muqabala
    Al-Khwarizmi's *Al-jabr wa-l-muqabala* is a foundational 9th-century mathematical treatise that systematically introduced and developed algebra as an independent discipline.
  • C. Ulugh Beg's Zij-i Sultani
    Ulugh Beg's Zij-i Sultani is a 15th-century astronomical star catalogue and set of planetary tables compiled at the Samarkand observatory, renowned for its remarkably accurate measurements and lasting influence on later astronomy.
  • D. Treatise on Astronomy
    Treatise on Astronomy is a 19th-century textbook by American mathematician and astronomer Elias Loomis that systematically presents the fundamental principles and observations of astronomy for students and general readers.
  • E. Al-Zarqali's Toledan Tables
    Al-Zarqali's Toledan Tables are a highly influential set of medieval astronomical tables, compiled in Toledo, that provided precise planetary positions and were widely used across the Islamic world and later in Europe.
  • 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_69c008593a44819081a07ae0efe6c574 completed March 22, 2026, 3:18 p.m.
NER Named-entity recognition batch_69c037bb538c8190acc514c2d49359f4 completed March 22, 2026, 6:40 p.m.
NED1 Entity disambiguation (via context triple) batch_69c0c02430bc8190a63b91b6dbdbc9f2 completed March 23, 2026, 4:23 a.m.
NEDg Description generation batch_69c0c0cb4fac8190b1f73d6707200112 completed March 23, 2026, 4:25 a.m.
NED2 Entity disambiguation (via description) batch_69c0c1f6fe60819080a00976740b6a9c completed March 23, 2026, 4:30 a.m.
Created at: March 22, 2026, 3:59 p.m.