Triple

T1148806
Position Surface form Disambiguated ID Type / Status
Subject Omar Khayyam E23627 entity
Predicate notableWork P4 FINISHED
Object 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.
E131567 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: Commentary on the Difficulties of Certain Postulates of Euclid | Statement: [Omar Khayyam, notableWork, Commentary on the Difficulties of Certain Postulates of Euclid]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Commentary on the Difficulties of Certain Postulates of Euclid
Context triple: [Omar Khayyam, notableWork, Commentary on the Difficulties of Certain Postulates of Euclid]
  • A. Euclides adauctus et methodicus
    Euclides adauctus et methodicus is a 17th-century mathematical treatise by Guarino Guarini that expands and systematizes Euclidean geometry for advanced study and architectural application.
  • B. Über die Hypothesen, welche der Geometrie zu Grunde liegen
    "Über die Hypothesen, welche der Geometrie zu Grunde liegen" is Bernhard Riemann’s seminal 1854 lecture that founded Riemannian geometry and revolutionized the understanding of space in mathematics and physics.
  • C. Ethica, ordine geometrico demonstrata
    Ethica, ordine geometrico demonstrata is Baruch Spinoza’s major philosophical work, a systematic treatise that presents his metaphysics, ethics, and theory of mind in a rigorous, geometrical style.
  • D. Principia Mathematica
    Principia Mathematica is a landmark three-volume work in mathematical logic and the foundations of mathematics, co-authored by Bertrand Russell and Alfred North Whitehead, which aimed to derive all mathematical truths from a formal system of symbolic logic.
  • E. Grundgesetze der Arithmetik, Volume II
    Grundgesetze der Arithmetik, Volume II is the second volume of Gottlob Frege’s foundational work in logic and the philosophy of mathematics, in which he further develops and applies his formal system for arithmetic.
  • 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: Commentary on the Difficulties of Certain Postulates of Euclid
Triple: [Omar Khayyam, notableWork, Commentary on the Difficulties of Certain Postulates of Euclid]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Commentary on the Difficulties of Certain Postulates of Euclid
Target entity description: 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.
  • A. Euclides adauctus et methodicus
    Euclides adauctus et methodicus is a 17th-century mathematical treatise by Guarino Guarini that expands and systematizes Euclidean geometry for advanced study and architectural application.
  • B. Über die Hypothesen, welche der Geometrie zu Grunde liegen
    "Über die Hypothesen, welche der Geometrie zu Grunde liegen" is Bernhard Riemann’s seminal 1854 lecture that founded Riemannian geometry and revolutionized the understanding of space in mathematics and physics.
  • C. Ethica, ordine geometrico demonstrata
    Ethica, ordine geometrico demonstrata is Baruch Spinoza’s major philosophical work, a systematic treatise that presents his metaphysics, ethics, and theory of mind in a rigorous, geometrical style.
  • D. Principia Mathematica
    Principia Mathematica is a landmark three-volume work in mathematical logic and the foundations of mathematics, co-authored by Bertrand Russell and Alfred North Whitehead, which aimed to derive all mathematical truths from a formal system of symbolic logic.
  • E. Grundgesetze der Arithmetik, Volume II
    Grundgesetze der Arithmetik, Volume II is the second volume of Gottlob Frege’s foundational work in logic and the philosophy of mathematics, in which he further develops and applies his formal system for arithmetic.
  • 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_69a493f0d32c8190ac74bad3c87f2641 completed March 1, 2026, 7:30 p.m.
NER Named-entity recognition batch_69a4bc7190308190ab104480ed208b22 completed March 1, 2026, 10:23 p.m.
NED1 Entity disambiguation (via context triple) batch_69ac5eb3ec3881908c8cb39b422fcc71 completed March 7, 2026, 5:21 p.m.
NEDg Description generation batch_69ac5f248db081908596810839ee6160 completed March 7, 2026, 5:23 p.m.
NED2 Entity disambiguation (via description) batch_69ac5fb242488190bf99f63956aeda13 completed March 7, 2026, 5:26 p.m.
Created at: March 1, 2026, 7:44 p.m.