Triple

T1148805
Position Surface form Disambiguated ID Type / Status
Subject Omar Khayyam E23627 entity
Predicate notableWork P4 FINISHED
Object 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.
E131566 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 Demonstration of Problems of Algebra | Statement: [Omar Khayyam, notableWork, Treatise on Demonstration of Problems of Algebra]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Treatise on Demonstration of Problems of Algebra
Context triple: [Omar Khayyam, notableWork, Treatise on Demonstration of Problems of Algebra]
  • A. 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.
  • B. Über die Bildung des Formensystems der ternären biquadratischen Form
    "Über die Bildung des Formensystems der ternären biquadratischen Form" is the 1907 doctoral dissertation of mathematician Emmy Noether, in which she investigates the invariant theory of certain higher-degree algebraic forms.
  • C. The Mathematical Analysis of Logic
    The Mathematical Analysis of Logic is George Boole’s pioneering 1847 work that laid the foundations of symbolic logic and helped initiate the algebraic treatment of logical reasoning.
  • D. Begriffsschrift
    Begriffsschrift is Gottlob Frege’s groundbreaking 1879 work that introduced a formal logical notation and is widely regarded as the foundation of modern 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: Treatise on Demonstration of Problems of Algebra
Triple: [Omar Khayyam, notableWork, Treatise on Demonstration of Problems of Algebra]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Treatise on Demonstration of Problems of Algebra
Target entity description: 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.
  • A. 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.
  • B. Über die Bildung des Formensystems der ternären biquadratischen Form
    "Über die Bildung des Formensystems der ternären biquadratischen Form" is the 1907 doctoral dissertation of mathematician Emmy Noether, in which she investigates the invariant theory of certain higher-degree algebraic forms.
  • C. The Mathematical Analysis of Logic
    The Mathematical Analysis of Logic is George Boole’s pioneering 1847 work that laid the foundations of symbolic logic and helped initiate the algebraic treatment of logical reasoning.
  • D. Begriffsschrift
    Begriffsschrift is Gottlob Frege’s groundbreaking 1879 work that introduced a formal logical notation and is widely regarded as the foundation of modern 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.