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.