Triple

T5658065
Position Surface form Disambiguated ID Type / Status
Subject Euclid E124667 entity
Predicate notableWork P4 FINISHED
Object On Divisions of Figures
On Divisions of Figures is an ancient mathematical treatise attributed to Euclid that systematically studies how geometric figures can be divided into parts with specified ratios or properties.
E537784 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: On Divisions of Figures | Statement: [Euclid, notableWork, On Divisions of Figures]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: On Divisions of Figures
Context triple: [Euclid, notableWork, On Divisions of Figures]
  • A. Euler’s polyhedron formula
    Euler’s polyhedron formula is a fundamental result in topology and geometry that relates the numbers of vertices, edges, and faces of a convex polyhedron through the equation V − E + F = 2.
  • B. “Solutio problematis ad geometriam situs pertinentis”
    “Solutio problematis ad geometriam situs pertinentis” is Leonhard Euler’s 1736 Latin paper that founded graph theory and topology by solving the Seven Bridges of Königsberg problem.
  • C. 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.
  • D. Checkerboard Division
    The Checkerboard Division is the nickname of the U.S. Army’s 99th Infantry Division, a World War II unit noted for its distinctive shoulder patch and its role in the Battle of the Bulge.
  • E. The Beauty of Geometry
    The Beauty of Geometry is a classic mathematical book by H. S. M. Coxeter that explores elegant geometric ideas and configurations through clear exposition and rich illustrations.
  • 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: On Divisions of Figures
Triple: [Euclid, notableWork, On Divisions of Figures]
Generated description
On Divisions of Figures is an ancient mathematical treatise attributed to Euclid that systematically studies how geometric figures can be divided into parts with specified ratios or properties.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: On Divisions of Figures
Target entity description: On Divisions of Figures is an ancient mathematical treatise attributed to Euclid that systematically studies how geometric figures can be divided into parts with specified ratios or properties.
  • A. Euler’s polyhedron formula
    Euler’s polyhedron formula is a fundamental result in topology and geometry that relates the numbers of vertices, edges, and faces of a convex polyhedron through the equation V − E + F = 2.
  • B. “Solutio problematis ad geometriam situs pertinentis”
    “Solutio problematis ad geometriam situs pertinentis” is Leonhard Euler’s 1736 Latin paper that founded graph theory and topology by solving the Seven Bridges of Königsberg problem.
  • C. 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.
  • D. Checkerboard Division
    The Checkerboard Division is the nickname of the U.S. Army’s 99th Infantry Division, a World War II unit noted for its distinctive shoulder patch and its role in the Battle of the Bulge.
  • E. The Beauty of Geometry
    The Beauty of Geometry is a classic mathematical book by H. S. M. Coxeter that explores elegant geometric ideas and configurations through clear exposition and rich illustrations.
  • 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_69c0082774a481909d7e63fb2aad56ac completed March 22, 2026, 3:17 p.m.
NER Named-entity recognition batch_69c022fd9b148190bd4aa9c43500949f completed March 22, 2026, 5:12 p.m.
NED1 Entity disambiguation (via context triple) batch_69c04da37ffc819095f33e7e66e7c1d0 completed March 22, 2026, 8:14 p.m.
NEDg Description generation batch_69c04edf30448190a60eda49b8b031a0 completed March 22, 2026, 8:19 p.m.
NED2 Entity disambiguation (via description) batch_69c04fb62690819083327781cb857ccc completed March 22, 2026, 8:23 p.m.
Created at: March 22, 2026, 3:42 p.m.