Triple

T4585421
Position Surface form Disambiguated ID Type / Status
Subject William Rowan Hamilton E101954 entity
Predicate notableWork P4 FINISHED
Object Elements of Quaternions
Elements of Quaternions is a foundational 19th-century mathematical treatise by William Rowan Hamilton that systematically develops the theory and applications of quaternions.
E455350 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: Elements of Quaternions | Statement: [William Rowan Hamilton, notableWork, Elements of Quaternions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Elements of Quaternions
Context triple: [William Rowan Hamilton, notableWork, Elements of Quaternions]
  • A. Lectures on Quaternions
    Lectures on Quaternions is a foundational 19th-century mathematical treatise in which William Rowan Hamilton systematically develops and expounds his theory of quaternions.
  • B. The Classical Groups: Their Invariants and Representations
    The Classical Groups: Their Invariants and Representations is a foundational mathematical monograph by Hermann Weyl that systematically develops the theory of classical Lie groups, their invariants, and their representation theory.
  • C. Neue Geometrie des Raumes
    Neue Geometrie des Raumes is a foundational 19th-century mathematical work by Julius Plücker that develops projective and line geometry in three-dimensional space.
  • D. 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.
  • E. 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.
  • 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: Elements of Quaternions
Triple: [William Rowan Hamilton, notableWork, Elements of Quaternions]
Generated description
Elements of Quaternions is a foundational 19th-century mathematical treatise by William Rowan Hamilton that systematically develops the theory and applications of quaternions.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Elements of Quaternions
Target entity description: Elements of Quaternions is a foundational 19th-century mathematical treatise by William Rowan Hamilton that systematically develops the theory and applications of quaternions.
  • A. Lectures on Quaternions chosen
    Lectures on Quaternions is a foundational 19th-century mathematical treatise in which William Rowan Hamilton systematically develops and expounds his theory of quaternions.
  • B. The Classical Groups: Their Invariants and Representations
    The Classical Groups: Their Invariants and Representations is a foundational mathematical monograph by Hermann Weyl that systematically develops the theory of classical Lie groups, their invariants, and their representation theory.
  • C. Neue Geometrie des Raumes
    Neue Geometrie des Raumes is a foundational 19th-century mathematical work by Julius Plücker that develops projective and line geometry in three-dimensional space.
  • D. 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.
  • E. 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.
  • F. None of above.

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_69bd43d4ce208190b53158c882b222e3 completed March 20, 2026, 12:55 p.m.
NER Named-entity recognition batch_69bd59056bb48190ba1e0b5beda9bdc4 completed March 20, 2026, 2:26 p.m.
NED1 Entity disambiguation (via context triple) batch_69bdfa33103081909e83155f712b821f completed March 21, 2026, 1:53 a.m.
NEDg Description generation batch_69bdfc87fd3881909f072cd85d6b58c2 completed March 21, 2026, 2:03 a.m.
NED2 Entity disambiguation (via description) batch_69bdfcfb3de08190b9345e36c5c0c01c completed March 21, 2026, 2:05 a.m.
Created at: March 20, 2026, 1:10 p.m.