Triple

T229002
Position Surface form Disambiguated ID Type / Status
Subject Emmy Noether E4369 entity
Predicate doctoralThesis P6 FINISHED
Object 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.
E29379 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: Über die Bildung des Formensystems der ternären biquadratischen Form | Statement: [Emmy Noether, doctoralThesis, Über die Bildung des Formensystems der ternären biquadratischen Form]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Über die Bildung des Formensystems der ternären biquadratischen Form
Context triple: [Emmy Noether, doctoralThesis, Über die Bildung des Formensystems der ternären biquadratischen Form]
  • A. Frege’s system in "Grundgesetze der Arithmetik"
    Frege’s system in "Grundgesetze der Arithmetik" is a foundational logical framework for arithmetic based on second-order logic and Basic Law V, whose inconsistency—revealed by Russell’s paradox—marked a turning point in the development of modern logic and set theory.
  • B. 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.
  • C. Dyson’s transform in number theory
    Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
  • 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. An Investigation of the Laws of Thought
    An Investigation of the Laws of Thought is George Boole’s foundational 1854 treatise that established Boolean algebra and helped lay the groundwork for modern mathematical logic and computer science.
  • 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: Über die Bildung des Formensystems der ternären biquadratischen Form
Triple: [Emmy Noether, doctoralThesis, Über die Bildung des Formensystems der ternären biquadratischen Form]
Generated description
"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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Über die Bildung des Formensystems der ternären biquadratischen Form
Target entity description: "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.
  • A. Frege’s system in "Grundgesetze der Arithmetik"
    Frege’s system in "Grundgesetze der Arithmetik" is a foundational logical framework for arithmetic based on second-order logic and Basic Law V, whose inconsistency—revealed by Russell’s paradox—marked a turning point in the development of modern logic and set theory.
  • B. 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.
  • C. Dyson’s transform in number theory
    Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
  • 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. An Investigation of the Laws of Thought
    An Investigation of the Laws of Thought is George Boole’s foundational 1854 treatise that established Boolean algebra and helped lay the groundwork for modern mathematical logic and computer science.
  • 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_69a257363ffc81909757bde7ab3404da completed Feb. 28, 2026, 2:47 a.m.
NER Named-entity recognition batch_69a25c9140c48190b90647400854b37e completed Feb. 28, 2026, 3:10 a.m.
NED1 Entity disambiguation (via context triple) batch_69a35b66359481908daf0412badd76bc completed Feb. 28, 2026, 9:17 p.m.
NEDg Description generation batch_69a35d280c8c81909dd05d5c45ffe616 completed Feb. 28, 2026, 9:24 p.m.
NED2 Entity disambiguation (via description) batch_69a35dc9ad808190a93a4a4c062ce69c completed Feb. 28, 2026, 9:27 p.m.
Created at: Feb. 28, 2026, 2:53 a.m.