Triple

T1382796
Position Surface form Disambiguated ID Type / Status
Subject Noether's theorem E29375 entity
Predicate publishedIn P309 FINISHED
Object "Invariante Variationsprobleme"
"Invariante Variationsprobleme" is Emmy Noether’s landmark 1918 paper that founded the deep connection between symmetries and conservation laws in physics and the calculus of variations.
E157399 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: "Invariante Variationsprobleme" | Statement: [Noether's theorem, publishedIn, "Invariante Variationsprobleme"]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: "Invariante Variationsprobleme"
Context triple: [Noether's theorem, publishedIn, "Invariante Variationsprobleme"]
  • A. Theorie der Transformationsgruppen
    Theorie der Transformationsgruppen is Sophus Lie’s foundational multi-volume work that established the theory of continuous transformation groups, now known as Lie groups, and their applications to differential equations and geometry.
  • B. Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe
    Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe is Bernhard Riemann’s seminal 1854 paper that laid foundational ideas for Fourier series and modern real analysis, including the concept now known as the Riemann integral.
  • C. Hilbert problems
    The Hilbert problems are a famous list of 23 unsolved mathematical problems presented by David Hilbert in 1900 that profoundly influenced the development of 20th-century mathematics.
  • 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. Entscheidungsproblem
    The Entscheidungsproblem is a foundational decision problem in mathematical logic that asks whether there exists a general algorithm to determine the truth or falsity of any given first-order logical statement.
  • 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: "Invariante Variationsprobleme"
Triple: [Noether's theorem, publishedIn, "Invariante Variationsprobleme"]
Generated description
"Invariante Variationsprobleme" is Emmy Noether’s landmark 1918 paper that founded the deep connection between symmetries and conservation laws in physics and the calculus of variations.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: "Invariante Variationsprobleme"
Target entity description: "Invariante Variationsprobleme" is Emmy Noether’s landmark 1918 paper that founded the deep connection between symmetries and conservation laws in physics and the calculus of variations.
  • A. Theorie der Transformationsgruppen
    Theorie der Transformationsgruppen is Sophus Lie’s foundational multi-volume work that established the theory of continuous transformation groups, now known as Lie groups, and their applications to differential equations and geometry.
  • B. Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe
    Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe is Bernhard Riemann’s seminal 1854 paper that laid foundational ideas for Fourier series and modern real analysis, including the concept now known as the Riemann integral.
  • C. Hilbert problems
    The Hilbert problems are a famous list of 23 unsolved mathematical problems presented by David Hilbert in 1900 that profoundly influenced the development of 20th-century mathematics.
  • 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. Entscheidungsproblem
    The Entscheidungsproblem is a foundational decision problem in mathematical logic that asks whether there exists a general algorithm to determine the truth or falsity of any given first-order logical statement.
  • 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_69a498d883a48190bfdca525296ef7ee completed March 1, 2026, 7:51 p.m.
NER Named-entity recognition batch_69a4c3361bf08190b3f6bbf82e17685b completed March 1, 2026, 10:52 p.m.
NED1 Entity disambiguation (via context triple) batch_69acd48c41f4819092f7e1302d803662 completed March 8, 2026, 1:44 a.m.
NEDg Description generation batch_69acd543a0ac8190b9fd5e921b5ad9ea completed March 8, 2026, 1:47 a.m.
NED2 Entity disambiguation (via description) batch_69acd5b8fa2481908fd52d94e55b6377 completed March 8, 2026, 1:49 a.m.
Created at: March 1, 2026, 7:59 p.m.