Triple

T2408491
Position Surface form Disambiguated ID Type / Status
Subject Alfred Clebsch E50330 entity
Predicate notableWork P4 FINISHED
Object Clebsch–Aronhold invariants
The Clebsch–Aronhold invariants are classical algebraic invariants associated with binary forms, particularly quartic forms, that play a key role in invariant theory and the classification of algebraic curves.
E262451 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: Clebsch–Aronhold invariants | Statement: [Alfred Clebsch, notableWork, Clebsch–Aronhold invariants]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Clebsch–Aronhold invariants
Context triple: [Alfred Clebsch, notableWork, Clebsch–Aronhold invariants]
  • A. Hilbert’s fourteenth problem
    Hilbert’s fourteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the finite generation of certain algebras of invariants in algebraic geometry and invariant theory.
  • B. Hilbert’s Nullstellensatz
    Hilbert’s Nullstellensatz is a foundational theorem in algebraic geometry that establishes a deep correspondence between ideals in polynomial rings and algebraic sets, linking algebra and geometry.
  • C. 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.
  • 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. Noether’s theorem in algebraic geometry (Noether’s AF+BG theorem)
    Noether’s AF+BG theorem is a foundational result in algebraic geometry that provides conditions under which a polynomial vanishing on the intersection of two plane curves can be expressed as a linear combination of their defining 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: Clebsch–Aronhold invariants
Triple: [Alfred Clebsch, notableWork, Clebsch–Aronhold invariants]
Generated description
The Clebsch–Aronhold invariants are classical algebraic invariants associated with binary forms, particularly quartic forms, that play a key role in invariant theory and the classification of algebraic curves.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Clebsch–Aronhold invariants
Target entity description: The Clebsch–Aronhold invariants are classical algebraic invariants associated with binary forms, particularly quartic forms, that play a key role in invariant theory and the classification of algebraic curves.
  • A. Hilbert’s fourteenth problem
    Hilbert’s fourteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the finite generation of certain algebras of invariants in algebraic geometry and invariant theory.
  • B. Hilbert’s Nullstellensatz
    Hilbert’s Nullstellensatz is a foundational theorem in algebraic geometry that establishes a deep correspondence between ideals in polynomial rings and algebraic sets, linking algebra and geometry.
  • C. 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.
  • 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. Noether’s theorem in algebraic geometry (Noether’s AF+BG theorem)
    Noether’s AF+BG theorem is a foundational result in algebraic geometry that provides conditions under which a polynomial vanishing on the intersection of two plane curves can be expressed as a linear combination of their defining equations.
  • 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_69a88b0339a88190a1207333cd271cc9 completed March 4, 2026, 7:41 p.m.
NER Named-entity recognition batch_69abc92408308190ad2d331ebee71d15 completed March 7, 2026, 6:43 a.m.
NED1 Entity disambiguation (via context triple) batch_69aeb3eba9d08190a2c63e590e08b4df completed March 9, 2026, 11:50 a.m.
NEDg Description generation batch_69aeb4a5e9c481908426fe51343a1342 completed March 9, 2026, 11:53 a.m.
NED2 Entity disambiguation (via description) batch_69aeb52bec1881909c589aea2af3684c completed March 9, 2026, 11:55 a.m.
Created at: March 4, 2026, 7:58 p.m.