Triple

T2408489
Position Surface form Disambiguated ID Type / Status
Subject Alfred Clebsch E50330 entity
Predicate notableWork P4 FINISHED
Object Clebsch diagonal surfaces
Clebsch diagonal surfaces are classical 19th-century algebraic surfaces in projective three-space, famous as the first explicit smooth cubic surface with all 27 lines defined over the real numbers.
E262450 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 diagonal surfaces | Statement: [Alfred Clebsch, notableWork, Clebsch diagonal surfaces]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Clebsch diagonal surfaces
Context triple: [Alfred Clebsch, notableWork, Clebsch diagonal surfaces]
  • A. Sur les courbes algébriques et les variétés qui s’en déduisent
    Sur les courbes algébriques et les variétés qui s’en déduisent is a foundational 1948 monograph by André Weil that helped establish modern algebraic geometry and introduced key ideas leading to the Weil conjectures.
  • B. 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.
  • C. 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.
  • D. 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.
  • E. Klein quartic
    The Klein quartic is a highly symmetric algebraic curve of genus 3 that plays a central role in complex geometry, group theory, and the study of Riemann surfaces.
  • 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 diagonal surfaces
Triple: [Alfred Clebsch, notableWork, Clebsch diagonal surfaces]
Generated description
Clebsch diagonal surfaces are classical 19th-century algebraic surfaces in projective three-space, famous as the first explicit smooth cubic surface with all 27 lines defined over the real numbers.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Clebsch diagonal surfaces
Target entity description: Clebsch diagonal surfaces are classical 19th-century algebraic surfaces in projective three-space, famous as the first explicit smooth cubic surface with all 27 lines defined over the real numbers.
  • A. Sur les courbes algébriques et les variétés qui s’en déduisent
    Sur les courbes algébriques et les variétés qui s’en déduisent is a foundational 1948 monograph by André Weil that helped establish modern algebraic geometry and introduced key ideas leading to the Weil conjectures.
  • B. 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.
  • C. 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.
  • D. 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.
  • E. Klein quartic
    The Klein quartic is a highly symmetric algebraic curve of genus 3 that plays a central role in complex geometry, group theory, and the study of Riemann surfaces.
  • 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.