Triple

T10543864
Position Surface form Disambiguated ID Type / Status
Subject Carl Ludwig Siegel E248763 entity
Predicate notableWork P4 FINISHED
Object Siegel upper half-space
The Siegel upper half-space is a higher-dimensional generalization of the complex upper half-plane that serves as a fundamental domain in the theory of Siegel modular forms and symplectic geometry.
E871400 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: Siegel upper half-space | Statement: [Carl Ludwig Siegel, notableWork, Siegel upper half-space]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Siegel upper half-space
Context triple: [Carl Ludwig Siegel, notableWork, Siegel upper half-space]
  • A. Poincaré upper half-plane model
    The Poincaré upper half-plane model is a standard representation of the hyperbolic plane using the complex numbers with positive imaginary part, equipped with a specific metric that makes geodesics appear as semicircles and vertical lines.
  • B. Hurwitz quaternions
    Hurwitz quaternions are a specific lattice of quaternions with integer and half-integer components that form a maximal order in the quaternion algebra and provide a natural algebraic framework for understanding representations of integers as sums of four squares.
  • C. 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.
  • D. Blaschke
    Blaschke is a German surname most notably associated with Wilhelm Blaschke, a prominent mathematician known for his contributions to differential and convex geometry.
  • E. Gaussian rationals ℚ(i)
    Gaussian rationals ℚ(i) are the field of complex numbers whose real and imaginary parts are rational, formed by adjoining the imaginary unit i to the rational numbers.
  • 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: Siegel upper half-space
Triple: [Carl Ludwig Siegel, notableWork, Siegel upper half-space]
Generated description
The Siegel upper half-space is a higher-dimensional generalization of the complex upper half-plane that serves as a fundamental domain in the theory of Siegel modular forms and symplectic geometry.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Siegel upper half-space
Target entity description: The Siegel upper half-space is a higher-dimensional generalization of the complex upper half-plane that serves as a fundamental domain in the theory of Siegel modular forms and symplectic geometry.
  • A. Poincaré upper half-plane model
    The Poincaré upper half-plane model is a standard representation of the hyperbolic plane using the complex numbers with positive imaginary part, equipped with a specific metric that makes geodesics appear as semicircles and vertical lines.
  • B. Hurwitz quaternions
    Hurwitz quaternions are a specific lattice of quaternions with integer and half-integer components that form a maximal order in the quaternion algebra and provide a natural algebraic framework for understanding representations of integers as sums of four squares.
  • C. 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.
  • D. Blaschke
    Blaschke is a German surname most notably associated with Wilhelm Blaschke, a prominent mathematician known for his contributions to differential and convex geometry.
  • E. Gaussian rationals ℚ(i)
    Gaussian rationals ℚ(i) are the field of complex numbers whose real and imaginary parts are rational, formed by adjoining the imaginary unit i to the rational numbers.
  • 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_69d381c733c08190ab1dd6239f5f34ae completed April 6, 2026, 9:49 a.m.
NER Named-entity recognition batch_69d51911b10481909e6e548879e8de36 completed April 7, 2026, 2:47 p.m.
NED1 Entity disambiguation (via context triple) batch_69d9343c5c308190952596e5254b6a65 completed April 10, 2026, 5:32 p.m.
NEDg Description generation batch_69d938c697f481908a93296ee7f82eae completed April 10, 2026, 5:52 p.m.
NED2 Entity disambiguation (via description) batch_69d940176c988190b7583ce9f2c21898 completed April 10, 2026, 6:23 p.m.
Created at: April 6, 2026, 12:32 p.m.