Triple

T11812504
Position Surface form Disambiguated ID Type / Status
Subject Elwin Bruno Christoffel E280907 entity
Predicate notableWork P4 FINISHED
Object Schwarz–Christoffel mapping
The Schwarz–Christoffel mapping is a conformal transformation that maps the upper half-plane (or unit disk) onto polygonal regions, playing a central role in complex analysis and applications such as fluid dynamics and electrostatics.
E947534 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: Schwarz–Christoffel mapping | Statement: [Elwin Bruno Christoffel, notableWork, Schwarz–Christoffel mapping]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Schwarz–Christoffel mapping
Context triple: [Elwin Bruno Christoffel, notableWork, Schwarz–Christoffel mapping]
  • A. Conformal Invariants
    Conformal Invariants is a foundational mathematical work by Lars Ahlfors that systematically develops the theory of quantities preserved under conformal mappings in complex analysis and geometric function theory.
  • B. Riemann mapping theorem
    The Riemann mapping theorem is a fundamental result in complex analysis stating that any non-empty simply connected open subset of the complex plane (other than the whole plane) can be conformally mapped onto the open unit disk.
  • C. Lectures on Quasiconformal Mappings
    Lectures on Quasiconformal Mappings is a classic mathematical monograph by Lars Ahlfors that systematically develops the theory of quasiconformal mappings in the complex plane and higher dimensions.
  • D. Möbius transformations
    Möbius transformations are conformal automorphisms of the extended complex plane represented by fractional linear functions that map circles and lines to circles and lines.
  • E. Bochner–Martinelli formula
    The Bochner–Martinelli formula is a fundamental integral representation in several complex variables that generalizes the Cauchy integral formula to higher dimensions.
  • 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: Schwarz–Christoffel mapping
Triple: [Elwin Bruno Christoffel, notableWork, Schwarz–Christoffel mapping]
Generated description
The Schwarz–Christoffel mapping is a conformal transformation that maps the upper half-plane (or unit disk) onto polygonal regions, playing a central role in complex analysis and applications such as fluid dynamics and electrostatics.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Schwarz–Christoffel mapping
Target entity description: The Schwarz–Christoffel mapping is a conformal transformation that maps the upper half-plane (or unit disk) onto polygonal regions, playing a central role in complex analysis and applications such as fluid dynamics and electrostatics.
  • A. Conformal Invariants
    Conformal Invariants is a foundational mathematical work by Lars Ahlfors that systematically develops the theory of quantities preserved under conformal mappings in complex analysis and geometric function theory.
  • B. Riemann mapping theorem
    The Riemann mapping theorem is a fundamental result in complex analysis stating that any non-empty simply connected open subset of the complex plane (other than the whole plane) can be conformally mapped onto the open unit disk.
  • C. Lectures on Quasiconformal Mappings
    Lectures on Quasiconformal Mappings is a classic mathematical monograph by Lars Ahlfors that systematically develops the theory of quasiconformal mappings in the complex plane and higher dimensions.
  • D. Möbius transformations
    Möbius transformations are conformal automorphisms of the extended complex plane represented by fractional linear functions that map circles and lines to circles and lines.
  • E. Bochner–Martinelli formula
    The Bochner–Martinelli formula is a fundamental integral representation in several complex variables that generalizes the Cauchy integral formula to higher dimensions.
  • 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_69d6ab26aae88190b2489efcb2a24234 completed April 8, 2026, 7:23 p.m.
NER Named-entity recognition batch_69d8a5cba708819097467bb7aca7fc65 completed April 10, 2026, 7:24 a.m.
NED1 Entity disambiguation (via context triple) batch_69f131a01aa48190bf5a70759ac886f6 completed April 28, 2026, 10:16 p.m.
NEDg Description generation batch_69f141b31c9081908f19ff870f5f3c33 completed April 28, 2026, 11:24 p.m.
NED2 Entity disambiguation (via description) batch_69f14fdb39d48190828668fc535d7f6a completed April 29, 2026, 12:24 a.m.
Created at: April 8, 2026, 9:42 p.m.