Triple

T11812505
Position Surface form Disambiguated ID Type / Status
Subject Elwin Bruno Christoffel E280907 entity
Predicate notableWork P4 FINISHED
Object Christoffel–Schwarz formula
The Christoffel–Schwarz formula is a fundamental result in complex analysis that provides an explicit conformal mapping from the upper half-plane onto polygonal regions in the complex plane.
E947535 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: Christoffel–Schwarz formula | Statement: [Elwin Bruno Christoffel, notableWork, Christoffel–Schwarz formula]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Christoffel–Schwarz formula
Context triple: [Elwin Bruno Christoffel, notableWork, Christoffel–Schwarz formula]
  • A. 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.
  • B. Cauchy–Pompeiu formula
    The Cauchy–Pompeiu formula is a fundamental result in complex analysis that extends the Cauchy integral formula to functions that are not necessarily holomorphic by expressing them via both boundary and area integrals.
  • C. Riemann–Hurwitz formula
    The Riemann–Hurwitz formula is a fundamental result in algebraic geometry and complex analysis that relates the genera of two Riemann surfaces connected by a branched covering map, accounting for the ramification data.
  • D. 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.
  • E. Noether’s formula
    Noether’s formula is a fundamental result in algebraic geometry that relates the holomorphic Euler characteristic of a smooth projective surface to its Chern numbers, serving as a special case of the Hirzebruch–Riemann–Roch theorem.
  • 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: Christoffel–Schwarz formula
Triple: [Elwin Bruno Christoffel, notableWork, Christoffel–Schwarz formula]
Generated description
The Christoffel–Schwarz formula is a fundamental result in complex analysis that provides an explicit conformal mapping from the upper half-plane onto polygonal regions in the complex plane.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Christoffel–Schwarz formula
Target entity description: The Christoffel–Schwarz formula is a fundamental result in complex analysis that provides an explicit conformal mapping from the upper half-plane onto polygonal regions in the complex plane.
  • A. 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.
  • B. Cauchy–Pompeiu formula
    The Cauchy–Pompeiu formula is a fundamental result in complex analysis that extends the Cauchy integral formula to functions that are not necessarily holomorphic by expressing them via both boundary and area integrals.
  • C. Riemann–Hurwitz formula
    The Riemann–Hurwitz formula is a fundamental result in algebraic geometry and complex analysis that relates the genera of two Riemann surfaces connected by a branched covering map, accounting for the ramification data.
  • D. 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.
  • E. Noether’s formula
    Noether’s formula is a fundamental result in algebraic geometry that relates the holomorphic Euler characteristic of a smooth projective surface to its Chern numbers, serving as a special case of the Hirzebruch–Riemann–Roch theorem.
  • 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.