Triple

T6376226
Position Surface form Disambiguated ID Type / Status
Subject Lars Ahlfors E143471 entity
Predicate notableWork P4 FINISHED
Object 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.
E588686 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: Conformal Invariants | Statement: [Lars Ahlfors, notableWork, Conformal Invariants]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Conformal Invariants
Context triple: [Lars Ahlfors, notableWork, Conformal Invariants]
  • A. Teichmüller theory
    Teichmüller theory is a branch of complex analysis and geometry that studies the deformation spaces of Riemann surfaces and their moduli, often via quasiconformal mappings.
  • B. Lempert function on convex domains
    The Lempert function on convex domains is a complex-analytic invariant that coincides with the Kobayashi distance and provides an extremal characterization of holomorphic mappings between convex domains in several complex variables.
  • C. Dynamics in One Complex Variable
    Dynamics in One Complex Variable is a foundational graduate-level textbook by John Milnor that introduces and develops the theory of complex dynamical systems, particularly the iteration of rational maps on the Riemann sphere.
  • D. Riemann surfaces
    Riemann surfaces are one-dimensional complex manifolds that provide the natural geometric setting for studying complex analytic functions and their multi-valued behavior.
  • E. 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.
  • 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: Conformal Invariants
Triple: [Lars Ahlfors, notableWork, Conformal Invariants]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Conformal Invariants
Target entity description: 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.
  • A. Teichmüller theory
    Teichmüller theory is a branch of complex analysis and geometry that studies the deformation spaces of Riemann surfaces and their moduli, often via quasiconformal mappings.
  • B. Lempert function on convex domains
    The Lempert function on convex domains is a complex-analytic invariant that coincides with the Kobayashi distance and provides an extremal characterization of holomorphic mappings between convex domains in several complex variables.
  • C. Dynamics in One Complex Variable
    Dynamics in One Complex Variable is a foundational graduate-level textbook by John Milnor that introduces and develops the theory of complex dynamical systems, particularly the iteration of rational maps on the Riemann sphere.
  • D. Riemann surfaces
    Riemann surfaces are one-dimensional complex manifolds that provide the natural geometric setting for studying complex analytic functions and their multi-valued behavior.
  • E. 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.
  • 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_69c008d9f4348190ab598a2913259a1c completed March 22, 2026, 3:20 p.m.
NER Named-entity recognition batch_69c0683bfc7081908b15c3c9a3c72e7b completed March 22, 2026, 10:07 p.m.
NED1 Entity disambiguation (via context triple) batch_69c62d9dd9dc8190b2aca25feda3e690 completed March 27, 2026, 7:11 a.m.
NEDg Description generation batch_69c62fb982088190ab4ccbd5ff23740d completed March 27, 2026, 7:20 a.m.
NED2 Entity disambiguation (via description) batch_69c6302e2f008190bd7ccdfbcddb3c07 completed March 27, 2026, 7:22 a.m.
Created at: March 22, 2026, 4:33 p.m.