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.