Triple
T6376227
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Lars Ahlfors |
E143471
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
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.
|
E588687
|
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: Lectures on Quasiconformal Mappings | Statement: [Lars Ahlfors, notableWork, Lectures on Quasiconformal Mappings]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Lectures on Quasiconformal Mappings Context triple: [Lars Ahlfors, notableWork, Lectures on Quasiconformal Mappings]
-
A.
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.
-
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.
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.
-
D.
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.
-
E.
Singular Integrals and Differentiability Properties of Functions
"Singular Integrals and Differentiability Properties of Functions" is a landmark mathematical monograph by Elias M. Stein that developed the modern theory of singular integral operators and their role in harmonic analysis and differentiability.
- 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: Lectures on Quasiconformal Mappings Triple: [Lars Ahlfors, notableWork, Lectures on Quasiconformal Mappings]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Lectures on Quasiconformal Mappings Target entity description: 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.
-
A.
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.
-
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.
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.
-
D.
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.
-
E.
Singular Integrals and Differentiability Properties of Functions
"Singular Integrals and Differentiability Properties of Functions" is a landmark mathematical monograph by Elias M. Stein that developed the modern theory of singular integral operators and their role in harmonic analysis and differentiability.
- 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.