Triple
T6376225
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Lars Ahlfors |
E143471
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Complex Analysis
Complex Analysis is a classic, widely used textbook that provides a rigorous introduction to the theory of functions of a complex variable.
|
E588685
|
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: Complex Analysis | Statement: [Lars Ahlfors, notableWork, Complex Analysis]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Complex Analysis Context triple: [Lars Ahlfors, notableWork, Complex Analysis]
-
A.
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.
-
B.
Runge approximation theorem
The Runge approximation theorem is a fundamental result in complex analysis stating that holomorphic functions on certain domains can be uniformly approximated by rational functions with poles outside those domains.
-
C.
Théorie des fonctions analytiques
Théorie des fonctions analytiques is a foundational mathematical treatise by Joseph-Louis Lagrange that systematically develops calculus using power series and analytic functions instead of geometric or infinitesimal arguments.
-
D.
Cauchy–Riemann equations
The Cauchy–Riemann equations are fundamental conditions in complex analysis that characterize when a complex-valued function is holomorphic (complex differentiable).
-
E.
Functional Analysis: Introduction to Further Topics in Analysis
"Functional Analysis: Introduction to Further Topics in Analysis" is an advanced graduate-level textbook by Elias Stein that develops modern functional analysis with applications to areas such as operator theory, harmonic analysis, and partial differential equations.
- 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: Complex Analysis Triple: [Lars Ahlfors, notableWork, Complex Analysis]
Generated description
Complex Analysis is a classic, widely used textbook that provides a rigorous introduction to the theory of functions of a complex variable.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Complex Analysis Target entity description: Complex Analysis is a classic, widely used textbook that provides a rigorous introduction to the theory of functions of a complex variable.
-
A.
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.
-
B.
Runge approximation theorem
The Runge approximation theorem is a fundamental result in complex analysis stating that holomorphic functions on certain domains can be uniformly approximated by rational functions with poles outside those domains.
-
C.
Théorie des fonctions analytiques
Théorie des fonctions analytiques is a foundational mathematical treatise by Joseph-Louis Lagrange that systematically develops calculus using power series and analytic functions instead of geometric or infinitesimal arguments.
-
D.
Cauchy–Riemann equations
The Cauchy–Riemann equations are fundamental conditions in complex analysis that characterize when a complex-valued function is holomorphic (complex differentiable).
-
E.
Functional Analysis: Introduction to Further Topics in Analysis
"Functional Analysis: Introduction to Further Topics in Analysis" is an advanced graduate-level textbook by Elias Stein that develops modern functional analysis with applications to areas such as operator theory, harmonic analysis, and partial differential equations.
- 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.