Triple
T20439490
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Edmund Landau |
E501345
|
entity |
| Predicate | knownFor |
P22
|
FINISHED |
| Object |
Landau notation
Landau notation is a mathematical notation, introduced by Edmund Landau, used to describe the asymptotic growth rates of functions, especially in analysis and computational complexity (e.g., Big O notation).
|
E679192
|
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: Landau notation | Statement: [Edmund Landau, knownFor, Landau notation]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Landau notation Context triple: [Edmund Landau, knownFor, Landau notation]
-
A.
Little-o notation
Little-o notation is a mathematical notation used in analysis and asymptotic theory to describe functions that grow strictly slower than a given reference function as the input approaches a limit.
-
B.
Big-O notation
Big-O notation is a mathematical tool used in computer science to describe how the running time or space requirements of an algorithm grow relative to the size of its input.
-
C.
Stirling's approximation
Stirling's approximation is a classical formula in mathematics that provides an efficient asymptotic estimate for factorials and the gamma function, especially for large arguments.
-
D.
Knuth’s up-arrow notation
Knuth’s up-arrow notation is a mathematical notation introduced by Donald Knuth to concisely represent very large integers using iterated exponentiation and its higher-order generalizations.
-
E.
von Mangoldt function Λ(n)
The von Mangoldt function Λ(n) is an arithmetic function in number theory that encodes the distribution of prime powers by assigning log p to integers n that are powers of a prime p and 0 otherwise.
- 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: Landau notation Triple: [Edmund Landau, knownFor, Landau notation]
Generated description
Landau notation is a mathematical notation, introduced by Edmund Landau, used to describe the asymptotic growth rates of functions, especially in analysis and computational complexity (e.g., Big O notation).
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Landau notation Target entity description: Landau notation is a mathematical notation, introduced by Edmund Landau, used to describe the asymptotic growth rates of functions, especially in analysis and computational complexity (e.g., Big O notation).
-
A.
Little-o notation
Little-o notation is a mathematical notation used in analysis and asymptotic theory to describe functions that grow strictly slower than a given reference function as the input approaches a limit.
-
B.
Big-O notation
chosen
Big-O notation is a mathematical tool used in computer science to describe how the running time or space requirements of an algorithm grow relative to the size of its input.
-
C.
Stirling's approximation
Stirling's approximation is a classical formula in mathematics that provides an efficient asymptotic estimate for factorials and the gamma function, especially for large arguments.
-
D.
Knuth’s up-arrow notation
Knuth’s up-arrow notation is a mathematical notation introduced by Donald Knuth to concisely represent very large integers using iterated exponentiation and its higher-order generalizations.
-
E.
von Mangoldt function Λ(n)
The von Mangoldt function Λ(n) is an arithmetic function in number theory that encodes the distribution of prime powers by assigning log p to integers n that are powers of a prime p and 0 otherwise.
- F. None of above.
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_69e0b4ab3cfc8190ac9bf32e932316b1 |
completed | April 16, 2026, 10:06 a.m. |
| NER | Named-entity recognition | batch_69e685f20fe08190b9370b523a20153d |
completed | April 20, 2026, 8 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a0883fd1af88190a34aef615ec3a23e |
completed | May 16, 2026, 2:49 p.m. |
| NEDg | Description generation | batch_6a0884d316148190b1fe155fc2dfbb7b |
completed | May 16, 2026, 2:53 p.m. |
| NED2 | Entity disambiguation (via description) | batch_6a088565cbcc81909b4bbc286d272ef6 |
completed | May 16, 2026, 2:55 p.m. |
Created at: April 16, 2026, 11:31 a.m.