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.