Triple

T3410522
Position Surface form Disambiguated ID Type / Status
Subject Srinivasa Ramanujan E71880 entity
Predicate notableWork P4 FINISHED
Object highly composite numbers
Highly composite numbers are positive integers that have more divisors than any smaller positive integer, extensively studied and characterized by Srinivasa Ramanujan.
E355438 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: highly composite numbers | Statement: [Srinivasa Ramanujan, notableWork, highly composite numbers]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: highly composite numbers
Context triple: [Srinivasa Ramanujan, notableWork, highly composite numbers]
  • A. Hardy–Ramanujan asymptotic formula
    The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
  • B. Chebyshev functions
    Chebyshev functions are arithmetic functions in number theory that encode information about the distribution of prime numbers and play a key role in analytic approaches to the prime number theorem.
  • C. Hardy–Littlewood circle method
    The Hardy–Littlewood circle method is a powerful analytic number theory technique that uses complex analysis and Fourier series to study additive problems such as Waring’s problem and the Goldbach conjecture.
  • D. Hardy–Littlewood conjectures
    The Hardy–Littlewood conjectures are a collection of influential unproven hypotheses in analytic number theory that generalize the prime number theorem to describe the distribution of prime numbers and prime constellations.
  • E. Jordan’s totient functions
    Jordan’s totient functions are a family of arithmetic functions in number theory that generalize Euler’s totient function to count k-tuples of integers modulo n with certain coprimality conditions.
  • 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: highly composite numbers
Triple: [Srinivasa Ramanujan, notableWork, highly composite numbers]
Generated description
Highly composite numbers are positive integers that have more divisors than any smaller positive integer, extensively studied and characterized by Srinivasa Ramanujan.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: highly composite numbers
Target entity description: Highly composite numbers are positive integers that have more divisors than any smaller positive integer, extensively studied and characterized by Srinivasa Ramanujan.
  • A. Hardy–Ramanujan asymptotic formula
    The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
  • B. Chebyshev functions
    Chebyshev functions are arithmetic functions in number theory that encode information about the distribution of prime numbers and play a key role in analytic approaches to the prime number theorem.
  • C. Hardy–Littlewood circle method
    The Hardy–Littlewood circle method is a powerful analytic number theory technique that uses complex analysis and Fourier series to study additive problems such as Waring’s problem and the Goldbach conjecture.
  • D. Hardy–Littlewood conjectures
    The Hardy–Littlewood conjectures are a collection of influential unproven hypotheses in analytic number theory that generalize the prime number theorem to describe the distribution of prime numbers and prime constellations.
  • E. Jordan’s totient functions
    Jordan’s totient functions are a family of arithmetic functions in number theory that generalize Euler’s totient function to count k-tuples of integers modulo n with certain coprimality conditions.
  • 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_69ad85ac312481909e7027ced1456a9f completed March 8, 2026, 2:20 p.m.
NER Named-entity recognition batch_69adb9094b2881909262e58a470ed9d0 completed March 8, 2026, 5:59 p.m.
NED1 Entity disambiguation (via context triple) batch_69b34bdd99248190823875cae2531609 completed March 12, 2026, 11:27 p.m.
NEDg Description generation batch_69b34e4972008190af3b84f26b4a3629 completed March 12, 2026, 11:37 p.m.
NED2 Entity disambiguation (via description) batch_69b34fc6c3f88190ba1a08243232df05 completed March 12, 2026, 11:44 p.m.
Created at: March 8, 2026, 3:15 p.m.