Triple

T3410521
Position Surface form Disambiguated ID Type / Status
Subject Srinivasa Ramanujan E71880 entity
Predicate notableWork P4 FINISHED
Object mock theta functions
Mock theta functions are a class of q-series introduced by Srinivasa Ramanujan that exhibit mysterious modular-like behavior and play a key role in modern number theory and the theory of modular forms.
E355437 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: mock theta functions | Statement: [Srinivasa Ramanujan, notableWork, mock theta functions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: mock theta functions
Context triple: [Srinivasa Ramanujan, notableWork, mock theta functions]
  • A. Riemann–Siegel theta function
    The Riemann–Siegel theta function is a special function that appears in the study of the Riemann zeta function, used to express its values on the critical line in a form suitable for high-precision numerical computation.
  • B. Jacobi triple product
    The Jacobi triple product is a fundamental identity in number theory and complex analysis that expresses an infinite product as an infinite sum, playing a key role in the theory of theta functions and q-series.
  • C. 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.
  • D. Jacobi elliptic functions
    Jacobi elliptic functions are a family of doubly periodic complex functions that generalize trigonometric functions and play a central role in the theory of elliptic integrals and many areas of mathematical physics.
  • E. Riemann–Siegel formula
    The Riemann–Siegel formula is an asymptotic expression that efficiently approximates the Riemann zeta function on the critical line, playing a key role in the numerical study of its zeros.
  • 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: mock theta functions
Triple: [Srinivasa Ramanujan, notableWork, mock theta functions]
Generated description
Mock theta functions are a class of q-series introduced by Srinivasa Ramanujan that exhibit mysterious modular-like behavior and play a key role in modern number theory and the theory of modular forms.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: mock theta functions
Target entity description: Mock theta functions are a class of q-series introduced by Srinivasa Ramanujan that exhibit mysterious modular-like behavior and play a key role in modern number theory and the theory of modular forms.
  • A. Riemann–Siegel theta function
    The Riemann–Siegel theta function is a special function that appears in the study of the Riemann zeta function, used to express its values on the critical line in a form suitable for high-precision numerical computation.
  • B. Jacobi triple product
    The Jacobi triple product is a fundamental identity in number theory and complex analysis that expresses an infinite product as an infinite sum, playing a key role in the theory of theta functions and q-series.
  • C. 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.
  • D. Jacobi elliptic functions
    Jacobi elliptic functions are a family of doubly periodic complex functions that generalize trigonometric functions and play a central role in the theory of elliptic integrals and many areas of mathematical physics.
  • E. Riemann–Siegel formula
    The Riemann–Siegel formula is an asymptotic expression that efficiently approximates the Riemann zeta function on the critical line, playing a key role in the numerical study of its zeros.
  • 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.