Triple

T14334622
Position Surface form Disambiguated ID Type / Status
Subject mock theta functions E355437 entity
Predicate introducedIn P513 FINISHED
Object Ramanujan’s last letter to G. H. Hardy
Ramanujan’s last letter to G. H. Hardy is a famous 1920 correspondence in which the mathematician Srinivasa Ramanujan outlined his mysterious mock theta functions, profoundly influencing later developments in number theory and modular forms.
E1094045 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: Ramanujan’s last letter to G. H. Hardy | Statement: [mock theta functions, introducedIn, Ramanujan’s last letter to G. H. Hardy]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Ramanujan’s last letter to G. H. Hardy
Context triple: [mock theta functions, introducedIn, Ramanujan’s last letter to G. H. Hardy]
  • A. Ramanujan’s lost notebook
    Ramanujan’s lost notebook is a posthumously discovered collection of Srinivasa Ramanujan’s final mathematical formulas and insights, many of which were decades ahead of their time in number theory and q-series.
  • B. 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.
  • C. Ramanujan partition congruences
    Ramanujan partition congruences are remarkable number-theoretic results discovered by Srinivasa Ramanujan that describe surprising modular patterns in the partition function, such as specific arithmetic progressions where the number of integer partitions of an integer is divisible by a given prime.
  • D. Ramanujan’s sum
    Ramanujan’s sum is a number-theoretic function introduced by Srinivasa Ramanujan, expressing certain periodic arithmetic functions as finite trigonometric sums over primitive roots of unity.
  • E. Three Pearls of Number Theory
    Three Pearls of Number Theory is a classic mathematical text that presents three elegant and accessible problems in number theory, illustrating deep ideas through simple, beautifully explained examples.
  • 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: Ramanujan’s last letter to G. H. Hardy
Triple: [mock theta functions, introducedIn, Ramanujan’s last letter to G. H. Hardy]
Generated description
Ramanujan’s last letter to G. H. Hardy is a famous 1920 correspondence in which the mathematician Srinivasa Ramanujan outlined his mysterious mock theta functions, profoundly influencing later developments in number theory and modular forms.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Ramanujan’s last letter to G. H. Hardy
Target entity description: Ramanujan’s last letter to G. H. Hardy is a famous 1920 correspondence in which the mathematician Srinivasa Ramanujan outlined his mysterious mock theta functions, profoundly influencing later developments in number theory and modular forms.
  • A. Ramanujan’s lost notebook
    Ramanujan’s lost notebook is a posthumously discovered collection of Srinivasa Ramanujan’s final mathematical formulas and insights, many of which were decades ahead of their time in number theory and q-series.
  • B. 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.
  • C. Ramanujan partition congruences
    Ramanujan partition congruences are remarkable number-theoretic results discovered by Srinivasa Ramanujan that describe surprising modular patterns in the partition function, such as specific arithmetic progressions where the number of integer partitions of an integer is divisible by a given prime.
  • D. Ramanujan’s sum
    Ramanujan’s sum is a number-theoretic function introduced by Srinivasa Ramanujan, expressing certain periodic arithmetic functions as finite trigonometric sums over primitive roots of unity.
  • E. Three Pearls of Number Theory
    Three Pearls of Number Theory is a classic mathematical text that presents three elegant and accessible problems in number theory, illustrating deep ideas through simple, beautifully explained examples.
  • 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_69d8278fa2108190bc0d0e7939c1eb03 completed April 9, 2026, 10:26 p.m.
NER Named-entity recognition batch_69de8c20d2148190bb534bef338e871d completed April 14, 2026, 6:49 p.m.
NED1 Entity disambiguation (via context triple) batch_69fd469634688190980df59ee482b792 completed May 8, 2026, 2:12 a.m.
NEDg Description generation batch_69fd47e2b8d481909ed8274a96615b36 completed May 8, 2026, 2:18 a.m.
NED2 Entity disambiguation (via description) batch_69fd4879b2688190ac208545ae226c93 completed May 8, 2026, 2:20 a.m.
Created at: April 10, 2026, 1:13 a.m.