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.