Triple

T14334459
Position Surface form Disambiguated ID Type / Status
Subject Ramanujan theta function E355433 entity
Predicate appearsIn P795 FINISHED
Object Ramanujan’s notebooks
Ramanujan’s notebooks are a collection of handwritten manuscripts by mathematician Srinivasa Ramanujan, filled with thousands of original formulas and conjectures in number theory, analysis, and related fields that have profoundly influenced modern mathematics.
E355440 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 notebooks | Statement: [Ramanujan theta function, appearsIn, Ramanujan’s notebooks]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Ramanujan’s notebooks
Context triple: [Ramanujan theta function, appearsIn, Ramanujan’s notebooks]
  • 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. 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.
  • C. 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.
  • 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. Unsolved Problems in Number Theory
    *Unsolved Problems in Number Theory* is a classic reference book that surveys a wide range of open questions and conjectures in number theory, often with historical context and extensive bibliographic notes.
  • 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 notebooks
Triple: [Ramanujan theta function, appearsIn, Ramanujan’s notebooks]
Generated description
Ramanujan’s notebooks are a collection of handwritten manuscripts by mathematician Srinivasa Ramanujan, filled with thousands of original formulas and conjectures in number theory, analysis, and related fields that have profoundly influenced modern mathematics.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Ramanujan’s notebooks
Target entity description: Ramanujan’s notebooks are a collection of handwritten manuscripts by mathematician Srinivasa Ramanujan, filled with thousands of original formulas and conjectures in number theory, analysis, and related fields that have profoundly influenced modern mathematics.
  • A. Ramanujan’s lost notebook chosen
    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. 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.
  • C. 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.
  • 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. Unsolved Problems in Number Theory
    *Unsolved Problems in Number Theory* is a classic reference book that surveys a wide range of open questions and conjectures in number theory, often with historical context and extensive bibliographic notes.
  • 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_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.