Triple

T18479225
Position Surface form Disambiguated ID Type / Status
Subject theory of divergent series E451513 entity
Predicate usesConcept P531 FINISHED
Object Ramanujan summation
Ramanujan summation is a technique in mathematical analysis that assigns finite values to certain divergent series in a way consistent with analytic continuation and other regularization methods.
E1325978 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 summation | Statement: [theory of divergent series, usesConcept, Ramanujan summation]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Ramanujan summation
Context triple: [theory of divergent series, usesConcept, Ramanujan summation]
  • A. 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.
  • B. Cesàro summation
    Cesàro summation is a method of assigning finite values to certain divergent series by averaging their partial sums.
  • C. Euler–Maclaurin summation formula
    The Euler–Maclaurin summation formula is a fundamental result in analysis that connects sums and integrals, providing powerful asymptotic expansions and error estimates for approximating series by integrals.
  • D. Abel summation
    Abel summation is a method in mathematical analysis for assigning values to certain divergent series by considering the limit of their power series as the variable approaches 1 from below.
  • E. Ramanujan tau function
    The Ramanujan tau function is a multiplicative arithmetic function arising from the Fourier coefficients of a modular discriminant form, central to the study of modular forms and number theory.
  • 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 summation
Triple: [theory of divergent series, usesConcept, Ramanujan summation]
Generated description
Ramanujan summation is a technique in mathematical analysis that assigns finite values to certain divergent series in a way consistent with analytic continuation and other regularization methods.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Ramanujan summation
Target entity description: Ramanujan summation is a technique in mathematical analysis that assigns finite values to certain divergent series in a way consistent with analytic continuation and other regularization methods.
  • A. 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.
  • B. Cesàro summation
    Cesàro summation is a method of assigning finite values to certain divergent series by averaging their partial sums.
  • C. Euler–Maclaurin summation formula
    The Euler–Maclaurin summation formula is a fundamental result in analysis that connects sums and integrals, providing powerful asymptotic expansions and error estimates for approximating series by integrals.
  • D. Abel summation
    Abel summation is a method in mathematical analysis for assigning values to certain divergent series by considering the limit of their power series as the variable approaches 1 from below.
  • E. Ramanujan tau function
    The Ramanujan tau function is a multiplicative arithmetic function arising from the Fourier coefficients of a modular discriminant form, central to the study of modular forms and number theory.
  • 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_69d8d38465a0819099b9b42d2a662ac1 completed April 10, 2026, 10:40 a.m.
NER Named-entity recognition batch_69e53065e8388190bb216dae89f8cf75 completed April 19, 2026, 7:43 p.m.
NED1 Entity disambiguation (via context triple) batch_6a043f2f64848190808075254008e6e1 completed May 13, 2026, 9:06 a.m.
NEDg Description generation batch_6a043fb7db388190bb50cfade4f025f9 completed May 13, 2026, 9:09 a.m.
NED2 Entity disambiguation (via description) batch_6a044063c6048190b65620af8ceed897 completed May 13, 2026, 9:12 a.m.
Created at: April 10, 2026, 11:35 a.m.