Triple

T4552234
Position Surface form Disambiguated ID Type / Status
Subject Divergent Series E120391 entity
Predicate topic P261 FINISHED
Object Euler summation E54271 NE FINISHED

How this triple was built (2 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: Euler summation | Statement: [Divergent Series, topic, Euler summation]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Euler summation
Context triple: [Divergent Series, topic, Euler summation]
  • A. Euler–Maclaurin summation formula chosen
    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.
  • B. Euler’s method of rearranging absolutely convergent series
    Euler’s method of rearranging absolutely convergent series is a technique introduced by Leonhard Euler to systematically reorder and manipulate convergent infinite series in order to derive new identities and product expansions, such as those appearing in analytic number theory.
  • C. Bernoulli numbers
    Bernoulli numbers are a sequence of rational numbers that play a central role in number theory and analysis, especially in formulas for sums of powers of integers and in the study of special functions like the Riemann zeta function.
  • 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. Euler’s theorem
    Euler’s theorem is a fundamental result in number theory stating that for any integer a coprime to n, a raised to the power of φ(n) is congruent to 1 modulo n.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69bd4636f1648190a701445c2fcd9c17 completed March 20, 2026, 1:05 p.m.
NER Named-entity recognition batch_69bd57f7b9748190af29d02fc77b02e0 completed March 20, 2026, 2:21 p.m.
NED1 Entity disambiguation (via context triple) batch_69bdb95b01b0819094a600752e41aa09 completed March 20, 2026, 9:17 p.m.
Created at: March 20, 2026, 1:09 p.m.