Triple

T5338260
Position Surface form Disambiguated ID Type / Status
Subject Hardy–Ramanujan asymptotic formula E123877 entity
Predicate improvedBy P6555 FINISHED
Object Rademacher convergent series for p(n) E123877 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: Rademacher convergent series for p(n) | Statement: [Hardy–Ramanujan asymptotic formula, improvedBy, Rademacher convergent series for p(n)]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Rademacher convergent series for p(n)
Context triple: [Hardy–Ramanujan asymptotic formula, improvedBy, Rademacher convergent series for p(n)]
  • A. Hardy–Ramanujan asymptotic formula chosen
    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.
  • 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. Ono’s partition congruences
    Ono’s partition congruences are modern number-theoretic results that extend Ramanujan’s classical congruences by proving the existence of infinitely many congruence relations for the partition function modulo various primes.
  • 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. Jacobi’s four-square theorem
    Jacobi’s four-square theorem is a fundamental result in number theory that gives a precise formula for the number of ways an integer can be expressed as a sum of four squares.
  • 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_69bd464b07f8819095aa76577c9829e4 completed March 20, 2026, 1:06 p.m.
NER Named-entity recognition batch_69bd85c6ec008190ad7a8a54360387d8 completed March 20, 2026, 5:37 p.m.
NED1 Entity disambiguation (via context triple) batch_69bf18c54ca4819095ca1d81ee061937 completed March 21, 2026, 10:16 p.m.
Created at: March 20, 2026, 2 p.m.