Triple

T18299118
Position Surface form Disambiguated ID Type / Status
Subject Ono’s partition congruences E438308 entity
Predicate relatedTo P37 FINISHED
Object Ramanujan’s partition congruences — NE NERFINISHED

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: Ramanujan’s partition congruences | Statement: [Ono’s partition congruences, relatedTo, Ramanujan’s partition congruences]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Ramanujan’s partition congruences
Context triple: [Ono’s partition congruences, relatedTo, Ramanujan’s partition congruences]
  • A. Ramanujan partition congruences chosen
    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.
  • B. 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.
  • C. Rogers–Ramanujan identities
    The Rogers–Ramanujan identities are two famous q-series equalities in number theory and combinatorics that relate infinite series to infinite products and have deep connections to partition theory and modular forms.
  • D. Rogers–Ramanujan-type identities
    Rogers–Ramanujan-type identities are a class of deep q-series and partition identities generalizing the classical Rogers–Ramanujan identities, with rich connections to combinatorics, number theory, and modular forms.
  • E. 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.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69d8b915e3e881909125d760c15d0c29 completed April 10, 2026, 8:47 a.m.
NER Named-entity recognition batch_69e5017d96588190ac1e326803142976 completed April 19, 2026, 4:23 p.m.
Created at: April 10, 2026, 10:35 a.m.