Triple

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).

Phrase: Rogers–Ramanujan-type identities | Statement: [Bailey chains, relatedTo, Rogers–Ramanujan-type identities]

Target entity: Rogers–Ramanujan-type identities
Context triple: [Bailey chains, relatedTo, Rogers–Ramanujan-type identities]

• A. Rogers–Ramanujan-type identities chosen
  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.
• 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. Euler pentagonal number theorem
  The Euler pentagonal number theorem is a fundamental result in number theory and combinatorics that gives a remarkable infinite product expansion for the generating function of partition numbers, involving exponents given by generalized pentagonal numbers.
• 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.