Triple

T4437402
Position Surface form Disambiguated ID Type / Status
Subject Rogers–Ramanujan-type identities E95684 entity
Predicate relatedTo P37 FINISHED
Object Andrews–Gordon identities
The Andrews–Gordon identities are a family of deep q-series and partition identities that generalize the classical Rogers–Ramanujan identities and play a key role in combinatorics and modular forms.
E95684 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: Andrews–Gordon identities | Statement: [Rogers–Ramanujan-type identities, relatedTo, Andrews–Gordon identities]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Andrews–Gordon identities
Context triple: [Rogers–Ramanujan-type identities, relatedTo, Andrews–Gordon identities]
  • A. 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.
  • B. Gelfand–Tsetlin basis
    The Gelfand–Tsetlin basis is a canonical, combinatorially defined basis for representations of certain Lie algebras and groups, particularly used in the representation theory of GL(n) and related structures.
  • 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 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.
  • E. Weyl character formula
    The Weyl character formula is a fundamental result in representation theory that gives an explicit expression for the characters of irreducible finite-dimensional representations of semisimple Lie algebras and Lie groups.
  • 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: Andrews–Gordon identities
Triple: [Rogers–Ramanujan-type identities, relatedTo, Andrews–Gordon identities]
Generated description
The Andrews–Gordon identities are a family of deep q-series and partition identities that generalize the classical Rogers–Ramanujan identities and play a key role in combinatorics and modular forms.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Andrews–Gordon identities
Target entity description: The Andrews–Gordon identities are a family of deep q-series and partition identities that generalize the classical Rogers–Ramanujan identities and play a key role in combinatorics and modular forms.
  • 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. Gelfand–Tsetlin basis
    The Gelfand–Tsetlin basis is a canonical, combinatorially defined basis for representations of certain Lie algebras and groups, particularly used in the representation theory of GL(n) and related structures.
  • 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 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.
  • E. Weyl character formula
    The Weyl character formula is a fundamental result in representation theory that gives an explicit expression for the characters of irreducible finite-dimensional representations of semisimple Lie algebras and Lie groups.
  • F. None of above.

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_69b3453ea2b48190a26f154b3b8fece5 completed March 12, 2026, 10:59 p.m.
NER Named-entity recognition batch_69b3558b1d4481909060ede5e0ded4bc completed March 13, 2026, 12:08 a.m.
NED1 Entity disambiguation (via context triple) batch_69b6137960908190814cbdf0b4e56542 completed March 15, 2026, 2:03 a.m.
NEDg Description generation batch_69b61439a86c8190849c5af718ddc647 completed March 15, 2026, 2:06 a.m.
NED2 Entity disambiguation (via description) batch_69b614d6106c81908a601f540622f934 completed March 15, 2026, 2:09 a.m.
Created at: March 12, 2026, 11:31 p.m.