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.