Triple

T17661332
Position Surface form Disambiguated ID Type / Status
Subject Andrews–Baxter–Forrester method E440257 entity
Predicate relatedTo P37 FINISHED
Object Rogers–Ramanujan continued fraction
The Rogers–Ramanujan continued fraction is a famous q-continued fraction introduced by Srinivasa Ramanujan that plays a central role in the theory of partitions, modular forms, and q-series.
E1281757 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: Rogers–Ramanujan continued fraction | Statement: [Andrews–Baxter–Forrester method, relatedTo, Rogers–Ramanujan continued fraction]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Rogers–Ramanujan continued fraction
Context triple: [Andrews–Baxter–Forrester method, relatedTo, Rogers–Ramanujan continued fraction]
  • A. Ramanujan theta function
    The Ramanujan theta function is a special type of q-series introduced by Srinivasa Ramanujan that plays a central role in the theory of modular forms, partitions, and mock theta functions.
  • B. 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.
  • C. 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.
  • 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. Ramanujan tau function
    The Ramanujan tau function is a multiplicative arithmetic function arising from the Fourier coefficients of a modular discriminant form, central to the study of modular forms and number theory.
  • 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: Rogers–Ramanujan continued fraction
Triple: [Andrews–Baxter–Forrester method, relatedTo, Rogers–Ramanujan continued fraction]
Generated description
The Rogers–Ramanujan continued fraction is a famous q-continued fraction introduced by Srinivasa Ramanujan that plays a central role in the theory of partitions, modular forms, and q-series.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Rogers–Ramanujan continued fraction
Target entity description: The Rogers–Ramanujan continued fraction is a famous q-continued fraction introduced by Srinivasa Ramanujan that plays a central role in the theory of partitions, modular forms, and q-series.
  • A. Ramanujan theta function
    The Ramanujan theta function is a special type of q-series introduced by Srinivasa Ramanujan that plays a central role in the theory of modular forms, partitions, and mock theta functions.
  • B. 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.
  • C. 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.
  • 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. Ramanujan tau function
    The Ramanujan tau function is a multiplicative arithmetic function arising from the Fourier coefficients of a modular discriminant form, central to the study of modular forms and number theory.
  • F. None of above. chosen

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_69d8b9e87e18819087104a44dc4dc5b1 completed April 10, 2026, 8:50 a.m.
NER Named-entity recognition batch_69e46ea67f8081909da164ca21a98675 completed April 19, 2026, 5:56 a.m.
NED1 Entity disambiguation (via context triple) batch_6a02232075b48190a3defc74027b775e completed May 11, 2026, 6:42 p.m.
NEDg Description generation batch_6a02258632d081909249af799f8d2adb completed May 11, 2026, 6:52 p.m.
NED2 Entity disambiguation (via description) batch_6a0225cb32c4819089ef592279cd64cb completed May 11, 2026, 6:54 p.m.
Created at: April 10, 2026, 9:43 a.m.