Triple

T4410542
Position Surface form Disambiguated ID Type / Status
Subject Ramanujan partition congruences E94841 entity
Predicate relatedTo P37 FINISHED
Object Ramanujan tau function E355432 NE FINISHED

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 tau function | Statement: [Ramanujan partition congruences, relatedTo, Ramanujan tau function]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Ramanujan tau function
Context triple: [Ramanujan partition congruences, relatedTo, Ramanujan tau function]
  • A. Ramanujan tau function chosen
    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.
  • B. 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.
  • C. 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.
  • D. Riemann–Siegel formula
    The Riemann–Siegel formula is an asymptotic expression that efficiently approximates the Riemann zeta function on the critical line, playing a key role in the numerical study of its zeros.
  • E. Riemann–Siegel theta function
    The Riemann–Siegel theta function is a special function that appears in the study of the Riemann zeta function, used to express its values on the critical line in a form suitable for high-precision numerical computation.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69b34539638c8190abfea3eb29425210 completed March 12, 2026, 10:59 p.m.
NER Named-entity recognition batch_69b354e4c58c8190b4190aad3095a1dd completed March 13, 2026, 12:05 a.m.
NED1 Entity disambiguation (via context triple) batch_69b5f60ea0808190a59418f7911d123d completed March 14, 2026, 11:58 p.m.
Created at: March 12, 2026, 11:29 p.m.