Triple
T14334728
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Ramanujan’s sum |
E355439
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Möbius function |
E865102
|
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: Möbius function | Statement: [Ramanujan’s sum, relatedTo, Möbius function]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Möbius function Context triple: [Ramanujan’s sum, relatedTo, Möbius function]
-
A.
Möbius function
chosen
The Möbius function is a multiplicative arithmetic function in number theory that assigns values based on the prime factorization of integers and plays a central role in inversion formulas and the study of prime distribution.
-
B.
Mertens function
The Mertens function is an arithmetic function in number theory defined as the cumulative sum of the Möbius function, playing a key role in the study of the distribution of prime numbers and the Riemann Hypothesis.
-
C.
Liouville function
The Liouville function is a completely multiplicative arithmetic function that assigns values based on the parity of the total number of prime factors of an integer, playing a key role in analytic number theory and the study of prime distribution.
-
D.
von Mangoldt function Λ(n)
The von Mangoldt function Λ(n) is an arithmetic function in number theory that encodes the distribution of prime powers by assigning log p to integers n that are powers of a prime p and 0 otherwise.
-
E.
Dirichlet convolution
Dirichlet convolution is a binary operation on arithmetic functions that combines them via summation over divisors and plays a central role in multiplicative number theory and Dirichlet series.
- 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_69d8278fa2108190bc0d0e7939c1eb03 |
completed | April 9, 2026, 10:26 p.m. |
| NER | Named-entity recognition | batch_69de8c20d2148190bb534bef338e871d |
completed | April 14, 2026, 6:49 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69fd469634688190980df59ee482b792 |
completed | May 8, 2026, 2:12 a.m. |
Created at: April 10, 2026, 1:13 a.m.